Subject Quotes (543 quotes)
... one of the main functions of an analogy or model is to suggest extensions of the theory by considering extensions of the analogy, since more is known about the analogy than is known about the subject matter of the theory itself … A collection of observable concepts in a purely formal hypothesis suggesting no analogy with anything would consequently not suggest either any directions for its own development.
'Operational Definition and Analogy in Physical Theories', British Journal for the Philosophy of Science (Feb 1952), 2, No. 8, 291.
… scientific thought does not mean thought about scientific subjects with long names. There are no scientific subjects. The subject of science is the human universe; that is to say, everything that is, or has been, or may be related to man.
'On the Aims and Instruments of Scientific Thought,' a Lecture delivered before the members of the British Association, at Brighton, on 19 Aug 1872, in Leslie Stephen and Frederick Pollock (eds.), Lectures and Essays, by the Late William Kingdon Clifford (1886), 86.
… what is physical is subject to the laws of mathematics, and what is spiritual to the laws of God, and the laws of mathematics are but the expression of the thoughts of God.
In 'The Uses of Mathesis', Bibliotheca Sacra, 32, 523.
...[T]he natural history of the rat is tragically similar to that of man ... some of the more obvious qualities in which rats resemble men — ferocity, omnivorousness, and adaptability to all climates ... the irresponsible fecundity with which both species breed at all seasons of the year with a heedlessness of consequences, which subjects them to wholesale disaster on the inevitable, occasional failure of the food supply.... [G]radually, these two have spread across the earth, keeping pace with each other and unable to destroy each other, though continually hostile. They have wandered from East to West, driven by their physical needs, and — unlike any other species of living things — have made war upon their own kind. The gradual, relentless, progressive extermination of the black rat by the brown has no parallel in nature so close as that of the similar extermination of one race of man by another...
Rats, Lice and History(1935)
“And how many hours a day did you do lessons?” said Alice, in a hurry to change the subject.
“Ten hours the first day,” said the Mock Turtle: “nine the next, and so on.”
“What a curious plan!” exclaimed Alice.
“That's the reason they’re called lessons,” the Gryphon remarked: “because they lessen from day to day.”
“Ten hours the first day,” said the Mock Turtle: “nine the next, and so on.”
“What a curious plan!” exclaimed Alice.
“That's the reason they’re called lessons,” the Gryphon remarked: “because they lessen from day to day.”
Alice's Adventures in Wonderland (1865, 1869), 145.
“Daddy,” she says, “which came first, the chicken or the egg?”
Steadfastly, even desperately, we have been refusing to commit ourselves. But our questioner is insistent. The truth alone will satisfy her. Nothing less. At long last we gather up courage and issue our solemn pronouncement on the subject: “Yes!”
So it is here.
“Daddy, is it a wave or a particle?”
“Yes.”
“Daddy, is the electron here or is it there?”
“Yes.”
“Daddy, do scientists really know what they are talking about?”
“Yes!”
Steadfastly, even desperately, we have been refusing to commit ourselves. But our questioner is insistent. The truth alone will satisfy her. Nothing less. At long last we gather up courage and issue our solemn pronouncement on the subject: “Yes!”
So it is here.
“Daddy, is it a wave or a particle?”
“Yes.”
“Daddy, is the electron here or is it there?”
“Yes.”
“Daddy, do scientists really know what they are talking about?”
“Yes!”
The Strange Story of the Quantum (1947), 156-7.
“Exobiology” … that peculiar science has no known subject matter.
In The Meaning of Evolution: A Study of the History of Life and of Its Significance for Man (Rev. Ed., 1967), 10, footnote.
“Heaven helps those who help themselves” is a well-tried maxim, embodying in a small compass the results of vast human experience. The spirit of self-help is the root of all genuine growth in the individual; and, exhibited in the lives of many, it constitutes the true source of national vigour and strength. Help from without is often enfeebling in its effects, but help from within invariably invigorates. Whatever is done for men or classes, to a certain extent takes away the stimulus and necessity of doing for themselves; and where men are subjected to over-guidance and over-government, the inevitable tendency is to render them comparatively helpless.
In Self-help: With Illustrations of Character and Conduct (1859, 1861), 15.
“Talent is a long patience.” We must look on what we wish to express long enough and with enough attention to discover an aspect that has not been seen and portrayed by another. There is, in everything, something unexplored, because we always use our eyes only with the recollection of what has been thought before on the subject we are contemplating.
From Pierre et Jean (1888), as translated by Alexina Loranger in 'Introduction', Pierre et Jean (Peter and John) (1890), 38-39. The opening words are quoted from Gustave Flaubert. From the original French, “Le talent est une longue patience. — Il s’agit de regarder tout ce qu’on veut exprimer assez longtemps et avec assez d’attention pour en découvrir un aspect qui n’ait été vu et dit par personne. Il y a, dans tout, de l’inexploré, parce que nous sommes habitués à ne nous servir de nos yeux qu’avec le souvenir de ce qu’on a pensé avant nous sur ce que nous contemplons.”
(1) I have told you more than I know about osteoporosis. (2) What I have told you is subject to change without notice. (3) I hope I raised more questions than I have given answers. (4) In any case, as usual, a lot more work is necessary.
Conclusion of one of his papers.
Conclusion of one of his papers.
In Barry G. Firkin, Judith A. Whitworth, Dictionary of Medical Eponyms (1996), 5.
[Among the books he chooses, a statesman] ought to read interesting books on history and government, and books of science and philosophy; and really good books on these subjects are as enthralling as any fiction ever written in prose or verse.
In Theodore Roosevelt: An Autobiography (1913), 333.
[At high school in Cape Town] my interests outside my academic work were debating, tennis, and to a lesser extent, acting. I became intensely interested in astronomy and devoured the popular works of astronomers such as Sir Arthur Eddington and Sir James Jeans, from which I learnt that a knowledge of mathematics and physics was essential to the pursuit of astronomy. This increased my fondness for those subjects.
'Autobiography of Allan M. Cormack,' Les Prix Nobel/Nobel Lectures 1979, editted by Wilhelm Odelberg.
[Before college] I was almost more interested in literature and history than in the exact sciences; I was equally good in all subjects including the classical languages.
As quoted in Paul Forman and Armin Hermann, 'Sommerfeld, Arnold (Johannes Wilhelm)', Biography in Dictionary of Scientific Biography (1975), Vol. 12, 526. Cited from 'Autobiographische Skizze', Gesammelte Schriften, Vol 4, 673–682.
[Euclid's Elements] has been for nearly twenty-two centuries the encouragement and guide of that scientific thought which is one thing with the progress of man from a worse to a better state. The encouragement; for it contained a body of knowledge that was really known and could be relied on, and that moreover was growing in extent and application. For even at the time this book was written—shortly after the foundation of the Alexandrian Museum—Mathematics was no longer the merely ideal science of the Platonic school, but had started on her career of conquest over the whole world of Phenomena. The guide; for the aim of every scientific student of every subject was to bring his knowledge of that subject into a form as perfect as that which geometry had attained. Far up on the great mountain of Truth, which all the sciences hope to scale, the foremost of that sacred sisterhood was seen, beckoning for the rest to follow her. And hence she was called, in the dialect of the Pythagoreans, ‘the purifier of the reasonable soul.’
From a lecture delivered at the Royal Institution (Mar 1873), collected postumously in W.K. Clifford, edited by Leslie Stephen and Frederick Pollock, Lectures and Essays, (1879), Vol. 1, 296.
[Experimental Physicist] Phys. I know that it is often a help to represent pressure and volume as height and width on paper; and so geometry may have applications to the theory of gases. But is it not going rather far to say that geometry can deal directly with these things and is not necessarily concerned with lengths in space?
[Mathematician] Math. No. Geometry is nowadays largely analytical, so that in form as well as in effect, it deals with variables of an unknown nature. …It is literally true that I do not want to know the significance of the variables x, y, z, t that I am discussing. …
Phys. Yours is a strange subject. You told us at the beginning that you are not concerned as to whether your propositions are true, and now you tell us you do not even care to know what you are talking about.
Math. That is an excellent description of Pure Mathematics, which has already been given by an eminent mathematician [Bertrand Russell].
[Mathematician] Math. No. Geometry is nowadays largely analytical, so that in form as well as in effect, it deals with variables of an unknown nature. …It is literally true that I do not want to know the significance of the variables x, y, z, t that I am discussing. …
Phys. Yours is a strange subject. You told us at the beginning that you are not concerned as to whether your propositions are true, and now you tell us you do not even care to know what you are talking about.
Math. That is an excellent description of Pure Mathematics, which has already been given by an eminent mathematician [Bertrand Russell].
In Space, Time and Gravitation: An Outline of the General Relativity Theory (1920, 1921), 14.
[Godfrey H. Hardy] personified the popular idea of the absent-minded professor. But those who formed the idea that he was merely an absent-minded professor would receive a shock in conversation, where he displayed amazing vitality on every subject under the sun. ... He was interested in the game of chess, but was frankly puzzled by something in its nature which seemed to come into conflict with his mathematical principles.
In 'Prof. G. H. Hardy: A Mathematician of Genius,' Obituary The Times.
[In junior high school] I liked math—that was my favorite subject—and I was very interested in astronomy and in physical science.
Interview conducted on Scholastic website (20 Nov 1998).
[John Wheeler] rejuvenated general relativity; he made it an experimental subject and took it away from the mathematicians
Quoted in Dennis Overbye, 'John A. Wheeler, Physicist Who Coined the Term Black Hole, Is Dead at 96', New York Times (14 Apr 2008).
[L]et us not overlook the further great fact, that not only does science underlie sculpture, painting, music, poetry, but that science is itself poetic. The current opinion that science and poetry are opposed is a delusion. … On the contrary science opens up realms of poetry where to the unscientific all is a blank. Those engaged in scientific researches constantly show us that they realize not less vividly, but more vividly, than others, the poetry of their subjects. Whoever will dip into Hugh Miller’s works on geology, or read Mr. Lewes's “Seaside Studies,” will perceive that science excites poetry rather than extinguishes it. And whoever will contemplate the life of Goethe will see that the poet and the man of science can co-exist in equal activity. Is it not, indeed, an absurd and almost a sacrilegious belief that the more a man studies Nature the less he reveres it? Think you that a drop of water, which to the vulgar eye is but a drop of water, loses anything in the eye of the physicist who knows that its elements are held together by a force which, if suddenly liberated, would produce a flash of lightning? Think you that what is carelessly looked upon by the uninitiated as a mere snow-flake, does not suggest higher associations to one who has seen through a microscope the wondrously varied and elegant forms of snow-crystals? Think you that the rounded rock marked with parallel scratches calls up as much poetry in an ignorant mind as in the mind of a geologist, who knows that over this rock a glacier slid a million years ago? The truth is, that those who have never entered upon scientific pursuits know not a tithe of the poetry by which they are surrounded. Whoever has not in youth collected plants and insects, knows not half the halo of interest which lanes and hedge-rows can assume. Whoever has not sought for fossils, has little idea of the poetical associations that surround the places where imbedded treasures were found. Whoever at the seaside has not had a microscope and aquarium, has yet to learn what the highest pleasures of the seaside are. Sad, indeed, is it to see how men occupy themselves with trivialities, and are indifferent to the grandest phenomena—care not to understand the architecture of the Heavens, but are deeply interested in some contemptible controversy about the intrigues of Mary Queen of Scots!—are learnedly critical over a Greek ode, and pass by without a glance that grand epic written by the finger of God upon the strata of the Earth!
In Education: Intellectual, Moral, and Physical (1889), 82-83.
[Mathematics] is that [subject] which knows nothing of observation, nothing of experiment, nothing of induction, nothing of causation.
In 'The Scientific Aspects of Positivism', Fortnightly Review (1898) in Lay Sermons, Addresses and Reviews, (1872), 169.
[My dream dinner guest is] Charles Darwin. It’s an obvious answer, but it’s the truth. Think of any problem and before you start theorising, just check up whether Charles Darwin mentioned it in one of those green books sitting on your shelf. Whether it’s earthworms, human gestures or the origin of species, the observations that man made are unbelievable. He touched on so many subjects. Then, Alexander von Humboldt, the last polymath. There was no aspect of the natural world that he wasn’t curious about or didn’t write about in Kosmos, an extraordinary book.
From interview with Alice Roberts, 'Attenborough: My Life on Earth', The Biologist (Aug 2015), 62, No. 4, 16.
[The earth’s rocks] were so arranged, in their formation, that they should best serve Man’s purposes. The strata were subjected to metamorphism, and so crystallized, that he might be provided with the most perfect material for his art, his statues, temples, and dwellings; at the same time, they were filled with veins, in order to supply him with gold and silver and other treasures. The rocks were also made to enclose abundant beds of coal and iron ore, that Man might have fuel for his hearths and iron for his utensils and machinery. Mountains were raised to temper hot climates, to diversify the earth’s productiveness, and, pre-eminently, to gather the clouds into river-channels, thence to moisten the fields for agriculture, afford facilities for travel, and supply the world with springs and fountains.
In 'Concluding Remarks', A Text-book of Geology: Designed for Schools and Academies (1863), 338.
[The mathematician's] subject is the most curious of all—there is none in which truth plays such odd pranks. It has the most elaborate and the most fascinating technique, and gives unrivaled openings for the display of sheer professional skill.
In A Mathematician’s Apology (1940, 1967), 80.
[We] can easily distinguish what relates to Mathematics in any question from that which belongs to the other sciences. But as I considered the matter carefully it gradually came to light that all those matters only were referred to Mathematics in which order and measurements are investigated, and that it makes no difference whether it be in numbers, figures, stars, sounds or any other object that the question of measurement arises. I saw consequently that there must be some general science to explain that element as a whole which gives rise to problems about order and measurement, restricted as these are to no special subject matter. This, I perceived was called “Universal Mathematics,” not a far-fetched asignation, but one of long standing which has passed into current use, because in this science is contained everything on account of which the others are called parts of Mathematics.
Rules for the Direction of the Mind (written 1628). As translated by Elizabeth Sanderson Haldane and George Robert Thomson Ross in The Philosophical Works of Descartes (1911, 1931), 13.
Dicere enim bene nemo potest, nisi qui prudenter intelligit.
No one can speak well, unless he thoroughly understands his subject.
No one can speak well, unless he thoroughly understands his subject.
Brutus VI., 23. In Thomas Benfield Harbottle, Dictionary of Quotations (classical) (3rd Ed., 1906), 45.
Ein Fachmann ist ein Mann, der einige der gröbsten Fehler kennt, die man in dem betreffenden Fach machen kann, und der sie deshalb zu vermeiden versteht.
An expert is someone who knows some of the worst mistakes that can be made in his subject, and how to avoid them.
An expert is someone who knows some of the worst mistakes that can be made in his subject, and how to avoid them.
From the original German, “Ein Fachmann ist ein Mann, der einige der gröbsten Fehler kennt, die man in dem betreffenden Fach machen kann, und der sie deshalb zu vermeiden versteht”, in Der Teil und das Ganze: Gespräche im Umkreis der Atomphysik (The Part and the Whole: Conversations in the Atomic Physics) (1969, 2001), 247. Excerpt in magazine article, 'Kein Chaos, aus dem nicht wieder Ordnung würde,' Die Zeit (22 August 1969), 34. English version in Werner Heisenberg and Arnold J. Pomerans (trans.), Physics and Beyond: Encounters and Conversations (1971), 210.
Les causes primordiales ne nous sont point connues; mais elles sont assujetties à des lois simples et constantes, que l’on peut découvrir par l’observation, et dont l’étude est l’objet de la philosophie naturelle.
Primary causes are unknown to us; but are subject to simple and constant laws, which may be discovered by observation, the study of them being the object of natural philosophy.
Primary causes are unknown to us; but are subject to simple and constant laws, which may be discovered by observation, the study of them being the object of natural philosophy.
Opening statement from 'Discours Préliminaire' to Théorie Analytique de la Chaleur (1822), i, translated by Alexander Freeman in The Analytical Theory of Heat (1878), 1.
Newsreader: A huge asteroid could destroy Earth! And by coincidence, that's the subject of tonight's miniseries.
Dogbert: In science, researchers proved that this simple device can keep idiots off your television screen. [TV remote control] Click.
Dogbert: In science, researchers proved that this simple device can keep idiots off your television screen. [TV remote control] Click.
Dilbert cartoon strip (30 Apr 1993).
~~[Attributed, authorship undocumented]~~ Mathematical demonstrations are a logic of as much or more use, than that commonly learned at schools, serving to a just formation of the mind, enlarging its capacity, and strengthening it so as to render the same capable of exact reasoning, and discerning truth from falsehood in all occurrences, even in subjects not mathematical. For which reason it is said, the Egyptians, Persians, and Lacedaemonians seldom elected any new kings, but such as had some knowledge in the mathematics, imagining those, who had not, men of imperfect judgments, and unfit to rule and govern.
From an article which appeared as 'The Usefulness of Mathematics', Pennsylvania Gazette (30 Oct 1735), No. 360. Collected, despite being without clear evidence of Franklin’s authorship, in The Works of Benjamin Franklin (1809), Vol. 4, 377. Evidence of actual authorship by Ben Franklin for the newspaper article has not been ascertained, and scholars doubt it. See Franklin documents at the website founders.archives.gov. The quote is included here to attach this caution.
1. Universal CHEMISTRY is the Art of resolving mixt, compound, or aggregate Bodies into their Principles; and of composing such Bodies from those Principles. 2. It has for its Subject all the mix’d, compound, and aggregate Bodies that are and resolvable and combinable and Resolution and Combination, or Destruction and Generation, for its Object. 3. Its Means in general, are either remote or immediate; that is, either Instruments or the Operations themselves. 4. Its End is either philosophical and theoretical; or medicinal, mechanical, œconomical, and practical. 5. Its efficient Cause is the Chemist.
In Philosophical Principles of Universal Chemistry: Or, The Foundation of a Scientifical Manner of Inquiring Into and Preparing the Natural and Artificial Bodies for the Uses of Life: Both in the Smaller Way of Experiment, and the Larger Way of Business (1730), 1. Footnote to (1.): “The justness of this Definition will appear from the scope and tenour of the Work; though it is rather adapted to the perfect, than the present imperfect state of Chemistry….” Footnote to (4): “Hence universal Chemistry is commodiously resolved into several Parts or Branches, under which it must be distinctly treated to give a just notion of its due extent and usefulness. For tho’ in common acceptation of the word, Chemistry is supposed to relate chiefly to the Art of Medicine, as it supplies that Art with Remedies, this in reality is but a very small part of its use, compared with the rest; numerous other Arts, Trades, and mechanical Employments, Merchandize itself, and all natural Philosophy, being as much, and some of them more, concern’d therewith….”
A common fallacy in much of the adverse criticism to which science is subjected today is that it claims certainty, infallibility and complete emotional objectivity. It would be more nearly true to say that it is based upon wonder, adventure and hope.
Quoted in E. J. Bowen's obituary of Hinshelwood, Chemistry in Britain (1967), Vol. 3, 536.
A good title should aim at making what follows as far as possible superfluous to those who know anything of the subject.
Samuel Butler, Henry Festing Jones (ed.), The Note-Books of Samuel Butler (1917), 229.
A great department of thought must have its own inner life, however transcendent may be the importance of its relations to the outside. No department of science, least of all one requiring so high a degree of mental concentration as Mathematics, can be developed entirely, or even mainly, with a view to applications outside its own range. The increased complexity and specialisation of all branches of knowledge makes it true in the present, however it may have been in former times, that important advances in such a department as Mathematics can be expected only from men who are interested in the subject for its own sake, and who, whilst keeping an open mind for suggestions from outside, allow their thought to range freely in those lines of advance which are indicated by the present state of their subject, untrammelled by any preoccupation as to applications to other departments of science. Even with a view to applications, if Mathematics is to be adequately equipped for the purpose of coping with the intricate problems which will be presented to it in the future by Physics, Chemistry and other branches of physical science, many of these problems probably of a character which we cannot at present forecast, it is essential that Mathematics should be allowed to develop freely on its own lines.
In Presidential Address British Association for the Advancement of Science, Sheffield, Section A,
Nature (1 Sep 1910), 84, 286.
A hundred years ago … an engineer, Herbert Spencer, was willing to expound every aspect of life, with an effect on his admiring readers which has not worn off today.
Things do not happen quite in this way nowadays. This, we are told, is an age of specialists. The pursuit of knowledge has become a profession. The time when a man could master several sciences is past. He must now, they say, put all his efforts into one subject. And presumably, he must get all his ideas from this one subject. The world, to be sure, needs men who will follow such a rule with enthusiasm. It needs the greatest numbers of the ablest technicians. But apart from them it also needs men who will converse and think and even work in more than one science and know how to combine or connect them. Such men, I believe, are still to be found today. They are still as glad to exchange ideas as they have been in the past. But we cannot say that our way of life is well-fitted to help them. Why is this?
Things do not happen quite in this way nowadays. This, we are told, is an age of specialists. The pursuit of knowledge has become a profession. The time when a man could master several sciences is past. He must now, they say, put all his efforts into one subject. And presumably, he must get all his ideas from this one subject. The world, to be sure, needs men who will follow such a rule with enthusiasm. It needs the greatest numbers of the ablest technicians. But apart from them it also needs men who will converse and think and even work in more than one science and know how to combine or connect them. Such men, I believe, are still to be found today. They are still as glad to exchange ideas as they have been in the past. But we cannot say that our way of life is well-fitted to help them. Why is this?
In 'The Unification of Biology', New Scientist (11 Jan 1962), 13, No. 269, 72.
A multitude of words doth rather obscure than illustrate, they being a burden to the memory, and the first apt to be forgotten, before we come to the last. So that he that uses many words for the explaining of any subject, doth, like the cuttle-fish, hide himself, for the most part, in his own ink.
— John Ray
The Wisdom of God Manifested in the Works of the Creation (1691).
A patient pursuit of facts, and cautious combination and comparison of them, is the drudgery to which man is subjected by his Maker, if he wishes to attain sure knowledge.
In 'Productions Mineral, Vegetable and Animal', Notes on the State of Virginia (1787), 112.
A person by study must try to disengage the subject from useless matter, and to seize on points capable of improvement. ... When subjects are viewed through the mists of prejudice, useful truths may escape.
In An Essay on Aërial Navigation, With Some Observations on Ships (1844), 80.
A physician’s subject of study is necessarily the patient, and his first field for observation is the hospital. But if clinical observation teaches him to know the form and course of diseases, it cannot suffice to make him understand their nature; to this end he must penetrate into the body to find which of the internal parts are injured in their functions. That is why dissection of cadavers and microscopic study of diseases were soon added to clinical observation. But to-day these various methods no longer suffice; we must push investigation further and, in analyzing the elementary phenomena of organic bodies, must compare normal with abnormal states. We showed elsewhere how incapable is anatomy alone to take account of vital phenenoma, and we saw that we must add study of all physico-chemical conditions which contribute necessary elements to normal or pathological manifestations of life. This simple suggestion already makes us feel that the laboratory of a physiologist-physician must be the most complicated of all laboratories, because he has to experiment with phenomena of life which are the most complex of all natural phenomena.
From An Introduction to the Study of Experimental Medicine (1865), as translated by Henry Copley Greene (1957), 140-141.
A professor … may be to produce a perfect mathematical work of art, having every axiom stated, every conclusion drawn with flawless logic, the whole syllabus covered. This sounds excellent, but in practice the result is often that the class does not have the faintest idea of what is going on. … The framework is lacking; students do not know where the subject fits in, and this has a paralyzing effect on the mind.
In A Concrete Approach to Abstract Algebra (1959), 1-2.
A professor is one who can speak on any subject—for precisely fifty minutes.
…...
A rock or stone is not a subject that, of itself, may interest a philosopher to study; but, when he comes to see the necessity of those hard bodies, in the constitution of this earth, or for the permanency of the land on which we dwell, and when he finds that there are means wisely provided for the renovation of this necessary decaying part, as well as that of every other, he then, with pleasure, contemplates this manifestation of design, and thus connects the mineral system of this earth with that by which the heavenly bodies are made to move perpetually in their orbits.
Theory of the Earth, with Proofs and l1lustrations, Vol. 1 (1795), 276.
A scientist may exhaust himself; he frequently exhausts his colleagues, always exhausts his money, but never exhausts his subject.
In The Development of Design (1981), 1.
A superficial knowledge of mathematics may lead to the belief that this subject can be taught incidentally, and that exercises akin to counting the petals of flowers or the legs of a grasshopper are mathematical. Such work ignores the fundamental idea out of which quantitative reasoning grows—the equality of magnitudes. It leaves the pupil unaware of that relativity which is the essence of mathematical science. Numerical statements are frequently required in the study of natural history, but to repeat these as a drill upon numbers will scarcely lend charm to these studies, and certainly will not result in mathematical knowledge.
In Primary Arithmetic: First Year, for the Use of Teachers (1897), 26-27.
A superficial knowledge of mathematics may lead to the belief that this subject can be taught incidentally, and that exercises akin to counting the petals of flowers or the legs of a grasshopper are mathematical. Such work ignores the fundamental idea out of which quantitative reasoning grows—the equality of magnitudes. It leaves the pupil unaware of that relativity which is the essence of mathematical science. Numerical statements are frequently required in the study of natural history, but to repeat these as a drill upon numbers will scarcely lend charm to these studies, and certainly will not result in mathematical knowledge.
In Primary Arithmetic: First Year, for the Use of Teachers (1897), 26-27.
Accordingly, we find Euler and D'Alembert devoting their talent and their patience to the establishment of the laws of rotation of the solid bodies. Lagrange has incorporated his own analysis of the problem with his general treatment of mechanics, and since his time M. Poinsôt has brought the subject under the power of a more searching analysis than that of the calculus, in which ideas take the place of symbols, and intelligent propositions supersede equations.
J. C. Maxwell on Louis Poinsôt (1777-1859) in 'On a Dynamical Top' (1857). In W. D. Niven (ed.), The Scientific Papers of James Clerk Maxwell (1890), Vol. 1, 248.
After five years' work I allowed myself to speculate on the subject, and drew up some short notes; these I enlarged in 1844 into a sketch of the conclusions, which then seemed to me probable: from that period to the present day I have steadily pursued the same object. I hope that I may be excused for entering on these personal details, as I give them to show that I have not been hasty in coming to a decision.
From On the Origin of Species by Means of Natural Selection; or, The Preservation of Favoured Races in the Struggle for Life (1861), 9.
All scientists must focus closely on limited targets. Whether or not one’s findings on a limited subject will have wide applicability depends to some extent on chance, but biologists of superior ability repeatedly focus on questions the answers to which either have wide ramifications or lead to new areas of investigation. One procedure that can be effective is to attempt both reduction and synthesis; that is, direct a question at a phenomenon on one integrative level, identify its mechanism at a simpler level, then extrapolate its consequences to a more complex level of integration.
In 'Scientific innovation and creativity: a zoologist’s point of view', American Zoologist (1982), 22, 230-231,
All that can be said upon the number and nature of elements is, in my opinion, confined to discussions entirely of a metaphysical nature. The subject only furnishes us with indefinite problems, which may be solved in a thousand different ways, not one of which, in all probability, is consistent with nature. I shall therefore only add upon this subject, that if, by the term elements, we mean to express those simple and indivisible atoms of which matter is composed, it is extremely probable we know nothing at all about them; but, if we apply the term elements, or principles of bodies, to express our idea of the last point which analysis is capable of reaching, we must admit, as elements, all the substances into which we are capable, by any means, to reduce bodies by decomposition.
Elements of Chemistry (1790), trans. R. Kerr, Preface, xxiv.
All true science must aim at objective truth, and that means that the human observer must never allow himself to get emotionally mixed up with his subject-matter. His concern is to understand the universe, not to improve it. Detachment is obligatory.
From transcript of BBC radio Reith Lecture (12 Nov 1967), 'A Runaway World', on the bbc.co.uk website.
Although the way ahead [for immunology] is full of pitfalls and difficulties, this is indeed an exhilarating prospect. There is no danger of a shortage of forthcoming excitement in the subject. Yet, as always, the highlights of tomorrow are the unpredictabilities of today.
From Nobel Lecture (8 Dec 1984), collected in Tore Frängsmyr and Jan Lindsten (eds.), Nobel Lectures in Physiology Or Medicine: 1981-1990 (1993), 267.
Amid all the revolutions of the globe, the economy of Nature has been uniform, ... and her laws are the only things that have resisted the general movement. The rivers and the rocks, the seas and the continents, have been changed in all their parts; but the laws which direct those changes, and the rules to which they are subject, have remained invariably the same.
Illustrations of the Huttonian Theory of the Earth (1802) collected in The Works of John Playfair (1822), Vol. 1, 415
An engineer, a physicist and a mathematician find themselves in an anecdote, indeed an anecdote quite similar to many that you have no doubt already heard.
After some observations and rough calculations the engineer realizes the situation and starts laughing.
A few minutes later the physicist understands too and chuckles to himself happily, as he now has enough experimental evidence to publish a paper.
This leaves the mathematician somewhat perplexed, as he had observed right away that he was the subject of an anecdote, and deduced quite rapidly the presence of humor from similar anecdotes, but considers this anecdote to be too trivial a corollary to be significant, let alone funny.
After some observations and rough calculations the engineer realizes the situation and starts laughing.
A few minutes later the physicist understands too and chuckles to himself happily, as he now has enough experimental evidence to publish a paper.
This leaves the mathematician somewhat perplexed, as he had observed right away that he was the subject of an anecdote, and deduced quite rapidly the presence of humor from similar anecdotes, but considers this anecdote to be too trivial a corollary to be significant, let alone funny.
In 'Zero Gravity: The Lighter Side of Science' APS News (Jun 2003), 12 No. 6.
An enthusiastic philosopher, of whose name we are not informed, had constructed a very satisfactory theory on some subject or other, and was not a little proud of it. “But the facts, my dear fellow,” said his friend, “the facts do not agree with your theory.”—“Don't they?” replied the philosopher, shrugging his shoulders, “then, tant pis pour les faits;”—so much the worse for the facts!
From Memoirs of Extraordinary Popular Delusions (1841), Vol. 3, 313, footnote.
And I believe there are many Species in Nature, which were never yet taken notice of by Man, and consequently of no use to him, which yet we are not to think were created in vain; but it’s likely … to partake of the overflowing Goodness of the Creator, and enjoy their own Beings. But though in this sense it be not true, that all things were made for Man; yet thus far it is, that all the Creatures in the World may be some way or other useful to us, at least to exercise our Wits and Understandings, in considering and contemplating of them, and so afford us Subject of Admiring and Glorifying their and our Maker. Seeing them, we do believe and assert that all things were in some sense made for us, we are thereby obliged to make use of them for those purposes for which they serve us, else we frustrate this End of their Creation.
— John Ray
The Wisdom of God Manifested in the Works of the Creation (1691), 169-70.
And new philosophy calls all in doubt,
The Element of fire is quite put out;
The Sun is lost, and th’earth, and no mans wit
Can well direct him where to look for it.
And freely men confesse that this world’s spent,
When in the Planets, and the Firmament
They seeke so many new; and then see that this
Is crumbled out againe to his Atomies.
’Tis all in pieces, all cohaerence gone;
All just supply, and all Relation;
Prince, Subject, Father, Sonne, are things forgot,
For every man alone thinkes he hath got
To be a phoenix, and that then can bee
None of that kinde, of which he is, but hee.
The Element of fire is quite put out;
The Sun is lost, and th’earth, and no mans wit
Can well direct him where to look for it.
And freely men confesse that this world’s spent,
When in the Planets, and the Firmament
They seeke so many new; and then see that this
Is crumbled out againe to his Atomies.
’Tis all in pieces, all cohaerence gone;
All just supply, and all Relation;
Prince, Subject, Father, Sonne, are things forgot,
For every man alone thinkes he hath got
To be a phoenix, and that then can bee
None of that kinde, of which he is, but hee.
An Anatomie of the World, I. 205-18. The Works of John Donne (Wordsworth edition 1994), 177.
Another diversity of Methods is according to the subject or matter which is handled; for there is a great difference in delivery of the Mathematics, which are the most abstracted of knowledges, and Policy, which is the most immersed…, yet we see how that opinion, besides the weakness of it, hath been of ill desert towards learning, as that which taketh the way to reduce learning to certain empty and barren generalities; being but the very husks and shells of sciences, all the kernel being forced out and expulsed with the torture and press of the method.
Advancement of Learning, Book 2. In James Spedding, The Works of Francis Bacon (1863), Vol. 6, 292-293. Peter Pešić, explains that 'By Mathematics, he had in mind a sterile and rigid scheme of logical classifications, called dichotomies in his time,' inLabyrinth: A Search for the Hidden Meaning of Science (2001), 73.
Any chemist reading this book can see, in some detail, how I have spent most of my mature life. They can become familiar with the quality of my mind and imagination. They can make judgements about my research abilities. They can tell how well I have documented my claims of experimental results. Any scientist can redo my experiments to see if they still work—and this has happened! I know of no other field in which contributions to world culture are so clearly on exhibit, so cumulative, and so subject to verification.
From Design to Discovery (1990), 119-20.
Archimedes possessed so high a spirit, so profound a soul, and such treasures of highly scientific knowledge, that though these inventions [used to defend Syracuse against the Romans] had now obtained him the renown of more than human sagacity, he yet would not deign to leave behind him any commentary or writing on such subjects; but, repudiating as sordid and ignoble the whole trade of engineering, and every sort of art that lends itself to mere use and profit, he placed his whole affection and ambition in those purer speculations where there can be no reference to the vulgar needs of life; studies, the superiority of which to all others is unquestioned, and in which the only doubt can be whether the beauty and grandeur of the subjects examined, or the precision and cogency of the methods and means of proof, most deserve our admiration.
— Plutarch
In John Dryden (trans.), Life of Marcellus.
Art and religion first; then philosophy; lastly science. That is the order of the great subjects of life, that’s their order of importance.
Dialog by the character Miss Brodie, in The Prime of Miss Jean Brodie (1961, 2004), 23-24.
Art arises in those strange complexities of action that are called human beings. It is a kind of human behavior. As such it is not magic, except as human beings are magical. Nor is it concerned in absolutes, eternities, “forms,” beyond those that may reside in the context of the human being and be subject to his vicissitudes. Art is not an inner state of consciousness, whatever that may mean. Neither is it essentially a supreme form of communication. Art is human behavior, and its values are contained in human behavior.
In Art Is Action: A Discussion of Nine Arts in a Modern World (1939), 1.
Art is an expression of the world order and is, therefore, orderly, organic, subject to mathematical law, and susceptible to mathematical analysis.
In 'The Theosophic View of the Art of Architecture', The Beautiful Necessity, Seven Essays on Theosophy and Architecture (2nd ed., 1922), Preface to the Second Edition, 11.
Art, science, discovery and invention, startle and bewilder us at every turn, by their rapid, vast and wonderful achievements. These forces have made men lords where they were vassals, masters where they were slaves, and kings where they were subjects. They have abolished the limitations of time and space and have brought the ends of the earth together.
From speech (20 Nov 1883) delivered to the Bethel Literary and Historical Association, Washington D.C.,'It Moves, or Philosophy of Reform' , collected in The Speeches of Frederick Douglass (2018), 387.
As few subjects are more interesting to society, so few have been more frequently written upon than the education of youth.
Essay No. VI, 'On Education', first published in The Bee (10 Nov 1759), collected in The Works of Oliver Goldsmith (1900), Vol. 5, 95. Reprinted as Essay VII under the title 'On the Education of Youth', (1765). The Bee was a weekly paper wholly the work of Goldsmith.
As for me ... I would much rather be a perfected ape than a degraded Adam. Yes, if it is shown to me that my humble ancestors were quadrupedal animals, arboreal herbivores, brothers or cousins of those who were also the ancestors of monkeys and apes, far from blushing in shame for my species because of its genealogy and parentage, I will be proud of all that evolution has accomplished, of the continuous improvement which takes us up to the highest order, of the successive triumphs that have made us superior to all of the other species ... the splendid work of progress.
I will conclude in saying: the fixity of species is almost impossible, it contradicts the mode of succession and of the distribution of species in the sequence of extant and extinct creatures. It is therefore extremely likely that species are variable and are subject to evolution. But the causes, the mechanisms of this evolution are still unknown.
I will conclude in saying: the fixity of species is almost impossible, it contradicts the mode of succession and of the distribution of species in the sequence of extant and extinct creatures. It is therefore extremely likely that species are variable and are subject to evolution. But the causes, the mechanisms of this evolution are still unknown.
'Discussion sur la Machoire Humaine de la Naulette (Belgique)', Bulletin de la Societé d'Anthropologie de Paris, 2nd Series, I (1866), 595. Trans. Erik Trinkaus and Pat Shipman, The Neanderthals: Changing the Image of Mankind (1993), 103-4.
As science is more and more subject to grave misuse as well as to use for human benefit it has also become the scientist's responsibility to become aware of the social relations and applications of his subject, and to exert his influence in such a direction as will result in the best applications of the findings in his own and related fields. Thus he must help in educating the public, in the broad sense, and this means first educating himself, not only in science but in regard to the great issues confronting mankind today.
Message to University Students Studying Science', Kagaku Asahi 11, no. 6 (1951), 28-29. Quoted in Elof Axel Carlson, Genes, Radiation, and Society: The Life and Work of H. J. Muller (1981), 371.
As to Science, she has never sought to ally herself to civil power. She has never attempted to throw odium or inflict social ruin on any human being. She has never subjected anyone to mental torment, physical torture, least of all to death, for the purpose of upholding or promoting her ideas. She presents herself unstained by cruelties and crimes. But in the Vatican—we have only to recall the Inquisition—the hands that are now raised in appeals to the Most Merciful are crimsoned. They have been steeped in blood!
History of the Conflict between Religion and Science (1875), xi.
At no period of [Michael Faraday’s] unmatched career was he interested in utility. He was absorbed in disentangling the riddles of the universe, at first chemical riddles, in later periods, physical riddles. As far as he cared, the question of utility was never raised. Any suspicion of utility would have restricted his restless curiosity. In the end, utility resulted, but it was never a criterion to which his ceaseless experimentation could be subjected.
'The Usefulness of Useless Knowledge', Harper's Magazine (Jun/Nov 1939), No. 179, 546. In Hispania (Feb 1944), 27, No. 1, 77.
At present good work in science pays less well very often than mediocrity in other subjects. This, as was pointed out by Sir Lyon Playfair in his Presidential Address to the British Association in 1885 helps to arrest progress in science teaching.
In Sir Norman Lockyer (ed.), 'Physical Science and the Woolwich Examinations', Nature (23 Feb 1888), 37, 386. Webmaster has assumed this unsigned lead article (editorial?) should be attributed to the Editor.
At that point, my sense of dissatisfaction was so strong that I firmly resolved to start thinking until I should find a purely arithmetic and absolutely rigorous foundation of the principles of infinitesimal analysis. … I achieved this goal on November 24th, 1858, … but I could not really decide upon a proper publication, because, firstly, the subject is not easy to present, and, secondly, the material is not very fruitful.
(1872). As quoted in Ernst Hairer and Gerhard Wanner, Analysis by Its History (2008), 177.
Bacteria are highly adaptable. They frequently change both morphologically and functionally. Their virulence is also an essentially fluctuating property, that increases or diminishes according to the conditions to which the pathogenic organism is subjected.
In Studies in Immunity (1909), 1.
Beasts have not the high advantages which we possess; but they have some which we have not. They have not our hopes, but then they have not our fears; they are subject like us to death, but it is without being aware of it; most of them are better able to preserve themselves than we are, and make a less bad use of their passions.
In Edwin Davies, Other Men's Minds, Or, Seven Thousand Choice Extracts (1800), 55.
Before delivering your lectures, the manuscript should be in such a perfect form that, if need be, it could be set in type. Whether you follow the manuscript during the delivery of the lecture is purely incidental. The essential point is that you are thus master of the subject matter.
Advice to his son. As quoted in Ralph Oesper, The Human Side Of Scientists (1975), 185.
Before I came here I was confused about this subject. Having listened to your lecture I am still confused. But on a higher level.
In A Dictionary of Scientific Quotations by Alan L. Mackay (1991).
Bertrand Russell had given a talk on the then new quantum mechanics, of whose wonders he was most appreciative. He spoke hard and earnestly in the New Lecture Hall. And when he was done, Professor Whitehead, who presided, thanked him for his efforts, and not least for “leaving the vast darkness of the subject unobscured.”
Quoted in Robert Oppenheimer, The Open Mind (1955), 102.
Bertrand, Darboux, and Glaisher have compared Cayley to Euler, alike for his range, his analytical power, and, not least, for his prolific production of new views and fertile theories. There is hardly a subject in the whole of pure mathematics at which he has not worked.
In Proceedings of London Royal Society (1895), 58, 21.
Biology can be divided into the study of proximate causes, the study of the physiological sciences (broadly conceived), and into the study of ultimate (evolutionary) causes, the subject of natural history.
The Growth of Biological Thought: Diversity, Evolution and Inheritance (1982), 67.
Biology cannot go far in its subject without being met by mind.
In 'The Brain Collaborates With Psyche', Man On His Nature: The Gifford Lectures, Edinburgh 1937-8 (1940), 290-291.
But as no two (theoreticians) agree on this (skin friction) or any other subject, some not agreeing today with what they wrote a year ago, I think we might put down all their results, add them together, and then divide by the number of mathematicians, and thus find the average coefficient of error. (1908)
In Artificial and Natural Flight (1908), 3. Quoted in John David Anderson, Jr., Hypersonic and High Temperature Gas Dynamics (2000), 335.
But for the persistence of a student of this university in urging upon me his desire to study with me the modern algebra I should never have been led into this investigation; and the new facts and principles which I have discovered in regard to it (important facts, I believe), would, so far as I am concerned, have remained still hidden in the womb of time. In vain I represented to this inquisitive student that he would do better to take up some other subject lying less off the beaten track of study, such as the higher parts of the calculus or elliptic functions, or the theory of substitutions, or I wot not what besides. He stuck with perfect respectfulness, but with invincible pertinacity, to his point. He would have the new algebra (Heaven knows where he had heard about it, for it is almost unknown in this continent), that or nothing. I was obliged to yield, and what was the consequence? In trying to throw light upon an obscure explanation in our text-book, my brain took fire, I plunged with re-quickened zeal into a subject which I had for years abandoned, and found food for thoughts which have engaged my attention for a considerable time past, and will probably occupy all my powers of contemplation advantageously for several months to come.
In Johns Hopkins Commemoration Day Address, Collected Mathematical Papers, Vol. 3, 76.
But nothing of a nature foreign to the duties of my profession [clergyman] engaged my attention while I was at Leeds so much as the, prosecution of my experiments relating to electricity, and especially the doctrine of air. The last I was led into a consequence of inhabiting a house adjoining to a public brewery, where first amused myself with making experiments on fixed air [carbon dioxide] which found ready made in the process of fermentation. When I removed from that house, I was under the necessity making the fixed air for myself; and one experiment leading to another, as I have distinctly and faithfully noted in my various publications on the subject, I by degrees contrived a convenient apparatus for the purpose, but of the cheapest kind. When I began these experiments I knew very little of chemistry, and had in a manner no idea on the subject before I attended a course of chymical lectures delivered in the Academy at Warrington by Dr. Turner of Liverpool. But I have often thought that upon the whole, this circumstance was no disadvantage to me; as in this situation I was led to devise an apparatus and processes of my own, adapted to my peculiar views. Whereas, if I had been previously accustomed to the usual chemical processes, I should not have so easily thought of any other; and without new modes of operation I should hardly have discovered anything materially new.
Memoirs of Dr. Joseph Priestley, in the Year 1795 (1806), Vol. 1, 61-2.
But the fact is that when wine is taken in moderation, it gives rise to a large amount of breath, whose character is balanced, and whose luminosity is strong and brilliant. Hence wine disposes greatly to gladness, and the person is subject to quite trivial exciting agents. The breath now takes up the impression of agents belonging to the present time more easily than it does those which relate to the future; it responds to agents conducive to delight rather than those conducive to a sense of beauty.
— Avicenna
'The External Causes of Delight and Sadness', in The Canon of Medicine, adapted by L. Bakhtiar (19-99), 149-50.
By science, then, I understand the consideration of all subjects, whether of a pure or mixed nature, capable of being reduced to measurement and calculation. All things comprehended under the categories of space, time and number properly belong to our investigations; and all phenomena capable of being brought under the semblance of a law are legitimate objects of our inquiries.
In Report of the British Association for the Advancement of Science (1833), xxviii.
Calculation touches, at most, certain phenomena of organic destruction. Organic creation, on the contrary, the evolutionary phenomena which properly constitute life, we cannot in any way subject to a mathematical treatment.
In Creative Evolution (1911).
Can we separate object and subject? Myself is nothing but a part of my body, my body is nothing but a part of my food, my food is nothing but a part of the earth, the earth is nothing but a part of the solar system.
In Sir William Withey Gull and Theodore Dyke Acland (ed.), A Collection of the Published Writings of William Withey Gull (1896), lii.
Casting off the dark fog of verbal philosophy and vulgar medicine, which inculcate names alone ... I tried a series of experiments to explain more clearly many phenomena, particularly those of physiology. In order that I might subject as far as possible the reasonings of the Galenists and Peripatetics to sensory criteria, I began, after trying experiments, to write dialogues in which a Galenist adduced the better-known and stronger reasons and arguments; these a mechanist surgeon refuted by citing to the contrary the experiments I had tried, and a third, neutral interlocutor weighed the reasons advanced by both and provided an opportunity for further progress.
'Malpighi at Pisa 1656-1659', in H. B. Adelmann (ed.), Marcello Malpighi and the Evolution of Embryology (1966), Vol. 1, 155-6.
Cayley was singularly learned in the work of other men, and catholic in his range of knowledge. Yet he did not read a memoir completely through: his custom was to read only so much as would enable him to grasp the meaning of the symbols and understand its scope. The main result would then become to him a subject of investigation: he would establish it (or test it) by algebraic analysis and, not infrequently, develop it so to obtain other results. This faculty of grasping and testing rapidly the work of others, together with his great knowledge, made him an invaluable referee; his services in this capacity were used through a long series of years by a number of societies to which he was almost in the position of standing mathematical advisor.
In Proceedings of London Royal Society (1895), 58, 11-12.
Changes That Have Occurred in the Globe: When we have seen with our own eyes a mountain progressing into a plain; that is to say, an immense boulder separating from this mountain and covering the fields; an entire castle broken into pieces over the ground; a river swallowed up which then bursts out from its abyss; clear marks of a vast amount of water having once flooded regions now inhabited, and a hundred vestiges of other transformations, then we are much more willing to believe that great changes altered the face of the earth, than a Parisian lady who knows only that the place where her house was built was once a cultivated field. However, a lady from Naples who has seen the buried ruins of Herculaneum, is much less subject to the bias which leads us to believe that everything has always been as it is today.
From article 'Changements arrivées dans le globe', in Dictionnaire philosophique (1764), collected in Œuvres Complètes de Voltaire (1878), Vol. 2, 427-428. Translated by Ian Ellis, from the original French: “Changements arrivées dans le globe: Quand on a vu de ses yeux une montagne s’avancer dans une plaine, c’est-à-dire un immense rocher de cette montagne se détacher et couvrir des champs, un château tout entier enfoncé dans la terre, un fleuve englouti qui sort ensuite de son abîme, des marques indubitables qu’un vaste amas d’eau inondait autrefois un pays habité aujourd’hui, et cent vestiges d’autres révolutions, on est alors plus disposé à croire les grands changements qui ont altéré la face du monde, que ne l’est une dame de Paris qui sait seulement que la place où est bâtie sa maison était autrefois un champ labourable. Mais une dame de Naples, qui a vu sous terre les ruines d’Herculanum, est encore moins asservie au préjugé qui nous fait croire que tout a toujours été comme il est aujourd’hui.”
Chemistry is yet, indeed, a mere embryon. Its principles are contested; experiments seem contradictory; their subjects are so minute as to escape our senses; and their result too fallacious to satisfy the mind. It is probably an age too soon to propose the establishment of a system.
Letter to Rev. James Madison (Paris, 19 Jul 1788). In Thomas Jefferson and John P. Foley (ed.), The Jeffersonian Cyclopedia (1900), 135. From H.A. Washington, The Writings of Thomas Jefferson (1853-54). Vol 2, 431.
Chlorine is a deadly poison gas employed on European battlefields in World War I. Sodium is a corrosive metal which burns upon contact with water. Together they make a placid and unpoisonous material, table salt. Why each of these substances has the properties it does is a subject called chemistry.
In Broca's Brain: The Romance of Science (1979), 18, footnote.
Civilized people can talk about anything. For them no subject is taboo…. In civilized societies there will be no intellectual bogeys at sight of which great grown-up babies are expected to hide their eyes
In Civilization: An Essay (1928), 138.
Coming to the question of life being found on other planets, Professor Haldane apologized for discoursing, as a mere biologist, on a subject on which we had been expecting a lecture by a physicist [J. D. Bernal]. He mentioned three hypotheses:
(a) That life had a supernatural origin,
(b) That it originated from inorganic materials, and (c) That life is a constituent of the Universe and can only arise from pre-existing life. The first hypothesis, he said, should be taken seriously, and he would proceed to do so. From the fact that there are 400,000 species of beetle on this planet, but only 8,000 species of mammals, he concluded that the Creator, if he exists, has a special preference for beetles, and so we might be more likely to meet them than any other type of animal on a planet which would support life.
(a) That life had a supernatural origin,
(b) That it originated from inorganic materials, and (c) That life is a constituent of the Universe and can only arise from pre-existing life. The first hypothesis, he said, should be taken seriously, and he would proceed to do so. From the fact that there are 400,000 species of beetle on this planet, but only 8,000 species of mammals, he concluded that the Creator, if he exists, has a special preference for beetles, and so we might be more likely to meet them than any other type of animal on a planet which would support life.
In Mark Williamson, 'Haldane’s Special Preference', The Linnean, 1992, 8, 14.
Communication of science as subject-matter has so far outrun in education the construction of a scientific habit of mind that to some extent the natural common sense of mankind has been interfered with to its detriment.
Address to Section L, Education, of the American Association for the Advancement of Science, at Boston (1909), 'Science as Subject-Matter and as Method'. Published in Science (28 Jan 1910), N.S. Vol. 31, No. 787, 126.
Concerning the gods, I have no means of knowing either that they exist or that they do not exist, nor what sort of form they may have; there are many reasons why knowledge on this subject is not possible, owing to the lack of evidence and the shortness of human life.
Protagoras, fr. 1, quoted in E. Hussey, The Pre-Socratics (1972), 109.
Cosmology, for centuries consisting of speculation based on a minimum of observational evidence and a maximum of philosophical predilection, became in the twentieth century an observational science, its theories now subject to verification or refutation to a degree previously unimaginable.
Opening sentence in 'Philosophical Values and Observation in Edwin Hubble's Choice of a Model of the Universe', Historical Studies in the Physical Sciences (1982), 13, No. 1, 41.
Cuvier had even in his address & manner the character of a superior Man, much general power & eloquence in conversation & great variety of information on scientific as well as popular subjects. I should say of him that he is the most distinguished man of talents I have ever known on the continent: but I doubt if He be entitled to the appellation of a Man of Genius.
J. Z. Fullmer, 'Davy's Sketches of his Contemporaries', Chymia, 1967, 12, 132.
Dead is when the chemists take over the subject.
Lecture at Stanford, 'Is Spectroscopy Dead?', as quoted in Steven Chu and Charles H. Townes, 'Arthur Schawlow', Biographical Memoirs of the National Academy of Sciences (2003), Vol. 83, 202.
Deaths, births, and marriages, considering how much they are separately dependent on the freedom of the human will, should seem to be subject to no law according to which any calculation could be made beforehand of their amount; and yet the yearly registers of these events in great countries prove that they go on with as much conformity to the laws of nature as the oscillations of the weather.
'Idea of a Universal history on a Cosmo-Political Plan' (1784). As translated by Thomas De Quinsey in The London Magazine (Oct 1824), 10, 385. Reprinted in 1859 by De Quincey in Vol. 8 of his Collective Edition of his writings.
Definition of Mathematics.—It has now become apparent that the traditional field of mathematics in the province of discrete and continuous number can only be separated from the general abstract theory of classes and relations by a wavering and indeterminate line. Of course a discussion as to the mere application of a word easily degenerates into the most fruitless logomachy. It is open to any one to use any word in any sense. But on the assumption that “mathematics” is to denote a science well marked out by its subject matter and its methods from other topics of thought, and that at least it is to include all topics habitually assigned to it, there is now no option but to employ “mathematics” in the general sense of the “science concerned with the logical deduction of consequences from the general premisses of all reasoning.”
In article 'Mathematics', Encyclopedia Britannica (1911, 11th ed.), Vol. 17, 880. In the 2006 DVD edition of the encyclopedia, the definition of mathematics is given as “The science of structure, order, and relation that has evolved from elemental practices of counting, measuring, and describing the shapes of objects.” [Premiss is a variant form of “premise”. —Webmaster]
Descartes' immortal conclusion cogito ergo sum was recently subjected to destruction testing by a group of graduate researchers at Princeton led by Professors Montjuic and Lauterbrunnen, and now reads, in the Shorter Harvard Orthodoxy:
(a) I think, therefore I am; or
(b) Perhaps I thought, therefore I was; but
(c) These days, I tend to leave that side of things to my wife.
(a) I think, therefore I am; or
(b) Perhaps I thought, therefore I was; but
(c) These days, I tend to leave that side of things to my wife.
— Tom Holt
Ye Gods! (1992), 223.
Despite rapid progress in the right direction, the program of the average elementary school has been primarily devoted to teaching the fundamental subjects, the three R’s, and closely related disciplines… Artificial exercises, like drills on phonetics, multiplication tables, and formal writing movements, are used to a wasteful degree. Subjects such as arithmetic, language, and history include content that is intrinsically of little value. Nearly every subject is enlarged unwisely to satisfy the academic ideal of thoroughness… Elimination of the unessential by scientific study, then, is one step in improving the curriculum.
Does it not seem as if Algebra had attained to the dignity of a fine art, in which the workman has a free hand to develop his conceptions, as in a musical theme or a subject for a painting? It has reached a point where every properly developed algebraical composition, like a skillful landscape, is expected to suggest the notion of an infinite distance lying beyond the limits of the canvas.
In 'Lectures on the Theory of Reciprocants', Lecture XXI, American Journal of Mathematics (Jul 1886), 9, No. 3, 136.
Einstein, twenty-six years old, only three years away from crude privation, still a patent examiner, published in the Annalen der Physik in 1905 five papers on entirely different subjects. Three of them were among the greatest in the history of physics. One, very simple, gave the quantum explanation of the photoelectric effect—it was this work for which, sixteen years later, he was awarded the Nobel prize. Another dealt with the phenomenon of Brownian motion, the apparently erratic movement of tiny particles suspended in a liquid: Einstein showed that these movements satisfied a clear statistical law. This was like a conjuring trick, easy when explained: before it, decent scientists could still doubt the concrete existence of atoms and molecules: this paper was as near to a direct proof of their concreteness as a theoretician could give. The third paper was the special theory of relativity, which quietly amalgamated space, time, and matter into one fundamental unity.
This last paper contains no references and quotes no authority. All of them are written in a style unlike any other theoretical physicist’s. They contain very little mathematics. There is a good deal of verbal commentary. The conclusions, the bizarre conclusions, emerge as though with the greatest of ease: the reasoning is unbreakable. It looks as though he had reached the conclusions by pure thought, unaided, without listening to the opinions of others. To a surprisingly large extent, that is precisely what he had done.
This last paper contains no references and quotes no authority. All of them are written in a style unlike any other theoretical physicist’s. They contain very little mathematics. There is a good deal of verbal commentary. The conclusions, the bizarre conclusions, emerge as though with the greatest of ease: the reasoning is unbreakable. It looks as though he had reached the conclusions by pure thought, unaided, without listening to the opinions of others. To a surprisingly large extent, that is precisely what he had done.
In Variety of Men (1966), 100-101. First published in Commentary magazine.
Ethnologists regard man as the primitive element of tribes, races, and peoples. The anthropologist looks at him as a member of the fauna of the globe, belonging to a zoölogical classification, and subject to the same laws as the rest of the animal kingdom. To study him from the last point of view only would be to lose sight of some of his most interesting and practical relations; but to be confined to the ethnologist’s views is to set aside the scientific rule which requires us to proceed from the simple to the compound, from the known to the unknown, from the material and organic fact to the functional phenomenon.
'Paul Broca and the French School of Anthropology'. Lecture delivered in the National Museum, Washington, D.C., 15 April 1882, by Dr. Robert Fletcher. In The Saturday Lectures (1882), 118.
Every discipline must be honored for reason other than its utility, otherwise it yields no enthusiasm for industry.
For both reasons, I consider mathematics the chief subject for the common school. No more highly honored exercise for the mind can be found; the buoyancy [Spannkraft] which it produces is even greater than that produced by the ancient languages, while its utility is unquestioned.
For both reasons, I consider mathematics the chief subject for the common school. No more highly honored exercise for the mind can be found; the buoyancy [Spannkraft] which it produces is even greater than that produced by the ancient languages, while its utility is unquestioned.
In 'Mathematischer Lehrplan für Realschulen' Werke [Kehrbach] (1890), Bd. 5, 167. (Mathematics Curriculum for Secondary Schools). As quoted, cited and translated in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-Book (1914), 61.
Every subject in Davy’s mind has the principle of Vitality. Living thoughts spring up like Turf under his feet.
Quoted in Joseph Cottle, Reminiscences of Samuel Taylor Coleridge and Robert Southey (1847), 329.
Everything material which is the subject of knowledge has number, order, or position; and these are her first outlines for a sketch of the universe. If our feeble hands cannot follow out the details, still her part has been drawn with an unerring pen, and her work cannot be gainsaid. So wide is the range of mathematical sciences, so indefinitely may it extend beyond our actual powers of manipulation that at some moments we are inclined to fall down with even more than reverence before her majestic presence. But so strictly limited are her promises and powers, about so much that we might wish to know does she offer no information whatever, that at other moments we are fain to call her results but a vain thing, and to reject them as a stone where we had asked for bread. If one aspect of the subject encourages our hopes, so does the other tend to chasten our desires, and he is perhaps the wisest, and in the long run the happiest, among his fellows, who has learned not only this science, but also the larger lesson which it directly teaches, namely, to temper our aspirations to that which is possible, to moderate our desires to that which is attainable, to restrict our hopes to that of which accomplishment, if not immediately practicable, is at least distinctly within the range of conception.
From Presidential Address (Aug 1878) to the British Association, Dublin, published in the Report of the 48th Meeting of the British Association for the Advancement of Science (1878), 31.
Evolutionary plasticity can be purchased only at the ruthlessly dear price of continuously sacrificing some individuals to death from unfavourable mutations. Bemoaning this imperfection of nature has, however, no place in a scientific treatment of this subject.
Genetics and the Origin of Species (1937), 127.
Evolutionists sometimes take as haughty an attitude toward the next level up the conventional ladder of disciplines: the human sciences. They decry the supposed atheoretical particularism of their anthropological colleagues and argue that all would be well if only the students of humanity regarded their subject as yet another animal and therefore yielded explanatory control to evolutionary biologists.
From book review, 'The Ghost of Protagoras', The New York Review of Books (22 Jan 1981), 27, No. 21 & 22. Collected in An Urchin in the Storm: Essays about Books and Ideas (1987, 2010), 64. The article reviewed two books: John Tyler Bonner, The Evolution of Culture and Peter J. Wilson, The Promising Primate.
Exobiology—a curious development in view of the fact that this “science” has yet to demonstrate that its subject matter exists!
In This View of Life: The World of the Evolutionist (1964), 254.
Experience is never at fault; it is only your judgment that is in error in promising itself such results from experience as are not caused by our experiments. For having given a beginning, what follows from it must necessarily be a natural development of such a beginning, unless it has been subject to a contrary influence, while, if it is affected by any contrary influence, the result which ought to follow from the aforesaid beginning will be found to partake of this contrary influence in a greater or less degree in proportion as the said influence is more or less powerful than the aforesaid beginning.
'Philosophy', in The Notebooks of Leonardo da Vinci, trans. E. MacCurdy (1938), Vol. 1, 70.
Extremely hazardous is the desire to explain everything, and to supply whatever appears a gap in history—for in this propensity lies the first cause and germ of all those violent and arbitrary hypotheses which perplex and pervert the science of history far more than the open avowal of our ignorance, or the uncertainty of our knowledge: hypotheses which give an oblique direction, or an exaggerated and false extension, to a view of the subject originally not incorrect.
In Friedrich von Schlegel and James Burton Robertson (trans.), The Philosophy of History (1835), 12.
Faraday, … by his untiring faithfulness in keeping his diary, contributes to our understanding the objects of his scientific research in magnetism, electricity and light, but he also makes us understand the scientist himself, as a living subject, the mind in action.
In 'The Scientific Grammar of Michael Faraday’s Diaries', Part I, 'The Classic of Science', A Classic and a Founder (1937), collected in Rosenstock-Huessy Papers (1981), Vol. 1, 2.
First, as concerns the success of teaching mathematics. No instruction in the high schools is as difficult as that of mathematics, since the large majority of students are at first decidedly disinclined to be harnessed into the rigid framework of logical conclusions. The interest of young people is won much more easily, if sense-objects are made the starting point and the transition to abstract formulation is brought about gradually. For this reason it is psychologically quite correct to follow this course.
Not less to be recommended is this course if we inquire into the essential purpose of mathematical instruction. Formerly it was too exclusively held that this purpose is to sharpen the understanding. Surely another important end is to implant in the student the conviction that correct thinking based on true premises secures mastery over the outer world. To accomplish this the outer world must receive its share of attention from the very beginning.
Doubtless this is true but there is a danger which needs pointing out. It is as in the case of language teaching where the modern tendency is to secure in addition to grammar also an understanding of the authors. The danger lies in grammar being completely set aside leaving the subject without its indispensable solid basis. Just so in Teaching of Mathematics it is possible to accumulate interesting applications to such an extent as to stunt the essential logical development. This should in no wise be permitted, for thus the kernel of the whole matter is lost. Therefore: We do want throughout a quickening of mathematical instruction by the introduction of applications, but we do not want that the pendulum, which in former decades may have inclined too much toward the abstract side, should now swing to the other extreme; we would rather pursue the proper middle course.
Not less to be recommended is this course if we inquire into the essential purpose of mathematical instruction. Formerly it was too exclusively held that this purpose is to sharpen the understanding. Surely another important end is to implant in the student the conviction that correct thinking based on true premises secures mastery over the outer world. To accomplish this the outer world must receive its share of attention from the very beginning.
Doubtless this is true but there is a danger which needs pointing out. It is as in the case of language teaching where the modern tendency is to secure in addition to grammar also an understanding of the authors. The danger lies in grammar being completely set aside leaving the subject without its indispensable solid basis. Just so in Teaching of Mathematics it is possible to accumulate interesting applications to such an extent as to stunt the essential logical development. This should in no wise be permitted, for thus the kernel of the whole matter is lost. Therefore: We do want throughout a quickening of mathematical instruction by the introduction of applications, but we do not want that the pendulum, which in former decades may have inclined too much toward the abstract side, should now swing to the other extreme; we would rather pursue the proper middle course.
In Ueber den Mathematischen Unterricht an den hoheren Schulen; Jahresbericht der Deutschen Mathematiker Vereinigung, Bd. 11, 131.
For between true Science, and erroneous Doctrines, Ignorance is in the middle. Naturall sense and imagination, are not subject to absurdity. Nature it selfe cannot erre: and as men abound in copiousnesses of language; so they become more wise, or more mad than ordinary. Nor is it possible without Letters for any man to become either excellently wise, or (unless his memory be hurt by disease, or ill constitution of organs) excellently foolish. For words are wise men's counters, they do but reckon by them; but they are the money of fools that value them by the authority of an Aristotle, a Cicero, or a Thomas, or any other Doctor whatsoever, if but a man.
Leviathan (1651), ed. C. B. Macpherson (1968), Part 1, Chapter 4, 106.
For ourselves, we may take as a basic assumption, clear from a survey of particular cases, that natural things are some or all of them subject to change.
In 'Physics', Book 1, Chapter 2, 185a13, as translated by William Charlton, Physics: Books I and II (1983), 2.
For, Mathematical Demonstrations being built upon the impregnable Foundations of Geometry and Arithmetick, are the only Truths, that can sink into the Mind of Man, void of all Uncertainty; and all other Discourses participate more or less of Truth, according as their Subjects are more or less capable of Mathematical Demonstration.
Inaugural lecture of Christopher Wren in his chair of astronomy at Gresham College (1657). From Parentelia (1741, 1951), 200-201.
Fourier’s Theorem … is not only one of the most beautiful results of modern analysis, but it may be said to furnish an indispensable instrument in the treatment of nearly every recondite question in modern physics. To mention only sonorous vibrations, the propagation of electric signals along a telegraph wire, and the conduction of heat by the earth’s crust, as subjects in their generality intractable without it, is to give but a feeble idea of its importance.
In William Thomson and Peter Guthrie Tait, Treatise on Natural Philosophy (1867), Vol. 1, 28.
Freudian psychoanalytical theory is a mythology that answers pretty well to Levi-Strauss's descriptions. It brings some kind of order into incoherence; it, too, hangs together, makes sense, leaves no loose ends, and is never (but never) at a loss for explanation. In a state of bewilderment it may therefore bring comfort and relief … give its subject a new and deeper understanding of his own condition and of the nature of his relationship to his fellow men. A mythical structure will be built up around him which makes sense and is believable-in, regardless of whether or not it is true.
From 'Science and Literature', The Hope of Progress: A Scientist Looks at Problems in Philosophy, Literature and Science (1973), 29.
From the age of 13, I was attracted to physics and mathematics. My interest in these subjects derived mostly from popular science books that I read avidly. Early on I was fascinated by theoretical physics and determined to become a theoretical physicist. I had no real idea what that meant, but it seemed incredibly exciting to spend one's life attempting to find the secrets of the universe by using one's mind.
From 'Autobiography', in Tore Frängsmyr (ed.) Les Prix Nobel. The Nobel Prizes 2004, (2005).
From the infinitely great down to the infinitely small, all things are subject to [the laws of nature]. The sun and the planets follow the laws discovered by Newton and Laplace, just as the atoms in their combinations follow the laws of chemistry, as living creatures follow the laws of biology. It is only the imperfections of the human mind which multiply the divisions of the sciences, separating astronomy from physics or chemistry, the natural sciences from the social sciences. In essence, science is one. It is none other than the truth.
From Cours d’Economie Politique (1896-97), as given in Archives Internationales d’Histoire des Sciences (1993), Issues 131-133, 67.
General preparatory instruction must continue to be the aim in the instruction at the higher institutions of learning. Exclusive selection and treatment of subject matter with reference to specific avocations is disadvantageous.
In Resolution adopted by the German Association for the Advancement of Scientific and Mathematical Instruction, in Jahresbericht der Deutschen Mathematiker Vereinigung (1896), 41. As translated in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-Book (1914), 72.
Genetics was, I would say, the first part of biology to become a pretty good theoretical subject, based on the theory of the gene and patterns of inheritance of characteristics.
From interview with Neil A. Campbell, in 'Crossing the Boundaries of Science', BioScience (Dec 1986), 36, No. 11, 738.
Geology has its peculiar difficulties, from which all other sciences are exempt. Questions in chemistry may be settled in the laboratory by experiment. Mathematical and philosophical questions may be discussed, while the materials for discussion are ready furnished by our own intellectual reflections. Plants, animals and minerals, may be arranged in the museum, and all questions relating to their intrinsic principles may be discussed with facility. But the relative positions, the shades of difference, the peculiar complexions, whether continuous or in subordinate beds, are subjects of enquiry in settling the character of rocks, which can be judged of while they are in situ only.
A Geological and Agricultural Survey of the District Adjoining the Erie Canal (1824), 8.
Good scholars struggle to understand the world in an integral way (pedants bite off tiny bits and worry them to death). These visions of reality ... demand our respect, for they are an intellectual’s only birthright. They are often entirely wrong and always flawed in serious ways, but they must be understood honorably and not subjected to mayhem by the excision of patches.
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Good work is no done by “humble” men. It is one of the first duties of a professor, for example, in any subject, to exaggerate a little both the importance of his subject and his own importance in it. A man who is always asking “Is what I do worth while?” and “Am I the right person to do it?” will always be ineffective himself and a discouragement to others. He must shut his eyes a little and think a little more of his subject and himself than they deserve. This is not too difficult: it is harder not to make his subject and himself ridiculous by shutting his eyes too tightly.
In A Mathematician’s Apology (1940, 1967), 66.
He [Samuel Johnson] bid me always remember this, that after a system is well settled upon positive evidence, a few objections ought not to shake it. “The human mind is so limited that it cannot take in all parts of a subject; so that there may be objections raised against anything. There are objections against a plenum, and objections against a vacuum. Yet one of them must certainly be true.”
Note: Whereas vacuum means devoid of matter, plenum regards a space with matter throughout.
He is a learned man that understands one subject, a very learned man that understands two.
In Hialmer Day Gould, New Practical Spelling (1905), 14.
Here the most sublime scene ever witnessed in the operating room was presented when the patient placed himself voluntarily upon the table, which was to become the altar of future fame. … The heroic bravery of the man who voluntarily placed himself upon the table, a subject for the surgeon’s knife, should be recorded and his name enrolled upon parchment, which should be hung upon the walls of the surgical amphitheatre in which the operation was performed. His name was Gilbert Abbott.
Description of the first public demonstration of ether at the Massachussetts General Hospital (16 Oct 1846).
Description of the first public demonstration of ether at the Massachussetts General Hospital (16 Oct 1846).
From the Semi-Centennial of Anesthesia, Massachusetts General Hospital (1897). In Logan Clendening, Source Book of Medical History (1960), 373.
His subject is the “Origin of Species,” & not the origin of Organization; & it seems a needless mischief to have opened the latter speculation at all.
In a letter to Fannie Wedgwood (13 Mar 1860), in Harriet Martineau's Letters to Fanny Wedgwood (1983), 189.
Historically, Statistics is no more than State Arithmetic, a system of computation by which differences between individuals are eliminated by the taking of an average. It has been used—indeed, still is used—to enable rulers to know just how far they may safely go in picking the pockets of their subjects.
In Facts from Figures (1951), 1.
How can he [Thomas Edison] call it a wonderful success when everyone acquainted with the subject will recognize it as a conspicuous failure?
In The New York Herald, (18 Dec 1879). As quoted and cited in Rob Kaplan (ed.), Science Says (2001), 200.
How can you shorten the subject? That stern struggle with the multiplication table, for many people not yet ended in victory, how can you make it less? Square root, as obdurate as a hardwood stump in a pasture nothing but years of effort can extract it. You can’t hurry the process. Or pass from arithmetic to algebra; you can’t shoulder your way past quadratic equations or ripple through the binomial theorem. Instead, the other way; your feet are impeded in the tangled growth, your pace slackens, you sink and fall somewhere near the binomial theorem with the calculus in sight on the horizon. So died, for each of us, still bravely fighting, our mathematical training; except for a set of people called “mathematicians”—born so, like crooks.
In Too Much College: Or, Education Eating up Life, with Kindred Essays in Education and Humour (1939), 8.
How could science be any enemy of religion when God commanded man to be a scientist the day He told him to rule the earth and subject it?
In The Life of All Living: the philosophy of life (1929, 1942), 212.
However, if we consider that all the characteristics which have been cited are only differences in degree of structure, may we not suppose that this special condition of organization of man has been gradually acquired at the close of a long period of time, with the aid of circumstances which have proved favorable? What a subject for reflection for those who have the courage to enter into it!
In Recherches sur l'Organization des corps vivans (1802), as translated in Alpheus Spring Packard, Lamarck, the Founder of Evolution: His Life and Work (1901), 363. Packard's italics.
I accepted the Copernican position several years ago and discovered from thence the causes of many natural effects which are doubtless inexplicable by the current theories. I have written up many reasons and refutations on the subject, but I have not dared until now to bring them into the open, being warned by the fortunes of Copernicus himself, our master, who procured for himself immortal fame among a few but stepped down among the great crowd (for this is how foolish people are to be numbered), only to be derided and dishonoured. I would dare publish my thoughts if there were many like you; but since there are not, I shall forbear.
Letter to Johannes Kepler, 4 Aug 1597. Quoted in G. de Santillana, Crime of Galileo (1955), 11.
I admitted, that the world had existed millions of years. I am astonished at the ignorance of the masses on these subjects. Hugh Miller has it right when he says that 'the battle of evidences must now be fought on the field of the natural sciences.'
Letter to Burke A. Hinsdale, president of Hiram College (10 Jan 1859), commenting on the audience at Garfield's debate with William Denton. Quoted in John Clark Ridpath, The Life and Work of James A. Garfield (1881), 80.
I am a strong advocate for free thought on all subjects, yet it appears to me (whether rightly or wrongly) that direct arguments against christianity & theism produce hardly any effect on the public; & freedom of thought is best promoted by the gradual illumination of men's minds, which follow[s] from the advance of science. It has, therefore, been always my object to avoid writing on religion, & I have confined myself to science. I may, however, have been unduly biassed by the pain which it would give some members of my family, if I aided in any way direct attacks on religion.
Letter to E.B. Aveling (13 Oct 1880).
I am never content until I have constructed a mechanical model of the subject I am studying. If I succeed in making one, I understand. Otherwise, I do not. [Attributed; source unverified.]
Note: Webmaster has been unable to verify this quotation allegedly from his Baltimore Lectures. Is is widely quoted, usually without citation. A few instances indicate the quote came from a guest lecture, Johns Hopkins University, Baltimore (1884). The lecture notes were published in Baltimore Lectures on Molecular Dynamics and the Wave Theory of Light (1904). Webmaster has found no citation giving a page number, and has been unable to find the quote in that text. Anyone with more specific information, please contact Webmaster.
I am not, personally, a believer or a religious man in any sense of institutional commitment or practice. But I have a great respect for religion, and the subject has always fascinated me, beyond almost all others (with a few exceptions, like evolution and paleontology).
Leonardo's Mountain of Clams and the Diet of Worms: Essays on Natural History (1998), 281.
I am of opinion, then, ... that, if there is any circumstance thoroughly established in geology, it is, that the crust of our globe has been subjected to a great and sudden revolution, the epoch of which cannot be dated much farther back than five or six thousand years ago; that this revolution had buried all the countries which were before inhabited by men and by the other animals that are now best known; that the same revolution had laid dry the bed of the last ocean, which now forms all the countries at present inhabited; that the small number of individuals of men and other animals that escaped from the effects of that great revolution, have since propagated and spread over the lands then newly laid dry; and consequently, that the human race has only resumed a progressive state of improvement since that epoch, by forming established societies, raising monuments, collecting natural facts, and constructing systems of science and of learning.
'Preliminary discourse', to Recherches sur les Ossemens Fossiles (1812), trans. R. Kerr Essay on the Theory of the Earth (1813), 171-2.
I am of the decided opinion, that mathematical instruction must have for its first aim a deep penetration and complete command of abstract mathematical theory together with a clear insight into the structure of the system, and doubt not that the instruction which accomplishes this is valuable and interesting even if it neglects practical applications. If the instruction sharpens the understanding, if it arouses the scientific interest, whether mathematical or philosophical, if finally it calls into life an esthetic feeling for the beauty of a scientific edifice, the instruction will take on an ethical value as well, provided that with the interest it awakens also the impulse toward scientific activity. I contend, therefore, that even without reference to its applications mathematics in the high schools has a value equal to that of the other subjects of instruction.
In 'Ueber das Lehrziel im mathemalischen Unterricht der höheren Realanstalten', Jahresbericht der Deutschen Mathematiker Vereinigung, 2, 192. (The Annual Report of the German Mathematical Association. As translated in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-Book (1914), 73.
I am only a physicist with nothing material to show for my labours. I have never even seen the ionosphere, although I have worked on the subject for thirty years. That does show how lucky people can be. If there had been no ionosphere I would not have been standing here this morning.
Response to receiving an honour from the Institute of Mechanical Engineers. As quoted in New Scientist (22 Nov 1956), 33.
I am particularly concerned to determine the probability of causes and results, as exhibited in events that occur in large numbers, and to investigate the laws according to which that probability approaches a limit in proportion to the repetition of events. That investigation deserves the attention of mathematicians because of the analysis required. It is primarily there that the approximation of formulas that are functions of large numbers has its most important applications. The investigation will benefit observers in identifying the mean to be chosen among the results of their observations and the probability of the errors still to be apprehended. Lastly, the investigation is one that deserves the attention of philosophers in showing how in the final analysis there is a regularity underlying the very things that seem to us to pertain entirely to chance, and in unveiling the hidden but constant causes on which that regularity depends. It is on the regularity of the main outcomes of events taken in large numbers that various institutions depend, such as annuities, tontines, and insurance policies. Questions about those subjects, as well as about inoculation with vaccine and decisions of electoral assemblies, present no further difficulty in the light of my theory. I limit myself here to resolving the most general of them, but the importance of these concerns in civil life, the moral considerations that complicate them, and the voluminous data that they presuppose require a separate work.
Philosophical Essay on Probabilities (1825), trans. Andrew I. Dale (1995), Introduction.
I believe myself to possess a most singular combination of qualities exactly fitted to make me pre-eminently a discoverer of the hidden realities of nature… the belief has been forced upon me…
Firstly: Owing to some peculiarity in my nervous system, I have perceptions of some things, which no one else has… and intuitive perception of… things hidden from eyes, ears, & ordinary senses…
Secondly: my sense reasoning faculties;
Thirdly: my concentration faculty, by which I mean the power not only of throwing my whole energy & existence into whatever I choose, but also of bringing to bear on anyone subject or idea, a vast apparatus from all sorts of apparently irrelevant & extraneous sources…
Well, here I have written what most people would call a remarkably mad letter; & yet certainly one of the most logical, sober-minded, cool, pieces of composition, (I believe), that I ever framed.
Firstly: Owing to some peculiarity in my nervous system, I have perceptions of some things, which no one else has… and intuitive perception of… things hidden from eyes, ears, & ordinary senses…
Secondly: my sense reasoning faculties;
Thirdly: my concentration faculty, by which I mean the power not only of throwing my whole energy & existence into whatever I choose, but also of bringing to bear on anyone subject or idea, a vast apparatus from all sorts of apparently irrelevant & extraneous sources…
Well, here I have written what most people would call a remarkably mad letter; & yet certainly one of the most logical, sober-minded, cool, pieces of composition, (I believe), that I ever framed.
Lovelace Papers, Bodleian Library, Oxford University, 42, folio 12 (6 Feb 1841). As quoted and cited in Dorothy Stein (ed.), 'This First Child of Mine', Ada: A Life and a Legacy (1985), 86.
I believe that there is but one way to learn any subject, and that is through study. The very name student tells what the person so named should be doing; and with a natural science, dealing with a most complex object, extending through three dimensions of space, any other method besides studying the object is practically useless.
As quoted from a paper by Mall (1896), in Florence R. Sabin, Franklin Paine Mall: The Story of a Mind. (1934), 142.
I can see him [Sylvester] now, with his white beard and few locks of gray hair, his forehead wrinkled o’er with thoughts, writing rapidly his figures and formulae on the board, sometimes explaining as he wrote, while we, his listeners, caught the reflected sounds from the board. But stop, something is not right, he pauses, his hand goes to his forehead to help his thought, he goes over the work again, emphasizes the leading points, and finally discovers his difficulty. Perhaps it is some error in his figures, perhaps an oversight in the reasoning. Sometimes, however, the difficulty is not elucidated, and then there is not much to the rest of the lecture. But at the next lecture we would hear of some new discovery that was the outcome of that difficulty, and of some article for the Journal, which he had begun. If a text-book had been taken up at the beginning, with the intention of following it, that text-book was most likely doomed to oblivion for the rest of the term, or until the class had been made listeners to every new thought and principle that had sprung from the laboratory of his mind, in consequence of that first difficulty. Other difficulties would soon appear, so that no text-book could last more than half of the term. In this way his class listened to almost all of the work that subsequently appeared in the Journal. It seemed to be the quality of his mind that he must adhere to one subject. He would think about it, talk about it to his class, and finally write about it for the Journal. The merest accident might start him, but once started, every moment, every thought was given to it, and, as much as possible, he read what others had done in the same direction; but this last seemed to be his real point; he could not read without finding difficulties in the way of understanding the author. Thus, often his own work reproduced what had been done by others, and he did not find it out until too late.
A notable example of this is in his theory of cyclotomic functions, which he had reproduced in several foreign journals, only to find that he had been greatly anticipated by foreign authors. It was manifest, one of the critics said, that the learned professor had not read Rummer’s elementary results in the theory of ideal primes. Yet Professor Smith’s report on the theory of numbers, which contained a full synopsis of Kummer’s theory, was Professor Sylvester’s constant companion.
This weakness of Professor Sylvester, in not being able to read what others had done, is perhaps a concomitant of his peculiar genius. Other minds could pass over little difficulties and not be troubled by them, and so go on to a final understanding of the results of the author. But not so with him. A difficulty, however small, worried him, and he was sure to have difficulties until the subject had been worked over in his own way, to correspond with his own mode of thought. To read the work of others, meant therefore to him an almost independent development of it. Like the man whose pleasure in life is to pioneer the way for society into the forests, his rugged mind could derive satisfaction only in hewing out its own paths; and only when his efforts brought him into the uncleared fields of mathematics did he find his place in the Universe.
A notable example of this is in his theory of cyclotomic functions, which he had reproduced in several foreign journals, only to find that he had been greatly anticipated by foreign authors. It was manifest, one of the critics said, that the learned professor had not read Rummer’s elementary results in the theory of ideal primes. Yet Professor Smith’s report on the theory of numbers, which contained a full synopsis of Kummer’s theory, was Professor Sylvester’s constant companion.
This weakness of Professor Sylvester, in not being able to read what others had done, is perhaps a concomitant of his peculiar genius. Other minds could pass over little difficulties and not be troubled by them, and so go on to a final understanding of the results of the author. But not so with him. A difficulty, however small, worried him, and he was sure to have difficulties until the subject had been worked over in his own way, to correspond with his own mode of thought. To read the work of others, meant therefore to him an almost independent development of it. Like the man whose pleasure in life is to pioneer the way for society into the forests, his rugged mind could derive satisfaction only in hewing out its own paths; and only when his efforts brought him into the uncleared fields of mathematics did he find his place in the Universe.
In Florian Cajori, Teaching and History of Mathematics in the United States (1890), 266-267.
I can’t think of any definition of the words mathematician or scientist that would apply to me. I think of myself as a journalist who knows just enough about mathematics to be able to take low-level math and make it clear and interesting to nonmathematicians. Let me say that I think not knowing too much about a subject is an asset for a journalist, not a liability. The great secret of my column is that I know so little about mathematics that I have to work hard to understand the subject myself. Maybe I can explain things more clearly than a professional mathematician can.
In Scot Morris, 'Interview: Martin Gardner', Omni, 4, No. 4 (Jan 1982), 68.
I cannot anyhow be contented to view this wonderful universe, and especially the nature of man, and to conclude that everything is the result of brute force. I am inclined to look at everything as resulting from designed laws, with the details, whether good or bad, left to the working out of what we call chance. Not that this notion at all satisfies me. I feel most deeply that the whole subject is too profound for the human intellect. A dog might as well speculate on the mind of Newton. Let each man hope and believe what he can.
Letter to Asa Gray (22 May 1860). In Charles Darwin and Francis Darwin (ed.), Charles Darwin: His Life Told in an Autobiographical Chapter, and in a Selected Series of His Published Letters (1892), 236.
I contend that the continued racial classification of Homo sapiens represents an outmoded approach to the general problem of differentiation within a species. In other words, I reject a racial classification of humans for the same reasons that I prefer not to divide into subspecies the prodigiously variable West Indian land snails that form the subject of my own research.
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I count Maxwell and Einstein, Eddington and Dirac, among “real” mathematicians. The great modern achievements of applied mathematics have been in relativity and quantum mechanics, and these subjects are at present at any rate, almost as “useless” as the theory of numbers.
In A Mathematician's Apology (1940, 2012), 131.
I do not believe that the present flowering of science is due in the least to a real appreciation of the beauty and intellectual discipline of the subject. It is due simply to the fact that power, wealth and prestige can only be obtained by the correct application of science.
In 'Some Reflections on the Present Status of Organic Chemistry', Science and Human Progress: Addresses at the Celebrations of the 50th Anniversary of the Mellon Institute (1963), 90.
I do not maintain that the chief value of the study of arithmetic consists in the lessons of morality that arise from this study. I claim only that, to be impressed from day to day, that there is something that is right as an answer to the questions with which one is able to grapple, and that there is a wrong answer—that there are ways in which the right answer can be established as right, that these ways automatically reject error and slovenliness, and that the learner is able himself to manipulate these ways and to arrive at the establishment of the true as opposed to the untrue, this relentless hewing to the line and stopping at the line, must color distinctly the thought life of the pupil with more than a tinge of morality. … To be neighborly with truth, to feel one’s self somewhat facile in ways of recognizing and establishing what is right, what is correct, to find the wrong persistently and unfailingly rejected as of no value, to feel that one can apply these ways for himself, that one can think and work independently, have a real, a positive, and a purifying effect upon moral character. They are the quiet, steady undertones of the work that always appeal to the learner for the sanction of his best judgment, and these are the really significant matters in school work. It is not the noise and bluster, not even the dramatics or the polemics from the teacher’s desk, that abide longest and leave the deepest and stablest imprint upon character. It is these still, small voices that speak unmistakably for the right and against the wrong and the erroneous that really form human character. When the school subjects are arranged on the basis of the degree to which they contribute to the moral upbuilding of human character good arithmetic will be well up the list.
In Arithmetic in Public Education (1909), 18. As quoted and cited in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-book (1914), 69.
I do not think the division of the subject into two parts - into applied mathematics and experimental physics a good one, for natural philosophy without experiment is merely mathematical exercise, while experiment without mathematics will neither sufficiently discipline the mind or sufficiently extend our knowledge in a subject like physics.
to Henry Roscoe, Professor of Chemistry at Owens College (2 Jun 1870), B.C.S Archive Quoted in R.H. Kargon, Science in Victorian Manchester (1977), 215.
I don’t know what your Company is feeling as of today about the work of Dr. Alice Hamilton on benzol [benzene] poisoning. I know that back in the old days some of your boys used to think that she was a plain nuisance and just picking on you for luck. But I have a hunch that as you have learned more about the subject, men like your good self have grown to realize the debt that society owes her for her crusade. I am pretty sure that she has saved the lives of a great many girls in can-making plants and I would hate to think that you didn’t agree with me.
Letter to S. P. Miller, technical director of a company that sold solvents, 9 Feb 1933. Alice Hamilton papers, no. 40, Schlesinger Library, Radcliffe College. Quoted in Barbara Sicherman, Alice Hamilton: A Life in Letters (1984).
I feel that, in a sense, the writer knows nothing any longer. He has no moral stance. He offers the reader the contents of his own head, a set of options and imaginative alternatives. His role is that of a scientist, whether on safari or in his laboratory, faced with an unknown terrain or subject. All he can do is to devise various hypotheses and test them against the facts.
Crash (1973, 1995), Introduction. In Barry Atkins, More Than A Game: the Computer Game as a Fictional Form (2003), 144.
I have a true aversion to teaching. The perennial business of a professor of mathematics is only to teach the ABC of his science; most of the few pupils who go a step further, and usually to keep the metaphor, remain in the process of gathering information, become only Halbwisser [one who has superficial knowledge of the subject], for the rarer talents do not want to have themselves educated by lecture courses, but train themselves. And with this thankless work the professor loses his precious time.
Letter to Heinrich Olbers (26 Oct 1802). Quoted in G. Waldo Dunnington, Carl Friedrich Gauss: Titan of Science (2004), 414.
I have been branded with folly and madness for attempting what the world calls impossibilities, and even from the great engineer, the late James Watt, who said ... that I deserved hanging for bringing into use the high-pressure engine. This has so far been my reward from the public; but should this be all, I shall be satisfied by the great secret pleasure and laudable pride that I feel in my own breast from having been the instrument of bringing forward new principles and new arrangements of boundless value to my country, and however much I may be straitened in pecuniary circumstances, the great honour of being a useful subject can never be taken from me, which far exceeds riches.
From letter to Davies Gilbert, written a few months before Trevithick's last illness. Quoted in Francis Trevithick, Life of Richard Trevithick: With an Account of his Inventions (1872), Vol. 2, 395-6.
I have been described on more than one occasion as belonging to something called the 'Functional School of Social Anthropology' and even as being its leader, or one of its leaders. This Functional School does not really exist; it is a myth invented by Professor Malinowski ... There is no place in natural science for 'schools' in this sense, and I regard social anthropology as a branch of natural science. ... I conceive of social anthropology as the theoretical natural science of human society, that is, the investigation of social phenomena by methods essentially similar to those used in the physical and biological sciences. I am quite willing to call the subject 'comparative sociology', if anyone so wishes.
In A. Kuper, Anthropologists and Anthropology: The Modern British School (1983), 36.
I have no doubt that certain learned men, now that the novelty of the hypotheses in this work has been widely reported—for it establishes that the Earth moves, and indeed that the Sun is motionless in the middle of the universe—are extremely shocked, and think that the scholarly disciplines, rightly established once and for all, should not be upset. But if they are willing to judge the matter thoroughly, they will find that the author of this work has committed nothing which deserves censure. For it is proper for an astronomer to establish a record of the motions of the heavens with diligent and skilful observations, and then to think out and construct laws for them, or rather hypotheses, whatever their nature may be, since the true laws cannot be reached by the use of reason; and from those assumptions the motions can be correctly calculated, both for the future and for the past. Our author has shown himself outstandingly skilful in both these respects. Nor is it necessary that these hypotheses should be true, nor indeed even probable, but it is sufficient if they merely produce calculations which agree with the observations. … For it is clear enough that this subject is completely and simply ignorant of the laws which produce apparently irregular motions. And if it does work out any laws—as certainly it does work out very many—it does not do so in any way with the aim of persuading anyone that they are valid, but only to provide a correct basis for calculation. Since different hypotheses are sometimes available to explain one and the same motion (for instance eccentricity or an epicycle for the motion of the Sun) an astronomer will prefer to seize on the one which is easiest to grasp; a philosopher will perhaps look more for probability; but neither will grasp or convey anything certain, unless it has been divinely revealed to him. Let us therefore allow these new hypotheses also to become known beside the older, which are no more probable, especially since they are remarkable and easy; and let them bring with them the vast treasury of highly learned observations. And let no one expect from astronomy, as far as hypotheses are concerned, anything certain, since it cannot produce any such thing, in case if he seizes on things constructed for another other purpose as true, he departs from this discipline more foolish than he came to it.
Although this preface would have been assumed by contemporary readers to be written by Copernicus, it was unsigned. It is now believed to have been written and added at press time by Andreas Osiander (who was then overseeing the printing of the book). It suggests the earth’s motion as described was merely a mathematical device, and not to be taken as absolute reality. Text as given in 'To the Reader on the Hypotheses in this Work', Copernicus: On the Revolutions of the Heavenly Spheres (1543), translated by Alistair Matheson Duncan (1976), 22-3. By adding this preface, Osiander wished to stave off criticism by theologians. See also the Andreas Osiander Quotes page of this website.
I have said that mathematics is the oldest of the sciences; a glance at its more recent history will show that it has the energy of perpetual youth. The output of contributions to the advance of the science during the last century and more has been so enormous that it is difficult to say whether pride in the greatness of achievement in this subject, or despair at his inability to cope with the multiplicity of its detailed developments, should be the dominant feeling of the mathematician. Few people outside of the small circle of mathematical specialists have any idea of the vast growth of mathematical literature. The Royal Society Catalogue contains a list of nearly thirty- nine thousand papers on subjects of Pure Mathematics alone, which have appeared in seven hundred serials during the nineteenth century. This represents only a portion of the total output, the very large number of treatises, dissertations, and monographs published during the century being omitted.
In Presidential Address British Association for the Advancement of Science, Sheffield, Section A,
Nature (1 Sep 1910), 84, 285.
I have spent much time in the study of the abstract sciences; but the paucity of persons with whom you can communicate on such subjects disgusted me with them. When I began to study man, I saw that these abstract sciences are not suited to him, and that in diving into them, I wandered farther from my real object than those who knew them not, and I forgave them for not having attended to these things. I expected then, however, that I should find some companions in the study of man, since it was so specifically a duty. I was in error. There are fewer students of man than of geometry.
Thoughts of Blaise Pascal (1846), 137.
I have stated, that in the thirteen species of ground-finches [in the Galapagos Islands], a nearly perfect gradation may be traced, from a beak extraordinarily thick, to one so fine, that it may be compared to that of a warbler. I very much suspect, that certain members of the series are confined to different islands; therefore, if the collection had been made on any one island, it would not have presented so perfect a gradation. It is clear, that if several islands have each their peculiar species of the same genera, when these are placed together, they will have a wide range of character. But there is not space in this work, to enter on this curious subject.
Journal of Researches: into the Natural History and Geology of the Countries Visited During the Voyage of H.M.S. Beagle Round the World (1839), ch. XIX, 475.
I have steadily endeavored to keep my mind free so as to give up any hypothesis, however much beloved (and I cannot resist forming one on every subject) as soon as the facts are shown to be opposed to it. … I cannot remember a single first formed hypothesis which had not after a time to be given up or be greatly modified.
In Darwin’s Life and Letters (1887), 103-104.
I have the vagary of taking a lively interest in mathematical subjects only where I may anticipate ingenious association of ideas and results recommending themselves by elegance or generality.
Letter to Heinrich Schumacher (17 Sep 1808). Quoted in G. Waldo Dunnington, Carl Friedrich Gauss: Titan of Science (2004), 416.
I heard Professor Cannon lecture last night, going partly on your account. His subject was a physiological substitute for war—which is international sports and I suppose motorcycle races—to encourage the secretion of the adrenal glands!
Letter from James McKeen Cattell to his son, McKeen. In S. Benison, A. C. Barger and E. L. Wolfe, Walter B Cannon: The Life and Times of a Young Scientist (1987), 319.
I purpose, in return for the honour you do us by coming to see what are our proceedings here, to bring before you, in the course of these lectures, the Chemical History of a Candle. I have taken this subject on a former occasion; and were it left to my own will, I should prefer to repeat it almost every year—so abundant is the interest that attaches itself to the subject, so wonderful are the varieties of outlet which it offers into the various departments of philosophy. There is not a law under which any part of this universe is governed which does not come into play, and is touched upon in these phenomena. There is no better, there is no more open door by which you can enter the study of natural philosophy, than by considering the physical phenomena of a candle.
A Course of Six Lectures on the Chemical History of a Candle (1861), 13-4.
I simply believe that some part of the human Self or Soul is not subject to the laws of space and time.
In The Guardian, (19 Jul 1975), 9. Also quoted in Kim Lim (ed.), 1,001 Pearls of Spiritual Wisdom: Words to Enrich, Inspire, and Guide Your Life (2014), 36
I took this view of the subject. The medulla spinalis has a central division, and also a distinction into anterior and posterior fasciculi, corresponding with the anterior and posterior portions of the brain. Further we can trace down the crura of the cerebrum into the anterior fasciculus of the spinal marrow, and the crura of the cerebellum into the posterior fasciculus. I thought that here I might have an opportunity of touching the cerebellum, as it were, through the posterior portion of the spinal marrow, and the cerebrum by the anterior portion. To this end I made experiments which, though they were not conclusive, encouraged me in the view I had taken. I found that injury done to the anterior portion of the spinal marrow, convulsed the animal more certainly than injury done to the posterior portion; but I found it difficult to make the experiment without injuring both portions.
Idea of a New Anatomy of the Brain (1811), 21-22.
I was often humiliated to see men disputing for a piece of bread, just as animals might have done. My feelings on this subject have very much altered since I have been personally exposed to the tortures of hunger. I have discovered, in fact, that a man, whatever may have been his origin, his education, and his habits, is governed, under certain circumstances, much more by his stomach than by his intelligence and his heart.
In François Arago, trans. by William Henry Smyth, Baden Powell and Robert Grant, 'The History of My Youth: An Autobiography of Francis Arago', Biographies of Distinguished Scientific Men (1859), Vol. 1, 55.
I was suffering from a sharp attack of intermittent fever, and every day during the cold and succeeding hot fits had to lie down for several hours, during which time I had nothing to do but to think over any subjects then particularly interesting me. One day something brought to my recollection Malthus's 'Principles of Population', which I had read about twelve years before. I thought of his clear exposition of 'the positive checks to increase'—disease, accidents, war, and famine—which keep down the population of savage races to so much lower an average than that of more civilized peoples. It then occurred to me that these causes or their equivalents are continually acting in the case of animals also; and as animals usually breed much more rapidly than does mankind, the destruction every year from these causes must be enormous in order to keep down the numbers of each species, since they evidently do not increase regularly from year to year, as otherwise the world would long ago have been densely crowded with those that breed most quickly. Vaguely thinking over the enormous and constant destruction which this implied, it occurred to me to ask the question, Why do some die and some live? The answer was clearly, that on the whole the best fitted live. From the effects of disease the most healthy escaped; from enemies, the strongest, swiftest, or the most cunning; from famine, the best hunters or those with the best digestion; and so on. Then it suddenly flashed upon me that this self-acting process would necessarily improve the race, because in every generation the inferior would inevitably be killed off and the superior would remain—that is, the fittest would survive.
[The phrase 'survival of the fittest,' suggested by the writings of Thomas Robert Malthus, was expressed in those words by Herbert Spencer in 1865. Wallace saw the term in correspondence from Charles Darwin the following year, 1866. However, Wallace did not publish anything on his use of the expression until very much later, and his recollection is likely flawed.]
[The phrase 'survival of the fittest,' suggested by the writings of Thomas Robert Malthus, was expressed in those words by Herbert Spencer in 1865. Wallace saw the term in correspondence from Charles Darwin the following year, 1866. However, Wallace did not publish anything on his use of the expression until very much later, and his recollection is likely flawed.]
My Life: A Record of Events and Opinions (1905), Vol. 1, 361-362, or in reprint (2004), 190.
I will ask you to mark again that rather typical feature of the development of our subject; how so much progress depends on the interplay of techniques, discoveries and new ideas, probably in that order of decreasing importance.
This is the original quote, which gave rise to the commonly seen misstated shortened quote as: “Progress in science depends on new techniques, new discoveries and new ideas, probably in that order”—with the qualifying words “interplay” and “decreasing importance” omitted. From Brenner’s own handwritten notes of a Speech (20 Mar 1980), 'Biology in the 1980s', at the Friedrich Miescher Institute in Basel, Switzerland. Reproduced in his article 'Life sentences: Detective Rummage investigates', The Scientist (19 Aug 2002), 16, No. 16, 15. He reflects on the original wording of the quote, from his notes that he “came across”, while rummaging through “the piles of papers that I have accumulated,” (hence “Detective Rummage” in the title). See more on the commonly seen misstated shortened quote also on the Sydney Brenner Quotes web page of this site, beginning, “Progress in science…”.
I wish the lecturers to treat their subject as a strictly natural science, the greatest of all possible sciences, indeed, in one sense, the only science, that of Infinite Being, without reference to or reliance upon any supposed special exception or so-called miraculous revelation. I wish it considered just as astronomy or chemistry is.
Statement in deed of foundation of the Gifford Lectures on natural theology (1885).
Statement in deed of foundation of the Gifford Lectures on natural theology (1885).
Quoted in Michael A. Arbib and Mary B. Hesse, The Construction of Reality (1986), 1.
I, Galileo Galilei, son of the late Vincenzo Galilei, of Florence, aged seventy years, being brought personally to judgment, and kneeling before your Most Eminent and Most Reverend Lords Cardinals, General Inquisitors of the universal Christian republic against heretical depravity, having before my eyes the Holy Gospels, which I touch with my own hands, swear that I have always believed, and now believe, and with the help of God will in future believe, every article which the Holy Catholic and Apostolic Church of Rome holds, teaches, and preaches. But because I have been enjoined by this Holy Office altogether to abandon the false opinion which maintains that the sun is the centre and immovable, and forbidden to hold, defend, or teach the said false doctrine in any manner, and after it hath been signified to me that the said doctrine is repugnant with the Holy Scripture, I have written and printed a book, in which I treat of the same doctrine now condemned, and adduce reasons with great force in support of the same, without giving any solution, and therefore have been judged grievously suspected of heresy; that is to say, that I held and believed that the sun is the centre of the universe and is immovable, and that the earth is not the centre and is movable; willing, therefore, to remove from the minds of your Eminences, and of every Catholic Christian, this vehement suspicion rightfully entertained toward me, with a sincere heart and unfeigned faith, I abjure, curse, and detest the said errors and heresies, and generally every other error and sect contrary to Holy Church; and I swear that I will never more in future say or assert anything verbally, or in writing, which may give rise to a similar suspicion of me; but if I shall know any heretic, or anyone suspected of heresy, that I will denounce him to this Holy Office, or to the Inquisitor or Ordinary of the place where I may be; I swear, moreover, and promise, that I will fulfil and observe fully, all the penances which have been or shall be laid on me by this Holy Office. But if it shall happen that I violate any of my said promises, oaths, and protestations (which God avert!), I subject myself to all the pains and punishments which have been decreed and promulgated by the sacred canons, and other general and particular constitutions, against delinquents of this description. So may God help me, and his Holy Gospels which I touch with my own hands. I, the above-named Galileo Galilei, have abjured, sworn, promised, and bound myself as above, and in witness thereof with my own hand have subscribed this present writing of my abjuration, which I have recited word for word. At Rome, in the Convent of Minerva, June 22, 1633. I, Galileo Galilei, have abjured as above with my own hand.
Abjuration, 22 Jun 1633. In J.J. Fahie, Galileo, His Life and Work (1903), 319-321.
I’m sorry to say that the subject I most disliked was mathematics. I have thought about it. I think the reason was that mathematics leaves no room for argument. If you made a mistake, that was all there was to it.
The Autobiography of Malcolm X (1965, 1999), 34.
If a specific question has meaning, it must be possible to find operations by which an answer may be given to it ... I believe that many of the questions asked about social and philosophical subjects will be found to be meaningless when examined from the point of view of operations.
The Logic of Modern Physics (1960), 28.
If a teacher is full of his subject, and can induce enthusiasm in his pupils; if his facts are concrete and naturally connected, the amount of material that an average child can assimilate without injury is as astonishing as is the little that will fag him if it is a trifle above or below or remote from him, or taught dully or incoherently.
In The North American Review (Mar 1883), No. 316, 289.
If an explanation is so vague in its inherent nature, or so unskillfully molded in its formulation, that specific deductions subject to empirical verification or refutation can not be based upon it, then it can never serve as a working hypothesis. A hypothesis with which one can not work is not a working hypothesis.
'Role of Analysis in Scientific Investigation', Bulletin of the Geological Society of America (1933), 44, 479.
If I want to stop a research program I can always do it by getting a few experts to sit in on the subject, because they know right away that it was a fool thing to try in the first place.
If I were summing up the qualities of a good teacher of medicine, I would enumerate human sympathy, moral and intellectual integrity, enthusiasm, and ability to talk, in addition, of course, to knowledge of his subject.
If one might wish for impossibilities, I might then wish that my children might be well versed in physical science, but in due subordination to the fulness and freshness of their knowledge on moral subjects. ... Rather than have it the principal thing in my son's mind, I would gladly have him think that the sun went round the earth, and that the stars were so many spangles set in the bright blue firmament.
Letter to Dr. Greenhill (9 May 1836). In Arthur Penrhyn Stanley, The Life and Correspondence of Thomas Arnold (2nd Ed., 1846), 277.
If there were some deep principle that drove organic systems towards living systems, the operation of the principle should easily be demonstrable in a test tube in half a morning. Needless to say, no such demonstration has ever been given. Nothing happens when organic materials are subjected to the usual prescription of showers of electrical sparks or drenched in ultraviolet light, except the eventual production of a tarry sludge.
…...
If we range through the whole territory of nature, and endeavour to extract from each department the rich stores of knowledge and pleasure they respectively contain, we shall not find a more refined or purer source of amusement, or a more interesting and unfailing subject for recreation, than that which the observation and examination of the structure, affinities, and habits of plants and vegetables, afford.
In A Practical Treatise on the Cultivation of the Dahlia (1838), 2.
If you are young, then I say: Learn something about statistics as soon as you can. Don’t dismiss it through ignorance or because it calls for thought. … If you are older and already crowned with the laurels of success, see to it that those under your wing who look to you for advice are encouraged to look into this subject. In this way you will show that your arteries are not yet hardened, and you will be able to reap the benefits without doing overmuch work yourself. Whoever you are, if your work calls for the interpretation of data, you may be able to do without statistics, but you won’t do as well.
In Facts from Figures (1951), 463.
If you look over my Scientific American columns you will see that they get progressively more sophisticated as I began reading math books and learning more about the subject. There is no better way to learn anything than to write about it!
In Kendrick Frazier, 'A Mind at Play: An Interview with Martin Gardner', Skeptical Inquirer (Mar/Apr 1998), 22, No. 2, 36.
In 1847 I gave an address at Newton, Mass., before a Teachers’ Institute conducted by Horace Mann. My subject was grasshoppers. I passed around a large jar of these insects, and made every teacher take one and hold it while I was speaking. If any one dropped the insect, I stopped till he picked it up. This was at that time a great innovation, and excited much laughter and derision. There can be no true progress in the teaching of natural science until such methods become general.
In a sense cosmology contains all subjects because it is the story of everything, including biology, psychology and human history. In that single sense it can be said to contain an explanation also of time's arrow. But this is not what is meant by those who advocate the cosmological explanation of irreversibility. They imply that in some way the time arrow of cosmology imposes its sense on the thermodynamic arrow. I wish to disagree with this view. The explanation assumes that the universe is expanding. While this is current orthodoxy, there is no certainty about it. The red-shifts might be due to quite different causes. For example, when light passes through the expanding clouds of gas it will be red-shifted. A large number of such clouds might one day be invoked to explain these red shifts. It seems an odd procedure to attempt to 'explain' everyday occurrences, such as the diffusion of milk into coffee, by means of theories of the universe which are themselves less firmly established than the phenomena to be explained. Most people believe in explaining one set of things in terms of others about which they are more certain, and the explanation of normal irreversible phenomena in terms of the cosmological expansion is not in this category.
'Thermodynamics, Cosmology) and the Physical Constants', in J. T. Fraser (ed.), The Study of Time III (1973), 117-8.
In college I largely wasted my opportunities. My worst subjects were drawing and science. Almost my only memory of the chemistry class was of making some sulfuric acid into a foul-smelling concoction and dropping it into another student's pocket.
From My Own Story (1957), 55.
In early times, when the knowledge of nature was small, little attempt was made to divide science into parts, and men of science did not specialize. Aristotle was a master of all science known in his day, and wrote indifferently treatises on physics or animals. As increasing knowledge made it impossible for any one man to grasp all scientific subjects, lines of division were drawn for convenience of study and of teaching. Besides the broad distinction into physical and biological science, minute subdivisions arose, and, at a certain stage of development, much attention was, given to methods of classification, and much emphasis laid on the results, which were thought to have a significance beyond that of the mere convenience of mankind.
But we have reached the stage when the different streams of knowledge, followed by the different sciences, are coalescing, and the artificial barriers raised by calling those sciences by different names are breaking down. Geology uses the methods and data of physics, chemistry and biology; no one can say whether the science of radioactivity is to be classed as chemistry or physics, or whether sociology is properly grouped with biology or economics. Indeed, it is often just where this coalescence of two subjects occurs, when some connecting channel between them is opened suddenly, that the most striking advances in knowledge take place. The accumulated experience of one department of science, and the special methods which have been developed to deal with its problems, become suddenly available in the domain of another department, and many questions insoluble before may find answers in the new light cast upon them. Such considerations show us that science is in reality one, though we may agree to look on it now from one side and now from another as we approach it from the standpoint of physics, physiology or psychology.
But we have reached the stage when the different streams of knowledge, followed by the different sciences, are coalescing, and the artificial barriers raised by calling those sciences by different names are breaking down. Geology uses the methods and data of physics, chemistry and biology; no one can say whether the science of radioactivity is to be classed as chemistry or physics, or whether sociology is properly grouped with biology or economics. Indeed, it is often just where this coalescence of two subjects occurs, when some connecting channel between them is opened suddenly, that the most striking advances in knowledge take place. The accumulated experience of one department of science, and the special methods which have been developed to deal with its problems, become suddenly available in the domain of another department, and many questions insoluble before may find answers in the new light cast upon them. Such considerations show us that science is in reality one, though we may agree to look on it now from one side and now from another as we approach it from the standpoint of physics, physiology or psychology.
In article 'Science', Encyclopedia Britannica (1911), 402.
In every science certain things must be accepted as first principles if the subject matter is to be understood; and these first postulates rest upon faith.
As quoted, without citation, in Ronald Keast, Dancing in the Dark: The Waltz in Wonder of Quantum Metaphysics (2009), 104-105. If you know a primary source, please contact Webmaster.
In like manner, the loadstone has from nature its two poles, a northern and a southern; fixed, definite points in the stone, which are the primary termini of the movements and effects, and the limits and regulators of the several actions and properties. It is to be understood, however, that not from a mathematical point does the force of the stone emanate, but from the parts themselves; and all these parts in the whole—while they belong to the whole—the nearer they are to the poles of the stone the stronger virtues do they acquire and pour out on other bodies. These poles look toward the poles of the earth, and move toward them, and are subject to them. The magnetic poles may be found in very loadstone, whether strong and powerful (male, as the term was in antiquity) or faint, weak, and female; whether its shape is due to design or to chance, and whether it be long, or flat, or four-square, or three-cornered or polished; whether it be rough, broken-off, or unpolished: the loadstone ever has and ever shows its poles.
On the Loadstone and Magnetic Bodies and on the Great Magnet the Earth: A New Physiology, Demonstrated with many Arguments and Experiments (1600), trans. P. Fleury Mottelay (1893), 23.
In my first publication I might have claimed that I had come to the conclusion, as a result of serious study of the literature and deep thought, that valuable antibacterial substances were made by moulds and that I set out to investigate the problem. That would have been untrue and I preferred to tell the truth that penicillin started as a chance observation. My only merit is that I did not neglect the observation and that I pursued the subject as a bacteriologist. My publication in 1929 was the starting-point of the work of others who developed penicillin especially in the chemical field.
'Penicillin', Nobel Lecture, 11 Dec 1945. In Nobel Lectures: Physiology or Medicine 1942-1962 (1964), 83.
In nature hybrid species are usually sterile, but in science the reverse is often true. Hybrid subjects are often astonishingly fertile, whereas if a scientific discipline remains too pure it usually wilts.
In What Mad Pursuit: A Personal View of Scientific Discovery (1988), 150.
In no subject is there a rule, compliance with which will lead to new knowledge or better understanding. Skilful observations, ingenious ideas, cunning tricks, daring suggestions, laborious calculations, all these may be required to advance a subject. Occasionally the conventional approach in a subject has to be studiously followed; on other occasions it has to be ruthlessly disregarded. Which of these methods, or in what order they should be employed is generally unpredictable. Analogies drawn from the history of science are frequently claimed to be a guide; but, as with forecasting the next game of roulette, the existence of the best analogy to the present is no guide whatever to the future. The most valuable lesson to be learnt from the history of scientific progress is how misleading and strangling such analogies have been, and how success has come to those who ignored them.
'Cosmology', in Arthur Beer (ed.), Vistas in Astronomy (1956), Vol. 2, 1722.
In other branches of science, where quick publication seems to be so much desired, there may possibly be some excuse for giving to the world slovenly or ill-digested work, but there is no such excuse in mathematics. The form ought to be as perfect as the substance, and the demonstrations as rigorous as those of Euclid. The mathematician has to deal with the most exact facts of Nature, and he should spare no effort to render his interpretation worthy of his subject, and to give to his work its highest degree of perfection. “Pauca sed matura” was Gauss’s motto.
In Presidential Address British Association for the Advancement of Science, Section A, (1890), Nature, 42, 467. [The Latin motto translates as “Few, but ripe”. —Webmaster]
In physical science a first essential step in the direction of learning any subject is to find principles of numerical reckoning and practicable methods for measuring some quality connected with it. I often say that when you can measure what you are speaking about, and express it in numbers, you know something about it; but when you cannot measure it, when you cannot express it in numbers, your knowledge is of a meagre and unsatisfactory kind; it may be the beginning of knowledge, but you have scarcely in your thoughts advanced to the stage of science, whatever the matter may be.
Often seen quoted in a condensed form: If you cannot measure it, then it is not science.
Often seen quoted in a condensed form: If you cannot measure it, then it is not science.
From lecture to the Institution of Civil Engineers, London (3 May 1883), 'Electrical Units of Measurement', Popular Lectures and Addresses (1889), Vol. 1, 80-81.
In science nothing can be permanently accepted but that which is true, and whatever is accepted as true is challenged again and again. It is an axiom in science that no truth can be so sacred that it may not be questioned. When that which has been accepted as true has the least doubt thrown upon it, scientific men at once re-examine the subject. No opinion is sacred. “It ought to be” is never heard in scientific circles. “It seems to be” and “we think it is” is the modest language of scientific literature.
From address (1 Oct 1884), at inauguration of the Corcoran School of Science and Arts, Columbian University, Washington, D.C. Published in 'The Larger Import of Scientific Education', Popular Science Monthly (Feb 1885), 26, 455.
In science, attempts at formulating hierarchies are always doomed to eventual failure. A Newton will always be followed by an Einstein, a Stahl by a Lavoisier; and who can say who will come after us? What the human mind has fabricated must be subject to all the changes—which are not progress—that the human mind must undergo. The 'last words' of the sciences are often replaced, more often forgotten. Science is a relentlessly dialectical process, though it suffers continuously under the necessary relativation of equally indispensable absolutes. It is, however, possible that the ever-growing intellectual and moral pollution of our scientific atmosphere will bring this process to a standstill. The immense library of ancient Alexandria was both symptom and cause of the ossification of the Greek intellect. Even now I know of some who feel that we know too much about the wrong things.
Voices in the Labyrinth: Nature, Man, and Science (1979), 46.
In science, each of us knows that what he has accomplished will be antiquated in ten, twenty, fifty years. That is the fate to which science is subjected; it is the very meaning of scientific work, to which it is devoted in a quite specific sense, as compared with other spheres of culture for which in general the same holds. Every scientific “fulfilment” raises new “questions”; it asks to be “surpassed” and outdated. Whoever wishes to serve science has to resign himself to this fact. Scientific works certainly can last as “gratifications” because of their artistic quality, or they may remain important as a means of training. Yet they will be surpassed scientifically—let that be repeated—for it is our common fate and, more our common goal. We cannot work without hoping that others will advance further than we have. In principle, this progress goes on ad infinitum.
From a Speech (1918) presented at Munich University, published in 1919, and collected in 'Wissenschaft als Beruf', Gessammelte Aufsätze zur Wissenschaftslehre (1922), 524-525. As given in H.H. Gerth and C. Wright-Mills (translators and eds.), 'Science as a Vocation', Max Weber: Essays in Sociology (1946), 138. A different translation of a shorter excerpt from this quote, beginning “[In] the realm of science, …” is also on the Max Weber Quotes web page on this site.
In summary, all great work is the fruit of patience and perseverance, combined with tenacious concentration on a subject over a period of months or years.
From Reglas y Consejos sobre Investigacíon Cientifica: Los tónicos de la voluntad. (1897), as translated by Neely and Larry W. Swanson, in Advice for a Young Investigator (1999), 38.
In the beginning there was an explosion. Not an explosion like those familiar on earth, starting from a definite center and spreading out to engulf more and more of the circumambient air, but an explosion which occurred simultaneously everywhere, filling all space from the beginning, with every particle of matter rushing apart from every other particle. ‘All space’ in this context may mean either all of an infinite universe, or all of a finite universe which curves back on itself like the surface of a sphere. Neither possibility is easy to comprehend, but this will not get in our way; it matters hardly at all in the early universe whether space is finite or infinite. At about one-hundredth of a second, the earliest time about which we can speak with any confidence, the temperature of the universe was about a hundred thousand million (1011) degrees Centigrade. This is much hotter than in the center of even the hottest star, so hot, in fact, that none of the components of ordinary matter, molecules, or atoms, or even the nuclei of atoms, could have held together. Instead, the matter rushing apart in this explosion consisted of various types of the so-called elementary particles, which are the subject of modern highenergy nuclear physics.
The First Three Minutes: A Modern View of the Origin of the Universe (1977), 5.
In the collecting of evidence upon any medical subject, there are but three sources from which we can hope to obtain it: viz. from observation of the living subject; from examination of the dead; and from experiments upon living animals.
Astley Cooper and Benjamin Travers, Surgical Essays (1821), Vol. 1, 84. In Ira M. Rutkow, The History of Surgery in the United States, 1775-1900 (1988), 394.
In the mathematical investigations I have usually employed such methods as present themselves naturally to a physicist. The pure mathematician will complain, and (it must be confessed) sometimes with justice, of deficient rigour. But to this question there are two sides. For, however important it may be to maintain a uniformly high standard in pure mathematics, the physicist may occasionally do well to rest content with arguments which are fairly satisfactory and conclusive from his point of view. To his mind, exercised in a different order of ideas, the more severe procedure of the pure mathematician may appear not more but less demonstrative. And further, in many cases of difficulty to insist upon the highest standard would mean the exclusion of the subject altogether in view of the space that would be required.
In Preface to second edition, The Theory of Sound (1894), Vol. 1, vii.
In the study of this membrane [the retina] I for the first time felt my faith in Darwinism (hypothesis of natural selection) weakened, being amazed and confounded by the supreme constructive ingenuity revealed not only in the retina and in the dioptric apparatus of the vertebrates but even in the meanest insect eye. ... I felt more profoundly than in any other subject of study the shuddering sensation of the unfathomable mystery of life.
Recollections of My Life (1898), 576. Quoted in Sidney Perkowitz, Empire of Light (1999), 16.
In trying to evaluate Hopkins' unique contribution to biochemistry it may perhaps be said that he alone amongst his contemporaries succeeded in formulating the subject. Among others whose several achievements in their own fields may have surpassed his, no one has ever attempted to unify and correlate biochemical knowledge so as to form a comprehensible picture of the cell and its relation to life, reproduction and function.
'Sir F. G. Hopkins' Teaching and Scientific Influence'. In J. Needham and E. Baldwin (eds.), Hopkins and Biochemistry, 1861-1947 (1949), 36.
Indeed, the aim of teaching [mathematics] should be rather to strengthen his [the pupil’s] faculties, and to supply a method of reasoning applicable to other subjects, than to furnish him with an instrument for solving practical problems.
In John Perry (ed.), Discussion on the Teaching of Mathematics (1901), 84. The discussion took place on 14 Sep 1901 at the British Association at Glasgow, during a joint meeting of the mathematics and physics sections with the education section. The proceedings began with an address by John Perry. Magnus spoke in the Discussion that followed.
Intelligence is important in psychology for two reasons. First, it is one of the most scientifically developed corners of the subject, giving the student as complete a view as is possible anywhere of the way scientific method can be applied to psychological problems. Secondly, it is of immense practical importance, educationally, socially, and in regard to physiology and genetics.
From Intelligence: Its Structure, Growth and Action: Its Structure, Growth and Action (1987), 1.
Is there perhaps some magical power in the subject [mathematics] that, although it had fought under the invincible banner of truth, has actually achieved its victories through some inner mysterious strength?
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It frequently happens that two persons, reasoning right on a mechanical subject, think alike and invent the same thing without any communication with each other.
As quoted by Coleman Sellers, Jr., in his Lecture (20 Nov 1885) delivered at the Franklin Institute. Printed in Coleman Sellers, Jr., 'Oliver Evans and his Inventions', Journal of the Franklin Institute (Jul 1886), 122, No. 1, 15.
It has sometimes been said that the success of the Origin proved “that the subject was in the air,” or “that men's minds were prepared for it.” I do not think that this is strictly true, for I occasionally sounded not a few naturalists, and never happened to come across a single one who seemed to doubt about the permanence of species.
In Charles Darwin and Francis Darwin (ed.), Charles Darwin: His Life Told in an Autobiographical Chapter, and in a Selected Series of His Published Letters (1892), 42.
It hath been an old remark, that Geometry is an excellent Logic. And it must be owned that when the definitions are clear; when the postulata cannot be refused, nor the axioms denied; when from the distinct contemplation and comparison of figures, their properties are derived, by a perpetual well-connected chain of consequences, the objects being still kept in view, and the attention ever fixed upon them; there is acquired a habit of reasoning, close and exact and methodical; which habit strengthens and sharpens the mind, and being transferred to other subjects is of general use in the inquiry after truth.
In 'The Analyst', in The Works of George Berkeley (1898), Vol. 3, 10.
It is a peculiar feature in the fortune of principles of such high elementary generality and simplicity as characterise the laws of motion, that when they are once firmly established, or supposed to be so, men turn with weariness and impatience from all questionings of the grounds and nature of their authority. We often feel disposed to believe that truths so clear and comprehensive are necessary conditions, rather than empirical attributes of their subjects: that they are legible by their own axiomatic light, like the first truths of geometry, rather than discovered by the blind gropings of experience.
In An Introduction to Dynamics (1832), x.
It is above all the duty of the methodical text-book to adapt itself to the pupil’s power of comprehension, only challenging his higher efforts with the increasing development of his imagination, his logical power and the ability of abstraction. This indeed constitutes a test of the art of teaching, it is here where pedagogic tact becomes manifest. In reference to the axioms, caution is necessary. It should be pointed out comparatively early, in how far the mathematical body differs from the material body. Furthermore, since mathematical bodies are really portions of space, this space is to be conceived as mathematical space and to be clearly distinguished from real or physical space. Gradually the student will become conscious that the portion of the real space which lies beyond the visible stellar universe is not cognizable through the senses, that we know nothing of its properties and consequently have no basis for judgments concerning it. Mathematical space, on the other hand, may be subjected to conditions, for instance, we may condition its properties at infinity, and these conditions constitute the axioms, say the Euclidean axioms. But every student will require years before the conviction of the truth of this last statement will force itself upon him.
In Methodisches Lehrbuch der Elementar-Mathemalik (1904), Teil I, Vorwort, 4-5.
It is also vital to a valuable education that independent critical thinking be developed in the young human being, a development that is greatly jeopardized by overburdening with too much and too varied subjects. Overburdening necessarily leads to superficiality.
From interview with Benjamin Fine, 'Einstein Stresses Critical Thinking', New York Times (5 Oct 1952), 37. [Here, “superficiality” has been inserted as a correction for a typo, “superciality”, in the original text. —Webmaster]
It is certainly true that all physical phenomena are subject to strictly mathematical conditions, and mathematical processes are unassailable in themselves. The trouble arises from the data employed. Most phenomena are so highly complex that one can never be quite sure that he is dealing with all the factors until the experiment proves it. So that experiment is rather the criterion of mathematical conclusions and must lead the way.
In Matter, Ether, Motion (1894), 89.
It is not Cayley’s way to analyze concepts into their ultimate elements. … But he is master of the empirical utilization of the material: in the way he combines it to form a single abstract concept which he generalizes and then subjects to computative tests, in the way the newly acquired data are made to yield at a single stroke the general comprehensive idea to the subsequent numerical verification of which years of labor are devoted. Cayley is thus the natural philosopher among mathematicians.
In Mathematische Annalen, Bd. 46 (1895), 479. As quoted and cited in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-book (1914), 146.
It is not knowledge, but the act of learning, not possession but the act of getting there, which grants the greatest enjoyment. When I have clarified and exhausted a subject, then I turn away from it, in order to go into darkness again; the never-satisfied man is so strange if he has completed a structure, then it is not in order to dwell in it peacefully,but in order to begin another. I imagine the world conqueror must feel thus, who, after one kingdom is scarcely conquered, stretches out his arms for others.
Letter to Farkas Wolfgang Bolyai (2 Sep 1808). Quoted in G. Waldo Dunnington, Carl Friedrich Gauss: Titan of Science (2004), 416.
It is not surprising that our language should be incapable of describing the processes occurring within the atoms, for, as has been remarked, it was invented to describe the experiences of daily life, and these consists only of processes involving exceedingly large numbers of atoms. Furthermore, it is very difficult to modify our language so that it will be able to describe these atomic processes, for words can only describe things of which we can form mental pictures, and this ability, too, is a result of daily experience. Fortunately, mathematics is not subject to this limitation, and it has been possible to invent a mathematical scheme—the quantum theory—which seems entirely adequate for the treatment of atomic processes; for visualization, however, we must content ourselves with two incomplete analogies—the wave picture and the corpuscular picture.
The Physical Principles of the Quantum Theory, trans. Carl Eckart and Frank C. Hoyt (1949), 11.
It is not, indeed, strange that the Greeks and Romans should not have carried ... any ... experimental science, so far as it has been carried in our time; for the experimental sciences are generally in a state of progression. They were better understood in the seventeenth century than in the sixteenth, and in the eighteenth century than in the seventeenth. But this constant improvement, this natural growth of knowledge, will not altogether account for the immense superiority of the modern writers. The difference is a difference not in degree, but of kind. It is not merely that new principles have been discovered, but that new faculties seem to be exerted. It is not that at one time the human intellect should have made but small progress, and at another time have advanced far; but that at one time it should have been stationary, and at another time constantly proceeding. In taste and imagination, in the graces of style, in the arts of persuasion, in the magnificence of public works, the ancients were at least our equals. They reasoned as justly as ourselves on subjects which required pure demonstration.
History (May 1828). In Samuel Austin Allibone, Prose Quotations from Socrates to Macaulay (1880), 36.
It is of great advantage to the student of any subject to read the original memoirs on that subject, for science is always most completely assimilated when it is in the nascent state.
A Treatise on Electricity and Magnetism (1873), Vol. 1, Preface, xiii-xiv.
It is one of the signs of the times that modern chemists hold themselves bound and consider themselves in a position to give an explanation for everything, and when their knowledge fails them to make sure of supernatural explanations. Such a treatment of scientific subjects, not many degrees removed from a belief in witches and spirit-rapping, even Wislicenus considers permissible.
In H. Kolbe, 'Sign of the Times', Journal für Praktische Chemie (1877), 15, 473. Trans. W. H. Brock.
It is perhaps a law of nature that when a species (or group) fits itself to a place not previously occupied, and in which it is subject to no opposition from beings of its own class, or where it attains so great a perfection as to be able easily to overcome all opposition, the character eventually loses its original plasticity, or tendency to vary, since improvement in such a case would be superfluous, and becomes, so to speak, crystallized in that form which continues thereafter unaltered. … [Such as] the humming-bird.
In The Naturalist in La Plata (1895), 40.
It is profitable nevertheless to permit ourselves to talk about 'meaningless' terms in the narrow sense if the preconditions to which all profitable operations are subject are so intuitive and so universally accepted as to form an almost unconscious part of the background of the public using the term. Physicists of the present day do constitute a homogenous public of this character; it is in the air that certain sorts of operation are valueless for achieving certain sorts of result. If one wants to know how many planets there are one counts them but does not ask a philosopher what is the perfect number.
Reflections of a Physicist (1950), 6.
It is rigid dogma that destroys truth; and, please notice, my emphasis is not on the dogma, but on the rigidity. When men say of any question, “This is all there is to be known or said of the subject; investigation ends here,” that is death. It may be that the mischief comes not from the thinker but for the use made of his thinking by late-comers. Aristotle, for example, gave us our scientific technique … yet his logical propositions, his instruction in sound reasoning which was bequeathed to Europe, are valid only within the limited framework of formal logic, and, as used in Europe, they stultified the minds of whole generations of mediaeval Schoolmen. Aristotle invented science, but destroyed philosophy.
Dialogues of Alfred North Whitehead, as recorded by Lucien Price (1954, 2001), 165.
It is sages and grey-haired philosophers who ought to sit up all night reading Alice in Wonderland in order to study that darkest problem of metaphysics, the borderland between reason and unreason, and the nature of the most erratic of spiritual forces, humour, which eternally dances between the two. That we do find a pleasure in certain long and elaborate stories, in certain complicated and curious forms of diction, which have no intelligible meaning whatever, is not a subject for children to play with; it is a subject for psychologists to go mad over.
In 'The Library of the Nursery', in Lunacy and Letters (1958), 26.
It is the great beauty of our science that advancement in it, whether in a degree great or small, instead of exhausting the subject of research, opens the doors to further and more abundant knowledge, overflowing with beauty and utility.
From 'Experimental Researches in Electricity: Series VII: § 13. On the absolute quantity of Electricity associated with the particles or atoms of Matter', Philosophic Transactions, (text dated 31 Dec 1833, received 9 Jan 1834, read 13 Feb 1834). Collected in Experimental Researches in Electricity (1839), Vol. 1, 257.
It is the lone worker who makes the first advance in a subject: the details may be worked out by a team, but the prime idea is due to the enterprise, thought, and perception of an individual.
In a speech at Edinburgh University (1951). As cited in John Bartlett, Bartlett’s Familiar Quotations (18th ed., 2012), 647.
It is this mythical, or rather this symbolic, content of the religious traditions which is likely to come into conflict with science. This occurs whenever this religious stock of ideas contains dogmatically fixed statements on subjects which be long in the domain of science. Thus, it is of vital importance for the preservation of true religion that such conflicts be avoided when they arise from subjects which, in fact, are not really essential for the pursuance of the religious aims.
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It may be conceit, but I believe the subject will interest the public, and I am sure that the views are original.
Letter to his publisher, John Murray (5 Apr 1959). In Charles Darwin and Francis Darwin (ed.), The Life and Letters of Charles Darwin (1887), Vol. 2, 155.
It may sound like a lot of work to keep up with organic chemistry, and it is; however, those who haven't the time to do it become subject to decay in the ability to teach and to contribute to the Science—a sort of first-order process the half-life of which can't be much more than a year or two.
Highlights of Organic Chemistry: An Advanced Textbook (1974), 112.
It need scarcely be pointed out that with such a mechanism complete isolation of portion of a species should result relatively rapidly in specific differentiation, and one that is not necessarily adaptive. The effective intergroup competition leading to adaptive advance may be between species rather than races. Such isolation is doubtless usually geographic in character at the outset but may be clinched by the development of hybrid sterility. The usual difference of the chromosome complements of related species puts the importance of chromosome aberration as an evolutionary process beyond question, but, as I see it, this importance is not in the character differences which they bring (slight in balanced types), but rather in leading to the sterility of hybrids and thus making permanent the isolation of two groups.
How far do the observations of actual species and their subdivisions conform to this picture? This is naturally too large a subject for more than a few suggestions.
That evolution involves non-adaptive differentiation to a large extent at the subspecies and even the species level is indicated by the kinds of differences by which such groups are actually distinguished by systematics. It is only at the subfamily and family levels that clear-cut adaptive differences become the rule. The principal evolutionary mechanism in the origin of species must thus be an essentially nonadaptive one.
How far do the observations of actual species and their subdivisions conform to this picture? This is naturally too large a subject for more than a few suggestions.
That evolution involves non-adaptive differentiation to a large extent at the subspecies and even the species level is indicated by the kinds of differences by which such groups are actually distinguished by systematics. It is only at the subfamily and family levels that clear-cut adaptive differences become the rule. The principal evolutionary mechanism in the origin of species must thus be an essentially nonadaptive one.
In Proceedings of the Sixth International Congress of Genetics: Ithaca, New York, 1932 (1932) Vol. 1, 363-364.
It often happens that men, even of the best understandings and greatest circumspection, are guilty of that fault in reasoning which the writers on logick call the insufficient, or imperfect enumeration of parts, or cases: insomuch that I will venture to assert, that this is the chief, and almost the only, source of the vast number of erroneous opinions, and those too very often in matters of great importance, which we are apt to form on all the subjects we reflect upon, whether they relate to the knowledge of nature, or the merits and motives of human actions. It must therefore be acknowledged, that the art which affords a cure to this weakness, or defect, of our understandings, and teaches us to enumerate all the possible ways in which a given number of things may be mixed and combined together, that we may be certain that we have not omitted anyone arrangement of them that can lead to the object of our inquiry, deserves to be considered as most eminently useful and worthy of our highest esteem and attention. And this is the business of the art, or doctrine of combinations ... It proceeds indeed upon mathematical principles in calculating the number of the combinations of the things proposed: but by the conclusions that are obtained by it, the sagacity of the natural philosopher, the exactness of the historian, the skill and judgement of the physician, and the prudence and foresight of the politician, may be assisted; because the business of all these important professions is but to form reasonable conjectures concerning the several objects which engage their attention, and all wise conjectures are the results of a just and careful examination of the several different effects that may possibly arise from the causes that are capable of producing them.
Ars conjectandi (1713). In F. Maseres, The Doctrine of Permutations and Combinations (1795), 36.
It seems that the increased number of scientific workers, their being split up into groups whose studies are limited to a small subject, and over-specialization have brought about a shrinking of intelligence. There is no doubt that the quality of any human group decreases when the number of the individuals composing this group increases beyond certain limits… The best way to increase the intelligence of scientists would be to decrease their number.
Man the Unknown (1935), 48-9.
It seems to me that the older subjects, classics and mathematics, are strongly to be recommended on the ground of the accuracy with which we can compare the relative performance of the students. In fact the definiteness of these subjects is obvious, and is commonly admitted. There is however another advantage, which I think belongs in general to these subjects, that the examinations can be brought to bear on what is really most valuable in these subjects.
In Conflict of Studies and other Essays (1873), 6-7.
It seems to me, he says, that the test of “Do we or not understand a particular subject in physics?” is, “Can we make a mechanical model of it?” I have an immense admiration for Maxwell’s model of electromagnetic induction. He makes a model that does all the wonderful things that electricity docs in inducing currents, etc., and there can be no doubt that a mechanical model of that kind is immensely instructive and is a step towards a definite mechanical theory of electromagnetism.
From stenographic report by A.S. Hathaway of the Lecture 20 Kelvin presented at Johns Hopkins University, Baltimore, on 'Molecular Dynamics and the Wave Theory of Light' (1884), 132. (Hathaway was a Mathematics fellow there.) This remark is not included in the first typeset publication—a revised version, printed twenty years later, in 1904, as Lord Kelvin’s Baltimore Lectures on Molecular Dynamics and the Wave Theory of Light. The original notes were reproduced by the “papyrograph” process. They are excerpted in Pierre Maurice Marie Duhem, Essays in the History and Philosophy of Science (1996), 54-55.
It took Galileo 16 years to master the universe. You have one night. It seems unfair. The genius had all that time. While you have a few short hours to learn sun spots from your satellites before the dreaded astronomy exam. On the other hand, Vivarin [caffeine tablets] help you keep awake and mentally alert… So even when the subject matter’s dull, your mind will remain razor sharp. If Galileo had used Vivarin, maybe he could have mastered the solar system faster, too.
Advertisement by Beecham for Vivarin, student newspaper, Columbia Daily Spectator (1 Dec 1988), Vol. 112, No. 186, 5.
It was astonishing that for some considerable distance around the mould growth the staphococcal colonies were undergoing lysis. What had formerly been a well-grown colony was now a faint shadow of its former self...I was sufficiently interested to pursue the subject.
[Sep 1928, the first observation of penicillin. Lysis is the dissolution or destruction of cells.]
[Sep 1928, the first observation of penicillin. Lysis is the dissolution or destruction of cells.]
Sarah R. Riedman and Elton T. Gustafson, Portraits of Nobel Laureates in Medicine and Physiology (1964), 72.
It was not alone the striving for universal culture which attracted the great masters of the Renaissance, such as Brunellesco, Leonardo da Vinci, Raphael, Michelangelo and especially Albrecht Dürer, with irresistible power to the mathematical sciences. They were conscious that, with all the freedom of the individual fantasy, art is subject to necessary laws, and conversely, with all its rigor of logical structure, mathematics follows aesthetic laws.
From Lecture (5 Feb 1891) held at the Rathhaus, Zürich, printed as Ueber den Antheil der mathematischen Wissenschaft an der Kultur der Renaissance (1892), 19. (The Contribution of the Mathematical Sciences to the Culture of the Renaissance.) As translated in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-Book (1914), 183.
It would seem at first sight as if the rapid expansion of the region of mathematics must be a source of danger to its future progress. Not only does the area widen but the subjects of study increase rapidly in number, and the work of the mathematician tends to become more and more specialized. It is, of course, merely a brilliant exaggeration to say that no mathematician is able to understand the work of any other mathematician, but it is certainly true that it is daily becoming more and more difficult for a mathematician to keep himself acquainted, even in a general way, with the progress of any of the branches of mathematics except those which form the field of his own labours. I believe, however, that the increasing extent of the territory of mathematics will always be counteracted by increased facilities in the means of communication. Additional knowledge opens to us new principles and methods which may conduct us with the greatest ease to results which previously were most difficult of access; and improvements in notation may exercise the most powerful effects both in the simplification and accessibility of a subject. It rests with the worker in mathematics not only to explore new truths, but to devise the language by which they may be discovered and expressed; and the genius of a great mathematician displays itself no less in the notation he invents for deciphering his subject than in the results attained. … I have great faith in the power of well-chosen notation to simplify complicated theories and to bring remote ones near and I think it is safe to predict that the increased knowledge of principles and the resulting improvements in the symbolic language of mathematics will always enable us to grapple satisfactorily with the difficulties arising from the mere extent of the subject.
In Presidential Address British Association for the Advancement of Science, Section A., (1890), Nature, 42, 466.
It... [can] be easily shown:
1. That all present mountains did not exist from the beginning of things.
2. That there is no growing of mountains.
3. That the rocks or mountains have nothing in common with the bones of animals except a certain resemblance in hardness, since they agree in neither matter nor manner of production, nor in composition, nor in function, if one may be permitted to affirm aught about a subject otherwise so little known as are the functions of things.
4. That the extension of crests of mountains, or chains, as some prefer to call them, along the lines of certain definite zones of the earth, accords with neither reason nor experience.
5. That mountains can be overthrown, and fields carried over from one side of a high road across to the other; that peaks of mountains can be raised and lowered, that the earth can be opened and closed again, and that other things of this kind occur which those who in their reading of history wish to escape the name of credulous, consider myths.
1. That all present mountains did not exist from the beginning of things.
2. That there is no growing of mountains.
3. That the rocks or mountains have nothing in common with the bones of animals except a certain resemblance in hardness, since they agree in neither matter nor manner of production, nor in composition, nor in function, if one may be permitted to affirm aught about a subject otherwise so little known as are the functions of things.
4. That the extension of crests of mountains, or chains, as some prefer to call them, along the lines of certain definite zones of the earth, accords with neither reason nor experience.
5. That mountains can be overthrown, and fields carried over from one side of a high road across to the other; that peaks of mountains can be raised and lowered, that the earth can be opened and closed again, and that other things of this kind occur which those who in their reading of history wish to escape the name of credulous, consider myths.
The Prodromus of Nicolaus Steno's Dissertation Concerning a Solid Body enclosed by Process of Nature within a Solid (1669), trans. J. G. Winter (1916), 232-4.
Just as it will never be successfully challenged that the French language, progressively developing and growing more perfect day by day, has the better claim to serve as a developed court and world language, so no one will venture to estimate lightly the debt which the world owes to mathematicians, in that they treat in their own language matters of the utmost importance, and govern, determine and decide whatever is subject, using the word in the highest sense, to number and measurement.
In 'Sprüche in Prosa', Natur, III, 868.
Just as mathematics aims to study such entities as numbers, functions, spaces, etc., the subject matter of metamathematics is mathematics itself.
In 'Mathematics: A Non-Technical Exposition', American Scientist (3 Jul 1954), 42, No. 3, 490.
Kurt Gödel’s achievement in modern logic is singular and monumental—indeed it is more than a monument, it is a landmark which will remain visible far in space and time. … The subject of logic has certainly completely changed its nature and possibilities with Gödel's achievement.
From remarks at the Presentation (Mar 1951) of the Albert Einstein Award to Dr. Gödel, as quoted in 'Tribute to Dr. Gödel', in Jack J. Bulloff, Thomas C. Holyok (eds.), Foundations of Mathematics: Symposium Papers Commemorating the Sixtieth Birthday of Kurt Gödel (1969), ix.
https://books.google.com/books?id=irZLAAAAMAAJ
Kurt Gödel, Jack J. Bulloff, Thomas C. Holyoke - 1969 -
Learn just enough of the subject [metaphysics] to enable your mind to get rid of it.
As quoted in Geoffrey Madan’s Notebooks: A Selection (1984), 61.
Learn the leading precognita of all things—no need to turn over leaf by leaf, but grasp the trunk hard and you will shake all the branches.
Advice cherished by Samuel Johnson that that, if one is to master any subject, one must first discover its general principles.
Advice cherished by Samuel Johnson that that, if one is to master any subject, one must first discover its general principles.
Advice from Rev. Cornelius Ford, a distant cousin, quoted in John P. Hardy, Samuel Johnson: A Critical Study (1979), 29.
Let me suggest to you a simple test one can apply to scientific activities to determine whether or not they can constitute the practice of physics. Is what you are doing beautiful? Many beautiful things are created without the use of physical knowledge, but I know of no really worthwhile physics that isn’t beautiful. Indeed, one of the most distressing symptoms of scientific illiteracy is the impression so often given to school children that science is a mechanistic activity subject to algorithmic description.
In 'Physics and the APS in 1979', Physics Today (Apr 1980), 33, No. 4, 50.
Let no one say that I have said nothing new; the arrangement of the subject is new. When we play tennis, we both play with the same ball, but one of us places it better.
In Pensées (1670), Section 7, No. 9. From Blaise Pascal and W.F. Trotter (trans.), 'Thoughts', collected in Charles W. Eliot (ed.), The Harvard Classics (1910), Vol. 48, 14. From the French, “Qu’on ne dise pas que je n’ai rien dit de nouveau: la disposition des matières est nouvelle. Quand on joue à la paume, c’est une même balle dont on joue l’un et l’autre; mais l’un la place mieux,” in Oeuvres Complètes de Blaise Pascal (1864), Vol. 1, 287.
Like almost every subject of human interest, this one [mathematics] is just as easy or as difficult as we choose to make it. A lifetime may be spent by a philosopher in discussing the truth of the simplest axiom. The simplest fact as to our existence may fill us with such wonder that our minds will remain overwhelmed with wonder all the time. A Scotch ploughman makes a working religion out of a system which appalls a mental philosopher. Some boys of ten years of age study the methods of the differential calculus; other much cleverer boys working at mathematics to the age of nineteen have a difficulty in comprehending the fundamental ideas of the calculus.
In Teaching of Mathematics (1902), 19-20.
Logic is not concerned with human behavior in the same sense that physiology, psychology, and social sciences are concerned with it. These sciences formulate laws or universal statements which have as their subject matter human activities as processes in time. Logic, on the contrary, is concerned with relations between factual sentences (or thoughts). If logic ever discusses the truth of factual sentences it does so only conditionally, somewhat as follows: if such-and-such a sentence is true, then such-and-such another sentence is true. Logic itself does not decide whether the first sentence is true, but surrenders that question to one or the other of the empirical sciences.
Logic (1937). In The Language of Wisdom and Folly: Background Readings in Semantics (1967), 44.
MAGNET, n. Something acted upon by magnetism.
MAGNETISM, n. Something acting upon a magnet.
The two definitions immediately foregoing are condensed from the works of one thousand eminent scientists, who have illuminated the subject with a great white light, to the inexpressible advancement of human knowledge.
MAGNETISM, n. Something acting upon a magnet.
The two definitions immediately foregoing are condensed from the works of one thousand eminent scientists, who have illuminated the subject with a great white light, to the inexpressible advancement of human knowledge.
The Collected Works of Ambrose Bierce (1911), Vol. 7, The Devil's Dictionary, 208.
Man, the molecule of society, is the subject of social science.
The Unity of Law: As exhibited in the relations of physical, social, mental and moral science (1872), 77.
Many people regard mathematicians as a race apart, possessed of almost supernatural powers. While this is very flattering for successful mathematicians, it is very bad for those who, for one reason or another, are attempting to learn the subject.
Opening paragraph in Chap. 1 of Mathematician's Delight (1943, 2012), 7.
Mathematic is either Pure or Mixed: To Pure Mathematic belong those sciences which handle Quantity entirely severed from matter and from axioms of natural philosophy. These are two, Geometry and Arithmetic; the one handling quantity continued, the other dissevered. … Mixed Mathematic has for its subject some axioms and parts of natural philosophy, and considers quantity in so far as it assists to explain, demonstrate and actuate these.
In De Augmentis, Bk. 3; Advancement of Learning, Bk. 2.
Mathematic stands forth as that which unites, mediates between Man and Nature, Inner and Outer world, Thought and Perception, [as no other subject does].
In Die Erziehung der Menschheit (1826). Adapted and translated in William Henry Herford, 'The School: Mathematic', The Student’s Froebel (1894), Vol. 1, 84.
Mathematical instruction, in this as well as in other countries, is laboring under a burden of century-old tradition. Especially is this so with reference to the teaching of geometry. Our texts in this subject are still patterned more or less closely after the model of Euclid, who wrote over two thousand years ago, and whose text, moreover, was not intended for the use of boys and girls, but for mature men.
In Lectures on Fundamental Concepts of Algebra and Geometry (1911), 5.
Mathematical knowledge is not—as all Cambridge men are surely aware—the result of any special gift. It is merely the development of those conceptions of form and number which every human being possesses; and any person of average intellect can make himself a fair mathematician if he will only pay continuous attention; in plain English, think enough about the subject.
'Science', a lecture delivered at the Royal Institution. The Works of Charles Kingsley (1880), 241.
Mathematical proofs are essentially of three different types: pre-formal; formal; post-formal. Roughly the first and third prove something about that sometimes clear and empirical, sometimes vague and ‘quasi-empirical’ stuff, which is the real though rather evasive subject of mathematics.
In Mathematics, Science and Epistemology (1980), Vol. 2, 69.
Mathematics … above all other subjects, makes the student lust after knowledge, fills him, as it were, with a longing to fathom the cause of things and to employ his own powers independently; it collects his mental forces and concentrates them on a single point and thus awakens the spirit of individual inquiry, self-confidence and the joy of doing; it fascinates because of the view-points which it offers and creates certainty and assurance, owing to the universal validity of its methods. Thus, both what he receives and what he himself contributes toward the proper conception and solution of a problem, combine to mature the student and to make him skillful, to lead him away from the surface of things and to exercise him in the perception of their essence. A student thus prepared thirsts after knowledge and is ready for the university and its sciences. Thus it appears, that higher mathematics is the best guide to philosophy and to the philosophic conception of the world (considered as a self-contained whole) and of one’s own being.
In Die Mathematik die Fackelträgerin einer neuen Zeit (1889), 40. As translated in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-book (1914), 49.
Mathematics … is man’s own handiwork, subject only to the limitations imposed by the laws of thought.
With co-author James R. Newman, in Mathematics and the Imagination (1940), 359.
Mathematics because of its nature and structure is peculiarly fitted for high school instruction [Gymnasiallehrfach]. Especially the higher mathematics, even if presented only in its elements, combines within itself all those qualities which are demanded of a secondary subject.
In Die Mathematik die Fackelträgerin einer neuen Zeit (1889), 40. As translated in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-book (1914), 49.
Mathematics has beauties of its own—a symmetry and proportion in its results, a lack of superfluity, an exact adaptation of means to ends, which is exceedingly remarkable and to be found only in the works of the greatest beauty. … When this subject is properly and concretely presented, the mental emotion should be that of enjoyment of beauty, not that of repulsion from the ugly and the unpleasant.
In The Teaching of Mathematics in the Elementary and the Secondary School (1906), 44-45.
Mathematics is not a contemplative but a creative subject.
In A Mathematician's Apology (1940, 2012), 43.
Mathematics is often considered a difficult and mysterious science, because of the numerous symbols which it employs. Of course, nothing is more incomprehensible than a symbolism which we do not understand. … But this is not because they are difficult in themselves. On the contrary they have invariably been introduced to make things easy. … [T]he symbolism is invariably an immense simplification. It … represents an analysis of the ideas of the subject and an almost pictorial representation of their relations to each other.
In Introduction to Mathematics (1911), 59-60.
Mathematics is often erroneously referred to as the science of common sense. Actually, it may transcend common sense and go beyond either imagination or intuition. It has become a very strange and perhaps frightening subject from the ordinary point of view, but anyone who penetrates into it will find a veritable fairyland, a fairyland which is strange, but makes sense, if not common sense.
With co-author James R. Newman, in Mathematics and the Imagination (1940), 359.
Mathematics is perfectly free in its development and is subject only to the obvious consideration, that its concepts must be free from contradictions in themselves, as well as definitely and orderly related by means of definitions to the previously existing and established concepts.
In Grundlagen einer allgemeinen Manigfaltigkeitslehre (1883), Sect. 8.
Mathematics may be defined as the the subject in which we never know what we are talking about, not whether what we are saying is true.
In 'Recent Work on the Principles of Mathematics', International Monthly (1901), 4, 84. This sentence is part of a longer quote that begins, “Pure mathematics consists entirely…”, on the Bertrand Russell Quotes page of this website.
Mathematics, among all school subjects, is especially adapted to further clearness, definite brevity and precision in expression, although it offers no exercise in flights of rhetoric. This is due in the first place to the logical rigour with which it develops thought, avoiding every departure from the shortest, most direct way, never allowing empty phrases to enter. Other subjects excel in the development of expression in other respects: translation from foreign languages into the mother tongue gives exercise in finding the proper word for the given foreign word and gives knowledge of laws of syntax, the study of poetry and prose furnish fit patterns for connected presentation and elegant form of expression, composition is to exercise the pupil in a like presentation of his own or borrowed thoughtsand their development, the natural sciences teach description of natural objects, apparatus and processes, as well as the statement of laws on the grounds of immediate sense-perception. But all these aids for exercise in the use of the mother tongue, each in its way valuable and indispensable, do not guarantee, in the same manner as mathematical training, the exclusion of words whose concepts, if not entirely wanting, are not sufficiently clear. They do not furnish in the same measure that which the mathematician demands particularly as regards precision of expression.
In Anleitung zum mathematischen Unterricht in höheren Schulen (1906), 17.
Meanwhile I flatter myself with so much success, that: students... will not be so easily mistaken in the subjects of the mineral kingdom, as has happened with me and others in following former systems; and I also hope to obtain some protectors against those who are so possessed with the figuromania, and so addicted to the surface of things, that they are shocked at the boldness of calling a marble a limestone, and of placing the Porphyry amongst the Saxa.
An Essay Towards a System of Mineralogy (1770), trans. G. Von Engestrom, xxi.
Mechanical action may be derived from heat, and heat may be generated by mechanical action, by means of forces either acting between contiguous parts of bodies, or due to electric excitation; but in no other way known, or even conceivable, in the present state of science. Hence thermo-dynamics falls naturally into two divisions, of which the subjects are respectively, the relation of heat to the forces acting between contiguous parts of bodies, and the relation of heat to electrical agency.
In 'On the Dynamical Theory of Heat, with Numerical Results Deduced from Mr Joule's Equivalent of a Thermal Unit, and M. Regnault's Observations on Steam' (1851). Part VI, 'Thermo Electric Currents' (1854). In Mathematical and Physical Papers (1882), Vol. 1, 232.
Men always fool themselves when they give up experience for systems born of the imagination. Man is the work of nature, he exists in nature, he is subject to its laws, he can not break free, he can not leave even in thought; it is in vain that his spirit wants to soar beyond the bounds of the visible world, he is always forced to return.
Opening statement of first chapter of Système de la Nature (1770), Vol. 1, 1. Translation by Webmaster using Google Translate. From the original French, “Les hommes se tromperont toujours, quand ils abandonneront l'expérience pour des systèmes enfantés par l’imagination. L’homme est l’ouvrage de la nature, il existe dans la nature, il est soumis à ses lois, il ne peut s’en affranchir, il ne peut même par la pensée en sortir; c’est en vain que son esprit veut s’élancer au delà des bornes du monde visible, il est toujours forcé d’y rentrer.” In the English edition (1820-21), Samuel Wilkinson gives this as “Man has always deceived himself when he abandoned experience to follow imaginary systems.—He is the work of nature.—He exists in Nature.—He is submitted to the laws of Nature.—He cannot deliver himself from them:—cannot step beyond them even in thought. It is in vain his mind would spring forward beyond the visible world: direful and imperious necessity ever compels his return.”
Men give me some credit for genius. All the genius I have lies in this: When I have a subject in hand, I study it profoundly. Day and night it is before me. I explore it in all its bearings. My mind becomes pervaded with it. Then the effort which I have made is what people are pleased to call the fruit of genius. It is the fruit of labor and thought.
Attributed as a comment to a friend. In J. C. Thomas, Manual of Useful Information (1893), 108.
Mere numbers cannot bring out … the intimate essence of the experiment. This conviction comes naturally when one watches a subject at work. … What things can happen! What reflections, what remarks, what feelings, or, on the other hand, what blind automatism, what absence of ideas! … The experimenter judges what may be going on in [the subject’s] mind, and certainly feels difficulty in expressing all the oscillations of a thought in a simple, brutal number, which can have only a deceptive precision. How, in fact, could it sum up what would need several pages of description!
In La Suggestibilité (1900), 119-20.
Method means that arrangement of subject matter which makes it most effective in use. Never is method something outside of the material.
Democracy and Education: an Introduction to the Philosophy of Education (1916), 194.
Modern cytological work involves an intricacy of detail, the significance of which can be appreciated by the specialist alone; but Miss Stevens had a share in a discovery of importance, and her work will be remembered for this, when the minutiae of detailed investigations that she carried out have become incorporated in the general body of the subject.
In obituary, 'The Scientific Work of Miss N.M. Steves', Science (11 Oct 1912), 36, No. 928, 468.
Most of the scientists in their twenties and thirties who went in 1939 to work on wartime problems were profoundly affected by their experience. The belief that Rutherford's boys were the best boys, that we could do anything that was do-able and could master any subject in a few days was of enormous value.
'The Effect of World War II on the Development of Knowledge in the Physical Sciences', Proceedings of the Royal Society of London, 1975, Series A, 342, 531.
My profession often gets bad press for a variety of sins, both actual and imagined: arrogance, venality, insensitivity to moral issues about the use of knowledge, pandering to sources of funding with insufficient worry about attendant degradation of values. As an advocate for science, I plead ‘mildly guilty now and then’ to all these charges. Scientists are human beings subject to all the foibles and temptations of ordinary life. Some of us are moral rocks; others are reeds. I like to think (though I have no proof) that we are better, on average, than members of many other callings on a variety of issues central to the practice of good science: willingness to alter received opinion in the face of uncomfortable data, dedication to discovering and publicizing our best and most honest account of nature’s factuality, judgment of colleagues on the might of their ideas rather than the power of their positions.
…...
Mythology is wondrous, a balm for the soul. But its problems cannot be ignored. At worst, it buys inspiration at the price of physical impossibility ... At best, it purveys the same myopic view of history that made this most fascinating subject so boring and misleading in grade school as a sequential take of monarchs and battles.
…...
Naturally, there is always a great diversity of opinion about a popular subject when it is not well understood. We all know how true this is of social, ethical and religious subjects, upon which no two persons ever really agree. The exact sciences, however, admit of no differences of opinion.
In The Science of Poetry and the Philosophy of Language (1910), x.
Nature does not consist entirely, or even largely, of problems designed by a Grand Examiner to come out neatly in finite terms, and whatever subject we tackle the first need is to overcome timidity about approximating.
As co-author with Bertha Swirles Jeffreys, in Methods of Mathematical Physics (1946, 1999), 8.
Nearly every subject has a shadow, or imitation. It would, I suppose, be quite possible to teach a deaf and dumb child to play the piano. When it played a wrong note, it would see the frown of its teacher, and try again. But it would obviously have no idea of what it was doing, or why anyone should devote hours to such an extraordinary exercise. It would have learnt an imitation of music. and it would fear the piano exactly as most students fear what is supposed to be mathematics.
In Mathematician's Delight (1943), 8.
Never leave an unsolved difficulty behind. I mean, don’t go any further in that book till the difficulty is conquered. In this point, Mathematics differs entirely from most other subjects. Suppose you are reading an Italian book, and come to a hopelessly obscure sentence—don’t waste too much time on it, skip it, and go on; you will do very well without it. But if you skip a mathematical difficulty, it is sure to crop up again: you will find some other proof depending on it, and you will only get deeper and deeper into the mud.
From letter to Edith Rix with hints for studying (about Mar 1885), in Stuart Dodgson Collingwood, The Life and Letters of Lewis Carroll (1898), 241.
Newton could not admit that there was any difference between him and other men, except in the possession of such habits as … perseverance and vigilance. When he was asked how he made his discoveries, he answered, “by always thinking about them;” and at another time he declared that if he had done anything, it was due to nothing but industry and patient thought: “I keep the subject of my inquiry constantly before me, and wait till the first dawning opens gradually, by little and little, into a full and clear light.”
In History of the Inductive Sciences, Bk. 7, chap, 1, sect. 5.
Next to ignorance of the grammar of one’s native language, nothing betrays want of information so soon as ignorance in matters of geography, without which it is almost impossible to carry on conversation long on any general subject.
In The Statistical Breviary: Shewing, on a Principle Entirely New, the Resources of Every State and Kingdom in Europe (1801), 5.
No branches of historical inquiry have suffered more from fanciful speculation than those which relate to the origin and attributes of the races of mankind. The differentiation of these races began in prehistoric darkness, and the more obscure a subject is, so much the more fascinating. Hypotheses are tempting, because though it may be impossible to verify them, it is, in the paucity of data, almost equally impossible to refute them.
Creighton Lecture delivered before the University of London on 22 Feb 1915. Race Sentiment as a Factor in History (1915), 3.
No man can be truly called an entomologist, sir; the subject is too vast for any single human
intelligence to grasp.
In 'The Poet at the Breakfast Table: II', The Atlantic Monthly (Feb 1872), 29, 231.
No other subject has such clear-cut or unanimously accepted standards, and the men who are remembered are almost always the men who merit it. Mathematical fame, if you have the cash to pay for it, is one of the soundest and steadiest of investments.
In A Mathematician's Apology (1940, 2012), 82.
No part of Mathematics suffers more from the triviality of its initial presentation to beginners than the great subject of series. Two minor examples of series, namely arithmetic and geometric series, are considered; these examples are important because they are the simplest examples of an important general theory. But the general ideas are never disclosed; and thus the examples, which exemplify nothing, are reduced to silly trivialities.
In An Introduction to Mathematics (1911), 194.
No physician, in so far as he is a physician, considers his own good in what he prescribes, but the good of his patient; for the true physician is also a ruler having the human body as a subject, and is not a mere money-maker.
— Plato
In Plato and B. Jowett (trans.), The Dialogues of Plato (1875), Vol. 3, 211.
No school subject so readily furnishes tasks whose purpose can be made so clear, so immediate and so appealing to the sober second-thought of the immature learner as the right sort of elementary school mathematics.
In Arithmetic in Public Education (1909), 8. As quoted and cited in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-book (1914), 50.
No scientific subject has ever aroused quite the same mixture of hopes and fears [as atomic energy].
In Presidential address to the Annual Meeting of the British Association (Sep 1947), as quoted in Brian Austin, Schonland: Scientist and Soldier: From Lightning on the Veld to Nuclear Power at Harwell: The Life of Field Marshal Montgomery's Scientific Adviser (2010), 459.
No study is less alluring or more dry and tedious than statistics, unless the mind and imagination are set to work, or that the person studying is particularly interested in the subject; which last can seldom be the case with young men in any rank of life.
In The Statistical Breviary: Shewing, on a Principle Entirely New, the Resources of Every State and Kingdom in Europe (1801), 16.
No subject of philosophical inquiry within the limits of human investigation is more calculated to excite admiration and to awaken curiosity than fire; and there is certainly none more extensively useful to mankind. It is owing, no doubt, to our being acquainted with it from our infancy, that we are not more struck with its appearance, and more sensible of the benefits we derive from it. Almost every comfort and convenience which man by his ingenuity procures for himself is obtained by its assistance; and he is not more distinguished from the brute creation by the use of speech, than by his power over that wonderful agent.
In The Complete Works of Count Rumford (1876), Vol. 4, 3-4.
Nobody, I suppose, could devote many years to the study of chemical kinetics without being deeply conscious of the fascination of time and change: this is something that goes outside science into poetry; but science, subject to the rigid necessity of always seeking closer approximations to the truth, itself contains many poetical elements.
From Nobel Lecture (11 Dec 1956), collected in Nobel Lectures in Chemistry (1999), 474.
Nothing afflicted Marcellus so much as the death of Archimedes, who was then, as fate would have it, intent upon working out some problem by a diagram, and having fixed his mind alike and his eyes upon the subject of his speculation, he never noticed the incursion of the Romans, nor that the city was taken. In this transport of study and contemplation, a soldier, unexpectedly coming up to him, commanded him to follow to Marcellus, which he declined to do before he had worked out his problem to a demonstration; the soldier, enraged, drew his sword and ran him through. Others write, that a Roman soldier, running upon him with a drawn sword, offered to kill him; and that Archimedes, looking back, earnestly besought him to hold his hand a little while, that he might not leave what he was at work upon inconclusive and imperfect; but the soldier, nothing moved by his entreaty, instantly killed him. Others again relate, that as Archimedes was carrying to Marcellus mathematical instruments, dials, spheres, and angles, by which the magnitude of the sun might be measured to the sight, some soldiers seeing him, and thinking that he carried gold in a vessel, slew him. Certain it is, that his death was very afflicting to Marcellus; and that Marcellus ever after regarded him that killed him as a murderer; and that he sought for his kindred and honoured them with signal favours.
— Plutarch
In John Dryden (trans.), Life of Marcellus.
Nothing afflicted Marcellus so much as the death of Archimedes, who was then, as fate would have it, intent upon working out some problem by a diagram, and having fixed his mind alike and his eyes upon the subject of his speculation, he never noticed the incursion of the Romans, nor that the city was taken. In this transport of study and contemplation, a soldier, unexpectedly coming up to him, commanded him to follow to Marcellus, which he declined to do before he had worked out his problem to a demonstration; the soldier, enraged, drew his sword and ran him through. Others write, that a Roman soldier, running upon him with a drawn sword, offered to kill him; and that Archimedes, looking back, earnestly besought him to hold his hand a little while, that he might not leave what he was at work upon inconclusive and imperfect; but the soldier, nothing moved by his entreaty, instantly killed him. Others again relate, that as Archimedes was carrying to Marcellus mathematical instruments, dials, spheres, and angles, by which the magnitude of the sun might be measured to the sight, some soldiers seeing him, and thinking that he carried gold in a vessel, slew him. Certain it is, that his death was very afflicting to Marcellus; and that Marcellus ever after regarded him that killed him as a murderer; and that he sought for his kindred and honoured them with signal favours.
— Plutarch
In John Dryden (trans.), Life of Marcellus.
Nothing could have been worse for the development of my mind than Dr. Butler's school, as it was strictly classical, nothing else being taught, except a little ancient geography and history. The school as a means of education to me was simply a blank. During my whole life I have been singularly incapable of mastering any language. Especial attention was paid to versemaking, and this I could never do well. I had many friends, and got together a good collection of old verses, which by patching together, sometimes aided by other boys, I could work into any subject.
In Charles Darwin and Francis Darwin (ed.), Charles Darwin: His Life Told in an Autobiographical Chapter, and in a Selected Series of His Published Letters (1892), 8.
Now I must take you to a very interesting part of our subject—to the relation between the combustion of a candle and that living kind of combustion which goes on within us. In every one of us there is a living process of combustion going on very similar to that of a candle, and I must try to make that plain to you. For it is not merely true in a poetical sense—the relation of the life of man to a taper; and if you will follow, I think I can make this clear.
A Course of Six Lectures on the Chemical History of a Candle (1861), 155-6.
O comfortable allurement, O ravishing perswasion, to deal with a Science, whose subject is so Auncient, so pure, so excellent, so surmounting all creatures... By Numbers propertie ... we may... arise, clime, ascend, and mount up (with Speculative winges) in spirit, to behold in the Glas of creation, the Forme of Formes, the Exemplar Number of all things Numerable... Who can remaine, therefore, unpersuaded, to love, allow, and honor the excellent sciehce of Arithmatike?
— John Dee
'Mathematicall Preface', in H. Billingsley, trans. The Elements of Geometry of the most Aunceint Philosopher Euclide of Megara (1570), in J. L. Hellbron, Weighing Imponderables and Other Quantitative Science around 1800 (1993), 2.
Of … habitable worlds, such as the Earth, all which we may suppose to be of a terrestrial or terraqueous nature, and filled with beings of the human species, subject to mortality, it may not be amiss in this place to compute how many may he conceived within our finite view every clear Star-light night. … In all together then we may safely reckon 170,000,000, and yet be much within compass, exclusive Of the Comets which I judge to be by far the most numerous part of the creation.
In The Universe and the Stars: Being an Original Theory on the Visible Creation, Founded on the Laws of Nature (1750, 1837), 131-132.
Of all many-sided subjects, [education] is the one which has the greatest number of sides.
Inaugural Address Delivered to the University of St. Andrews, Feb. 1st, 1867 (1867), 3.
Of all regions of the earth none invites speculation more than that which lies beneath our feet, and in none is speculation more dangerous; yet, apart from speculation, it is little that we can say regarding the constitution of the interior of the earth. We know, with sufficient accuracy for most purposes, its size and shape: we know that its mean density is about 5½ times that of water, that the density must increase towards the centre, and that the temperature must be high, but beyond these facts little can be said to be known. Many theories of the earth have been propounded at different times: the central substance of the earth has been supposed to be fiery, fluid, solid, and gaseous in turn, till geologists have turned in despair from the subject, and become inclined to confine their attention to the outermost crust of the earth, leaving its centre as a playground for mathematicians.
'The Constitution of the Interior of the Earth, as Revealed by Earthquakes', Quarterly Journal of the Geological Society (1906), 62, 456.
Of all the intellectual faculties, judgment is the last to arrive at maturity. The child should give its attention either to subjects where no error is possible at all, such as mathematics, or to those in which there is no particular danger in making a mistake, such as languages, natural science, history, and so on.
In Arthur Schopenhauer and T. Bailey (ed., trans.) Essays of Arthur Schopenhauer (1902), 67.
On all levels primary, and secondary and undergraduate - mathematics is taught as an isolated subject with few, if any, ties to the real world. To students, mathematics appears to deal almost entirely with things whlch are of no concern at all to man.
In editorial in Focus, a Journal of the Mathematical Association of America (1986), quoted in obituary by Eric Pace, New York Times (11 Jun 1992).
On our planet, all objects are subject to continual and inevitable changes which arise from the essential order of things. These changes take place at a variable rate according to the nature, condition, or situation of the objects involved, but are nevertheless accomplished within a certain period of time. Time is insignificant and never a difficulty for Nature. It is always at her disposal and represents an unlimited power with which she accomplishes her greatest and smallest tasks.
Hydrogéologie (1802), trans. A. V. Carozzi (1964), 61.
On the whole, at least in the author's experience, the preparation of species-specific antiserum fractions and the differentiation of closely related species with precipitin sera for serum proteins does not succeed so regularly as with agglutinins and lysins for blood cells. This may be due to the fact that in the evolutional scale the proteins undergo continuous variations whereas cell antigens are subject to sudden changes not linked by intermediary stages.
The Specificity of Serological Reactions (1936), 12-3.
One of the great challenges in this world is knowing enough about a subject to think you’re right, but not enough about the subject to know you’re wrong.
From video trailer, 'Neil deGrasse Tyson Teaches Scientific Thinking and Communication', Masterclass (19 Dec 2019)
One of the principal objects of theoretical research in my department of knowledge is to find the point of view from which the subject appears in its greatest simplicity.
In letter published in Proceedings of the American Academy of Arts and Sciences (1881), 420.
Our failure to discern a universal good does not record any lack of insight or ingenuity, but merely demonstrates that nature contains no moral messages framed in human terms. Morality is a subject for philosophers, theologians, students of the humanities, indeed for all thinking people. The answers will not be read passively from nature; they do not, and cannot, arise from the data of science. The factual state of the world does not teach us how we, with our powers for good and evil, should alter or preserve it in the most ethical manner.
…...
Our most distinguished “man of science” was the then veteran John Dalton. He was rarely absent from his seat in a warm corner of the room during the meetings of the Literary and Philosophical Society. Though a sober-minded Quaker, he was not devoid of some sense of fun; and there was a tradition amongst us, not only that he had once been a poet, but that, although a bachelor, two manuscript copies were still extant of his verses on the subject of matrimonial felicity; and it is my belief there was foundation for the tradition. The old man was sensitive on the subject of his age. Dining one day ... he was placed between two ladies ... [who] resolved to extract from him some admission on the tender point, but in vain. Though never other than courteous, Dalton foiled all their feminine arts and retained his secret. ... Dalton's quaint and diminutive figure was a strongly individualized one.
In Reminiscences of a Yorkshire Naturalist (1896), 73-74.
Our progress in education has truly been a curious one. We have gone from the hard and arbitrary curriculum, with its primary insistence upon training the memory and the consequent devitalization of valuable and beneficial subjects, to the free elective system, with its wholesale invitations to follow the paths of least resistance, back to a half-hearted compromise somewhere between the two extremes, and we have arrived at what? Certainly at little more than an educational jumble. A maelstrom in which the maximum amount of theory and the minimum amount of practice whirl those who are thrown into it round and round for definitely fixed periods of time, to be cast out as flotsam for another period until corporate business and industrial organizations can accomplish that which could and should have been done by general education.
Co-author with Louis Jay Heath, in A New Basis for Social Progress (1917), 151-152.
Our treatment of this science will be adequate, if it achieves the amount of precision which belongs to its subject matter.
In Nicomachean Ethics, Book 1, Chap 3. In Harris Rackham (trans.), Aristotle’s Ethics for English Readers (1943), 14.
Paris ... On this side of the ocean it is difficult to understand the susceptibility of American citizens on the subject and precisely why they should so stubbornly cling to the biblical version. It is said in Genesis the first man came from mud and mud is not anything very clean. In any case if the Darwinian hypothesis should irritate any one it should only be the monkey. The monkey is an innocent animal—a vegetarian by birth. He never placed God on a cross, knows nothing of the art of war, does not practice lynch law and never dreams of assassinating his fellow beings. The day when science definitely recognizes him as the father of the human race the monkey will have no occasion to be proud of his descendants. That is why it must be concluded that the American Association which is prosecuting the teacher of evolution can be no other than the Society for Prevention of Cruelty to Animals.
[A cynical article in the French press on the Scopes Monkey Trial, whether it will decide “a monkey or Adam was the grandfather of Uncle Sam.”]
[A cynical article in the French press on the Scopes Monkey Trial, whether it will decide “a monkey or Adam was the grandfather of Uncle Sam.”]
Article from a French daily newspaper on the day hearings at the Scopes Monkey Trial began, Paris Soir (13 Jul 1925), quoted in 'French Satirize the Case', New York Times (14 Jul 1925), 3.
Philosophers no longer write for the intelligent, only for their fellow professionals. The few thousand academic philosophers in the world do not stint themselves: they maintain more than seventy learned journals. But in the handful that cover more than one subdivision of philosophy, any given philosopher can hardly follow more than one or two articles in each issue. This hermetic condition is attributed to “technical problems” in the subject. Since William James, Russell, and Whitehead, philosophy, like history, has been confiscated by scholarship and locked away from the contamination of general use.
In The Culture We Deserve (1989), 9.
Philosophy, and science, and the springs
Of wonder, and th wisdom of the world,
I have essayed; and in my mind there is
A power to make these subject to itself...
Of wonder, and th wisdom of the world,
I have essayed; and in my mind there is
A power to make these subject to itself...
From poem 'Manfred'.
Physics does not change the nature of the world it studies, and no science of behavior can change the essential nature of man, even though both sciences yield technologies with a vast power to manipulate their subject matters.
In article 'Man', Proceedings of the American Philosophical Society (1964), 108, 482-85. Collected in Cumulative Record: Definitive Edition (2015).
Physics, owing to the simplicity of its subject matter, has reached a higher state of development than any other science. (1931)
In The Scientific Outlook (1931, 2009), 42.
Placed in a universe of constant change, on an isolated globe surrounded by distant celestial objects on all sides, subjected to influences of various kinds, it is a sublime occupation to measure the earth and weigh the planets, to predict their changes, and even to discover the materials of which they are composed; to investigate the causes of the tempest and volcano; to bring the lightning from the clouds; to submit it to experiment by which it shall reveal its character; and to estimate the size and weight of those invisible atoms which constitute the universe of things.
In Letter (3 Feb 1873) to the Committee of Arrangements, in Proceedings of the Farewell Banquet to Professor Tyndall (4 Feb 1873), 19. Reprinted as 'On the Importance of the Cultivation of Science', The Popular Science Monthly (1873), Vol. 2, 645.
Poor teaching leads to the inevitable idea that the subject [mathematics] is only adapted to peculiar minds, when it is the one universal science and the one whose four ground-rules are taught us almost in infancy and reappear in the motions of the universe.
In Mathematical Teaching (1907), 19.
Pope has elegantly said a perfect woman's but a softer man. And if we take in the consideration, that there can be but one rule of moral excellence for beings made of the same materials, organized after the same manner, and subjected to similar laws of Nature, we must either agree with Mr. Pope, or we must reverse the proposition, and say, that a perfect man is a woman formed after a coarser mold.
Letter XXII. 'No Characteristic Difference in Sex'. In Letters on Education with Observations on Religious and Metaphysical Subjects (1790), 128.
Power politics existed before Machiavelli was ever heard of; it will exist long after his name is only a faint memory. What he did, like Harvey, was to recognize its existence and subject it to scientific study.
The Prince and the Discourses by Niccolò Machiavelli, with an Introduction by Max Lerner (1950), xliii.
Professor Sylvester’s first high class at the new university Johns Hopkins consisted of only one student, G. B. Halsted, who had persisted in urging Sylvester to lecture on the modem algebra. The attempt to lecture on this subject led him into new investigations in quantics.
In Teaching and History of Mathematics in the United States (1890), 264.
Pure mathematics and physics are becoming ever more closely connected, though their methods remain different. One may describe the situation by saying that the mathematician plays a game in which he himself invents the rules while the while the physicist plays a game in which the rules are provided by Nature, but as time goes on it becomes increasingly evident that the rules which the mathematician finds interesting are the same as those which Nature has chosen. … Possibly, the two subjects will ultimately unify, every branch of pure mathematics then having its physical application, its importance in physics being proportional to its interest in mathematics.
From Lecture delivered on presentation of the James Scott prize, (6 Feb 1939), 'The Relation Between Mathematics And Physics', printed in Proceedings of the Royal Society of Edinburgh (1938-1939), 59, Part 2, 124.
Pure mathematics consists entirely of such asseverations as that, if such and such is a proposition is true of anything, then such and such another propositions is true of that thing. It is essential not to discuss whether the first proposition is really true, and not to mention what the anything is of which it is supposed to be true. Both these points would belong to applied mathematics. … If our hypothesis is about anything and not about some one or more particular things, then our deductions constitute mathematics. Thus mathematics may be defined as the the subject in which we never know what we are talking about, not whether what we are saying is true. People who have been puzzled by the beginnings of mathematics will, I hope, find comfort in this definition, and will probably agree that it is accurate.
In 'Recent Work on the Principles of Mathematics', International Monthly (1901), 4, 84.
Quite distinct from the theoretical question of the manner in which mathematics will rescue itself from the perils to which it is exposed by its own prolific nature is the practical problem of finding means of rendering available for the student the results which have been already accumulated, and making it possible for the learner to obtain some idea of the present state of the various departments of mathematics. … The great mass of mathematical literature will be always contained in Journals and Transactions, but there is no reason why it should not be rendered far more useful and accessible than at present by means of treatises or higher text-books. The whole science suffers from want of avenues of approach, and many beautiful branches of mathematics are regarded as difficult and technical merely because they are not easily accessible. … I feel very strongly that any introduction to a new subject written by a competent person confers a real benefit on the whole science. The number of excellent text-books of an elementary kind that are published in this country makes it all the more to be regretted that we have so few that are intended for the advanced student. As an example of the higher kind of text-book, the want of which is so badly felt in many subjects, I may mention the second part of Prof. Chrystal’s Algebra published last year, which in a small compass gives a great mass of valuable and fundamental knowledge that has hitherto been beyond the reach of an ordinary student, though in reality lying so close at hand. I may add that in any treatise or higher text-book it is always desirable that references to the original memoirs should be given, and, if possible, short historic notices also. I am sure that no subject loses more than mathematics by any attempt to dissociate it from its history.
In Presidential Address British Association for the Advancement of Science, Section A (1890), Nature, 42, 466.
Religions are tough. Either they make no contentions which are subject to disproof or they quickly redesign doctrine after disproof. … near the core of the religious experience is something remarkably resistant to rational inquiry.
From 'A Sunday Sermon', in Broca's Brain: Reflections on the Romance of Science (1975, 2011), 332-333.
Remember this, the rule for giving an extempore lecture is—let the the mind rest from the subject entirely for an interval preceding the lecture, after the notes are prepared; the thoughts will ferment without your knowing it, and enter into new combinations; but if you keep the mind active upon the subject up to the moment, the subject will not ferment but stupefy.
In Letter (10 Jul 1854) to William Rowan Hamilton, collected in Robert Perceval Graves, Life of Sir William Rowan Hamilton (1882-89), Vol. 3, 487.
Science and knowledge are subject, in their extension and increase, to laws quite opposite to those which regulate the material world. Unlike the forces of molecular attraction, which cease at sensible distances; or that of gravity, which decreases rapidly with the increasing distance from the point of its origin; the farther we advance from the origin of our knowledge, the larger it becomes, and the greater power it bestows upon its cultivators, to
add new fields to its dominions.
In 'Future Prospects', On the Economy of Machinery and Manufactures (1st ed., 1832), chap. 32, 277-278.
Science deals with judgments on which it is possible to obtain universal agreement. These judgments do not concern individual facts and events, but the invariable association of facts and events known as the laws of science. Agreement is secured by observation and experiment—impartial courts of appeal to which all men must submit if they wish to survive. The laws are grouped and explained by theories of ever increasing generality. The theories at first are ex post facto—merely plausible interpretations of existing bodies of data. However, they frequently lead to predictions that can be tested by experiments and observations in new fields, and, if the interpretations are verified, the theories are accepted as working hypotheses until they prove untenable. The essential requirements are agreement on the subject matter and the verification of predictions. These features insure a body of positive knowledge that can be transmitted from person to person, and that accumulates from generation to generation.
From manuscript on English Science in the Renaissance (1937), Edwin Hubble collection, Box 2, Huntington Library, San Marino, California. As cited by Norriss S. Hetherington in 'Philosophical Values and Observation in Edwin Hubble's Choice of a Model of the Universe', Historical Studies in the Physical Sciences (1982), 13, No. 1, 41. (Hetherington comments parenthetically that the references to court, judgment and appeal may be attributable to his prior experiences as a Rhodes Scholar reading Roman law at Oxford, and to a year's practice as an attorney in Louisville, Kentucky.)
Science does not present itself to man until mind conquers matter in striving to subject the result of experimental investigation to rational combinations.
In Alexander Humboldt and E.C. Otté (trans.), 'Introduction', Cosmos: Sketch of a Physical Description of the Universe (1852), Vol. 1, 76. The translator’s preface is dated 1844.
Science fiction films are not about science. They are about disaster, which is one of the oldest subjects of art.
From essay 'The Imagination of Disaster', collected in Against Interpretation and Other Essays (1966, 2001), 213.
Science is best defined as a careful, disciplined, logical search for knowledge about any and all aspects of the universe, obtained by examination of the best available evidence and always subject to correction and improvement upon discovery of better evidence. What's left is magic. And it doesn't work.
The Mask of Nostradamus: The Prophecies of the World’s Most Famous Seer (1993), 66.
Science is uncertain. Theories are subject to revision; observations are open to a variety of interpretations, and scientists quarrel amongst themselves. This is disillusioning for those untrained in the scientific method, who thus turn to the rigid certainty of the Bible instead. There is something comfortable about a view that allows for no deviation and that spares you the painful necessity of having to think.
The 'Threat' of Creationism. In Ashley Montagu (ed.), Science and Creationism (1984), 192.
Science is, according to Mach, nothing but the comparison and orderly arrangement of factually given contents of our consciousness, in accord with certain gradually acquired points of view and methods. Therefore, physics and psychology differ from each other not so much in the subject matter, but rather only in the points of view of the arrangement and connection of the various topics.
Translation from obituary, 'Ernst Mach', Physikalische Zeitschrift (1 Apr 1916), 102. From the original German text: “Nach Mach ist Wissenschaft nichts anderes, als Vergleichung und Ordnung der uns tatsächlich gegebenen Bewußtseinsinhalte nach gewissen, von uns allmählich ertasteten Gesichtspunkten und Methoden. Physik und Psychologie unterscheiden sich also voneinander nicht in dem Gegenstände, sondern nur in den Gesichtspunkten der Anordnung und Verknüpfung des Stoffes.”
Science only begins for man from the moment when his mind lays hold of matter—when he tries to subject the mass accumulated by experience to rational combinations.
In 'Introduction', Cosmos: Sketch of a Physical Description of the Universe (1849), Vol. 1, 64. Translation “under the superintendence of” Edward Sabine.
Science, regarded as the pursuit of truth, which can only be attained by patient and unprejudiced investigation, wherein nothing is to be attempted, nothing so minute as to be justly disregarded, must ever afford occupation of consummate interest, and subject of elevated meditation.
On the Connexion of the Physical Sciences (1858), 2-3.
Scientific knowledge scarcely exists amongst the higher classes of society. The discussion in the Houses of Lords or of Commons, which arise on the occurrence of any subjects connected with science, sufficiently prove this fact…
In Reflections on the Decline of Science in England (1830), 8.
Scientific method is not just a method which it has been found profitable to pursue in this or that abstruse subject for purely technical reasons. It represents the only method of thinking that has proved fruitful in any subject—that is what we mean when we call it scientific. It is not a peculiar
development of thinking for highly specialized ends; it is thinking, so far as thought has become conscious of its proper ends and of the equipment indispensable for success in their pursuit ... When our schools truly become laboratories of knowledge-making, not mills fitted out with information-hoppers, there will no longer be need to discuss the place of science in education.
Address to Section L, Education, of the American Association for the Advancement of Science, at Boston (1909), 'Science as Subject-Matter and as Method'. Published in Science (28 Jan 1910), N.S. Vol. 31, No. 787, 127.
Scientific subjects do not progress necessarily on the lines of direct usefulness. Very many applications of the theories of pure mathematics have come many years, sometimes centuries, after the actual discoveries themselves. The weapons were at hand, but the men were not able to use them.
In Perry, Teaching of Mathematics (1902), 35.
Scientists and particularly the professional students of evolution are often accused of a bias toward mechanism or materialism, even though believers in vitalism and in finalism are not lacking among them. Such bias as may exist is inherent in the method of science. The most successful scientific investigation has generally involved treating phenomena as if they were purely materialistic, rejecting any metaphysical hypothesis as long as a physical hypothesis seems possible. The method works. The restriction is necessary because science is confined to physical means of investigation and so it would stultify its own efforts to postulate that its subject is not physical and so not susceptible to its methods.
The Meaning of Evolution: A Study of the History of Life and of its Significance for Man (1949), 127.
Select such subjects that your pupils cannot walk out without seeing them. Train your pupils to be observers, and have them provided with the specimens about which you speak. If you can find nothing better, take a house-fly or a cricket, and let each one hold a specimen and examine it as you talk.
Lecture at a teaching laboratory on Penikese Island, Buzzard's Bay. Quoted from the lecture notes by David Starr Jordan, Science Sketches (1911), 146.
She knew only that if she did or said thus-and-so, men would unerringly respond with the complimentary thus-and-so. It was like a mathematical formula and no more difficult, for mathematics was the one subject that had come easy to Scarlett in her schooldays.
In Gone With the Wind (1936), 60.
Simplification of modes of proof is not merely an indication of advance in our knowledge of a subject, but is also the surest guarantee of readiness for farther progress.
In Lord Kelvin and Peter Guthrie Tait Elements of Natural Philosophy (1873), Preface.
Since many cases are known in which the specificities of antigens and enzymes appear to bear a direct relation to gene specificities, it seems reasonable to suppose that the gene’s primary and possibly sole function is in directing the final configurations of protein molecules.
Assuming that each specific protein of the organism has its unique configuration copied from that of a gene, it follows that every enzyme whose specificity depends on a protein should be subject to modification or inactivation through gene mutation. This would, of course, mean that the reaction normally catalyzed by the enzyme in question would either have its rate or products modified or be blocked entirely.
Such a view does not mean that genes directly “make” proteins. Regardless of precisely how proteins are synthesized, and from what component parts, these parts must themselves be synthesized by reactions which are enzymatically catalyzed and which in turn depend on the functioning of many genes. Thus in the synthesis of a single protein molecule, probably at least several hundred different genes contribute. But the final molecule corresponds to only one of them and this is the gene we visualize as being in primary control.
Assuming that each specific protein of the organism has its unique configuration copied from that of a gene, it follows that every enzyme whose specificity depends on a protein should be subject to modification or inactivation through gene mutation. This would, of course, mean that the reaction normally catalyzed by the enzyme in question would either have its rate or products modified or be blocked entirely.
Such a view does not mean that genes directly “make” proteins. Regardless of precisely how proteins are synthesized, and from what component parts, these parts must themselves be synthesized by reactions which are enzymatically catalyzed and which in turn depend on the functioning of many genes. Thus in the synthesis of a single protein molecule, probably at least several hundred different genes contribute. But the final molecule corresponds to only one of them and this is the gene we visualize as being in primary control.
In 'Genetics and Metabolism in Neurospora', Physiological Reviews, 1945, 25, 660.
Since my first discussions of ecological problems with Professor John Day around 1950 and since reading Konrad Lorenz's “King Solomon's Ring,” I have become increasingly interested in the study of animals for what they might teach us about man, and the study of man as an animal. I have become increasingly disenchanted with what the thinkers of the so-called Age of Enlightenment tell us about the nature of man, and with what the formal religions and doctrinaire political theorists tell us about the same subject.
'Autobiography of Allan M. Cormack,' Les Prix Nobel/Nobel Lectures 1979, editted by Wilhelm Odelberg.
Since the stomach gives no obvious external sign of its workings, investigators of gastric movements have hitherto been obliged to confine their studies to pathological subjects or to animals subjected to serious operative interference. Observations made under these necessarily abnormal conditions have yielded a literature which is full of conflicting statements and uncertain results. The only sure conclusion to be drawn from this material is that when the stomach receives food, obscure peristaltic contractions are set going, which in some way churn the food to a liquid chyme and force it into the intestines. How imperfectly this describes the real workings of the stomach will appear from the following account of the actions of the organ studied by a new method. The mixing of a small quantity of subnitrate of bismuth with the food allows not only the contractions of the gastric wall, but also the movements of the gastric contents to be seen with the Röntgen rays in the uninjured animal during normal digestion.
In 'The Movements of the Stomach Studied by Means of the Röntgen Rays,' American Journal of Physiology (1898), 1, 359-360.
Sir, the reason is very plain; knowledge is of two kinds. We know a subject ourselves, or we know where we can find information upon it.
In James Boswell, The Life of Samuel Johnson, LL.D. (1820), Vol. 1, 418.
So many of the properties of matter, especially when in the gaseous form, can be deduced from the hypothesis that their minute parts are in rapid motion, the velocity increasing with the temperature, that the precise nature of this motion becomes a subject of rational curiosity. Daniel Bernoulli, Herapath, Joule, Kronig, Clausius, &c., have shewn that the relations between pressure, temperature and density in a perfect gas can be explained by supposing the particles move with uniform velocity in straight lines, striking against the sides of the containing vessel and thus producing pressure. (1860)
In W.D. Niven (ed.) 'Illustrations of the Dynamical Theory of Gases,' The Scientific Papers of James Clerk Maxwell, Vol 1, 377. Quoted in John David Anderson, Jr., Hypersonic and High Temperature Gas Dynamics (2000), 468.
So the astronomer is on common ground with the physicist both in the subject and in the predicate of the conclusion, but the physicist demonstrates the predicate to belong to the subject by nature, whereas the astronomer does not care whether it belongs by nature or not. What, therefore, is the predicate for the physicist, is abstracted as the subject for the pure mathematician.
As quoted in Alistair Cameron Crombie, Robert Grosseteste and the Origins of Experimental Science, 1100-1700 (1971), 94.
Some beliefs may be subject to such instant, brutal and unambiguous rejection. For example: no left-coiling periwinkle has ever been found among millions of snails examined. If I happen to find one during my walk on Nobska beach tomorrow morning, a century of well nurtured negative evidence will collapse in an instant.
'A Foot Soldier for Evolution', In Eight Little Piggies (1994), 452.
Some one once asked Rutherford how it was that he always managed to keep on the crest of the wave. “Well” said Rutherford “that isn’t difficult. I made the wave, why shouldn’t I be at the top of it.” I hasten to say that my own subject is a very minor ripple compared to Rutherford’s.
From Speech (10 Dec 1963) at the Nobel Banquet in Stockholm, Sweden. Collected inGöran Liljestrand (ed.), Les Prix Nobel en 1963, (1964).
Sometimes I wonder whether there is any such thing as biology. The word was invented rather late—in 1809—and other words like botany, zoology, physiology, anatomy, have much longer histories and in general cover more coherent and unified subject matters. … I would like to see the words removed from dictionaries and college catalogues. I think they do more harm than good because they separate things that should not be separated…
In The Forest and the Sea (1960), 6-7.
Statistical accounts are to be referred to as a dictionary by men of riper years, and by young men as a grammar, to teach them the relations and proportions of different statistical subjects, and to imprint them on the mind at a time when the memory is capable of being impressed in a lasting and durable manner, thereby laying the foundation for accurate and valuable knowledge.
In The Statistical Breviary: Shewing, on a Principle Entirely New, the Resources of Every State and Kingdom in Europe (1801), 5-6.
Suppose then I want to give myself a little training in the art of reasoning; suppose I want to get out of the region of conjecture and probability, free myself from the difficult task of weighing evidence, and putting instances together to arrive at general propositions, and simply desire to know how to deal with my general propositions when I get them, and how to deduce right inferences from them; it is clear that I shall obtain this sort of discipline best in those departments of thought in which the first principles are unquestionably true. For in all our thinking, if we come to erroneous conclusions, we come to them either by accepting false premises to start with—in which case our reasoning, however good, will not save us from error; or by reasoning badly, in which case the data we start from may be perfectly sound, and yet our conclusions may be false. But in the mathematical or pure sciences,—geometry, arithmetic, algebra, trigonometry, the calculus of variations or of curves,— we know at least that there is not, and cannot be, error in our first principles, and we may therefore fasten our whole attention upon the processes. As mere exercises in logic, therefore, these sciences, based as they all are on primary truths relating to space and number, have always been supposed to furnish the most exact discipline. When Plato wrote over the portal of his school. “Let no one ignorant of geometry enter here,” he did not mean that questions relating to lines and surfaces would be discussed by his disciples. On the contrary, the topics to which he directed their attention were some of the deepest problems,— social, political, moral,—on which the mind could exercise itself. Plato and his followers tried to think out together conclusions respecting the being, the duty, and the destiny of man, and the relation in which he stood to the gods and to the unseen world. What had geometry to do with these things? Simply this: That a man whose mind has not undergone a rigorous training in systematic thinking, and in the art of drawing legitimate inferences from premises, was unfitted to enter on the discussion of these high topics; and that the sort of logical discipline which he needed was most likely to be obtained from geometry—the only mathematical science which in Plato’s time had been formulated and reduced to a system. And we in this country [England] have long acted on the same principle. Our future lawyers, clergy, and statesmen are expected at the University to learn a good deal about curves, and angles, and numbers and proportions; not because these subjects have the smallest relation to the needs of their lives, but because in the very act of learning them they are likely to acquire that habit of steadfast and accurate thinking, which is indispensable to success in all the pursuits of life.
In Lectures on Teaching (1906), 891-92.
Sylvester was incapable of reading mathematics in a purely receptive way. Apparently a subject either fired in his brain a train of active and restless thought, or it would not retain his attention at all. To a man of such a temperament, it would have been peculiarly helpful to live in an atmosphere in which his human associations would have supplied the stimulus which he could not find in mere reading. The great modern work in the theory of functions and in allied disciplines, he never became acquainted with …
What would have been the effect if, in the prime of his powers, he had been surrounded by the influences which prevail in Berlin or in Gottingen? It may be confidently taken for granted that he would have done splendid work in those domains of analysis, which have furnished the laurels of the great mathematicians of Germany and France in the second half of the present century.
What would have been the effect if, in the prime of his powers, he had been surrounded by the influences which prevail in Berlin or in Gottingen? It may be confidently taken for granted that he would have done splendid work in those domains of analysis, which have furnished the laurels of the great mathematicians of Germany and France in the second half of the present century.
In Address delivered at a memorial meeting at the Johns Hopkins University (2 May 1897), published in Bulletin of the American Mathematical Society (Jun 1897), 303. Also in Johns Hopkins University Circulars, 16 (1897), 54.
Sylvester’s writings are flowery and eloquent. He was able to make the dullest subject bright, fresh and interesting. His enthusiasm is evident in every line. He would get quite close up to his subject, so that everything else looked small in comparison, and for the time would think and make others think that the world contained no finer matter for contemplation. His handwriting was bad, and a trouble to his printers. His papers were finished with difficulty. No sooner was the manuscript in the editor’s hands than alterations, corrections, ameliorations and generalizations would suggest themselves to his mind, and every post would carry further directions to the editors and printers.
In Nature (1897), 55, 494.
Tait once urged the advantage of Quaternions on Cayley (who never used them), saying: “You know Quaternions are just like a pocket-map.” “That may be,” replied Cayley, “but you’ve got to take it out of your pocket, and unfold it, before it’s of any use.” And he dismissed the subject with a smile.
In Life of Lord Kelvin (1910), 1137.
Taxonomy is often regarded as the dullest of subjects, fit only for mindless ordering and sometimes denigrated within science as mere “stamp collecting” (a designation that this former philatelist deeply resents). If systems of classification were neutral hat racks for hanging the facts of the world, this disdain might be justified. But classifications both reflect and direct our thinking. The way we order represents the way we think. Historical changes in classification are the fossilized indicators of conceptual revolutions.
In Hen’s Teeth and Horse’s Toes: Further Reflections in Natural History (1983, 2010), 72
Teachers should be able to teach subjects, not manuals merely.
Annual Reports of the Secretary of the Board of Education of Massachusetts for the years 1839-1844, Life and Works of Horace Mann (1891), Vol. 3, 58.
That a free, or at least an unsaturated acid usually exists in the stomachs of animals, and is in some manner connected with the important process of digestion, seems to have been the general opinion of physiologists till the time of SPALLANZANI. This illustrious philosopher concluded, from his numerous experiments, that the gastric fluids, when in a perfectly natural state, are neither acid nor alkaline. Even SPALLANZANI, however, admitted that the contents of the stomach are very generally acid; and this accords not only with my own observation, but with that, I believe, of almost every individual who has made any experiments on the subject. ... The object of the present communication is to show, that the acid in question is the muriatic [hydrochloric] acid, and that the salts usually met with in the stomach, are the alkaline muriates.
'On the Nature of the Acid and Saline Matters Usually Existing in the Stomachs of Animals', Philosophical Transactions of the Royal Society of London (1824), 114, 45-6.
That ability to impart knowledge … what does it consist of? … a deep belief in the interest and importance of the thing taught, a concern about it amounting to a sort of passion. A man who knows a subject thoroughly, a man so soaked in it that he eats it, sleeps it and dreams it—this man can always teach it with success, no matter how little he knows of technical pedagogy. That is because there is enthusiasm in him, and because enthusiasm is almost as contagious as fear or the barber’s itch. An enthusiast is willing to go to any trouble to impart the glad news bubbling within him. He thinks that it is important and valuable for to know; given the slightest glow of interest in a pupil to start with, he will fan that glow to a flame. No hollow formalism cripples him and slows him down. He drags his best pupils along as fast as they can go, and he is so full of the thing that he never tires of expounding its elements to the dullest.
This passion, so unordered and yet so potent, explains the capacity for teaching that one frequently observes in scientific men of high attainments in their specialties—for example, Huxley, Ostwald, Karl Ludwig, Virchow, Billroth, Jowett, William G. Sumner, Halsted and Osler—men who knew nothing whatever about the so-called science of pedagogy, and would have derided its alleged principles if they had heard them stated.
This passion, so unordered and yet so potent, explains the capacity for teaching that one frequently observes in scientific men of high attainments in their specialties—for example, Huxley, Ostwald, Karl Ludwig, Virchow, Billroth, Jowett, William G. Sumner, Halsted and Osler—men who knew nothing whatever about the so-called science of pedagogy, and would have derided its alleged principles if they had heard them stated.
In Prejudices: third series (1922), 241-2.
For a longer excerpt, see H.L. Mencken on Teaching, Enthusiasm and Pedagogy.
For a longer excerpt, see H.L. Mencken on Teaching, Enthusiasm and Pedagogy.
That this subject [of imaginary magnitudes] has hitherto been considered from the wrong point of view and surrounded by a mysterious obscurity, is to be attributed largely to an ill-adapted notation. If, for example, +1, -1, and the square root of -1 had been called direct, inverse and lateral units, instead of positive, negative and imaginary (or even impossible), such an obscurity would have been out of the question.
Theoria Residiorum Biquadraticorum, Commentario secunda', Werke (1863), Vol. 2. Quoted in Robert Edouard Moritz, Memorabilia Mathematica (1914), 282.
The ability to imagine relations is one of the most indispensable conditions of all precise thinking. No subject can be named, in the investigation of which it is not imperatively needed; but it can be nowhere else so thoroughly acquired as in the study of mathematics.
In Darwinism and other Essays (1893), 296.
The actual evolution of mathematical theories proceeds by a process of induction strictly analogous to the method of induction employed in building up the physical sciences; observation, comparison, classification, trial, and generalisation are essential in both cases. Not only are special results, obtained independently of one another, frequently seen to be really included in some generalisation, but branches of the subject which have been developed quite independently of one another are sometimes found to have connections which enable them to be synthesised in one single body of doctrine. The essential nature of mathematical thought manifests itself in the discernment of fundamental identity in the mathematical aspects of what are superficially very different domains. A striking example of this species of immanent identity of mathematical form was exhibited by the discovery of that distinguished mathematician … Major MacMahon, that all possible Latin squares are capable of enumeration by the consideration of certain differential operators. Here we have a case in which an enumeration, which appears to be not amenable to direct treatment, can actually be carried out in a simple manner when the underlying identity of the operation is recognised with that involved in certain operations due to differential operators, the calculus of which belongs superficially to a wholly different region of thought from that relating to Latin squares.
In Presidential Address British Association for the Advancement of Science, Sheffield, Section A,
Nature (1 Sep 1910), 84, 290.
The art of reasoning consists in getting hold of the subject at the right end, of seizing on the few general ideas that illuminate the whole, and of persistently organizing all subsidiary facts round them.
In 'Presidential Address to the London Branch of the Mathematical Association', Mathematical Gazette (Mar 1913), 7, No. 104, 92.
The attempted synthesis of paleontology and genetics, an essential part of the present study, may be particularly surprising and possibly hazardous. Not long ago, paleontologists felt that a geneticist was a person who shut himself in a room, pulled down the shades, watched small flies disporting themselves in milk bottles, and thought that he was studying nature. A pursuit so removed from the realities of life, they said, had no significance for the true biologist. On the other hand, the geneticists said that paleontology had no further contributions to make to biology, that its only point had been the completed demonstration of the truth of evolution, and that it was a subject too purely descriptive to merit the name 'science'. The paleontologist, they believed, is like a man who undertakes to study the principles of the internal combustion engine by standing on a street corner and watching the motor cars whiz by.
Tempo and Mode in Evolution (1944), 1.
The automatic computing engine now being designed at N.P.L. [National Physics Laboratory] is atypical large scale electronic digital computing machine. In a single lecture it will not be possible to give much technical detail of this machine, and most of what I shall say will apply equally to any other machine of this type now being planned. From the point of view of the mathematician the property of being digital should be of greater interest than that of being electronic. That it is electronic is certainly important because these machines owe their high speed to this, and without the speed it is doubtful if financial support for their construction would be forthcoming. But this is virtually all that there is to be said on that subject. That the machine is digital however has more subtle significance. It means firstly that numbers are represented by sequences of digits which can be as long as one wishes. One can therefore work to any desired degree of accuracy. This accuracy is not obtained by more careful machining of parts, control of temperature variations, and such means, but by a slight increase in the amount of equipment in the machine.
Lecture to the London Mathematical Society, 20 February 1947. Quoted in B. E. Carpenter and R. W. Doran (eds.), A. M. Turing's Ace Report of 1946 and Other Papers (1986), 106.
The average English author [of mathematical texts] leaves one under the impression that he has made a bargain with his reader to put before him the truth, the greater part of the truth, and nothing but the truth; and that if he has put the facts of his subject into his book, however difficult it may be to unearth them, he has fulfilled his contract with his reader. This is a very much mistaken view, because effective teaching requires a great deal more than a bare recitation of facts, even if these are duly set forth in logical order—as in English books they often are not. The probable difficulties which will occur to the student, the objections which the intelligent student will naturally and necessarily raise to some statement of fact or theory—these things our authors seldom or never notice, and yet a recognition and anticipation of them by the author would be often of priceless value to the student. Again, a touch of humour (strange as the contention may seem) in mathematical works is not only possible with perfect propriety, but very helpful; and I could give instances of this even from the pure mathematics of Salmon and the physics of Clerk Maxwell.
In Perry, Teaching of Mathematics (1902), 59-61.
The claims of certain so-called scientific men as to 'science overthrowing religion' are as baseless as the fears of certain sincerely religious men on the same subject. The establishment of the doctrine of evolution in out time offers no more justification for upsetting religious beliefs than the discovery of the facts concerning the solar system a few centuries ago. Any faith sufficiently robust to stand the—surely very slight—strain of admitting that the world is not flat and does not move round the sun need have no apprehensions on the score of evolution, and the materialistic scientists who gleefully hail the discovery of the principle of evolution as establishing their dreary creed might with just as much propriety rest it upon the discovery of the principle of gravity.
'The Search for Truth in a Reverent Spirit', (originally published in The Outlook, 2 Dec 1911). In The Works of Theodore Roosevelt (1913), Vol. 26, 256.
The conception of the atom stems from the concepts of subject and substance: there has to be “something” to account for any action. The atom is the last descendant of the concept of the soul.
Epigraph, without citation, in Edward C. Stark, Essential Chemistry (1979), 97. Also without citation in Isaac Asimov and Jason A. Shulman (eds.), Isaac Asimov’s Book of Science and Nature Quotations (1988), 32. Webmaster has not yet been able to identify the primary source (can you help?).
The contents of this section will furnish a very striking illustration of the truth of a remark, which I have more than once made in my philosophical writings, and which can hardly be too often repeated, as it tends greatly to encourage philosophical investigations viz. That more is owing to what we call chance, that is, philosophically speaking, to the observation of events arising from unknown causes, than to any proper design, or pre-conceived theory in this business. This does not appear in the works of those who write synthetically upon these subjects; but would, I doubt not, appear very strikingly in those who are the most celebrated for their philosophical acumen, did they write analytically and ingenuously.
'On Dephlogisticated Air, and the Constitution of the Atmosphere', in The Discovery of Oxygen, Part I, Experiments by Joseph Priestley 1775 (Alembic Club Reprint, 1894), 5.
The degree of exactness of the intuition of space may be different in different individuals, perhaps even in different races. It would seem as if a strong naive space-intuition were an attribute pre-eminently of the Teutonic race, while the critical, purely logical sense is more fully developed in the Latin and Hebrew races. A full investigation of this subject, somewhat on the lines suggested by Francis Gallon in his researches on heredity, might be interesting.
In The Evanston Colloquium Lectures (1894), 46.
The development doctrines are doing much harm on both sides of the Atlantic, especially among intelligent mechanics, and a class of young men engaged in the subordinate departments of trade and the law. And the harm thus considerable in amount must be necessarily more than considerable in degree. For it invariably happens, that when persons in these walks become materialists, they become turbulent subjects and bad men.
The Foot-prints of the Creator: Or, The Asterolepis of Stromness (1850, 1859), Preface, vi.
The difference between science and the fuzzy subjects is that science requires reasoning while those other subjects merely require scholarship.
In Time Enough For Love: the Lives of Lazarus Long (1973), 366.
The digestive canal is in its task a complete chemical factory. The raw material passes through a long series of institutions in which it is subjected to certain mechanical and, mainly, chemical processing, and then, through innumerable side-streets, it is brought into the depot of the body. Aside from this basic series of institutions, along which the raw material moves, there is a series of lateral chemical manufactories, which prepare certain reagents for the appropriate processing of the raw material.
Speech to the Society of Russian Physicians (Dec 1874). as translated in Daniel P. Todes, Pavlov’s Physiology Factory: Experiment, Interpretation, Laboratory Enterprise (2002), 155.
The distinction is, that the science or knowledge of the particular subject-matter furnishes the evidence, while logic furnishes the principles and rules of the estimation of evidence.
In A System of Logic, Ratiocinative and Inductive: Being a Connected View of the Principles of Evidence, and the Methods of Scientific Investigation (1843), Vol. 1, 11.
The enthusiasm of Sylvester for his own work, which manifests itself here as always, indicates one of his characteristic qualities: a high degree of subjectivity in his productions and publications. Sylvester was so fully possessed by the matter which for the time being engaged his attention, that it appeared to him and was designated by him as the summit of all that is important, remarkable and full of future promise. It would excite his phantasy and power of imagination in even a greater measure than his power of reflection, so much so that he could never marshal the ability to master his subject-matter, much less to present it in an orderly manner.
Considering that he was also somewhat of a poet, it will be easier to overlook the poetic flights which pervade his writing, often bombastic, sometimes furnishing apt illustrations; more damaging is the complete lack of form and orderliness of his publications and their sketchlike character, … which must be accredited at least as much to lack of objectivity as to a superfluity of ideas. Again, the text is permeated with associated emotional expressions, bizarre utterances and paradoxes and is everywhere accompanied by notes, which constitute an essential part of Sylvester’s method of presentation, embodying relations, whether proximate or remote, which momentarily suggested themselves. These notes, full of inspiration and occasional flashes of genius, are the more stimulating owing to their incompleteness. But none of his works manifest a desire to penetrate the subject from all sides and to allow it to mature; each mere surmise, conceptions which arose during publication, immature thoughts and even errors were ushered into publicity at the moment of their inception, with utmost carelessness, and always with complete unfamiliarity of the literature of the subject. Nowhere is there the least trace of self-criticism. No one can be expected to read the treatises entire, for in the form in which they are available they fail to give a clear view of the matter under contemplation.
Sylvester’s was not a harmoniously gifted or well-balanced mind, but rather an instinctively active and creative mind, free from egotism. His reasoning moved in generalizations, was frequently influenced by analysis and at times was guided even by mystical numerical relations. His reasoning consists less frequently of pure intelligible conclusions than of inductions, or rather conjectures incited by individual observations and verifications. In this he was guided by an algebraic sense, developed through long occupation with processes of forms, and this led him luckily to general fundamental truths which in some instances remain veiled. His lack of system is here offset by the advantage of freedom from purely mechanical logical activity.
The exponents of his essential characteristics are an intuitive talent and a faculty of invention to which we owe a series of ideas of lasting value and bearing the germs of fruitful methods. To no one more fittingly than to Sylvester can be applied one of the mottos of the Philosophic Magazine:
“Admiratio generat quaestionem, quaestio investigationem investigatio inventionem.”
Considering that he was also somewhat of a poet, it will be easier to overlook the poetic flights which pervade his writing, often bombastic, sometimes furnishing apt illustrations; more damaging is the complete lack of form and orderliness of his publications and their sketchlike character, … which must be accredited at least as much to lack of objectivity as to a superfluity of ideas. Again, the text is permeated with associated emotional expressions, bizarre utterances and paradoxes and is everywhere accompanied by notes, which constitute an essential part of Sylvester’s method of presentation, embodying relations, whether proximate or remote, which momentarily suggested themselves. These notes, full of inspiration and occasional flashes of genius, are the more stimulating owing to their incompleteness. But none of his works manifest a desire to penetrate the subject from all sides and to allow it to mature; each mere surmise, conceptions which arose during publication, immature thoughts and even errors were ushered into publicity at the moment of their inception, with utmost carelessness, and always with complete unfamiliarity of the literature of the subject. Nowhere is there the least trace of self-criticism. No one can be expected to read the treatises entire, for in the form in which they are available they fail to give a clear view of the matter under contemplation.
Sylvester’s was not a harmoniously gifted or well-balanced mind, but rather an instinctively active and creative mind, free from egotism. His reasoning moved in generalizations, was frequently influenced by analysis and at times was guided even by mystical numerical relations. His reasoning consists less frequently of pure intelligible conclusions than of inductions, or rather conjectures incited by individual observations and verifications. In this he was guided by an algebraic sense, developed through long occupation with processes of forms, and this led him luckily to general fundamental truths which in some instances remain veiled. His lack of system is here offset by the advantage of freedom from purely mechanical logical activity.
The exponents of his essential characteristics are an intuitive talent and a faculty of invention to which we owe a series of ideas of lasting value and bearing the germs of fruitful methods. To no one more fittingly than to Sylvester can be applied one of the mottos of the Philosophic Magazine:
“Admiratio generat quaestionem, quaestio investigationem investigatio inventionem.”
In Mathematische Annalen (1898), 50, 155-160. As translated in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-book (1914), 176-178.
The equations of dynamics completely express the laws of the historical method as applied to matter, but the application of these equations implies a perfect knowledge of all the data. But the smallest portion of matter which we can subject to experiment consists of millions of molecules, not one of which ever becomes individually sensible to us. We cannot, therefore, ascertain the actual motion of anyone of these molecules; so that we are obliged to abandon the strict historical method, and to adopt the statistical method of dealing with large groups of molecules … Thus molecular science teaches us that our experiments can never give us anything more than statistical information, and that no law derived from them can pretend to absolute precision. But when we pass from the contemplation of our experiments to that of the molecules themselves, we leave a world of chance and change, and enter a region where everything is certain and immutable.
'Molecules' (1873). In W. D. Niven (ed.), The Scientific Papers of James Clerk Maxwell (1890), Vol. 2, 374.
The Excellence of Modern Geometry is in nothing more evident, than in those full and adequate Solutions it gives to Problems; representing all possible Cases in one view, and in one general Theorem many times comprehending whole Sciences; which deduced at length into Propositions, and demonstrated after the manner of the Ancients, might well become the subjects of large Treatises: For whatsoever Theorem solves the most complicated Problem of the kind, does with a due Reduction reach all the subordinate Cases.
In 'An Instance of the Excellence of Modern Algebra, etc', Philosophical Transactions, 1694, 960.
The fact is that there are few more “popular” subjects than mathematics. Most people have some appreciation of mathematics, just as most people can enjoy a pleasant tune; and there are probably more people really interested in mathematics than in music. Appearances may suggest the contrary, but there are easy explanations. Music can be used to stimulate mass emotion, while mathematics cannot; and musical incapacity is recognized (no doubt rightly) as mildly discreditable, whereas most people are so frightened of the name of mathematics that they are ready, quite unaffectedly, to exaggerate their own mathematical stupidity.
In A Mathematician's Apology (1940, reprint with Foreward by C.P. Snow 1992), 86.
The fading of ideals is sad evidence of the defeat of human endeavour. In the schools of antiquity philosophers aspired to impart wisdom, in modern colleges our humbler aim is to teach subjects
Opening lines of 'The Rhythmic Claims of Freedom and Discipline', The Aims of Education: & Other Essays (1917), 45.
The first fundamental rule of historical science and research, when by these is sought a knowledge of the general destinies of mankind, is to keep these and every object connected with them steadily in view, without losing ourselves in the details of special inquiries and particular facts, for the multitude and variety of these subjects is absolutely boundless; and on the ocean of historical science the main subject easily vanishes from the eye.
In Friedrich von Schlegel and James Burton Robertson (trans.), The Philosophy of History (1835), 8.
The flights of the imagination which occur to the pure mathematician are in general so much better described in his formulas than in words, that it is not remarkable to find the subject treated by outsiders as something essentially cold and uninteresting— … the only successful attempt to invest mathematical reasoning with a halo of glory—that made in this section by Prof. Sylvester—is known to a comparative few, …
In Presidential Address British Association for the Advancement of Science (1871), Nature Vol. 4, 271,
The following general conclusions are drawn from the propositions stated above, and known facts with reference to the mechanics of animal and vegetable bodies:—
There is at present in the material world a universal tendency to the dissipation of mechanical energy.
Any restoration of mechanical energy, without more than an equivalent of dissipation, is impossible in inanimate material processes, and is probably never effected by means of organized matter, either endowed with vegetable life, or subjected to the will of an animated creature.
Within a finite period of time past the earth must have been, and within a finite period of time to come the earth must again be, unfit for the habitation of man as at present constituted, unless operations have been, or are to be performed, which are impossible under the laws to which the known operations going on at present in the material world are subject.
There is at present in the material world a universal tendency to the dissipation of mechanical energy.
Any restoration of mechanical energy, without more than an equivalent of dissipation, is impossible in inanimate material processes, and is probably never effected by means of organized matter, either endowed with vegetable life, or subjected to the will of an animated creature.
Within a finite period of time past the earth must have been, and within a finite period of time to come the earth must again be, unfit for the habitation of man as at present constituted, unless operations have been, or are to be performed, which are impossible under the laws to which the known operations going on at present in the material world are subject.
In 'On a Universal Tendency in Nature to the Dissipation of Mechanical Energy', Proceedings of the Royal Society of Edinburgh, 1852, 3, 141-142. In Mathematical and Physical Papers (1882-1911), Vol. 1, 513-514.
The Frog—that arch-martyr to science—affords the most convenient subject.
In Rudiments of Pathological Histology (1855), trans. and ed. by George Busk, 15.
The functional validity of a working hypothesis is not a priori certain, because often it is initially based on intuition. However, logical deductions from such a hypothesis provide expectations (so-called prognoses) as to the circumstances under which certain phenomena will appear in nature. Such a postulate or working hypothesis can then be substantiated by additional observations ... The author calls such expectations and additional observations the prognosis-diagnosis method of research. Prognosis in science may be termed the prediction of the future finding of corroborative evidence of certain features or phenomena (diagnostic facts). This method of scientific research builds up and extends the relations between the subject and the object by means of a circuit of inductions and deductions.
In 'The Scientific Character of Geology', The Journal of Geology (Jul 1961), 69, No. 4, 454-5.
The game of chess has always fascinated mathematicians, and there is reason to suppose that the possession of great powers of playing that game is in many features very much like the possession of great mathematical ability. There are the different pieces to learn, the pawns, the knights, the bishops, the castles, and the queen and king. The board possesses certain possible combinations of squares, as in rows, diagonals, etc. The pieces are subject to certain rules by which their motions are governed, and there are other rules governing the players. … One has only to increase the number of pieces, to enlarge the field of the board, and to produce new rules which are to govern either the pieces or the player, to have a pretty good idea of what mathematics consists.
In Book review, 'What is Mathematics?', Bulletin American Mathematical Society (May 1912), 18, 386-387.
The genius of Laplace was a perfect sledge hammer in bursting purely mathematical obstacles; but, like that useful instrument, it gave neither finish nor beauty to the results. In truth, in truism if the reader please, Laplace was neither Lagrange nor Euler, as every student is made to feel. The second is power and symmetry, the third power and simplicity; the first is power without either symmetry or simplicity. But, nevertheless, Laplace never attempted investigation of a subject without leaving upon it the marks of difficulties conquered: sometimes clumsily, sometimes indirectly, always without minuteness of design or arrangement of detail; but still, his end is obtained and the difficulty is conquered.
In 'Review of “Théorie Analytique des Probabilites” par M. le Marquis de Laplace, 3eme edition. Paris. 1820', Dublin Review (1837), 2, 348.
The geometrical problems and theorems of the Greeks always refer to definite, oftentimes to rather complicated figures. Now frequently the points and lines of such a figure may assume very many different relative positions; each of these possible cases is then considered separately. On the contrary, present day mathematicians generate their figures one from another, and are accustomed to consider them subject to variation; in this manner they unite the various cases and combine them as much as possible by employing negative and imaginary magnitudes. For example, the problems which Apollonius treats in his two books De sectione rationis, are solved today by means of a single, universally applicable construction; Apollonius, on the contrary, separates it into more than eighty different cases varying only in position. Thus, as Hermann Hankel has fittingly remarked, the ancient geometry sacrifices to a seeming simplicity the true simplicity which consists in the unity of principles; it attained a trivial sensual presentability at the cost of the recognition of the relations of geometric forms in all their changes and in all the variations of their sensually presentable positions.
In 'Die Synthetische Geometrie im Altertum und in der Neuzeit', Jahresbericht der Deutschen Mathematiker Vereinigung (1902), 2, 346-347. As translated in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-book (1914), 112. The spelling of the first “Apollonius” has been corrected from “Appolonius” in the original English text. From the original German, “Die geometrischen Probleme und Sätze der Griechen beziehen sich allemal auf bestimmte, oft recht komplizierte Figuren. Nun können aber die Punkte und Linien einer solchen Figur häufig sehr verschiedene Lagen zu einander annehmen; jeder dieser möglichen Fälle wird alsdann für sich besonders erörtert. Dagegen lassen die heutigen Mathematiker ihre Figuren aus einander entstehen und sind gewohnt, sie als veränderlich zu betrachten; sie vereinigen so die speziellen Fälle und fassen sie möglichst zusammen unter Benutzung auch negativer und imaginärer Gröfsen. Das Problem z. B., welches Apollonius in seinen zwei Büchern de sectione rationis behandelt, löst man heutzutage durch eine einzige, allgemein anwendbare Konstruktion; Apollonius selber dagegen zerlegt es in mehr als 80 nur durch die Lage verschiedene Fälle. So opfert, wie Hermann Hankel treffend bemerkt, die antike Geometrie einer scheinbaren Einfachheit die wahre, in der Einheit der Prinzipien bestehende; sie erreicht eine triviale sinnliche Anschaulichkeit auf Kosten der Erkenntnis vom Zusammenhang geometrischer Gestalten in aller Wechsel und in aller Veränderlichkeit ihrer sinnlich vorstellbaren Lage.”
The gradual advance of Geology, during the last twenty years, to the dignity of a science, has arisen from the laborious and extensive collection of facts, and from the enlightened spirit in which the inductions founded on those facts have been deduced and discussed. To those who are unacquainted with this science, or indeed to any person not deeply versed in the history of this and kindred subjects, it is impossible to convey a just impression of the nature of that evidence by which a multitude of its conclusions are supported:—evidence in many cases so irresistible, that the records of the past ages, to which it refers, are traced in language more imperishable than that of the historian of any human transactions; the relics of those beings, entombed in the strata which myriads of centuries have heaped upon their graves, giving a present evidence of their past existence, with which no human testimony can compete.
The Ninth Bridgewater Treatise (1838), 47-8.
The great art consists in devising décisive experiments, leaving no place to the imagination of the observer. Imagination is needed to give wings to thought at the beginning of experimental investigations on any given subject. When, however, the time has come to conclude, and to interpret the facts derived from observations, imagination must submit to the factual results of the experiments.
Speech (8 Jul 1876), to the French Academy of Medicine. As translated in René J. Dubos, Louis Pasteur, Free Lance of Science (1950, 1986), 376. Date of speech identified in Maurice B. Strauss, Familiar Medical Quotations (1968), 502.
The great difference between science and technology is a difference of initial attitude. The scientific man follows his method whithersoever it may take him. He seeks acquaintance with his subjectmatter, and he does not at all care about what he shall find, what shall be the content of his knowledge when acquaintance-with is transformed into knowledge-about. The technologist moves in another universe; he seeks the attainment of some determinate end, which is his sole and obsessing care; and he therefore takes no heed of anything that he cannot put to use as means toward that end.
Systematic Psychology: Prolegomena (1929), 66.
The great problem of today is, how to subject all physical phenomena to dynamical laws. With all the experimental devices, and all the mathematical appliances of this generation, the human mind has been baffled in its attempts to construct a universal science of physics.
'President's Address', Proceedings of the American Association for the Advancement of Science (1874), 23, 34-5.
The Greeks made Space the subject-matter of a science of supreme simplicity and certainty. Out of it grew, in the mind of classical antiquity, the idea of pure science. Geometry became one of the most powerful expressions of that sovereignty of the intellect that inspired the thought of those times. At a later epoch, when the intellectual despotism of the Church, which had been maintained through the Middle Ages, had crumbled, and a wave of scepticism threatened to sweep away all that had seemed most fixed, those who believed in Truth clung to Geometry as to a rock, and it was the highest ideal of every scientist to carry on his science “more geometrico.”
In Space,Time, Matter, translated by Henry Leopold Brose (1952), 1.
The idea of making a fault a subject of study and not an object to be merely determined has been the most important step in the course of my methods of observation. If I have obtained some new results it is to this that I owe it.
'Notice sur les Travaux Scientifiques de Marcel Bertrand' (1894). In Geological Society of London, The Quarterly Journal of the Geological Society of London (May 1908), 64, li.
The idea that aptitude for mathematics is rarer than aptitude for other subjects is merely an illusion which is caused by belated or neglected beginners.
In 'Umriss pädagogischer Vorlesungen', Werke [Kehrbach] (1902), Bd. 10, 101. As quoted, cited and translated in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-Book (1914), 74.
The ideas which these sciences, Geometry, Theoretical Arithmetic and Algebra involve extend to all objects and changes which we observe in the external world; and hence the consideration of mathematical relations forms a large portion of many of the sciences which treat of the phenomena and laws of external nature, as Astronomy, Optics, and Mechanics. Such sciences are hence often termed Mixed Mathematics, the relations of space and number being, in these branches of knowledge, combined with principles collected from special observation; while Geometry, Algebra, and the like subjects, which involve no result of experience, are called Pure Mathematics.
In The Philosophy of the Inductive Sciences (1868), Part 1, Bk. 2, chap. 1, sect. 4.
The importance of a result is largely relative, is judged differently by different men, and changes with the times and circumstances. It has often happened that great importance has been attached to a problem merely on account of the difficulties which it presented; and indeed if for its solution it has been necessary to invent new methods, noteworthy artifices, etc., the science has gained more perhaps through these than through the final result. In general we may call important all investigations relating to things which in themselves are important; all those which have a large degree of generality, or which unite under a single point of view subjects apparently distinct, simplifying and elucidating them; all those which lead to results that promise to be the source of numerous consequences; etc.
From 'On Some Recent Tendencies in Geometric Investigations', Rivista di Matematica (1891), 44. In Bulletin American Mathematical Society (1904), 444.
The inhibitory nerves are of as fundamental importance in the economy of the body as the motor nerves. No evidence exists that the same nerve fibre is sometimes capable of acting as a motor nerve, sometimes as a nerve of inhibition, but on the contrary the latter nerves form a separate and complete nervous system subject to as definite anatomical and histological laws as the former.
'On the Structure, Distribution and Function of the Nerves which Innervate the Visceral and Vascular Systems', The Journal of Physiology, 1886, 7, 40.
The intensity and quantity of polemical literature on scientific problems frequently varies inversely as the number of direct observations on which the discussions are based: the number and variety of theories concerning a subject thus often form a coefficient of our ignorance. Beyond the superficial observations, direct and indirect, made by geologists, not extending below about one two-hundredth of the Earth's radius, we have to trust to the deductions of mathematicians for our ideas regarding the interior of the Earth; and they have provided us successively with every permutation and combination possible of the three physical states of matter—solid, liquid, and gaseous.
'Address delivered by the President of Section [Geology] at Sydney (Friday, Aug 21), Report of the Eighty-Fourth Meeting of the British Association for the Advancement of Science: Australia 1914, 1915, 345.
The invention of the differential calculus marks a crisis in the history of mathematics. The progress of science is divided between periods characterized by a slow accumulation of ideas and periods, when, owing to the new material for thought thus patiently collected, some genius by the invention of a new method or a new point of view, suddenly transforms the whole subject on to a higher level.
In An Introduction to Mathematics (1911), 217. Whitehead continued by quoting the poet, Percy Shelley, who compared the slow accumulation of thoughts leading to an avalanche following the laying down of a great truth. See the poetic quote beginning, “The sun-awakened avalanche…” on the Percy Shelley Quotations page.
The Johns Hopkins University certifies that John Wentworth Doe does not know anything but Biochemistry. Please pay no attention to any pronouncements he may make on any other subject, particularly when he joins with others of his kind to save the world from something or other. However, he worked hard for this degree and is potentially a most valuable citizen. Please treat him kindly.
[An imaginary academic diploma reworded to give a more realistic view of the value of the training of scientists.]
[An imaginary academic diploma reworded to give a more realistic view of the value of the training of scientists.]
'Our Splintered Learning and the Nature of Scientists', Science (15 Apr 1955), 121, 516.
The knowledge of Natural-History, being Observation of Matters of Fact, is more certain than most others, and in my slender Opinion, less subject to Mistakes than Reasonings, Hypotheses, and Deductions are; ... These are things we are sure of, so far as our Senses are not fallible; and which, in probability, have been ever since the Creation, and will remain to the End of the World, in the same Condition we now find them.
A Voyage to the Islands Madera, Barbados, Nieves, S. Christophers and Jamaica: With the Natural History of the Herbs and Trees, Four-footed Beasts, Fishes, Birds, Insects, Reptiles, &c. of the Last of those Islands (1707), Vol. 1, 1.
The logic of the subject [algebra], which, both educationally and scientifically speaking, is the most important part of it, is wholly neglected. The whole training consists in example grinding. What should have been merely the help to attain the end has become the end itself. The result is that algebra, as we teach it, is neither an art nor a science, but an ill-digested farrago of rules, whose object is the solution of examination problems. … The result, so far as problems worked in examinations go, is, after all, very miserable, as the reiterated complaints of examiners show; the effect on the examinee is a well-known enervation of mind, an almost incurable superficiality, which might be called Problematic Paralysis—a disease which unfits a man to follow an argument extending beyond the length of a printed octavo page.
In Presidential Address British Association for the Advancement of Science (1885), Nature, 32, 447-448.
The mathematic, then, is an art. As such it has its styles and style periods. It is not, as the layman and the philosopher (who is in this matter a layman too) imagine, substantially unalterable, but subject like every art to unnoticed changes form epoch to epoch. The development of the great arts ought never to be treated without an (assuredly not unprofitable) side-glance at contemporary mathematics.
In Oswald Spengler and Charles Francis Atkinson (trans.), The Decline of the West (1926), 62.
The method of inquiry which all our ingenious Theorists of the Earth have pursued is certainly erroneous. They first form an hypothesis to solve the phenomena, but in fact the Phenomena are always used as a prop to the hypothesis.
Instead therefore of attempting to cut the gordian knot by Hypothetical analysis, we shall follow the synthetic method of inquiry and content ourselves with endeavouring to establish facts rather than attempt solutions and try by experiments how far that method may leave us thro' the mazes of this subject
Instead therefore of attempting to cut the gordian knot by Hypothetical analysis, we shall follow the synthetic method of inquiry and content ourselves with endeavouring to establish facts rather than attempt solutions and try by experiments how far that method may leave us thro' the mazes of this subject
Introduction to his lecture course. In Robert Jameson, edited by H. W. Scott, Lectures on Geology, (1966), 27. In Patrick Wyse Jackson, Four Centuries of Geological Travel (2007), 33.
The moment one has offered an original explanation for a phenomenon which seems satisfactory, that moment affection for his intellectual child springs into existence, and as the explanation grows into a definite theory his parental affections cluster about his offspring and it grows more and more dear to him. ... There springs up also unwittingly a pressing of the theory to make it fit the facts and a pressing of the facts to make them fit the theory... To avoid this grave danger, the method of multiple working hypotheses is urged. It differs from the simple working hypothesis in that it distributes the effort and divides the affections... In developing the multiple hypotheses, the effort is to bring up into view every rational exploration of the phenomenon in hand and to develop every tenable hypothesis relative to its nature, cause or origin, and to give to all of these as impartially as possible a working form and a due place in the investigation. The investigator thus becomes the parent of a family of hypotheses; and by his parental relations to all is morally forbidden to fasten his affections unduly upon anyone. ... Each hypothesis suggests its own criteria, its own method of proof, its own method of developing the truth, and if a group of hypotheses encompass the subject on all sides, the total outcome of means and of methods is full and rich.
'Studies for Students. The Method of Multiple Working Hypotheses', Journal of Geology (1897), 5, 840-6.
The Moon and the weather
May change together;
But change of the Moon
Does not change the weather.
If we’d no moon at all,
And that may seem strange,
We still should have weather
That’s subject to change.
May change together;
But change of the Moon
Does not change the weather.
If we’d no moon at all,
And that may seem strange,
We still should have weather
That’s subject to change.
Cited as “heard many years ago” in Notes and Queries (23 Sep 1882), 246. Quoted in George Frederick Chambers, The Story of the Weather Simply Told for General Readers (1897), 197.
The more a science advances, the more will it be possible to understand immediately results which formerly could be demonstrated only by means of lengthy intermediate considerations: a mathematical subject cannot be considered as finally completed until this end has been attained.
In Formensystem binärer Formen (1875), 2.
The more the subject is examined the more complex must we suppose the constitution of matter in order to explain the remarkable effects observed.
In Radio-activity (1905), 1.
The morphological characteristics of plant and animal species form the chief subject of the descriptive natural sciences and are the criteria for their classification. But not until recently has it been recognized that in living organisms, as in the realm of crystals, chemical differences parallel the variation in structure.
The Specificity of Serological Reactions (1936), 3.
The mythology of science asserts that with many different scientists all asking their own questions and evaluating the answers independently, whatever personal bias creeps into their individual answers is cancelled out when the large picture is put together. This might conceivably be so if scientists were women and men from all sorts of different cultural and social backgrounds who came to science with very different ideologies and interests. But since, in fact, they have been predominantly university-trained white males from privileged social backgrounds, the bias has been narrow and the product often reveals more about the investigator than about the subject being researched.
'Have Only Men Evolved?' Women Look at Biology Looking At Women, eds. Ruth Hubbard, Mary Sue Henifin, and Barbara Fried (1979).
The nature of light is a subject of no material importance to the concerns of life or to the practice of the arts, but it is in many other respects extremely interesting.
Lecture 39, 'On the Nature of Light and Colours', A Course of Lectures on Natural Philosophy and the Mechanical Arts (1845), Vol. 1, 359.
The next object which I have observed is the essence or substance of the Milky Way. By the aid of a telescope anyone may behold this in a manner which so distinctly appeals to the senses that all the disputes which have tormented philosophers through so many ages are exploded at once by the irrefragable evidence of our eyes, and we are freed from wordy disputes upon this subject, for the Galaxy is nothing else but a mass of innumerable stars planted together in clusters.
In pamphlet, The Sidereal Messenger (1610), reprinted in The Sidereal Messenger of Galileo Galilei: And a Part of the Preface to the Preface to Kepler's Dioptrics Containing the Original Account of Galileo's Astronomical Discoveries (1880), 42.
The nicest constitutions of government are often like the finest pieces of clock-work, which, depending on so many motions, are therefore more subject to be out of order.
'Thoughts On Various Subjects', The Works of Alexander Pope (1806), Vol. 6, 406.
The object of pure mathematics is those relations which may be conceptually established among any conceived elements whatsoever by assuming them contained in some ordered manifold; the law of order of this manifold must be subject to our choice; the latter is the case in both of the only conceivable kinds of manifolds, in the discrete as well as in the continuous.
In Über das System der rein mathematischen Wissenschaften, Jahresbericht der Deutschen Mathematiker-Vereinigung, Bd. 1, 36. As quoted and cited in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-book (1914), 3.
The objects which astronomy discloses afford subjects of sublime contemplation, and tend to elevate the soul above vicious passions and groveling pursuits.
In Elijah H. Burritt, 'Introduction', The Geography of the Heavens (1844), 16.
The observing mind is not a physical system, it cannot interact with any physical system. And it might be better to reserve the term ‘subject ‘ for the observing mind ... For the subject, if anything, is the thing that senses and thinks. Sensations and thoughts do not belong to the ‘world of energy.’
…...
The opinion of Bacon on this subject [geometry] was diametrically opposed to that of the ancient philosophers. He valued geometry chiefly, if not solely, on account of those uses, which to Plato appeared so base. And it is remarkable that the longer Bacon lived the stronger this feeling became. When in 1605 he wrote the two books on the Advancement of Learning, he dwelt on the advantages which mankind derived from mixed mathematics; but he at the same time admitted that the beneficial effect produced by mathematical study on the intellect, though a collateral advantage, was “no less worthy than that which was principal and intended.” But it is evident that his views underwent a change. When near twenty years later, he published the De Augmentis, which is the Treatise on the Advancement of Learning, greatly expanded and carefully corrected, he made important alterations in the part which related to mathematics. He condemned with severity the pretensions of the mathematicians, “delidas et faslum mathematicorum.” Assuming the well-being of the human race to be the end of knowledge, he pronounced that mathematical science could claim no higher rank than that of an appendage or an auxiliary to other sciences. Mathematical science, he says, is the handmaid of natural philosophy; she ought to demean herself as such; and he declares that he cannot conceive by what ill chance it has happened that she presumes to claim precedence over her mistress.
In 'Lord Bacon', Edinburgh Review (Jul 1837). Collected in Critical and Miscellaneous Essays: Contributed to the Edinburgh Review (1857), Vol. 1, 395.
The ordinary man (or woman) thinks he knows what time is but cannot say. The learned man, physicist or philosopher, is not sure he knows but is ready to write volumes on the subject of his speculation and ignorance.
In Revolution in Time: Clocks and the Making of the Modern World (1983), 1.
The organism cannot be regarded as simply the passive object of autonomous internal and external forces; it is also the subject of its own evolution.
Co-author with American biologist Richard Charles Lewontin (1929- )
Co-author with American biologist Richard Charles Lewontin (1929- )
The Dialectical Biologist (1985), 89.
The physicist can never subject an isolated hypothesis to experimental test, but only a whole group of hypotheses.
The Aim and Structure of Physical Theory (1906), 2nd edition (1914), trans. Philip P. Wiener (1954), 187.
The process of mutation is the only known source of the raw materials of genetic variability, and hence of evolution. It is subject to experimental study, and considerable progress has been accomplished in this study in recent years. An apparent paradox has been disclosed. Although the living matter becomes adapted to its environment through formation of superior genetic patterns from mutational components, the process of mutation itself is not adaptive. On the contrary, the mutants which arise are, with rare exceptions, deleterious to their carriers, at least in the environments which the species normally encounters. Some of them are deleterious apparently in all environments. Therefore, the mutation process alone, not corrected and guided by natural selection, would result in degeneration and extinction rather than in improved adaptedness.
'On Methods of Evolutionary Biology and Anthropology', American Scientist, 1957, 45, 385.
The professor may choose familiar topics as a starting point. The students collect material, work problems, observe regularities, frame hypotheses, discover and prove theorems for themselves. … the student knows what he is doing and where he is going; he is secure in his mastery of the subject, strengthened in confidence of himself. He has had the experience of discovering mathematics. He no longer thinks of mathematics as static dogma learned by rote. He sees mathematics as something growing and developing, mathematical concepts as something continually revised and enriched in the light of new knowledge. The course may have covered a very limited region, but it should leave the student ready to explore further on his own.
In A Concrete Approach to Abstract Algebra (1959), 1-2.
The propositions of mathematics have, therefore, the same unquestionable certainty which is typical of such propositions as “All bachelors are unmarried,” but they also share the complete lack of empirical content which is associated with that certainty: The propositions of mathematics are devoid of all factual content; they convey no information whatever on any empirical subject matter.
From 'On the Nature of Mathematical Truth', collected in Carl Hempel and James H. Fetzer (ed.), The Philosophy of Carl G. Hempel: Studies in Science, Explanation, and Rationality (2001), Chap. 1, 13. Also Carl Hempel, 'On the Nature of Mathematical Truth', collected in J.R. Newman (ed.), The World of Mathematics (1956), Vol. 3, 1631.
The Reader may here observe the Force of Numbers, which can be successfully applied, even to those things, which one would imagine are subject to no Rules. There are very few things which we know, which are not capable of being reduc’d to a Mathematical Reasoning, and when they cannot, it’s a sign our Knowledge of them is very small and confus’d; and where a mathematical reasoning can be had, it’s as great folly to make use of any other, as to grope for a thing in the dark when you have a Candle standing by you.
From 'Preface' to Of the Laws of Chance, or, a Method of the Hazards of Game (1692), The book was Arbuthnot’s translation of Christiaan Huygen, Tractatus de Rationciniis in Aleae Ludo, in which Huygen expanded on the work of Blaise Pascal in probability and statistics.
The reader will find no figures in this work. The methods which I set forth do not require either constructions or geometrical or mechanical reasonings: but only algebraic operations, subject to a regular and uniform rule of procedure.
From the original French, “On ne trouvera point de Figures dans set Ouvrage. Les méthodes que j’y expose ne demandent ni constructions, ni raisonnements géométriqus ou méchaniques, mais seulement des opérations algébriques, assujetties à une march régulière et uniforme.” In 'Avertissement', Mécanique Analytique (1788, 1811), Vol. 1, i. English version as given in Cornelius Lanczos, The Variational Principles of Mechanics (1966), Vol. 1, 347.
The researches of many commentators have already thrown much darkness on this subject, and it is probable that, if they continue, we shall soon know nothing at all about it.
In The Sciences, September-October 1989.
The result of teaching small parts of a large number of subjects is the passive reception of disconnected ideas, not illuminated with any spark of vitality. Let the main ideas which are introduced into a child’s education be few and important, and let them be thrown into every combination possible.
In The Organisation of Thought: Educational and Scientific (1917), 5.
The scientist has to take 95 per cent of his subject on trust. He has to because he can't possibly do all the experiments, therefore he has to take on trust the experiments all his colleagues and predecessors have done. Whereas a mathematician doesn't have to take anything on trust. Any theorem that's proved, he doesn't believe it, really, until he goes through the proof himself, and therefore he knows his whole subject from scratch. He's absolutely 100 per cent certain of it. And that gives him an extraordinary conviction of certainty, and an arrogance that scientists don't have.
Essay, 'Private Games', in Lewis Wolpert and Alison Richards, (eds.), A Passion for Science (1988), 61.
The scientist knows that the ultimate of everything is unknowable. No matter What subject you take, the current theory of it if carried to the ultimate becomes ridiculous. Time and space are excellent examples of this.
As quoted in 'Electricity Will Keep The World From Freezing Up', New York Times (12 Nov 1911), SM4.
The Secretary of the Navy [Josephus Daniels] has decided that the science of aerial navigation has reached that point where aircraft must form a large part of our naval force for offensive and defensive operations. Nearly all countries having a Navy are giving attention to this subject. This country has not fully realized the value of aeronautics in preparation for war, but it is believed we should take our proper place.
Statement on the future of U.S. Naval Aviation made on the eve of World War I.
Statement on the future of U.S. Naval Aviation made on the eve of World War I.
News release, U.S. Navy Department, 10 Jan 1914. In Aviation in the United States Navy (1965), 5. In Kevin L. Falk, Why Nations Put to Sea (2000), 48.
The sense for style … is an aesthetic sense, based on admiration for the direct attainment of a foreseen end, simply and without waste. Style in art, style in literature, style in science, style in logic, style in practical execution have fundamentally the same aesthetic qualities, namely, attainment and restraint. The love of a subject in itself and for itself, where it is not the sleepy pleasure of pacing a mental quarter-deck, is the love of style as manifested in that study. Here we are brought back to the position from which we started, the utility of education. Style, in its finest sense, is the last acquirement of the educated mind; it is also the most useful. It pervades the whole being. The administrator with a sense for style hates waste; the engineer with a sense for style economises his material; the artisan with a sense for style prefers good work. Style is the ultimate morality of the mind.
In 'The Aims of Education', The Aims of Education and Other Essays (1929), 23.
The serum, when subjected to heat, coagulates and hardens like egg. This property is one of its striking characteristics; it is attributed to a particular substance which is thereby readily recognizable, and which is called albumine, because it is the one present in egg white, termed albumen.
Système des Connaissances Chimiques (1801), Vol. 5, 117. Trans. Joseph S. Fmton, Proteins, Enzymes, Genes: The Interplay of Chemistry and Biology (1999), 161.
The specialist is a man who fears the other subjects.
Martin H. Fischer, Howard Fabing (ed.) and Ray Marr (ed.), Fischerisms (1944).
The stories of Whitney’s love for experimenting are legion. At one time he received a letter asking if insects could live in a vacuum. Whitney took the letter to one of the members of his staff and asked the man if he cared to run an experiment on the subject. The man replied that there was no point in it, since it was well established that life could not exist without a supply of oxygen. Whitney, who was an inveterate student of wild life, replied that on his farm he had seen turtles bury themselves in mud each fall, and, although the mud was covered with ice and snow for months, emerge again in the spring. The man exclaimed, “Oh, you mean hibernation!” Whitney answered, “I don’t know what I mean, but I want to know if bugs can live in a vacuum.”
He proceeded down the hall and broached the subject to another member of the staff. Faced with the same lack of enthusiasm for pursuing the matter further, Whitney tried another illustration. “I’ve been told that you can freeze a goldfish solidly in a cake of ice, where he certainly can’t get much oxygen, and can keep him there for a month or two. But if you thaw him out carefully he seems none the worse for his experience.” The second scientist replied, “Oh, you mean suspended animation.” Whitney once again explained that his interest was not in the terms but in finding an answer to the question.
Finally Whitney returned to his own laboratory and set to work. He placed a fly and a cockroach in a bell jar and removed the air. The two insects promptly keeled over. After approximately two hours, however, when he gradually admitted air again, the cockroach waved its feelers and staggered to its feet. Before long, both the cockroach and the fly were back in action.
He proceeded down the hall and broached the subject to another member of the staff. Faced with the same lack of enthusiasm for pursuing the matter further, Whitney tried another illustration. “I’ve been told that you can freeze a goldfish solidly in a cake of ice, where he certainly can’t get much oxygen, and can keep him there for a month or two. But if you thaw him out carefully he seems none the worse for his experience.” The second scientist replied, “Oh, you mean suspended animation.” Whitney once again explained that his interest was not in the terms but in finding an answer to the question.
Finally Whitney returned to his own laboratory and set to work. He placed a fly and a cockroach in a bell jar and removed the air. The two insects promptly keeled over. After approximately two hours, however, when he gradually admitted air again, the cockroach waved its feelers and staggered to its feet. Before long, both the cockroach and the fly were back in action.
'Willis Rodney Whitney', National Academy of Sciences, Biographical Memoirs (1960), 357-358.
The student of medicine can no more hope to advance in the mastery of his subject with a loose and careless mind than the student of mathematics. If the laws of abstract truth require such rigid precision from those who study them, we cannot believe the laws of nature require less. On the contrary, they would seem to require more; for the facts are obscure, the means of inquiry imperfect, and in every exercise of the mind there are peculiar facilities to err.
From Address (Oct 1874) delivered at Guy’s Hospital, 'On The Study of Medicine', printed in British Medical journal (1874), 2, 425. Collected in Sir William Withey Gull and Theodore Dyke Acland (ed.), A Collection of the Published Writings of William Withey Gull (1896), 6.
The study of … simple cases would, I think, often be of advantage even to students whose mathematical attainments are sufficient to enable them to follow the solution of the more general cases. For in these simple cases the absence of analytical difficulties allows attention to be more easily concentrated on the physical aspects of the question, and thus gives the student a more vivid idea and a more manageable grasp of the subject than he would be likely to attain if he merely regarded electrical phenomena through a cloud of analytical symbols.
Elements of the Mathematical Theory of Electricity and Magnetism (189S), v-vi.
The study of economics does not seem to require any specialised gifts of an unusually high order. Is it not, intellectually regarded, a very easy subject compared with the higher branches of philosophy and pure science? Yet good, or even competent, economists are the rarest of birds. An easy subject, at which very few excel! The paradox finds its explanation, perhaps, in that the master-economist must possess a rare combination of gifts. He must reach a high standard in several different directions and must combine talents not often found together. He must be mathematician, historian, statesman, philosopher—in some degree. He must understand symbols and speak in words. He must contemplate the particular in terms of the general, and touch abstract and concrete in the same flight of thought. He must study the present in the light of the past for the purposes of the future. No part of man's nature or his institutions must lie entirely outside his regard. He must be purposeful and disinterested in a simultaneous mood; as aloof and incorruptible as an artist, yet sometimes as near the earth as a politician.
'Alfred Marshall: 1842-1924' (1924). In Geoffrey Keynes (ed.), Essays in Biography (1933), 170.
The subject matter of the scientist is a crowd of natural events at all times; he presupposes that this crowd is not real but apparent, and seeks to discover the true place of events in the system of nature. The subject matter of the poet is a crowd of historical occasions of feeling recollected from the past; he presupposes that this crowd is real but should not be, and seeks to transform it into a community. Both science and art are primarily spiritual activities, whatever practical applications may be derived from their results. Disorder, lack of meaning, are spiritual not physical discomforts, order and sense spiritual not physical satisfactions.
The Dyer’s Hand and Other Essays (1965), 66.
The subject may appear an insignificant one, but we shall see that it possesses some interest; and the maxim “de minimis lex non curat” [the law is not concerned with trifles] does not apply to science.
In The Formation of Vegetable Mould Through the Action of Worms, With Some Observations on Their Habits. (1881), 2.
The subject-matter of Archaeology is threefold—the Oral, the Written and the Monumental.
In Lecture to the Oxford meeting of the Archaeological Institute (18 Jun 1850), printed in 'On the Study of Achaeology', Archaeological Journal (1851), 8, 2.
The subject, cosmic physics, of her inaugural lecture was reported as 'cosmetic physics' in the press (more plausible with a female Dozent!).
Biographical Memoirs of Fellows of the Royal Society (1970), 16, 408.
The sublime can only be found in the great subjects. Poetry, history and philosophy all have the same object, and a very great object—Man and Nature. Philosophy describes and depicts Nature. Poetry paints and embellishes it. It also paints men, it aggrandizes them, it exaggerates them, it creates heroes and gods. History only depicts man, and paints him such as he is.
'Discours Prononcé a L' Académie française par M. De Buffon. Le Jour de sa Reception 25 Aout 1753'. Supplement a T.iv (1753), Histoire Naturelle, Générale et Particulière, Avec la Description du Cabinet du Roi (1777), 11. Trans. Phillip R. Sloan.
The theoretical broadening which comes from having many humanities subjects on the campus is offset by the general dopiness of the people who study these things and by the Department of Home Economics.
Letter to Robert Bacher (6 Apr 1950), as quoted in James Gleick, Genius: The Life and Science of Richard Feynman (1992), 278.
The theory here developed is that mega-evolution normally occurs among small populations that become preadaptive and evolve continuously (without saltation, but at exceptionally rapid rates) to radically different ecological positions. The typical pattern involved is probably this: A large population is fragmented into numerous small isolated lines of descent. Within these, inadaptive differentiation and random fixation of mutations occur. Among many such inadaptive lines one or a few are preadaptive, i.e., some of their characters tend to fit them for available ecological stations quite different from those occupied by their immediate ancestors. Such groups are subjected to strong selection pressure and evolve rapidly in the further direction of adaptation to the new status. The very few lines that successfully achieve this perfected adaptation then become abundant and expand widely, at the same time becoming differentiated and specialized on lower levels within the broad new ecological zone.
Tempo and Mode in Evolution (1944), 123.
The trend of mathematics and physics towards unification provides the physicist with a powerful new method of research into the foundations of his subject. … The method is to begin by choosing that branch of mathematics which one thinks will form the basis of the new theory. One should be influenced very much in this choice by considerations of mathematical beauty. It would probably be a good thing also to give a preference to those branches of mathematics that have an interesting group of transformations underlying them, since transformations play an important role in modern physical theory, both relativity and quantum theory seeming to show that transformations are of more fundamental importance than equations.
From Lecture delivered on presentation of the James Scott prize, (6 Feb 1939), 'The Relation Between Mathematics And Physics', printed in Proceedings of the Royal Society of Edinburgh (1938-1939), 59, Part 2, 122.
The truth is, when all is said and done, one does not teach a subject, one teaches a student how to learn it.
Begin Here: The Forgotten Conditions of Teaching and Learning (1991), 35. In Richard J. Cox, Managing Records as Evidence and Information (2001), 217.
The universality of parasitism as an offshoot of the predatory habit negatives the position taken by man that it is a pathological phenomenon or a deviation from the normal processes of nature. The pathological manifestations are only incidents in a developing parasitism. As human beings intent on maintaining man's domination over nature we may regard parasitism as pathological insofar as it becomes a drain upon human resources. In our efforts to protect ourselves we may make every kind of sacrifice to limit, reduce, and even eliminate parasitism as a factor in human life. Science attempts to define the terms on which this policy of elimination may or may not succeed. We must first of all thoroughly understand the problem, put ourselves in possession of all the facts in order to estimate the cost. Too often it has been assumed that parasitism was abnormal and that it needed only a slight force to reestablish what was believed to be a normal equilibrium without parasitism. On the contrary, biology teaches us that parasitism is a normal phenomenon and if we accept this view we shall be more ready to pay the price of freedom as a permanent and ever recurring levy of nature for immunity from a condition to which all life is subject. The greatest victory of man over nature in the physical realm would undoubtedly be his own delivery from the heavy encumbrance of parasitism with which all life is burdened.
Parasitism and Disease (1934), 4.
The validity of mathematical propositions is independent of the actual world—the world of existing subject-matters—is logically prior to it, and would remain unaffected were it to vanish from being. Mathematical propositions, if true, are eternal verities.
In The Pastures of Wonder: The Realm of Mathematics and the Realm of Science (1929), 99.
The visible universe is subject to quantification, and is so by necessity. … Between you and me only reason will be the judge … since you proceed according to the rational method, so shall I. … I will also give reason and take it. … This generation has an innate vice. It can’t accept anything that has been discovered by a contemporary!
As quoted in James Burke, The Day the Universe Changed (1985), 41. Burke also quotes the first sentence in The Axemaker's Gift (1995), 112, but after the first ellipsis, is substituted “If you wish to hear more from me, give and take reason, because I am not the kind of man to satisfy his hunger on the picture of a steak!”
The vulgar opinion, then, which, on health reasons, condemns vegetable food and so much praises animal food, being so ill-founded, I have always thought it well to oppose myself to it, moved both by experience and by that refined knowledge of natural things which some study and conversation with great men have given me. And perceiving now that such my constancy has been honoured by some learned and wise physicians with their authoritative adhesion (della autorevole sequela), I have thought it my duty publicly to diffuse the reasons of the Pythagorean diet, regarded as useful in medicine, and, at the same time, as full of innocence, of temperance, and of health. And it is none the less accompanied with a certain delicate pleasure, and also with a refined and splendid luxury (non è privo nemmeno d’una certa delicate voluttà e d’un lusso gentile e splendido ancora), if care and skill be applied in selection and proper supply of the best vegetable food, to which the fertility and the natural character of our beautiful country seem to invite us. For my part I have been so much the more induced to take up this subject, because I have persuaded myself that I might be of service to intending diet-reformers, there not being, to my knowledge, any book of which this is the sole subject, and which undertakes exactly to explain the origin and the reasons of it.
From Dell Vitto Pitagorico (1743), (The Pythagorean Diet: for the Use of the Medical Faculty), as translated quotes in Howard Williams, The Ethics of Diet: A Catena of Authorities Deprecatory of the Practice of Flesh-Eating (1883), 158.
The whole subject of the X rays is opening out wonderfully, Bragg has of course got in ahead of us, and so the credit all belongs to him, but that does not make it less interesting. We find that an X ray bulb with a platinum target gives out a sharp line spectrum of five wavelengths which the crystal separates out as if it were a diffraction grating. In this way one can get pure monochromatic X rays. Tomorrow we search for the spectra of other elements. There is here a whole new branch of spectroscopy, which is sure to tell one much about the nature of an atom.
Letter to his mother (18 May 1913). In J. L. Heilbron (ed.), H. G. J. Moseley: The Life and Letters of an English Physicist 1887-1915 (1974), 205.
The whole subject-matter of exact science consists of pointer readings and similar indications.
From Gifford Lecture, Edinburgh, (1927), 'The New Quantum Theory', collected in The Nature of the Physical World (1928), 219.
The wise man should study the acquisition of science and riches as if he were not subject to sickness and death; but to the duties of religion he should attend as if death had seized him by the hair.
In Charles Wilkins (trans.) Fables and Proverbs from the Sanskrit: being the Hitopadesa (1885), 18.
The work of the inventor consists of conceptualizing, combining, and ordering what is possible according to the laws of nature. This inner working out which precedes the external has a twofold characteristic: the participation of the subconscious in the inventing subject; and that encounter with an external power which demands and obtains complete subjugation, so that the way to the solution is experienced as the fitting of one's own imagination to this power.
Philosophie der Technik (1927). 'Technology in Its Proper Sphere' translated by William Carroll. In Carl Mitcham (ed.) and Robert Mackey (ed.), Philosophy and Technology: Readings in the Philosophical Problems of Technology, (1972), Vol. 14, 321. In David Lovekin, Technique, Discourse, and Consciousness (1991), 73.
The world is given to me only once, not one existing and one perceived. Subject and object are only one. The barrier between them cannot be said to have broken down as a result of recent experience in the physical sciences, for this barrier does not exist.
Concluding remark in Lecture, 'The Principle of Objectivation', the Tarner Lectures Delivered at Trinity College, Cambridge (Oct 1956), published in Mind and Matter (1958). Reprinted in collection What is Life?: With Mind and Matter and Autobiographical Sketches (1992, 2006), 127
Theology, Mr. Fortune found, is a more accommodating subject than mathematics; its technique of exposition allows greater latitude. For instance when you are gravelled for matter there is always the moral to fall back upon. Comparisons too may be drawn, leading cases cited, types and antetypes analysed and anecdotes introduced. Except for Archimedes mathematics is singularly naked of anecdotes.
In Mr. Fortune’s Maggot (1927), 168.
Theoretical chemistry is a peculiar subject. It is based on an equation that can hardly ever be solved.
'Orbital Update', review of R. McWenny, Methods of Molecular Quantum Mechanics (1989). Nature, 1990, 343, 222.
There are four subjects which must be taught: reading, writing and arithmetic, and the fear of God. The most difficult of these is arithmetic.
Quoted as a filler, without citation in The Record (3 Nov 1948), 40, No. 8, 2. (Student newspaper of the New York State College for Teachers.)
There are three ways to encourage initiative. One is to cut off people’s heads as they do in Russia. Another is to subject people to public criticism, which is impossible in such secret work as this. A third way is to set up competition. This is Livermore’s most valuable function: simply to be a competitor.
Explaining the merit in setting up a second laboratory, at Livermore, California, to continue his thermonuclear research after he left Los Alamos due to disagreements he had there. As quoted in Robert Coughlan, 'Dr. Edward Teller’s Magnificent Obsession', Life (6 Sep 1954), 70-72.
There is always a strong inclination for a body of professionals to oppose an unorthodox view. Such a group has a considerable investment in orthodoxy: they have learned to interpret a large body of data in terms of the old view, and they have prepared lectures and perhaps written books with the old background. To think the whole subject through again when one is no longer young is not easy and involves admitting a partially misspent youth.
Referring to attitudes such as early opposition to Wegener’s theory of continental drift. In 'The Emergence of Plate Tectonics: a Personal View', Annual Review of Earth and Planetary Sciences, 3, 5.
There is an attraction and a charm inherent in the colossal that is not subject to ordinary theories of art … The tower will be the tallest edifice ever raised by man. Will it therefore be imposing in its own way?
Quoted in J. Harriss, The Tallest Tower: Eiffel and the Belle Epoque (1975), 25. Cited by David P. Billington, 'Bridges and the New Art of Structural Engineering,' in National Research Council (U.S.). Transportation Research Board Subcommittee on Bridge Aesthetics, Bridge Aesthetics Around the World (1991), 67. From the original French in interview of Eiffel by Paul Bourde, in the newspaper Le Temps (14 Feb 1887). Reprinted in 'Au Jour le Jour: Les Artistes Contre la Tour Eiffel', Gazette Anecdotique, Littéraire, Artistique et Bibliographique (Feb 1887), 126, and in Gustave Eiffel, Travaux Scientifiques Exécutés à la Tour de 300 Mètres de 1889 à 1900 (1900), 14. “Il y a du reste dans le colossal une attraction, un charme propre auxquels les théories d’art ordinaires ne sont guère applicables. … Ma tour sera le plus haut édifice qu'aient jamais élevé les hommes. Ne serat-elle donc pas grandiose aussi a sa façon?
There is an influence which is getting strong and stronger day by day, which shows itself more and more in all departments of human activity, and influence most fruitful and beneficial—the influence of the artist. It was a happy day for the mass of humanity when the artist felt the desire of becoming a physician, an electrician, an engineer or mechanician or—whatnot—a mathematician or a financier; for it was he who wrought all these wonders and grandeur we are witnessing. It was he who abolished that small, pedantic, narrow-grooved school teaching which made of an aspiring student a galley-slave, and he who allowed freedom in the choice of subject of study according to one's pleasure and inclination, and so facilitated development.
'Roentgen Rays or Streams', Electrical Review (12 Aug 1896). Reprinted in The Nikola Tesla Treasury (2007), 307.
By Nikola Tesla
There is no area in our minds reserved for superstition, such as the Greeks had in their mythology; and superstition, under cover of an abstract vocabulary, has revenged itself by invading the entire realm of thought. Our science is like a store filled with the most subtle intellectual devices for solving the most complex problems, and yet we are almost incapable of applying the elementary principles of rational thought. In every sphere, we seem to have lost the very elements of intelligence: the ideas of limit, measure, degree, proportion, relation, comparison, contingency, interdependence, interrelation of means and ends. To keep to the social level, our political universe is peopled exclusively by myths and monsters; all it contains is absolutes and abstract entities. This is illustrated by all the words of our political and social vocabulary: nation, security, capitalism, communism, fascism, order, authority, property, democracy. We never use them in phrases such as: There is democracy to the extent that… or: There is capitalism in so far as… The use of expressions like “to the extent that” is beyond our intellectual capacity. Each of these words seems to represent for us an absolute reality, unaffected by conditions, or an absolute objective, independent of methods of action, or an absolute evil; and at the same time we make all these words mean, successively or simultaneously, anything whatsoever. Our lives are lived, in actual fact, among changing, varying realities, subject to the casual play of external necessities, and modifying themselves according to specific conditions within specific limits; and yet we act and strive and sacrifice ourselves and others by reference to fixed and isolated abstractions which cannot possibly be related either to one another or to any concrete facts. In this so-called age of technicians, the only battles we know how to fight are battles against windmills.
From 'The Power of Words', collected in Siân Miles (ed.), Simone Weil: An Anthology (2000), 222-223.
There is no subject more captivating, more worthy of study, than nature. To understand this great mechanism, to discover the forces which are active, and the laws which govern them, is the highest aim of the intellect of man.
Lecture (20 May 1891) to American Institute of Electrical Engineers, Columbia College, N. Y., 'Experiments With Alternate Currents Of Very High Frequencv And Their Application To Methods Of Artificial Illumination', collected in Nikola Tesla and Thomas Commerford Martin (ed.), The Inventions, Researches and Writings of Nikola Tesla: With Special Reference to His Work in Polyphase Currents and High Potential Lighting (1894), 145.
There is only one subject matter for education, and that is Life in all its manifestations. Instead of this single unity, we offer children—Algebra, from which nothing follows; Geometry, from which nothing follows; Science, from which nothing follows; History, from which nothing follows; a Couple of Languages, never mastered; and lastly, most dreary of all, Literature, represented by plays of Shakespeare, with philological notes and short analyses of plot and character to be in substance committed to memory.
In 'The Aims of Education', The Aims of Education: & Other Essays (1917), 10.
There's nothing situate under heaven's eye
But hath his bond in earth, in sea, in sky.
The beasts, the fishes, and the winged fowls
Are their males' subjects and at their controls.
Man, more divine, the master of all these,
Lord of the wide world and wild wat'ry seas,
Indu'd with intellectual sense and souls,
Of more pre-eminence than fish and fowls,
Are masters to their females, and their lords;
Then let your will attend on their accords.
But hath his bond in earth, in sea, in sky.
The beasts, the fishes, and the winged fowls
Are their males' subjects and at their controls.
Man, more divine, the master of all these,
Lord of the wide world and wild wat'ry seas,
Indu'd with intellectual sense and souls,
Of more pre-eminence than fish and fowls,
Are masters to their females, and their lords;
Then let your will attend on their accords.
The Comedy of Errors (1594), II, i.
Thermodynamics is a funny subject. The first time you go through it, you don’t understand it at all The second time you go through it, you think you understand it, except for one or two points. The third time you go through it, you know you don't understand it, but by that time you are so used to the subject, it doesn't bother you anymore.
Quoted, without citation, in Stanley W. Angrist and Loren G. Hepler, Order and Chaos: Laws of Energy and Entropy (1967), 215. The authors identify it as “perhaps apocryphal.” The quote is used as epigraph, dated as 1950 in Anton Z. Capri, Quips, Quotes, and Quanta: An Anecdotal History of Physics (2011), 50. The quote is introduced as “When asked why he did not write on that field he replied somewhat as follows,” by Keith J. Laidler in Physical Chemistry with Biological Applications (1978), 145.
These Disciplines [mathematics] serve to inure and corroborate the Mind to a constant Diligence in Study; to undergo the Trouble of an attentive Meditation, and cheerfully contend with such Difficulties as lie in the Way. They wholly deliver us from a credulous Simplicity, most strongly fortify us against the Vanity of Scepticism, effectually restrain from a rash Presumption, most easily incline us to a due Assent, perfectly subject us to the Government of right Reason, and inspire us with Resolution to wrestle against the unjust Tyranny of false Prejudices. If the Fancy be unstable and fluctuating, it is to be poized by this Ballast, and steadied by this Anchor, if the Wit be blunt it is sharpened upon this Whetstone; if luxuriant it is pared by this Knife; if headstrong it is restrained by this Bridle; and if dull it is rouzed by this Spur. The Steps are guided by no Lamp more clearly through the dark Mazes of Nature, by no Thread more surely through the intricate Labyrinths of Philosophy, nor lastly is the Bottom of Truth sounded more happily by any other Line. I will not mention how plentiful a Stock of Knowledge the Mind is furnished from these, with what wholesome Food it is nourished, and what sincere Pleasure it enjoys. But if I speak farther, I shall neither be the only Person, nor the first, who affirms it; that while the Mind is abstracted and elevated from sensible Matter, distinctly views pure Forms, conceives the Beauty of Ideas, and investigates the Harmony of Proportions; the Manners themselves are sensibly corrected and improved, the Affections composed and rectified, the Fancy calmed and settled, and the Understanding raised and excited to more divine Contemplations. All which I might defend by Authority, and confirm by the Suffrages of the greatest Philosophers.
Prefatory Oration in Mathematical Lectures (1734), xxxi.
These sciences, Geometry, Theoretical Arithmetic and Algebra, have no principles besides definitions and axioms, and no process of proof but deduction; this process, however, assuming a most remarkable character; and exhibiting a combination of simplicity and complexity, of rigour and generality, quite unparalleled in other subjects.
In The Philosophy of the Inductive Sciences (1858), Part 1, Bk. 2, chap. 1, sect. 2.
These specimens, which I could easily multiply, may suffice to justify a profound distrust of Auguste Comte, wherever he may venture to speak as a mathematician. But his vast general ability, and that personal intimacy with the great Fourier, which I most willingly take his own word for having enjoyed, must always give an interest to his views on any subject of pure or applied mathematics.
In R. Graves, Life of W. R. Hamilton (1882-89), Vol. 3, 475.
They who clamor loudest for freedom are often the ones least likely to be happy in a free society. The frustrated, oppressed by their shortcomings, blame their failure on existing restraints. Actually, their innermost desire is for an end to the “free for all.” They want to eliminate free competition and the ruthless testing to which the individual is continually subjected in a free society.
In The True Believer: Thoughts on the Nature of Mass Movements (1951), 32.
Things of all kinds are subject to a universal law which may be called the law of large numbers. It consists in the fact that, if one observes very considerable numbers of events of the same nature, dependent on constant causes and causes which vary irregularly, sometimes in one direction, sometimes in the other, it is to say without their variation being progressive in any definite direction, one shall find, between these numbers, relations which are almost constant.
Poisson’s Law of Large Numbers (16 Nov 1837), in Recherches sur la Probabilités (1837), 7. English version by Webmaster using Google Translate, from the original French, “Les choses de toutes natures sont soumises à une loi universelle qu’on) peut appeler la loi des grands nombres. Elle consiste en ce que, si l’on observe des nombres très considérables d’événements d’une même nature, dépendants de causes constantes et de causes qui varient irrégulièrement, tantôt dans un sens, tantôt daus l’autre, c’est-à-dire sans que leur variation soit progressive dans aucun sens déterminé, on trouvera, entre ces nombres, des rapports a très peu près constants.”
This is one of man's oldest riddles. How can the independence of human volition be harmonized with the fact that we are integral parts of a universe which is subject to the rigid order of nature's laws?
In Max Planck and James Vincent Murphy (trans.), Where is Science Going?, (1932), 107.
This splendid subject [mathematics], queen of all exact sciences, and the ideal and norm of all careful thinking...
Educational Problems (1911), Vol. 2, 393.
Those of us who were familiar with the state of inorganic chemistry in universities twenty to thirty years ago will recall that at that time it was widely regarded as a dull and uninteresting part of the undergraduate course. Usually, it was taught almost entirely in the early years of the course and then chiefly as a collection of largely unconnected facts. On the whole, students concluded that, apart from some relationships dependent upon the Periodic table, there was no system in inorganic chemistry comparable with that to be found in organic chemistry, and none of the rigour and logic which characterised physical chemistry. It was widely believed that the opportunities for research in inorganic chemistry were few, and that in any case the problems were dull and uninspiring; as a result, relatively few people specialized in the subject... So long as inorganic chemistry is regarded as, in years gone by, as consisting simply of the preparations and analysis of elements and compounds, its lack of appeal is only to be expected. The stage is now past and for the purpose of our discussion we shall define inorganic chemistry today as the integrated study of the formation, composition, structure and reactions of the chemical elements and compounds, excepting most of those of carbon.
Inaugural Lecture delivered at University College, London (1 Mar 1956). In The Renaissance of Inorganic Chemistry (1956), 4-5.
Those that can readily master the difficulties of Mathematics find a considerable charm in the study, sometimes amounting to fascination. This is far from universal; but the subject contains elements of strong interest of a kind that constitutes the pleasures of knowledge. The marvellous devices for solving problems elate the mind with the feeling of intellectual power; and the innumerable constructions of the science leave us lost in wonder.
In Education as a Science (1879), 153.
Those who have occasion to enter into the depths of what is oddly, if generously, called the literature of a scientific subject, alone know the difficulty of emerging with an unsoured disposition. The multitudinous facts presented by each corner of Nature form in large part the scientific man's burden to-day, and restrict him more and more, willy-nilly, to a narrower and narrower specialism. But that is not the whole of his burden. Much that he is forced to read consists of records of defective experiments, confused statement of results, wearisome description of detail, and unnecessarily protracted discussion of unnecessary hypotheses. The publication of such matter is a serious injury to the man of science; it absorbs the scanty funds of his libraries, and steals away his poor hours of leisure.
'Physiology, including Experimental Pathology and Experimental Physiology', Reports of the British Association for the Advancement of Science, 1899, 891-2.
Those who nod sagely and quote the tragedy of the commons in relation to environmental problems from pollution of the atmosphere to poaching of national parks tend to forget that Garrett Hardin revised his conclusions many times…. He recognized, most importantly, that anarchy did not prevail on the common pastures of medieval England in the way he had described…. “A managed commons, though it may have other defects, is not automatically subject to the tragic fate of the unmanaged commons,” wrote Hardin…. At sea, where a common exists in most waters… None of Hardin’s requirements for a successfully managed common is fulfilled by high-seas fishery regimes.
In The End of the Line: How Overfishing is Changing the World and what We Eat (2004), 153-155.
Thus a eukaryotic cell may be thought of as an empire directed by a republic of sovereign chromosomes in the nucleus. The chromosomes preside over the outlying cytoplasm in which formerly independent but now subject and degenerate prokaryotes carry out a variety of specialized service functions.
Molecular Genetics: An Introductory Narrative (1971), 622. Cell;Empire;Republic;Sovereign;Chromosome;Nucleus;Cytoplasm;Eukaryote;Prokaryote;Specialization;Service;Function
Thus far I have produced a various and, in my judgement, incontrovertible body of facts, to show that the whole earth has been subjected to a recent and universal inundation.
Reliquire Diluvianae (1824), 224.
Time was when all the parts of the subject were dissevered, when algebra, geometry, and arithmetic either lived apart or kept up cold relations of acquaintance confined to occasional calls upon one another; but that is now at an end; they are drawn together and are constantly becoming more and more intimately related and connected by a thousand fresh ties, and we may confidently look forward to a time when they shall form but one body with one soul.
In Presidential Address to British Association (19 Aug 1869), 'A Plea for the Mathematician', published in Nature (6 Jan 1870), 1, 262.
To demonstrate experimentally that a microscopic organism actually is the cause of a disease and the agent of contagion, I know no other way, in the present state of Science, than to subject the microbe (the new and happy term introduced by M. Sédillot) to the method of cultivation out of the body.
Paper read to the French Academy of Sciences (29 Apr 1878), published in Comptes Rendus de l'Academie des Sciences, 86, 1037-43, as translated by H.C.Ernst. Collected in Charles W. Eliot (ed.) The Harvard Classics, Vol. 38; Scientific Papers: Physiology, Medicine, Surgery, Geology (1910), 364.
To emphasize this opinion that mathematicians would be unwise to accept practical issues as the sole guide or the chief guide in the current of their investigations, ... let me take one more instance, by choosing a subject in which the purely mathematical interest is deemed supreme, the theory of functions of a complex variable. That at least is a theory in pure mathematics, initiated in that region, and developed in that region; it is built up in scores of papers, and its plan certainly has not been, and is not now, dominated or guided by considerations of applicability to natural phenomena. Yet what has turned out to be its relation to practical issues? The investigations of Lagrange and others upon the construction of maps appear as a portion of the general property of conformal representation; which is merely the general geometrical method of regarding functional relations in that theory. Again, the interesting and important investigations upon discontinuous two-dimensional fluid motion in hydrodynamics, made in the last twenty years, can all be, and now are all, I believe, deduced from similar considerations by interpreting functional relations between complex variables. In the dynamics of a rotating heavy body, the only substantial extension of our knowledge since the time of Lagrange has accrued from associating the general properties of functions with the discussion of the equations of motion. Further, under the title of conjugate functions, the theory has been applied to various questions in electrostatics, particularly in connection with condensers and electrometers. And, lastly, in the domain of physical astronomy, some of the most conspicuous advances made in the last few years have been achieved by introducing into the discussion the ideas, the principles, the methods, and the results of the theory of functions. … the refined and extremely difficult work of Poincare and others in physical astronomy has been possible only by the use of the most elaborate developments of some purely mathematical subjects, developments which were made without a thought of such applications.
In Presidential Address British Association for the Advancement of Science, Section A, (1897), Nature, 56, 377.
To engage in experiments on heat was always one of my most agreeable employments. This subject had already begun to excite my attention when, in my seventeenth year, I read Boerhave’s admirable Treatise on Fire. Subsequently, indeed, I was often prevented by other matters from devoting my attention to it, but whenever I could snatch a moment I returned to it anew, and always with increased interest.
In 'Historical Review of the Various Experiments of the Author on the Subject of Heat', The Complete Works of Count Rumford (1873), Vol. 2, 188. It is translated from the original German, in Vol. IV, of Rumford’s Kleine Schriften.
To Monsieur Lavoisier by appointment. Madame Lavoisier, a lively, sensible, scientific lady, had prepared a dejuné Anglois of tea and coffee, but her conversation on Mr. Kirwan’s Essay on Phlogiston, which she is translating from the English, and on other subjects, which a woman of understanding, that works with her husband in his laboratory, knows how to adorn, was the best repast.
Entry for 16 Oct 1787. In Arthur Young, Travels in France During the Years, 1787, 1788 and 1789 (1792), 64.
To present a scientific subject in an attractive and stimulating manner is an artistic task, similar to that of a novelist or even a dramatic writer. The same holds for writing textbooks.
— Max Born
My Life & My Views (1968), 48.
To speak of this subject you must... explain the nature of the resistance of the air, in the second the anatomy of the bird and its wings, in the third the method of working the wings in their various movements, in the fourth the power of the wings and the tail when the wings are not being moved and when the wind is favorable to serve as guide in various movements.
…...
To teach effectively a teacher must develop a feeling for his subject; he cannot make his students sense its vitality if he does not sense it himself. He cannot share his enthusiasm when he has no enthusiasm to share. How he makes his point may be as important as the point he makes; he must personally feel it to be important.
Mathematical Methods in Science (1963, 1977), 1.
To the Philosopher, the Physician, the Meteorologist, and the Chemist, there is perhaps no subject more attractive than that of Ozone.
Ozone and Antozone (1873), 1.
To wage war with Marchand or anyone else again will benefit nobody and bring little profit to science. You consume yourself in this way, you ruin your liver and eventually your nerves with Morrison pills. Imagine the year 1900 when we have disintegrated into carbonic acid, ammonia and water and our bone substance is perhaps once more a constituent of the bones of the dog who defiles our graves. Who will then worry his head as to whether we have lived in peace or anger, who then will know about your scientific disputes and of your sacrifice of health and peace of mind for science? Nobody. But your good ideas and the discoveries you have made, cleansed of all that is extraneous to the subject, will still be known and appreciated for many years to come. But why am I trying to advise the lion to eat sugar.
Letter from Wohler to Liebig (9 Mar 1843). In A. W. Hofmann (ed.), Aus Justus Liebigs und Friedrich Wohlers Briefwechsel (1888), Vol. 1, 224. Trans. Ralph Oesper, The Human Side of Scientists (1975), 205.
To write about history or language is supposed to be within the reach of every man. To write about natural science is allowed to be within the reach only of those who have mastered the subjects on which they write.
The Methods of Historical Study (1886), 91.
Today we no longer ask what really goes on in an atom; we ask what is likely to be observed—and with what likelihood—when we subject atoms to any specified influences such as light or heat, magnetic fields or electric currents.
What Little I Remember (1979), 20.
Today when the public thinks of the products of science it is likely to think about environmental problems, an unproductive armament industry, careless or dishonest 'scientific' reports, Livermore cheers for 'nukes forever' and a huge amount of self-serving noise on every subject from global warming to 'the face of God'.
'Hard Times', Physics Today (Oct 1992), 45, 9.
Truths are known to us in two ways: some are known directly, and of themselves; some through the medium of other truths. The former are the subject of Intuition, or Consciousness; the latter, of Inference; the latter of Inference. The truths known by Intuition are the original premisses, from which all others are inferred.
A System of Logic, Ratiocinative and Inductive (1858), 3.
Tyndall declared that he saw in Matter the promise and potency of all forms of life, and with his Irish graphic lucidity made a picture of a world of magnetic atoms, each atom with a positive and a negative pole, arranging itself by attraction and repulsion in orderly crystalline structure. Such a picture is dangerously fascinating to thinkers oppressed by the bloody disorders of the living world. Craving for purer subjects of thought, they find in the contemplation of crystals and magnets a happiness more dramatic and less childish than the happiness found by mathematicians in abstract numbers, because they see in the crystals beauty and movement without the corrupting appetites of fleshly vitality.
In Back to Methuselah: A Metabiological Pentateuch (1921), lxi-lxii.
Under certain given circumstances, and only under those circumstances, an agglomeration of men presents new characteristics very different from those of the individuals composing it. The sentiments and ideas of all the persons in the gathering take one and the same direction, and their conscious personality vanishes. A collective mind is formed, doubtless transitory, but presenting very clearly defined characteristics. The gathering has thus become what, in the absence of a better expression, I will call an organized crowd, or, if the term is considered preferable, a psychological crowd. It forms a single being and is subject to the law of the mental unity of crowds.
From Psychologie des Foules (1895), 12. English text in The Crowd: A Study of the Popular Mind (1897), Book 1, Chap. 1, 1-2. The original French text is, “Dans certaines circonstances données, et seulement dans ces circonstances, une agglomération d’hommes possède des caractères nouveaux fort différents de ceux des individus composant cette agglomération. La personnalité consciente s’évanouit, les sentiments et les idées de toutes les unités sont orientés dans une même direction. Il se forme une âme collective, transitoire sans doute, mais présentant des caractères très nets. La collectivité est alors devenue ce que, faute d’une expression meilleure, j’appellerai une foule organisée, ou, si l’on préfère, une foule psychologique. Elle forme un seul être et se trouve soumise à la loi de l'unité mentale des foules.”
Unhappily for the physiologist, the subjects of the principal department of his science, that of animal physiology, are sentient beings; and every experiment, every new or unusual situation of such a being, is necessarily attended by pain or suffering of a bodily or mental kind.
A Critical and Experimental Essay on the Circulation of the Blood (1831), 1.
Unless our laboratory results are to give us artificialities, mere scientific curiosities, they must be subjected to interpretation by gradual re-approximation to conditions of life.
'Psychology and Social Practice', The Psychological Review, 1900, 7, 119.
Until I became a published writer, I remained completely ignorant of books on how to write and courses on the subject ... they would have spoiled my natural style; made me observe caution; would have hedged me with rules.
In Isaac Asimov and Janet Asimov (ed.), It's Been a Good Life (2002), 38.
Until recently even the most generous assessment places the subject [of the origin of the universe] at the edges of objective inquiry if not entirely outside the scientific method.
As quoted in John Noble Wilford, 'Sizing up the Cosmos: An Astronomers Quest', New York Times (12 Mar 1991), C10.
Very few people realize the enormous bulk of contemporary mathematics. Probably it would be easier to learn all the languages of the world than to master all mathematics at present known. The languages could, I imagine, be learnt in a lifetime; mathematics certainly could not. Nor is the subject static.
In 'The Extent of Mathematics', Prelude to Mathematics (1955), 11.
We are as remote from adequate explanation of the nature and causes of mechanical evolution of the hard parts of animals as we were when Aristotle first speculated on this subject … I think it is possible that we may never fathom all the causes of mechanical evolution or of the origin of new mechanical characters, but shall have to remain content with observing the modes of mechanical evolution, just as embryologists and geneticists are observing the modes of development, from the fertilized ovum to the mature individual, without in the least understanding either the cause or the nature of the process of development which goes on under their eyes every day
From 'Orthogenesis as observed from paleontological evidence beginning in the year 1889', American Naturalist (1922) 56, 141-142. As quoted and cited in 'G.G. Simpson, Paleontology, and the Modern Synthesis', collected in Ernst Mayr, William B. Provine (eds.), The Evolutionary Synthesis: Perspectives on the Unification of Biology (1998), 171.
We are concerned to understand the motivation for the development of pure mathematics, and it will not do simply to point to aesthetic qualities in the subject and leave it at that. It must be remembered that there is far more excitement to be had from creating something than from appreciating it after it has been created. Let there be no mistake about it, the fact that the mathematician is bound down by the rules of logic can no more prevent him from being creative than the properties of paint can prevent the artist. … We must remember that the mathematician not only finds the solutions to his problems, he creates the problems themselves.
In A Signpost to Mathematics (1951), 19. As quoted and cited in William L. Schaaf, 'Memorabilia Mathematica', The Mathematics Teacher (Mar 1957), 50, No. 3, 230. Note that this paper incorrectly attributes “A.H. Head”.
We begin with the hypothesis that any subject can be taught effectively in some intellectually honest form to any child at any stage of development.
The Process of Education (1960), 31.
We can trace the development of a nervous system, and correlate with it the parallel phenomena of sensation and thought. We see with undoubting certainty that they go hand in hand. But we try to soar in a vacuum the moment we seek to comprehend the connexion between them … Man the object is separated by an impassable gulf from man the subject.
In 'Address Delivered Before The British Association Assembled at Belfast' (19 Aug 1874), in Fragments of Science for Unscientific People: A Series of Detached Essays, Lectures, and Reviews (1892), Vol. 2, 194-195.
We expect that the study of lunar geology will help to answer some longstanding questions about the early evolution of the earth. The moon and the earth are essentially a two-planet system, and the two bodies are probably closely related in origin. In this connection the moon is of special interest because its surface has not been subjected to the erosion by running water that has helped to shape the earth’s surface.
In Scientific American (Sep 1964). As cited in '50, 100 & 150 Years Ago', Scientific American (Dec 2014), 311, No. 6, 98.
We have corrupted the term research to mean study and experiment and development toward selected objectives, and we have even espoused secret and classified projects. This was not the old meaning of university research. We need a new term, or the revival of a still older one, to refer to the dedicated activities of the scholar, the intensive study of special aspects of a subject for its own sake, motivated by the love of knowledge and truth.
In 'Technology and National Research Policy', Bulletin of the Atomic Scientists (Oct 1953), 292.
We may as well cut out group theory. That is a subject that will never be of any use in physics.
Discussing mathematics curriculum reform at Princeton University (1910), as quoted in Abraham P. Hillman, Gerald L. Alexanderson, Abstract Algebra: A First Undergraduate Course (1994), 94.
We may lay it down that a happy person never phantasises, only an unsatisfied one... The motive forces of phantasies are unsatisfied wishes, and every single phantasy is the fulfilment of a wish, a correction of unsatisfying reality. These motivating wishes vary according to the sex, character and circumstances of the person who is having the phantasy; but they fall naturally into two main groups. They are either ambitious wishes, which serve to elevate the subject's personality; or they are erotic ones. It was shocking when Nietzsche said this, but today it is commonplace; our historical position—and no end to it is in sight—is that of having to philosophise without 'foundations'.
Creative Writers and Day-Dreaming (1906), In James Strachey (ed.), The Standard Edition of the Complete Psychcological Works of Sigmund Freud (1959), Vol 9, 146-7.
We must make practice in thinking, or, in other words, the strengthening of reasoning power, the constant object of all teaching from infancy to adult age, no matter what may be the subject of instruction. … Effective training of the reasoning powers cannot be secured simply by choosing this subject or that for study. The method of study and the aim in studying are the all-important things.
From 'Wherein Popular Education has Failed' Forum (Dec 1892), collected in American Contributions to Civilization: And Other Essays and Addresses (1897), 229 & 231.
We pass with admiration along the great series of mathematicians, by whom the science of theoretical mechanics has been cultivated, from the time of Newton to our own. There is no group of men of science whose fame is higher or brighter. The great discoveries of Copernicus, Galileo, Newton, had fixed all eyes on those portions of human knowledge on which their successors employed their labors. The certainty belonging to this line of speculation seemed to elevate mathematicians above the students of other subjects; and the beauty of mathematical relations and the subtlety of intellect which may be shown in dealing with them, were fitted to win unbounded applause. The successors of Newton and the Bernoullis, as Euler, Clairaut, D’Alembert, Lagrange, Laplace, not to introduce living names, have been some of the most remarkable men of talent which the world has seen.
In History of the Inductive Sciences, Vol. 1, Bk. 4, chap. 6, sect. 6.
We say that knowing begins in our intrigue about some subject, but that intrigue is the result of the subject’s action upon us: geologists are people who hear rocks speak, historians are people who hear the voices of the long dead, writers are people who hear the music of words.
In The Courage to Teach: Exploring the Inner Landscape of a Teacher’s Life (1998), 105.
We should not argue with the blind man who maintained that sight was an illusion to which some abnormal people were subject. Therefore in speaking of religious experience I do not attempt to prove the existence of religious experience…
Swarthmore Lecture (1929) at Friends’ House, London, printed in Science and the Unseen World (1929), 48-49.
We…know…that the smallest units of many materials are not atoms but molecules, which are groups of atoms, closely bound to each other. If we are to understand the structure of matter, we must understand not only the structure of atoms but also the reason atoms join and form molecules. We must understand what is called the chemical bond, which keeps the atoms together within the molecule, and we must get acquainted with a few typical molecules and their properties. The chemical bond and the properties of molecules are the subjects of chemistry.
In 'The Chemical Bond', Knowledge and Wonder (1962, Rev. ed. 1966), 142.
What a chimera ... is man ! What a novelty, what a monster, what a chaos, what a subject of contradiction, what a prodigy! A judge of all things, feeble worm of the earth, depository of the truth, cloacae of uncertainty and error, the glory and the shame of the universe!
…...
What a master a man would be in his own subject if he taught nothing useless!
In The Maxims and Reflections of Goethe (1906), 196.
What an amateur is, is a lover of a subject. I’m a lover of facts. The fact is the savior, as long as you don’t jam it into some preconceived pattern.
From interview, Carol Krucoff, 'The 6 O’Clock Scholar: Librarian of Congress Daniel Boorstin And His Love Affair With Books', The Washington Post (29 Jan 1984), K8.
What attracted me to immunology was that the whole thing seemed to revolve around a very simple experiment: take two different antibody molecules and compare their primary sequences. The secret of antibody diversity would emerge from that. Fortunately at the time I was sufficiently ignorant of the subject not to realise how naive I was being.
From Nobel Lecture (8 Dec 1984), collected in Tore Frängsmyr and Jan Lindsten (eds.), Nobel Lectures in Physiology Or Medicine: 1981-1990 (1993), 248.
What is this subject, which may be called indifferently either mathematics or logic? Is there any way in which we can define it? Certain characteristics of the subject are clear. To begin with, we do not, in this subject, deal with particular things or particular properties: we deal formally with what can be said about any thing or any property. We are prepared to say that one and one are two, but not that Socrates and Plato are two, because, in our capacity of logicians or pure mathematicians, we have never heard of Socrates or Plato. A world in which there were no such individuals would still be a world in which one and one are two. It is not open to us, as pure mathematicians or logicians, to mention anything at all, because, if we do so we introduce something irrelevant and not formal.
In Introduction to Mathematical Philosophy (1920), 196-197.
What makes the theory of relativity so acceptable to physicists in spite of its going against the principle of simplicity is its great mathematical beauty. This is a quality which cannot be defined, any more than beauty in art can be defined, but which people who study mathematics usually have no difficulty in appreciating. … The restricted theory changed our ideas of space and time in a way that may be summarised by stating that the group of transformations to which the space-time continuum is subject must be changed from the Galilean group to the Lorentz group.
From Lecture delivered on presentation of the James Scott prize, (6 Feb 1939), 'The Relation Between Mathematics And Physics', printed in Proceedings of the Royal Society of Edinburgh (1938-1939), 59, Part 2, 123.
What we remember, belonging more particularly to some special active pattern, is always normally checked by the reconstructed or the striking material of other active settings. It is, accordingly, apt to take on a peculiarity of some kind which, in any given case, expresses the temperament, or the character, of the person who effects the recall. This may be why, in almost all psychological descriptions of memory processes, memory is said to have a characteristically personal flavour … depending upon an interplay of appetites, instincts, interests and ideals peculiar to any given subject.
In Chapter 10, 'A Theory of Remembering', Remembering: A Study in Experimental and Social Psychology (1932, 1995), 213.
Whatever advantage can be attributed to logic in directing and strengthening the action of the understanding is found in a higher degree in mathematical study, with the immense added advantage of a determinate subject, distinctly circumscribed, admitting of the utmost precision, and free from the danger which is inherent in all abstract logic—of leading to useless and puerile rules, or to vain ontological speculations. The positive method, being everywhere identical, is as much at home in the art of reasoning as anywhere else: and this is why no science, whether biology or any other, can offer any kind of reasoning, of which mathematics does not supply a simpler and purer counterpart. Thus, we are enabled to eliminate the only remaining portion of the old philosophy which could even appear to offer any real utility; the logical part, the value of which is irrevocably absorbed by mathematical science.
In Auguste Comte and Harriet Martineau (trans.), Positive Philosophy (1858), Vol. 1, 326-327.
When Benjamin Franklin invented the lightning-rod, the clergy, both in England and America, with the enthusiastic support of George III, condemned it as an impious attempt to defeat the will of God. For, as all right-thinking people were aware, lightning is sent by God to punish impiety or some other grave sin—the virtuous are never struck by lightning. Therefore if God wants to strike any one, Benjamin Franklin [and his lightning-rod] ought not to defeat His design; indeed, to do so is helping criminals to escape. But God was equal to the occasion, if we are to believe the eminent Dr. Price, one of the leading divines of Boston. Lightning having been rendered ineffectual by the “iron points invented by the sagacious Dr. Franklin,” Massachusetts was shaken by earthquakes, which Dr. Price perceived to be due to God’s wrath at the “iron points.” In a sermon on the subject he said,“In Boston are more erected than elsewhere in New England, and Boston seems to be more dreadfully shaken. Oh! there is no getting out of the mighty hand of God.” Apparently, however, Providence gave up all hope of curing Boston of its wickedness, for, though lightning-rods became more and more common, earthquakes in Massachusetts have remained rare.
In An Outline of Intellectual Rubbish (1943), 6-7.
When Cayley had reached his most advanced generalizations he proceeded to establish them directly by some method or other, though he seldom gave the clue by which they had first been obtained: a proceeding which does not tend to make his papers easy reading. …
His literary style is direct, simple and clear. His legal training had an influence, not merely upon his mode of arrangement but also upon his expression; the result is that his papers are severe and present a curious contrast to the luxuriant enthusiasm which pervades so many of Sylvester’s papers. He used to prepare his work for publication as soon as he carried his investigations in any subject far enough for his immediate purpose. … A paper once written out was promptly sent for publication; this practice he maintained throughout life. … The consequence is that he has left few arrears of unfinished or unpublished papers; his work has been given by himself to the world.
His literary style is direct, simple and clear. His legal training had an influence, not merely upon his mode of arrangement but also upon his expression; the result is that his papers are severe and present a curious contrast to the luxuriant enthusiasm which pervades so many of Sylvester’s papers. He used to prepare his work for publication as soon as he carried his investigations in any subject far enough for his immediate purpose. … A paper once written out was promptly sent for publication; this practice he maintained throughout life. … The consequence is that he has left few arrears of unfinished or unpublished papers; his work has been given by himself to the world.
In Proceedings of London Royal Society (1895), 58, 23-24.
When I examine the conclusion [on experiments with the electric light bulb experiments published in the Herald] which everyone acquainted with the subject will recognize as a conspicuous failure, trumpeted as a wonderful success, I [conclude]... that the writer ... must either be very ignorant, and the victim of deceit, or a conscious accomplice in what is nothing less than a fraud upon the public.
Letter to the Sanitary Engineer (22 Dec 1880). Quoted in Charles Bazermanl, The Languages of Edison's Light (2002), 186.
When I quitted business and took to science as a career, I thought I had left behind me all the petty meannesses and small jealousies which hinder man in his moral progress; but I found myself raised into another sphere, only to find poor human nature just the same everywhere—subject to the same weaknesses and the same self-seeking, however exalted the intellect.
As quoted “as well as I can recollect” by Mrs. Cornelia Crosse, wife of the scientist Andrew Crosse. She was with him during a visit by Andrew to see his friend Faraday at the Royal Institution, and she had some conversation with him. This was Faraday’s reply to her comment that he must be happy to have elevated himself (presumably, from his apprenticeship as a bookbinder) above all the “meaner aspects and lower aims of common life.” As stated in John Hall Gladstone, Michael Faraday (1872), 117.
When I was living with the Indians, my hostess, a fine looking woman, who wore numberless bracelets, and rings in her ears and on her fingers, and painted her face like a brilliant sunset, one day gave away a very fine horse. I was surprised, for I knew there had been no family talk on the subject, so I asked: “Will your husband like to have you give the horse away?” Her eyes danced, and, breaking into a peal of laughter, she hastened to tell the story to the other women gathered in the tent, and I became the target of many merry eyes. I tried to explain how a white woman would act, but laughter and contempt met my explanation of the white man’s hold upon his wife’s property.
Speech on 'The Legal Conditions of Indian Women', delivered to Evening Session (Thur 29 Mar 1888), collected in Report of the International Council of Women: Assembled by the National Woman Suffrage Association, Washington, D.C., U.S. of America, March 25 to April 1, 1888 (1888), Vol. 1, 240.
When in Ames, I had charge of a football team and a track team. I was the official ‘rubber.’ Now we call them ‘Masseurs.’ But we weren’t so stylish in those days, so my title was that of a ‘rubber.’ I noticed then that there was something lacking in the oils used for such purposes, which set me thinking. When I came to Tuskegee, I found a healing strength in peanut oil not found in other oils. I have found great possibilities in it. I am simply a scientist attempting to work out a complete oil therapy. In my investigations I find that the peanut oils give better results when skillfully applied than any of the 44 other oils that I have used. So far my success is very gratifying. I have more than 6,000 letters before me on this subject, and there are people who come to consult with me every day.
As quoted in 'Chemistry and Peace', Atlanta Daily World (3 Jan 1943), 4.
When the war finally came to an end, 1 was at a loss as to what to do. ... I took stock of my qualifications. A not-very-good degree, redeemed somewhat by my achievements at the Admiralty. A knowledge of certain restricted parts of magnetism and hydrodynamics, neither of them subjects for which I felt the least bit of enthusiasm.
No published papers at all … [Only gradually did I realize that this lack of qualification could be an advantage. By the time most scientists have reached age thirty they are trapped by their own expertise. They have invested so much effort in one particular field that it is often extremely difficult, at that time in their careers, to make a radical change. I, on the other hand, knew nothing, except for a basic training in somewhat old-fashioned physics and mathematics and an ability to turn my hand to new things. … Since I essentially knew nothing, I had an almost completely free choice. …
No published papers at all … [Only gradually did I realize that this lack of qualification could be an advantage. By the time most scientists have reached age thirty they are trapped by their own expertise. They have invested so much effort in one particular field that it is often extremely difficult, at that time in their careers, to make a radical change. I, on the other hand, knew nothing, except for a basic training in somewhat old-fashioned physics and mathematics and an ability to turn my hand to new things. … Since I essentially knew nothing, I had an almost completely free choice. …
In What Mad Pursuit (1988).
When two minds of a high order, interested in kindred subjects, come together, their conversation is chiefly remarkable for the summariness of its allusions and the rapidity of its transitions. Before one of them is half through a sentence the other knows his meaning and replies. ... His mental lungs breathe more deeply, in an atmosphere more broad and vast...
In The Principles of Psychology (1918), Vol. 2, 370.
When two plants, constantly different in one or several traits, are crossed, the traits they have in common are transmitted unchanged to the hybrids and their progeny, as numerous experiments have proven; a pair of differing traits, on the other hand, are united in the hybrid to form a new trait, which usually is subject to changes in the hybrids' progeny.
'Experiments on Plant Hybrids' (1865). In Curt Stern and Eva R. Sherwood (eds.), The Origin of Genetics: A Mendel Source Book (1966), 5.
When we reflect that all the aspects of Nature, all the emotions of the soul, and all the events of life, have been the subjects of poetry for hundreds and thousands of years, we can hardly wonder that there should be so many resemblances and coincidences of expression among poets, but rather that they are not more numerous and more striking.
In 'Table-Talk', The Poetical Works of Henry Wadsworth Longfellow: Volume 3 (1883), 1355.
When you are identifying science of the motion of water, remember to include under each subject its application and use, so that the science will be useful.
…...
When you have made a thorough and reasonably long effort, to understand a thing, and still feel puzzled by it, stop, you will only hurt yourself by going on. Put it aside till the next morning; and if then you can’t make it out, and have no one to explain it to you, put it aside entirely, and go back to that part of the subject which you do understand.
From letter to Edith Rix with hints for studying (about Mar 1885), in Stuart Dodgson Collingwood, The Life and Letters of Lewis Carroll (1898), 240.
While the vaccine discovery was progressive, the joy I felt at the prospect before me of being the instrument destined to take away from the world one of its greatest calamities [smallpox], blended with the fond hope of enjoying independence and domestic peace and happiness, was often so excessive that, in pursuing my favourite subject among the meadows, I have sometimes found myself in a kind of reverie.
John Baron, The Life of Dr. Jenner (1827), 140.
Why did I decide to undertake my doctorate research in the exotic field of boron hydrides? As it happened, my girl friend, Sarah Baylen, soon to become my wife, presented me with a graduation gift, Alfred Stock's book, The Hydrides of Boron and Silicon. I read this book and became interested in the subject. How did it happen that she selected this particular book? This was the time of the Depression. None of us had much money. It appears she selected as her gift the most economical chemistry book ($2.06) available in the University of Chicago bookstore. Such are the developments that can shape a career.
'From Little Acorns Through to Tall Oaks From Boranes Through Organoboranes', Nobel Lecture (8 Dec) 1979. In Nobel Lectures: Chemistry, 1971-1980 (1993), 341.
Why we love science. It’s more than a school subject, or the periodic table, or the properties of waves. It is an approach to the world, a critical way to understand and explore and engage with the world, and then have the capacity to change that world, and to share this accumulated knowledge. It’s a mindset that says we that can use reason and logic and honest inquiry to reach new conclusions and solve big problems.
From remarks at the fifth White House Science Fair, in Press Release (23 Mar 2015).
Why, then, are we surprised that comets, such a rare spectacle in the universe, are not known, when their return is at vast intervals?. … The time will come when diligent research over long periods will bring to light things which now lie hidden. A single lifetime, even though entirely devoted to the sky, would not be enough for the investigation of so vast a subject … And so this knowledge will be unfolded only through long successive ages. There will come a time when our descendants will be amazed that we did not know things that are so plain to them …. Many discoveries are reserved for ages still to come, when memory of us will have been effaced. Our universe is a sorry little affair unless it has in it something for every age to investigate … Nature does not reveal her mysteries once and for all. Someday there will be a man who will show in what regions comets have their orbit, why they travel so remote from other celestial bodies, how large they are and what sort they are.
Natural Questions, Book 7. As translated by Thomas H. Corcoran in Seneca in Ten Volumes: Naturales Quaestiones II (1972), 279 and 293.
Will fluorine ever have practical applications?
It is very difficult to answer this question. I may, however, say in all sincerity that I gave this subject little thought when I undertook my researches, and I believe that all the chemists whose attempts preceded mine gave it no more consideration.
A scientific research is a search after truth, and it is only after discovery that the question of applicability can be usefully considered.
It is very difficult to answer this question. I may, however, say in all sincerity that I gave this subject little thought when I undertook my researches, and I believe that all the chemists whose attempts preceded mine gave it no more consideration.
A scientific research is a search after truth, and it is only after discovery that the question of applicability can be usefully considered.
Proceedings of the Royal Institution (1897). In Annual Report of the Board of Regents of the Smithsonian Institution to July 1897 (1898), 261.
Xenophanes of Kolophon ... says that nothing comes into being, nor is anything destroyed, nor moved; and that the universe is one and is not subject to change.
Doxographists, Epiph. adv. Haer. iii. 9; Dox. 590. Quoted in Arthur Fairbanks (ed. And trans.), The First Philosophers of Greece (1898), 83.
You can't really discover the most interesting conflicts and problems in a subject until you've tried to write about them. At that point, one discovers discontinuities in the data, perhaps, or in one's own thinking; then the act of writing forces you to work harder to resolve these contradictions.
From Robert S. Grumet, 'An Interview with Anthony F. C. Wallace', Ethnohistory (Winter 1998), 45, No. 1, 109.
You cannot do without one specialty. You must have some base-line to measure the work and attainments of others. For a general view of the subject, study the history of the sciences. Broad knowledge of all Nature has been the possession of no naturalist except Humboldt, and general relations constituted his specialty.
Lecture at a teaching laboratory on Penikese Island, Buzzard's Bay. Quoted from the lecture notes by David Starr Jordan, Science Sketches (1911), 146.
You, in this country [the USA], are subjected to the British insularity in weights and measures; you use the foot, inch and yard. I am obliged to use that system, but must apologize to you for doing so, because it is so inconvenient, and I hope Americans will do everything in their power to introduce the French metrical system. ... I look upon our English system as a wickedly, brain-destroying system of bondage under which we suffer. The reason why we continue to use it, is the imaginary difficulty of making a change, and nothing else; but I do not think in America that any such difficulty should stand in the way of adopting so splendidly useful a reform.
Journal of the Franklin Institute, Nov 1884, 118, 321-341
In science it often happens that scientists say, 'You know that's a really good argument; my position is mistaken,' and then they would actually change their minds and you never hear that old view from them again. They really do it. It doesn't happen as often as it should, because scientists are human and change is sometimes painful. But it happens every day. I cannot recall the last time something like that happened in politics or religion.
(1987) -- 
