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Who said: “The Columbia is lost; there are no survivors.”
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Least Quotes (75 quotes)

...what would be observed (if not with one’s actual eyes at least with those of the mind) if an eagle, carried by the force of the wind, were to drop a rock from its talons?
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Every teacher certainly should know something of non-euclidean geometry. Thus, it forms one of the few parts of mathematics which, at least in scattered catch-words, is talked about in wide circles, so that any teacher may be asked about it at any moment. … Imagine a teacher of physics who is unable to say anything about Röntgen rays, or about radium. A teacher of mathematics who could give no answer to questions about non-euclidean geometry would not make a better impression.
On the other hand, I should like to advise emphatically against bringing non-euclidean into regular school instruction (i.e., beyond occasional suggestions, upon inquiry by interested pupils), as enthusiasts are always recommending. Let us be satisfied if the preceding advice is followed and if the pupils learn to really understand euclidean geometry. After all, it is in order for the teacher to know a little more than the average pupil.
In George Edward Martin, The Foundations of Geometry and the Non-Euclidean Plane (1982), 72.
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Here, you see, it takes all the running you can do, to keep in the same place. If you want to get somewhere else, you must run at least twice as fast as that!
Said by the fictional Red Queen character, in Through the Looking Glass and What Alice Found There (1872, 1896), 36.
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A good ornithologist should be able to distinguish birds by their air as well as by their colors and shape; on the ground as well as on the wing, and in the bush as well as in the hand. For, though it must not be said that every species of birds has a manner peculiar to itself, yet there is somewhat, in most genera at least, that at first sight discriminates them and enables a judicious observer to pronounce upon them with some certainty.
Letter (7 Aug 1778) to Daines Barrington, collected in The Natural History of Selborne (1829), 274.
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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.
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A great nation is any mob of people which produces at least one honest man a century.
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A man who is convinced of the truth of his religion is indeed never tolerant. At the least, he is to feel pity for the adherent of another religion but usually it does not stop there. The faithful adherent of a religion will try first of all to convince those that believe in another religion and usually he goes on to hatred if he is not successful. However, hatred then leads to persecution when the might of the majority is behind it.
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A science in its infancy is the least satisfactory, and, at the same time, the most profitable theme for a general description.
In Modern Astrophysics (1924), Preface, v.
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Among people I have met, the few whom I would term “great” all share a kind of unquestioned, fierce dedication; an utter lack of doubt about the value of their activities (or at least an internal impulse that drives through any such angst); and above all, a capacity to work (or at least to be mentally alert for unexpected insights) at every available moment of every day of their lives.
From The Lying Stones of Marrakech: Penultimate Reflections in Natural History (2000), 76.
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As a graduate student at Columbia University, I remember the a priori derision of my distinguished stratigraphy professor toward a visiting Australian drifter ... Today my own students would dismiss with even more derision anyone who denied the evident truth of continental drift–a prophetic madman is at least amusing; a superannuated fuddy-duddy is merely pitiful.
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At the planet’s very heart lies a solid rocky core, at least five times larger than Earth, seething with the appalling heat generated by the inexorable contraction of the stupendous mass of material pressing down to its centre. For more than four billion years Jupiter’s immense gravitational power has been squeezing the planet slowly, relentlessly, steadily, converting gravitational energy into heat, raising the temperature of that rocky core to thirty thousand degrees, spawning the heat flow that warms the planet from within. That hot, rocky core is the original protoplanet seed from the solar system’s primeval time, the nucleus around which those awesome layers of hydrogen and helium and ammonia, methane, sulphur compounds and water have wrapped themselves.
Ben Bova
Jupiter
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Biodiversity is our most valuable but least appreciated resource.
In 'Unmined Riches', The Diversity of Life (1992), 281.
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Biological disciplines tend to guide research into certain channels. One consequence is that disciplines are apt to become parochial, or at least to develop blind spots, for example, to treat some questions as “interesting” and to dismiss others as “uninteresting.” As a consequence, readily accessible but unworked areas of genuine biological interest often lie in plain sight but untouched within one discipline while being heavily worked in another. For example, historically insect physiologists have paid relatively little attention to the behavioral and physiological control of body temperature and its energetic and ecological consequences, whereas many students of the comparative physiology of terrestrial vertebrates have been virtually fixated on that topic. For the past 10 years, several of my students and I have exploited this situation by taking the standard questions and techniques from comparative vertebrate physiology and applying them to insects. It is surprising that this pattern of innovation is not more deliberately employed.
In 'Scientific innovation and creativity: a zoologist’s point of view', American Zoologist (1982), 22, 233.
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Consider the plight of a scientist of my age. I graduated from the University of California at Berkeley in 1940. In the 41 years since then the amount of biological information has increased 16 fold; during these 4 decades my capacity to absorb new information has declined at an accelerating rate and now is at least 50% less than when I was a graduate student. If one defines ignorance as the ratio of what is available to be known to what is known, there seems no alternative to the conclusion that my ignorance is at least 25 times as extensive as it was when I got my bachelor’s degree. Although I am sure that my unfortunate condition comes as no surprise to my students and younger colleagues, I personally find it somewhat depressing. My depression is tempered, however, by the fact that all biologists, young or old, developing or senescing, face the same melancholy situation because of an interlocking set of circumstances.
In 'Scientific innovation and creativity: a zoologist’s point of view', American Zoologist (1982), 22, 228.
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Engineering is the science of economy, of conserving the energy, kinetic and potential, provided and stored up by nature for the use of man. It is the business of engineering to utilize this energy to the best advantage, so that there may be the least possible waste.
(1908). Quoted, without source, in Appendix A, 'Some Definitions of Engineering' in Theodore Jesse Hoover and John Charles Lounsbury Fish, The Engineering Profession (1941), 463.
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Every good mathematician is at least half a philosopher, and every good philosopher at least half a mathematician.
Quoted, without citation, in 'Gottlob Frege', The New Encyclopedia Britannica (1992), Vol. 4, 968. If you know a primary source, please contact Webmaster.
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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.
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Experimentation is the least arrogant method of gaining knowledge. The experimenter humbly asks a question of nature.
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For many planet hunters, though, the ultimate goal is still greater (or actually, smaller) prey: terrestrial planets, like Earth, circling a star like the Sun. Astronomers already know that three such planets orbit at least one pulsar. But planet hunters will not rest until they are in sight of a small blue world, warm and wet, in whose azure skies and upon whose wind-whipped oceans shines a bright yellow star like our own.
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From this fountain (the free will of God) it is those laws, which we call the laws of nature, have flowed, in which there appear many traces of the most wise contrivance, but not the least shadow of necessity. These therefore we must not seek from uncertain conjectures, but learn them from observations and experimental. He who is presumptuous enough to think that he can find the true principles of physics and the laws of natural things by the force alone of his own mind, and the internal light of his reason, must either suppose the world exists by necessity, and by the same necessity follows the law proposed; or if the order of Nature was established by the will of God, the [man] himself, a miserable reptile, can tell what was fittest to be done.
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General Relativity is at least very close to the truth.
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He that in ye mine of knowledge deepest diggeth, hath, like every other miner, ye least breathing time, and must sometimes at least come to terr. alt. for air.
[Explaining how he writes a letter as break from his study.]
Letter to Dr. Law (15 Dec 1716) as quoted in Norman Lockyer, (ed.), Nature (25 May 1881), 24, 39. The source refers to it as an unpublished letter.
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I can understand your aversion to the use of the term ‘religion’ to describe an emotional and psychological attitude which shows itself most clearly in Spinoza ... I have not found a better expression than ‘religious’ for the trust in the rational nature of reality that is, at least to a certain extent, accessible to human reason.
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I hate science. It denies a man’s responsibility for his own deeds, abolishes the brotherhood that springs from God’s fatherhood. It is a hectoring, dictating expertise, which makes the least lovable of the Church Fathers seem liberal by contrast. It is far easier for a Hitler or a Stalin to find a mock-scientific excuse for persecution than it was for Dominic to find a mock-Christian one.
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I strive that in public dissection the students do as much as possible so that if even the least trained of them must dissect a cadaver before a group of spectators, he will be able to perform it accurately with his own hands; and by comparing their studies one with another they will properly understand, this part of medicine.
In De Humani Corporis Fabrica Libri Septem [Seven Books on the Structure of the Human Body] (1543), 547. Quoted and trans. in Charles Donald O'Malley, Andreas Vesalius of Brussels, 1514-1564 (1964), 144.
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I think that I cannot preserve my health and spirits, unless I spend four hours a day at least—and it is commonly more than that—sauntering through the woods and over the hills and fields, absolutely free from all worldly engagements.
In 'Walking', The Atlantic (Jun 1862), 9, No. 56, 657-674. Collected in Walking (1841, 1914), 9.
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In abstract mathematical theorems, the approximation to absolute truth is perfect. … In physical science, on the contrary, we treat of the least quantities which are perceptible.
In The Principles of Science: A Treatise on Logic and Scientific Method (1913), 478.
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In every phase of business life, keep at least one year ahead of the other fellow.
As quoted by H.M. Davidson, in System: The Magazine of Business (Apr 1922), 41, 412.
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In order to comprehend and fully control arithmetical concepts and methods of proof, a high degree of abstraction is necessary, and this condition has at times been charged against arithmetic as a fault. I am of the opinion that all other fields of knowledge require at least an equally high degree of abstraction as mathematics,—provided, that in these fields the foundations are also everywhere examined with the rigour and completeness which is actually necessary.
In 'Die Theorie der algebraischen Zahlkorper', Vorwort, Jahresbericht der Deutschen Mathematiker Vereinigung, Bd. 4.
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In science, one can learn the most by studying what seems to be the least.
John Mitchinson and John Lloyd, If Ignorance Is Bliss, Why Aren't There More Happy People?: Smart Quotes for Dumb Times (2009), 217.
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Is it not true that for every person the course of life is along the line of least resistance, and that in this the movement of humanity is like the movement of material bodies?
In preface to Scientific Memoirs (1878), xiv.
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It is now necessary to indicate more definitely the reason why mathematics not only carries conviction in itself, but also transmits conviction to the objects to which it is applied. The reason is found, first of all, in the perfect precision with which the elementary mathematical concepts are determined; in this respect each science must look to its own salvation .... But this is not all. As soon as human thought attempts long chains of conclusions, or difficult matters generally, there arises not only the danger of error but also the suspicion of error, because since all details cannot be surveyed with clearness at the same instant one must in the end be satisfied with a belief that nothing has been overlooked from the beginning. Every one knows how much this is the case even in arithmetic, the most elementary use of mathematics. No one would imagine that the higher parts of mathematics fare better in this respect; on the contrary, in more complicated conclusions the uncertainty and suspicion of hidden errors increases in rapid progression. How does mathematics manage to rid itself of this inconvenience which attaches to it in the highest degree? By making proofs more rigorous? By giving new rules according to which the old rules shall be applied? Not in the least. A very great uncertainty continues to attach to the result of each single computation. But there are checks. In the realm of mathematics each point may be reached by a hundred different ways; and if each of a hundred ways leads to the same point, one may be sure that the right point has been reached. A calculation without a check is as good as none. Just so it is with every isolated proof in any speculative science whatever; the proof may be ever so ingenious, and ever so perfectly true and correct, it will still fail to convince permanently. He will therefore be much deceived, who, in metaphysics, or in psychology which depends on metaphysics, hopes to see his greatest care in the precise determination of the concepts and in the logical conclusions rewarded by conviction, much less by success in transmitting conviction to others. Not only must the conclusions support each other, without coercion or suspicion of subreption, but in all matters originating in experience, or judging concerning experience, the results of speculation must be verified by experience, not only superficially, but in countless special cases.
In Werke [Kehrbach] (1890), Bd. 5, 105. As quoted, cited and translated in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-Book (1914), 19.
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It seems to me that there is a good deal of ballyhoo about scientific method. I venture to think that the people who talk most about it are the people who do least about it. Scientific method is what working scientists do, not what other people or even they themselves may say about it. No working scientist, when he plans an experiment in the laboratory, asks himself whether he is being properly scientific, nor is he interested in whatever method he may be using as method.
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It’s that moment, that brief epiphany when the universe opens up and shows us something, and in that instant we get just a sense of an order greater than Heaven and, as yet at least, beyond the grasp of Stephen Hawking.
Quoted in Kim Lim (ed.), 1,001 Pearls of Spiritual Wisdom: Words to Enrich, Inspire, and Guide Your Life (2014), 109
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Law springs from experiment, but not immediately. Experiment is individual, the law deduced from it is general; experiment is only approximate, the law is precise, or at least pretends to be. Experiment is made under conditions always complex, the enunciation of the law eliminates these complications. This is what is called ‘correcting the systematic errors’.
From La Valeur de la Science (1904), 142, as translated by George Bruce Halsted (trans.), in The Value of Science (1907), 77. From the French, “La loi sort de l’expérience, mais elle n’en sort pas immédiatement. L’expérience est individuelle, la loi qu’on en tire est générale, l’expérience n’est qu’approchée, la loi est précise ou du moins prétend l’élre. L’expérience se fait dans des conditions toujours complexes, l’énoncé de la loi élimine ces complications. C’est ce qu’on appelle ‘corriger les erreurs systématiques’.”
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Looking back over the geological record it would seem that Nature made nearly every possible mistake before she reached her greatest achievement Man—or perhaps some would say her worst mistake of all. ... At last she tried a being of no great size, almost defenseless, defective in at least one of the more important sense organs; one gift she bestowed to save him from threatened extinction—a certain stirring, a restlessness, in the organ called the brain.
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Nothing is so firmly believed as what we least know; nor any people so confident as those who entertain us with fabulous stories, such as your alchemists, judicial astrologers, fortune-tellers, and physicians.
In Charles Cotton (trans.), Essays of Michael Seigneur de Montaigne: In Three Books (1693), Vol. 1, 339.
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Our credulity is greatest concerning the things we know least about. And since we know least about ourselves, we are ready to believe all that is said about us. Hence the mysterious power of both flattery and calumny.... It is thus with most of us: we are what other people say we are. We know ourselves chiefly by hearsay.
In The Passionate State of Mind (1955), 80.
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Probably I am very naive, but I also think I prefer to remain so, at least for the time being and perhaps for the rest of my life.
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Rulers and generals muster their troops. Magnates muster the sums of money which give them power. The fascist dictators muster the irrational human reactions which make it possible for them to attain and maintain their power over the masses. The scientists muster knowledge and means of research. But, thus far, no organization fighting for freedom has ever mustered the biological arsenal where the weapons are to be found for the establishment and the maintenance of human freedom. All precision of our social existence notwithstanding, there is as yet no definition of the word freedom which would be in keeping with natural science. No word is more misused and misunderstood. To define freedom is the same as to define sexual health. But nobody will openly admit this. The advocacy of personal and social freedom is connected with anxiety and guilt feelings. As if to be free were a sin or at least not quite as it should be. Sex-economy makes this guilt feeling comprehensible: freedom without sexual self-determination is in itself a contradiction. But to be sexual means—according to the prevailing human structure—to be sinful or guilty. There are very few people who experience sexual love without guilt feeling. “Free love” has acquired a degrading meaning: it lost the meaning given it by the old fighters for freedom. In films and in books, to be genital and to be criminal are presented as the same thing.
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Science progresses by a series of combinations in which chance plays not the least role. Its life is rough and resembles that of minerals which grow by juxtaposition [accretion]. This applies not only to science such as it emerges [results] from the work of a series of scientists, but also to the particular research of each one of them. In vain would analysts dissimulate: (however abstract it may be, analysis is no more our power than that of others); they do not deduce, they combine, they compare: (it must be sought out, sounded out, solicited.) When they arrive at the truth it is by cannoning from one side to another that they come across it.
English translation from manuscript, in Évariste Galois and Peter M. Neumann, 'Dossier 12: On the progress of pure analysis', The Mathematical Writings of Évariste Galois (2011), 263. A transcription of the original French is on page 262. In the following quote from that page, indicated deletions are omitted, and Webmaster uses parentheses to enclose indications of insertions above the original written line. “La science progresse par une série de combinaisons où le hazard ne joue pas le moindre rôle; sa vie est brute et ressemble à celle des minéraux qui croissent par juxtà position. Cela s’applique non seulement à la science telle qu’elle résulte des travaux d’une série de savants, mais aussi aux recherches particulières à chacun d’eux. En vain les analystes voudraient-ils se le dissimuler: (toute immatérielle qu’elle wst analyse n’est pas pas plus en notre pouvoir que des autres); ils ne déduisent pas, ils combinent, ils comparent: (il faut l’epier, la sonder, la solliciter) quand ils arrivent à la vérité, c’est en heurtant de côté et d’autre qu’il y sont tombés.” Webmaster corrected from typo “put” to “but” in the English text.
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Since the examination of consistency is a task that cannot be avoided, it appears necessary to axiomatize logic itself and to prove that number theory and set theory are only parts of logic. This method was prepared long ago (not least by Frege’s profound investigations); it has been most successfully explained by the acute mathematician and logician Russell. One could regard the completion of this magnificent Russellian enterprise of the axiomatization of logic as the crowning achievement of the work of axiomatization as a whole.
Address (11 Sep 1917), 'Axiomatisches Denken' delivered before the Swiss Mathematical Society in Zürich. Translated by Ewald as 'Axiomatic Thought', (1918), in William Bragg Ewald, From Kant to Hilbert (1996), Vol. 2, 1113.
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Sociology is the science with the greatest number of methods and the least results.
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Strong, deeply rooted desire is the starting point of all achievement. Just as the electron is the last unit of matter discernible to the scientist. DESIRE is the seed of all achievement; the starting place, back of which there is nothing, or at least there is nothing of which we have any knowledge.
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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.
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The dexterous management of terms and being able to fend and prove with them, I know has and does pass in the world for a great part of learning; but it is learning distinct from knowledge, for knowledge consists only in perceiving the habitudes and relations of ideas one to another, which is done without words; the intervention of sounds helps nothing to it. And hence we see that there is least use of distinction where there is most knowledge: I mean in mathematics, where men have determined ideas with known names to them; and so, there being no room for equivocations, there is no need of distinctions.
In Conduct of the Understanding, Sect. 31.
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The difference between what the most and the least learned people know is inexpressibly trivial in relation to that which is unknown.
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The fact that astronomies change while the stars abide is a true analogy of every realm of human life and thought, religion not least of all.
In The Living of These Days: An Autobiography (1956), 230.
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The genesis of mathematical invention is a problem that must inspire the psychologist with the keenest interest. For this is the process in which the human mind seems to borrow least from the exterior world, in which it acts, or appears to act, only by itself and on itself, so that by studying the process of geometric thought, we may hope to arrive at what is most essential in the human mind
As translated in Arthur I. Miller, Imagery in Scientific Thought Creating 20th-Century Physics (1984, 2013), 307. Opening of Paper delivered at Conference at the Institut Général Psychologique, Paris, 'L’Invention Mathématique', published in Enseignment Mathématique (1908), 10, 357. From the original French, “La genèse do l’Invention mathématique est un problème qui doit inspirer le plus vif intérêt au psychologue. C’est l’acte dans lequel l’esprit humain semble le moins emprunter au monde extérieur, où il n’agit ou ne paraît agir que par lui-même et sur lui-même, de sorte, qu’en étudiant le processus de la pensée géométrique, c’est ce qu’il y a de plus essentiel dans l’esprit humain que nous pouvons espérer atteindre.”
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The great science [mathematics] occupies itself at least just as much with the power of imagination as with the power of logical conclusion.
In 'Pestalozzi's Idee eines A B C der Anschauung', Werke[Kehrbach] (1890), Bd.l, 174. As quoted, cited and translated in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-Book (1914), 31.
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The history of science teaches only too plainly the lesson that no single method is absolutely to be relied upon, that sources of error lurk where they are least expected, and that they may escape the notice of the most experienced and conscientious worker.
Transactions of the Sections', Reports of the British Association for the Advancement of Science (1883), 438.
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The Internet is like a herd of performing elephants with diarrhea—massive, difficult to redirect, awe-inspiring, entertaining and a source of mind-boggling amounts of excrement when you least expect it.
Posted to a mailing list (1992), and circulated from there by some newsgroups. As authenticated in 'Quotable Spaf' on his faculty webpage at purdue.com
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The least thing contains something of the unknown. Let us find it. To describe a fire that flames and a tree in a field, we must remain facing that fire and that tree until they no longer resemble, to us, any other tree, or fire. This is the way we become original.
From 'Le Roman', Pierre et Jean (1888), as translated by Alexina Loranger in 'Introduction: The Novel', Pierre et Jean (Peter and John) (1890), 39. The opening words are quoted from Gustave Flaubert. From the original French, “La moindre chose contient un peu d’inconnu. Trouvons-le. Pour décrire un feu qui flambe et un arbre dans une plaine, demeurons en face de ce feu et de cet arbre jusqu’à ce 'qu’ils ne ressemblent plus, pour nous, à aucun autre arbre et à aucun autre feu. C’est de cette façon qu’on devient original.” [Because “devient” is present tense, where the original text gave “became”, the present tense “become” has been substituted in the above quote by Webmaster.]
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The mathematician pays not the least regard either to testimony or conjecture, but deduces everything by demonstrative reasoning, from his definitions and axioms. Indeed, whatever is built upon conjecture, is improperly called science; for conjecture may beget opinion, but cannot produce knowledge.
In Essays on the Intellectual Powers of Man, Essay 1, chap. 3.
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The more man inquires into the laws which regulate the material universe, the more he is convinced that all its varied forms arise from the action of a few simple principles. These principles themselves converge, with accelerating force, towards some still more comprehensive law to which all matter seems to be submitted. Simple as that law may possibly be, it must be remembered that it is only one amongst an infinite number of simple laws: that each of these laws has consequences at least as extensive as the existing one, and therefore that the Creator who selected the present law must have foreseen the consequences of all other laws.
In Passages from the Life of a Philosopher (1864), 402.
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The most beautiful and deepest experience a man can have is the sense of the mysterious. It is the underlying principle of religion as well as all serious endeavour in art and science. He who never had this experience seems to me, if not dead, then at least blind. To sense that behind anything that can be experienced there is a something that our mind cannot grasp and whose beauty and sublimity reaches us only indirectly and as a feeble reflection, this is religiousness.
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The only thing we know for sure about the future is that it will be radically different from the past. In the face of this enormous uncertainty, the least we can do for future generations is to pass on as many of the planet’s resources as possible.
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The reputation of science which ought to be the most lasting, as synonymous with truth, is often the least so. One discovery supersedes another; and the progress of light throws the past into obscurity. What is become of the Blacks, the Lavoisiers, the Priestleys, in chemistry? … When any set of men think theirs the only science worth studying, and themselves the only infallible persons in it, it is a sign how frail the traces are of past excellence in it.
Characteristics: In the Manner of Rochefoucault's Maxims (1837), 148-149.
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The Sun truly “comes up like thunder,” and it sets just as fast. Each sunrise and sunset lasts only a few seconds. But in that time you see at least eight different bands of color come and go, from a brilliant red to the brightest and deepest blue. And you see sixteen sunrises and sixteen sunsets every day you’re in space. No sunrise or sunset is ever the same.
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The Universe forces those who live in it to understand it. Those creatures who find everyday experience a muddled jumble of events with no predictability, no regularity, are in grave peril. The Universe belongs to those who, at least to some degree, have figured it out.
In Broca’s Brain: Reflections on the Romance of Science (1979, 1980), 19.
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There must be some one quality without which a work of art cannot exist; possessing which, in the least degree, no work is altogether worthless.
In Art (1913), 7.
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There was this huge world out there, independent of us human beings and standing before us like a great, eternal riddle, at least partly accessible to our inspection and thought. The contemplation of that world beckoned like a liberation.
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These two orders of mountains [Secondary and Tertiary] offer the most ancient chronicle of our globe, least liable to falsifications and at the same time more legible than the writing of the primitive ranges. They are Nature's archives, prior to even the most remote records and traditions that have been preserved for our observant century to investigate, comment on and bring to the light of day, and which will not be exhausted for several centuries after our own.
Observations sur la Formation des Montagnes', Acta Academiae Scientiarum Imperialis Petropolitanae (1777) [1778], 46. Trans. Albert Carozzi.
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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.
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This is the way physicians mend or end us
Secundum artem; but although we sneer
In health-when ill, we call them to attend us,
Without the least propensity to jeer;
While that hiatus maxime deplendus
To be fill’d by spade or mattock, ‘s nea
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This is what nonscientists don’t know, and this is what scientists are too bashful to talk about publicly, at least until they grow old enough to be shameless. Science at its highest level is ultimately the organization of, the systematic pursuit of, and
John Mitchinson and John Lloyd, If Ignorance Is Bliss, Why Aren't There More Happy People?: Smart Quotes for Dumb Times (2009), 274.
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Those who assert that the mathematical sciences make no affirmation about what is fair or good make a false assertion; for they do speak of these and frame demonstrations of them in the most eminent sense of the word. For if they do not actually employ these names, they do not exhibit even the results and the reasons of these, and therefore can be hardly said to make any assertion about them. Of what is fair, however, the most important species are order and symmetry, and that which is definite, which the mathematical sciences make manifest in a most eminent degree. And since, at least, these appear to be the causes of many things—now, I mean, for example, order, and that which is a definite thing, it is evident that they would assert, also, the existence of a cause of this description, and its subsistence after the same manner as that which is fair subsists in.
Aristotle
In Metaphysics [MacMahon] Bk. 12, chap. 3.
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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.
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To the east was our giant neighbor Makalu, unexplored and unclimbed, and even on top of Everest the mountaineering instinct was sufficient strong to cause me to spend some moments conjecturing as to whether a route up that mountain might not exist. Far away across the clouds the great bulk of Kangchenjunga loomed on the horizon. To the west, Cho Oyu, our old adversary from 1952, dominated the scene and we could see the great unexplored ranges of Nepal stretching off into the distance. The most important photograph, I felt, was a shot down the north ridge, showing the North Col and the old route that had been made famous by the struggles of those great climbers of the 1920s and 1930s. I had little hope of the results being particularly successful, as I had a lot of difficulty in holding the camera steady in my clumsy gloves, but I felt that they would at least serve as a record. After some ten minutes of this, I realized that I was becoming rather clumsy-fingered and slow-moving, so I quickly replaced my oxygen set and experience once more the stimulating effect of even a few liters of oxygen. Meanwhile, Tenzing had made a little hole in the snow and in it he placed small articles of food – a bar of chocolate, a packet of biscuits and a handful of lollies. Small offerings, indeed, but at least a token gifts to the gods that all devoted Buddhists believe have their home on this lofty summit. While we were together on the South Col two days before, Hunt had given me a small crucifix that he had asked me to take to the top. I, too, made a hole in the snow and placed the crucifix beside Tenzing’s gifts.
As quoted in Whit Burnett, The Spirit of Adventure: The Challenge (1955), 349.
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To us, men of the West, a very strange thing happened at the turn of the century; without noticing it, we lost science, or at least the thing that had been called by that name for the last four centuries. What we now have in place of it is something different, radically different, and we don’t know what it is. Nobody knows what it is.
From La Science et Nous (1941), translated as 'Classical Science and After', in Richard Rees (ed.), On Science, Necessity and the Love of God (1968), as quoted and cited in Robert Andrews, The Columbia Dictionary of Quotations (1993), 809-810. Also seen translated as, “Something happened to the people of the Western world at the beginning of the century, something quite strange: we lost science without even being aware of it, or at least, what had been called science for the last four centuries. What we now have under this name is something else, something radically different, and we do not know what it is. Probably no one knows what it is”, collected in Simone Weil: Late Philosophical Writings (2015), Chap. 10.
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We must therefore bear the undoubtedly bad effect s of the weak surviving and propagating their kind; but there appears to be at least one check in steady action, namely that the weaker and inferior members of society do not marry so freely as the sound; and this check might be indefinitely increased by the weak in body or mind refraining from marriage, though this is more to be hoped for than expected.
…...
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What I chiefly admired, and thought altogether unaccountable, was the strong disposition I observed in them [the mathematicians of Laputa] towards news and politics; perpetually inquiring into public affairs; giving their judgments in matters of state; and passionately disputing every inch of party opinion. I have indeed observed the same disposition among most of the mathematicians I have known in Europe, although I could never discover the least analogy between the two sciences.
In Gulliver's Travels, Part 8, chap. 2.
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What is common sense? That which attracts the least opposition: that which brings most agreeable and worthy results
In Sinner Sermons: A Selection of the Best Paragraphs of E. W. Howe (1926), 44.
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When the world is mad, a mathematician may find in mathematics an incomparable anodyne. For mathematics is, of all the arts and sciences, the most austere and the most remote, and a mathematician should be of all men the one who can most easily take refuge where, as Bertrand Russell says, “one at least of our nobler impulses can best escape from the dreary exile of the actual world.”
In A Mathematician's Apology (1940, 2012), 43.
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~~[Orphan]~~ Mathematicians are like lovers. Grant a mathematician the least principle, and he will draw from it a consequence which you must also grant him, and from this consequence another.
As quoted, without citation, in Eric Temple Bell, Men of Mathematics (1937), Vol. 2, xlix. Webmaster has so far been unable to find the primary source. Can you help? Until then, consider it an unverified orphan quote.
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Carl Sagan Thumbnail 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) -- Carl Sagan
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