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Today in Science History - Quickie Quiz
Who said: “I seem to have been only like a boy playing on the seashore, ... finding a smoother pebble or a prettier shell ... whilst the great ocean of truth lay all undiscovered before me.”
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Give Quotes (202 quotes)


...there is no prescribed route to follow to arrive at a new idea. You have to make the intuitive leap. But the difference is that once you’ve made the intuitive leap you have to justify it by filling in the intermediate steps. In my case, it often happens that I have an idea, but then I try to fill in the intermediate steps and find that they don’t work, so I have to give it up.
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...We must be on our guard against giving interpretations that are hazardous or opposed to science, and so exposing the Word of God to the ridicule of unbelievers.
Genesis in the Literal Sense
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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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Le lezioni non si dànno, si prendono.
Lessons are not given. They are taken.
Diary entry for 18th Aug 1946, In Il mestiere di vivere (1947), 303. Translated as The Burning Brand: Diaries 1935-1950 (1961), 296.
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Lepidoptera are for children to play with, pretty to look at, so some think. Give me the Coleoptera, and the kings of the Coleoptera are the beetles! Lepidoptera and Neuroptera for little folks; Coleoptera for men, sir!
In 'The Poet at the Breakfast Table: III', The Atlantic Monthly (Mar 1872), 29, 344.
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Q: Why did the chicken cross the road?
A: Pierre de Fermat: I just don’t have room here to give the full explanation.
Anonymous
[Note: Pierre de Fermat is famous for an enigmatic marginal note in his notebook, “I have discovered a truly remarkable proof which this margin is too small to contain.”]
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Quand on demande à nos philosophes à quoi sert ce nombre prodigieux d’étoiles fixes, dont une partie suffirait pour faire ce qu’elles font toutes, ils vous répondent froidement qu’elles servent à leur réjouir la vue.
When our philosophers are asked what is the use of these countless myriads of fixed stars, of which a small part would be sufficient to do what they all do, they coolly tell us that they are made to give delight to their eyes.
In 'Premier Soir', Entretiens Sur La Pluralité Des Mondes (1686, 1863), 29. French and translation in Craufurd Tait Ramage, Beautiful Thoughts from French and Italian Authors (1866), 117.
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A man has a very insecure tenure of a property which another can carry away with his eyes. A few months reduced me to the cruel necessity either of destroying my machine, or of giving it to the public. To destroy it, I could not think of; to give up that for which I had laboured so long, was cruel. I had no patent, nor the means of purchasing one. In preference to destroying, I gave it to the public.
[On his inability to keep for himself a profitable income from his invention of the Spinning Mule.]
As quoted in James Mason, The Great Triumphs of Great Men (1875), 579.
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A possible explanation for the observed excess noise is the one given by Dicke, Peebles, Roll, and Wilkinson (1965) in a companion letter in this issue.
[The low-key announcement of the detection of the cosmic microwave background radiation which is the afterglow of the Big Bang. Co-author with Robert Wilson. They received the 1978 Nobel Prize for their discovery.]
'A measurement of excess antenna temperature at 4080 Mc/s'. In Astrophysical Journal (1965). Reprinted in R. B. Partridge, 3 K the cosmic microwave background radiation? (1995), Appendix A, 355.
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A reference to the two sorts of doctors is also found in the Republic: “Now you know that when patients do not require medicine, but have only to be put under a regimen, the inferior sort of practitioner is deemed to be good enough; but when medicine has to be given, then the doctor should be more of a man.”
Osler is referring to Plato’s Dialogues, iii, 153. In Address (1893) to the Johns Hopkins Hospital Historical Club, 'Physic and Physicians as Depicted in Plato', collected in Aequanimitas: With Other Addresses to Medical Students, Nurses and Practitioners of Medicine (1904), 70.
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A scientist works largely by intuition. Given enough experience, a scientist examining a problem can leap to an intuition as to what the solution ‘should look like.’ ... Science is ultimately based on insight, not logic.
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A teacher of mathematics has a great opportunity. If he fills his allotted time with drilling his students in routine operations he kills their interest, hampers their intellectual development, and misuses his opportunity. But if he challenges the curiosity of his students by setting them problems proportionate to their knowledge, and helps them to solve their problems with stimulating questions, he may give them a taste for, and some means of, independent thinking.
In How to Solve It (1948), Preface.
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Algebra is generous; she often gives more than is asked of her.
Quoted in Bulletin American Mathematical Society (1905), 2, 285. As cited in Memorabilia Mathematica; Or, The Philomath’s Quotation-Book (1914), 275.
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All power, all subordination rests on the executioner: he is the horror and the bond of human association. Remove this incomprehensible agent from the world, and the very moment order gives way to chaos, thrones topple, and society disappears
In Joseph de Maistre and Richard A. Lebrun (trans.), The St. Petersburg Dialogues (1993), 20.
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Another great and special excellence of mathematics is that it demands earnest voluntary exertion. It is simply impossible for a person to become a good mathematician by the happy accident of having been sent to a good school; this may give him a preparation and a start, but by his own individual efforts alone can he reach an eminent position.
In Conflict of Studies (1873), 2.
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Any man who can drive safely while kissing a pretty girl is simply not giving the kiss the attention it deserves.
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Archimedes … had stated that given the force, any given weight might be moved, and even boasted, we are told, relying on the strength of demonstration, that if there were another earth, by going into it he could remove this. Hiero being struck with amazement at this, and entreating him to make good this problem by actual experiment, and show some great weight moved by a small engine, he fixed accordingly upon a ship of burden out of the king’s arsenal, which could not be drawn out of the dock without great labor and many men; and, loading her with many passengers and a full freight, sitting himself the while far off with no great endeavor, but only holding the head of the pulley in his hand and drawing the cords by degrees, he drew the ship in a straight line, as smoothly and evenly, as if she had been in the sea. The king, astonished at this, and convinced of the power of the art, prevailed upon Archimedes to make him engines accommodated to all the purposes, offensive and defensive, of a siege. … the apparatus was, in most opportune time, ready at hand for the Syracusans, and with it also the engineer himself.
Plutarch
In John Dryden (trans.), Life of Marcellus.
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As soon as somebody demonstrates the art of flying, settlers from our species of man will not be lacking [on the moon and Jupiter]… Given ships or sails adapted to the breezes of heaven, there will be those who will not shrink from even that vast expanse.
(1610) As translated by Edward Rosen in Kepler’s Conversation with Galileo’s Sidereal Messenger (1965), 39.
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Astronomy was thus the cradle of the natural sciences and the starting point of geometrical theories. The stars themselves gave rise to the concept of a ‘point’; triangles, quadrangles and other geometrical figures appeared in the constellations; the circle was realized by the disc of the sun and the moon. Thus in an essentially intuitive fashion the elements of geometrical thinking came into existence.
In George Edward Martin, The Foundations of Geometry and the Non-Euclidean Plane (1982), 72.
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At the present time all property is personal; the man owns his own ponies and other belongings he has personally acquired; the woman owns her horses, dogs, and all the lodge equipments; children own their own articles; and parents do not control the possessions of their children. There is no family property as we use the term. A wife is as independent as the most independent man in our midst. If she chooses to give away or sell all of her property, there is no one to gainsay her.
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, 239-240.
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Be glad of life, because it gives you the chance to love and to work and to play and to look up at the stars.
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Biological evolution is a system of constant divergence without subsequent joining of branches. Lineages, once distinct, are separate forever. In human history, transmission across lineages is, perhaps, the major source of cultural change. Europeans learned about corn and potatoes from Native Americans and gave them smallpox in return.
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Blessed is the man who, having nothing to say, abstains from giving in words evidence of the fact.
(Mary Ann Evans, English Novelist)
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Bowing to the reality of harried lives, Rudwick recognizes that not everyone will read every word of the meaty second section; he even explicitly gives us permission to skip if we get ‘bogged down in the narrative.’ Readers absolutely must not do such a thing; it should be illegal. The publisher should lock up the last 60 pages, and deny access to anyone who doesn’t pass a multiple-choice exam inserted into the book between parts two and three.
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Building goes on briskly at the therapeutic Tower of Babel; what one recommends another condemns; what one gives in large doses another scarce dares to prescribe in small doses; and what one vaunts as a novelty another thinks not worth rescuing from merited oblivion. All is confusion, contradiction, inconceivable chaos. Every country, every place, almost every doctor, have their own pet remedies, without which they imagine their patients can not be cured; and all this changes every year, aye every mouth.
Weekly Medical Gazette, of Vienna
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But here I stop–short of any deterministic speculation that attributes specific behaviors to the possession of specific altruist or opportunist genes. Our genetic makeup permits a wide range of behaviors–from Ebenezer Scrooge before to Ebenezer Scrooge after. I do not believe that the miser hoards through opportunist genes or that the philanthropist gives because nature endowed him with more than the normal complement of altruist genes. Upbringing, culture, class, status, and all the intangibles that we call ‘free will,’ determine how we restrict our behaviors from the wide spectrum–extreme altruism to extreme selfishness–that our genes permit.
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Cavendish gave me once some bits of platinum for my experiments, and came to see my results on the decomposition of the alkalis, and seemed to take an interest in them; but he encouraged no intimacy with any one, and received nobody at his own house. … He was acute, sagacious, and profound, and, I think, the most accomplished British philosopher of his time.
As quoted in Victor Robinson, Pathfinders in Medicine (1912), 143.
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Comets giveth and comets taketh away.
In Comet (1885, 1997), 337. [Note the context refers to the idea that although perhaps comets seeded life on earth, later comet collisions with Earth could cause mass extinctions.]
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Commitment becomes hysterical when those who have nothing to give advocate generosity, and those who have nothing to give up preach renunciation.
In Reflections on the Human Condition (1973), 31.
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Common Sense is that which judges the things given to it by other senses.
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Dalton transformed the atomic concept from a philosophical speculation into a scientific theory—framed to explain quantitative observations, suggesting new tests and experiments, and capable of being given quantitative form through the establishment of relative masses of atomic particles.
Development of Concepts of Physics. In Clifford A. Pickover, Archimedes to Hawking: Laws of Science and the Great Minds Behind Them (2008), 175.
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Debate is an art form. It is about the winning of arguments. It is not about the discovery of truth. There are certain rules and procedures to debate that really have nothing to do with establishing fact–which creationists have mastered. Some of those rules are: never say anything positive about your own position because it can be attacked, but chip away at what appear to be the weaknesses in your opponent’s position. They are good at that. I don’t think I could beat the creationists at debate. I can tie them. But in courtrooms they are terrible, because in courtrooms you cannot give speeches. In a courtroom you have to answer direct questions about the positive status of your belief. We destroyed them in Arkansas. On the second day of the two-week trial we had our victory party!
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Does there truly exist an insuperable contradiction between religion and science? Can religion be superseded by science? The answers to these questions have, for centuries, given rise to considerable dispute and, indeed, bitter fighting. Yet, in my own mind there can be no doubt that in both cases a dispassionate consideration can only lead to a negative answer. What complicates the solution, however, is the fact that while most people readily agree on what is meant by ‘science,’ they are likely to differ on the meaning of ‘religion.’
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Don’t think of organ donations as giving up part of yourself to keep a total stranger alive. It’s really a total stranger giving up almost all of themselves to keep part of you alive.
Anonymous
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Each of the major sciences has contributed an essential ingredient in our long retreat from an initial belief in our own cosmic importance. Astronomy defined our home as a small planet tucked away in one corner of an average galaxy among millions; biology took away our status as paragons created in the image of God; geology gave us the immensity of time and taught us how little of it our own species has occupied.
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Einstein has not ... given the lie to Kant’s deep thoughts on the idealization of space and time; he has, on the contrary, made a large step towards its accomplishment.
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Euclid always contemplates a straight line as drawn between two definite points, and is very careful to mention when it is to be produced beyond this segment. He never thinks of the line as an entity given once for all as a whole. This careful definition and limitation, so as to exclude an infinity not immediately apparent to the senses, was very characteristic of the Greeks in all their many activities. It is enshrined in the difference between Greek architecture and Gothic architecture, and between Greek religion and modern religion. The spire of a Gothic cathedral and the importance of the unbounded straight line in modern Geometry are both emblematic of the transformation of the modern world.
In Introduction to Mathematics (1911), 119.
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Euler could repeat the Aeneid from the beginning to the end, and he could even tell the first and last lines in every page of the edition which he used. In one of his works there is a learned memoir on a question in mechanics, of which, as he himself informs us, a verse of Aeneid gave him the first idea. [“The anchor drops, the rushing keel is staid.”]
In Letters of Euler (1872), Vol. 1, 24.
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Everybody likes to hear about a man laying down his life for his country, but nobody wants to hear about a country giving her shirt for her planet.
In 'The Wild Flag', The New Yorker (9 Sep 1944), 35. Quote collected in In the Words of E.B. White: Quotations from America’s Most Companionable of Writers (2011), 150.
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Everything flows and nothing abides; everything gives way and nothing stays fixed.
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Few will deny that even in the first scientific instruction in mathematics the most rigorous method is to be given preference over all others. Especially will every teacher prefer a consistent proof to one which is based on fallacies or proceeds in a vicious circle, indeed it will be morally impossible for the teacher to present a proof of the latter kind consciously and thus in a sense deceive his pupils. Notwithstanding these objectionable so-called proofs, so far as the foundation and the development of the system is concerned, predominate in our textbooks to the present time. Perhaps it will be answered, that rigorous proof is found too difficult for the pupil’s power of comprehension. Should this be anywhere the case,—which would only indicate some defect in the plan or treatment of the whole,—the only remedy would be to merely state the theorem in a historic way, and forego a proof with the frank confession that no proof has been found which could be comprehended by the pupil; a remedy which is ever doubtful and should only be applied in the case of extreme necessity. But this remedy is to be preferred to a proof which is no proof, and is therefore either wholly unintelligible to the pupil, or deceives him with an appearance of knowledge which opens the door to all superficiality and lack of scientific method.
In 'Stücke aus dem Lehrbuche der Arithmetik', Werke, Bd. 2 (1904), 296.
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Forty years ago the philosopher Alfred North Whitehead thought it self-evident that you would get a good government if you took power out of the hands of the acquisitive and gave it to the learned and the cultivated. At present, a child in kindergarten knows better than that.
In Before the Sabbath (1979), 40-41.
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Give 'em 2.5 cm, and they'll take 1.6 km.
Anonymous
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Give me an ounce of civit, good apothecary, to sweeten my imagination.
In Raymond C. Rowe, Joseph Chamberlain, A Spoonful of Sugar (2007),
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Give people facts and you feed their minds for an hour. Awaken curiosity and they feed their own minds for a lifetime.
Originally written for an ECSITE Newsletter, Food for Thought article, used for a long time as a personal e-mail signature, then posted on the website of interactives.co.uk
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Given angel’s wings, where might you fly?
In what sweet heaven might you find your love?
Unwilling to be bound, where might you move,
Lost between the wonder and the why?...
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God gives every bird his food, but does not throw it into the nest.
Seen, for example, in 'Home and Foreign Gossip', Harpers Weekly: A Journal of Civilization (1869), 13, 187, identified with other examples as a "Danish proverb".
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God gives every bird his food, but he does not throw it into the nest.
As quoted, without citation, in John Walker, A Fork in the Road: Answers to Daily Dilemmas from the Teachings of Jesus Christ (2005), 99.
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God has given you one face, and you make yourself another.
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Guido was as much enchanted by the rudiments of algebra as he would have been if I had given him an engine worked by steam, with a methylated spirit lamp to heat the boiler; more enchanted, perhaps for the engine would have got broken, and, remaining always itself, would in any case have lost its charm, while the rudiments of algebra continued to grow and blossom in his mind with an unfailing luxuriance. Every day he made the discovery of something which seemed to him exquisitely beautiful; the new toy was inexhaustible in its potentialities.
In Young Archimedes: And Other Stories (1924), 299. The fictional character, Guido, is a seven year old boy. Methylated spirit is an alcohol fuel.
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Half the time of all medical men is wasted keeping life in human wrecks who have no more intelligible reason for hanging on than a cow has for giving milk.
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He who gives a portion of his time and talent to the investigation of mathematical truth will come to all other questions with a decided advantage over his opponents. He will be in argument what the ancient Romans were in the field: to them the day of battle was a day of comparative recreation, because they were ever accustomed to exercise with arms much heavier than they fought; and reviews differed from a real battle in two respects: they encountered more fatigue, but the victory was bloodless.
Reflection 352, in Lacon: or Many things in Few Words; Addressed to Those Who Think (1820), 159.
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He who joyfully marches to music in rank and file has already earned my contempt. He has been given a large brain by mistake, since for him the spinal cord would fully suffice. This disgrace to civilisation should be done away with at once. Heroism at command, senseless brutality, deplorable love-of-country stance, how violently I hate all this, how despicable and ignoble war is; I would rather be torn to shreds than be part of so base an action! It is my conviction that killing under the cloak of war is nothing but an act of murder.
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Holding then to science with one hand—the left hand—we give the right hand to religion, and cry: ‘Open Thou mine eyes, that I may behold wondrous things, more wondrous than the shining worlds can tell.’ Obedient to the promise, religion does awaken faculties within us, does teach our eyes to the beholding of more wonderful things. Those great worlds blazing like suns die like feeble stars in the glory of the morning, in the presence of this new light. The soul knows that an infinite sea of love is all about it, throbbing through it, everlasting arms of affection lift it, and it bathes itself in the clear consciousness of a Father’s love.
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How can cosmic religious feeling be communicated from one person to another, if it can give rise to no definite notion of a God and no theology? In my view, it is the most important function of art and science to awaken this feeling and keep it alive in those who are receptive to it.
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I am more of a sponge than an inventor. I absorb ideas from every source. I take half-matured schemes for mechanical development and make them practical. I am a sort of middleman between the long-haired and impractical inventor and the hard-headed businessman who measures all things in terms of dollars and cents. My principal business is giving commercial value to the brilliant but misdirected ideas of others.
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I am very astonished that the scientific picture of the real world around me is deficient. It gives a lot of factual information, puts all our experience in a magnificently consistent order, but it is ghastly silent about all and sundry that is really near to our heart, that really matters to us. It cannot tell us a word about red and blue, bitter and sweet, physical pain and physical delight; it knows nothing of beautiful and ugly, good or bad, God and eternity. Science sometimes pretends to answer questions in these domains, but the answers are very often so silly that we are not inclined to take them seriously.
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Florence Nightingale quote: I attribute my success to this:— I never gave or took an excuse.
I attribute my success to this:— I never gave or took an excuse.
Letter (1861) to Miss H. Bonham Carter, transcribed in Edward Cook, The Life of Florence Nightingale (1913, 1914), Vol. 1, 506.
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I believe that the useful methods of mathematics are easily to be learned by quite young persons, just as languages are easily learned in youth. What a wondrous philosophy and history underlie the use of almost every word in every language—yet the child learns to use the word unconsciously. No doubt when such a word was first invented it was studied over and lectured upon, just as one might lecture now upon the idea of a rate, or the use of Cartesian co-ordinates, and we may depend upon it that children of the future will use the idea of the calculus, and use squared paper as readily as they now cipher. … When Egyptian and Chaldean philosophers spent years in difficult calculations, which would now be thought easy by young children, doubtless they had the same notions of the depth of their knowledge that Sir William Thomson might now have of his. How is it, then, that Thomson gained his immense knowledge in the time taken by a Chaldean philosopher to acquire a simple knowledge of arithmetic? The reason is plain. Thomson, when a child, was taught in a few years more than all that was known three thousand years ago of the properties of numbers. When it is found essential to a boy’s future that machinery should be given to his brain, it is given to him; he is taught to use it, and his bright memory makes the use of it a second nature to him; but it is not till after-life that he makes a close investigation of what there actually is in his brain which has enabled him to do so much. It is taken because the child has much faith. In after years he will accept nothing without careful consideration. The machinery given to the brain of children is getting more and more complicated as time goes on; but there is really no reason why it should not be taken in as early, and used as readily, as were the axioms of childish education in ancient Chaldea.
In Teaching of Mathematics (1902), 14.
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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.
In Florian Cajori, Teaching and History of Mathematics in the United States (1890), 266-267.
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I have never looked upon ease and happiness as ends in themselves–this critical basis I call the ideal of a pigsty. The ideals that have lighted my way, and time after time have given me new courage to face life cheerfully, have been Kindness, Beauty, and Truth. Without the sense of kinship with men of like mind, without the occupation with the objective world, the eternally unattainable in the field of art and scientific endeavors, life would have seemed empty to me. The trite objects of human efforts–possessions, outward success, luxury–have always seemed to me contemptible.
In 'What I Believe,' Forum and Century (1930).
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I have no doubt that it is possible to give a new direction to technological development, a direction that shall lead it back to the real needs of man, and that also means: to the actual size of man. Man is small, and, therefore, small is beautiful. To go
Small is Beautiful (1973).
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I have no dress except the one I wear every day. If you are going to be kind enough to give me one, please let it be practical and dark so that I can put it on afterwards to go to the laboratory.
[Referring to her wedding dress.]
In Eve Curie, Madame Curie: a biography by Eve Curie (1937, 2007), 136-37.
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I never pick up an item without thinking of how I might improve it. I never perfected an invention that I did not think about in terms of the service it might give others. I want to save and advance human life, not destroy it. I am proud of the fact that I never invented weapons to kill. The dove is my emblem.
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I should like to draw attention to the inexhaustible variety of the problems and exercises which it [mathematics] furnishes; these may be graduated to precisely the amount of attainment which may be possessed, while yet retaining an interest and value. It seems to me that no other branch of study at all compares with mathematics in this. When we propose a deduction to a beginner we give him an exercise in many cases that would have been admired in the vigorous days of Greek geometry. Although grammatical exercises are well suited to insure the great benefits connected with the study of languages, yet these exercises seem to me stiff and artificial in comparison with the problems of mathematics. It is not absurd to maintain that Euclid and Apollonius would have regarded with interest many of the elegant deductions which are invented for the use of our students in geometry; but it seems scarcely conceivable that the great masters in any other line of study could condescend to give a moment’s attention to the elementary books of the beginner.
In Conflict of Studies (1873), 10-11.
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I will give no deadly medicine to any one if asked, nor suggest any such counsel; and in like manner I will not give any woman the instrument to procure abortion. … I will not cut a person who is suffering with stone, but will leave this to be done by men who are practitioners of such work.
From 'The Oath', as translated by Francis Adams in The Genuine Works of Hippocrates (1849), Vol. 2, 780.
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If a man would be alone, let him look at the stars. … One might think the atmosphere was made transparent with this design, to give man, in the heavenly bodies, the perpetual presence of the sublime.
In 'Nature', The Prose Works of Ralph Waldo Emerson (1870), Vol. 1, Chap 1, 7.
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If any philosopher had been asked for a definition of infinity, he might have produced some unintelligible rigmarole, but he would certainly not have been able to give a definition that had any meaning at all.
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If God wanted man to become a space faring species, He would have given man a moon.
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If I am given a sign [formula], and I am ignorant of its meaning, it cannot teach me anything, but if I already know it what does the formula teach me?
In De Magistro (400s), Book 1, chap 10, 23. As quoted in Ettore Carruccio, Mathematics And Logic in History And in Contemporary Thought (1964), 152.
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If I give you a pfennig, you will be one pfennig richer and I’ll be one pfennig poorer. But if I give you an idea, you will have a new idea, but I shall still have it, too.
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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.
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If you throw a stone in a pond... the waves which strike against the shores are thrown back towards the spot where the stone struck; and on meeting other waves they never intercept each other’s course... In a small pond one and the same stroke gives birth to many motions of advance and recoil.
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If you want my opinion on the mystery of life and all that, I can give it to you in a nutshell; the universe is like a safe to which there is a key. But the key is locked up in the safe.
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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If you want to build a ship, don’t recruit the men to gather the wood, divide the work and give orders. Instead, teach them to yearn for vast and endless sea.
Not found as such in a work by Saint-Exupéry. Probably an anonymous paraphrase of a related passage in Citadelle (1948), section 75, 687. See the quote beginning, “One will weave the canvas…” on the Antoine de Saint-Exupéry Quotes page of this website.
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In Euclid each proposition stands by itself; its connection with others is never indicated; the leading ideas contained in its proof are not stated; general principles do not exist. In modern methods, on the other hand, the greatest importance is attached to the leading thoughts which pervade the whole; and general principles, which bring whole groups of theorems under one aspect, are given rather than separate propositions. The whole tendency is toward generalization. A straight line is considered as given in its entirety, extending both ways to infinity, while Euclid is very careful never to admit anything but finite quantities. The treatment of the infinite is in fact another fundamental difference between the two methods. Euclid avoids it, in modern mathematics it is systematically introduced, for only thus is generality obtained.
In 'Geometry', Encyclopedia Britannica (9th edition).
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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]
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Induction and analogy are the special characteristics of modern mathematics, in which theorems have given place to theories and no truth is regarded otherwise than as a link in an infinite chain. “Omne exit in infinitum” is their favorite motto and accepted axiom.
In 'A Plea for the Mathematician', Nature, Vol. 1, 861. [The Latin phrase “Omne exit in infinitum” means “Everything goes to infinity”.
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Is there anyone whose name cannot be twisted into either praise or satire? I have had given to me,
Thomas Babington Macaulay
Mouths big: a Cantab anomaly.

In Budget of Paradoxes (1872), 83. [Macaulay’s full name is followed by an anagram of it. —Webmaster]
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It has often been said that power corrupts. But it is perhaps equally important to realize that weakness, too, corrupts. Power corrupts the few, while weakness corrupts the many. Hatred, malice, rudeness, intolerance, and suspicion are the faults of weakness. The resentment of the weak does not spring from any injustice done to them but from the sense of inadequacy and impotence. We cannot win the weak by sharing our wealth with them. They feel our generosity as oppression. St. Vincent De Paul cautioned his disciples to deport themselves so that the poor “will forgive them the bread you give them.”
In 'The Awakening of Asia', The Ordeal of Change (1963), 12.
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It is a good thing for a physician to have prematurely grey hair and itching piles. The first makes him appear to know more than he does, and the second gives him an expression of concern which the patient interprets as being on his behalf.
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It is admitted by all that a finished or even a competent reasoner is not the work of nature alone; the experience of every day makes it evident that education develops faculties which would otherwise never have manifested their existence. It is, therefore, as necessary to learn to reason before we can expect to be able to reason, as it is to learn to swim or fence, in order to attain either of those arts. Now, something must be reasoned upon, it matters not much what it is, provided it can be reasoned upon with certainty. The properties of mind or matter, or the study of languages, mathematics, or natural history, may be chosen for this purpose. Now of all these, it is desirable to choose the one which admits of the reasoning being verified, that is, in which we can find out by other means, such as measurement and ocular demonstration of all sorts, whether the results are true or not. When the guiding property of the loadstone was first ascertained, and it was necessary to learn how to use this new discovery, and to find out how far it might be relied on, it would have been thought advisable to make many passages between ports that were well known before attempting a voyage of discovery. So it is with our reasoning faculties: it is desirable that their powers should be exerted upon objects of such a nature, that we can tell by other means whether the results which we obtain are true or false, and this before it is safe to trust entirely to reason. Now the mathematics are peculiarly well adapted for this purpose, on the following grounds:
1. Every term is distinctly explained, and has but one meaning, and it is rarely that two words are employed to mean the same thing.
2. The first principles are self-evident, and, though derived from observation, do not require more of it than has been made by children in general.
3. The demonstration is strictly logical, taking nothing for granted except self-evident first principles, resting nothing upon probability, and entirely independent of authority and opinion.
4. When the conclusion is obtained by reasoning, its truth or falsehood can be ascertained, in geometry by actual measurement, in algebra by common arithmetical calculation. This gives confidence, and is absolutely necessary, if, as was said before, reason is not to be the instructor, but the pupil.
5. There are no words whose meanings are so much alike that the ideas which they stand for may be confounded. Between the meaning of terms there is no distinction, except a total distinction, and all adjectives and adverbs expressing difference of degrees are avoided.
In On the Study and Difficulties of Mathematics (1898), chap. 1.
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It is not possible to find in all geometry more difficult and more intricate questions or more simple and lucid explanations [than those given by Archimedes]. Some ascribe this to his natural genius; while others think that incredible effort and toil produced these, to all appearance, easy and unlaboured results. No amount of investigation of yours would succeed in attaining the proof, and yet, once seen, you immediately believe you would have discovered it; by so smooth and so rapid a path he leads you to the conclusion required.
Plutarch
In John Dryden (trans.), Life of Marcellus.
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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 is the duty of every citizen according to his best capacities to give validity to his convictions in political affairs.
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It is therefore easy to see why the churches have always fought science and persecuted its devotees. On the other hand, I maintain that the cosmic religious feeling is the strongest and noblest motive for scientific research. Only those who realize the immense efforts and, above all, the devotion without which pioneer work in theoretical science cannot be achieved are able to grasp the strength of the emotion out of which alone such work, remote as it is from the immediate realities of life, can issue. What a deep conviction of the rationality of the universe and what a yearning to understand, were it but a feeble reflection of the mind revealed in this world, Kepler and Newton must have had to enable them to spend years of solitary labor in disentangling the principles of celestial mechanics! Those whose acquaintance with scientific research is derived chiefly from its practical results easily develop a completely false notion of the mentality of the men who, surrounded by a skeptical world, have shown the way to kindred spirits scattered wide through the world and through the centuries. Only one who has devoted his life to similar ends can have a vivid realization of what has inspired these men and given them the strength to remain true to their purpose in spite of countless failures. It is cosmic religious feeling that gives a man such strength. A contemporary has said, not unjustly, that in this materialistic age of ours the serious scientific workers are the only profoundly religious people.
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It may well be doubted whether, in all the range of Science, there is any field so fascinating to the explorer—so rich in hidden treasures—so fruitful in delightful surprises—as that of Pure Mathematics. The charm lies chiefly, I think, in the absolute certainty of its results: for that is what, beyond all mental treasures, the human intellect craves for. Let us only be sure of something! More light, more light … “And if our fate be death, give light and let us die” This is the cry that, through all the ages, is going up from perplexed Humanity, and Science has little else to offer, that will really meet the demands of its votaries, than the conclusions of Pure Mathematics.
Opening of 'Introduction', A New Theory of Parallels (1890), xv. As a non-fiction work, the author’s name on the title page of this book was Charles Lutwidge Dodgson. Being better known for his works of fiction as Lewis Carroll, all quotes relating to this one person, published under either name, are gathered on this single web page under his pen name.
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It might be said of psychoanalysis that if you give it your little finger, it will soon have your whole hand.
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It must happen that in some cases the author is not understood, or is very imperfectly understood; and the question is what is to be done. After giving a reasonable amount of attention to the passage, let the student pass on, reserving the obscurity for future efforts. … The natural tendency of solitary students, I believe, is not to hurry away prematurely from a hard passage, but to hang far too long over it; the just pride that does not like to acknowledge defeat, and the strong will that cannot endure to be thwarted, both urge to a continuance of effort even when success seems hopeless. It is only by experience we gain the conviction that when the mind is thoroughly fatigued it has neither the power to continue with advantage its course in .an assigned direction, nor elasticity to strike out a new path; but that, on the other hand, after being withdrawn for a time from the pursuit, it may return and gain the desired end.
In 'Private Study of Mathematics', Conflict of Studies and other Essays (1873), 68.
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It must not be forgotten that although a high standard of morality gives a slight or no advantage to each individual man and his children over the other men of the same tribe, yet an advancement in the standard of morality will certainly give an immense advantage to one tribe over another.
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It would not be difficult to come to an agreement as to what we understand by science. Science is the century-old endeavor to bring together by means of systematic thought the perceptible phenomena of this world into as thoroughgoing an association as possible. To put it boldly, it is the attempt at the posterior reconstruction of existence by the process of conceptualization. But when asking myself what religion is I cannot think of the answer so easily. And even after finding an answer which may satisfy me at this particular moment, I still remain convinced that I can never under any circumstances bring together, even to a slight extent, the thoughts of all those who have given this question serious consideration.
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I’ve learned that life sometimes gives you a second chance.
Fifth stanza of poem 'On Turning 70'. The poem is printed in Michigan Office of Services to the Aging, Annual Report 2004 (2005), no page number.
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Learn to reverence night and to put away the vulgar fear of it, for, with the banishment of night from the experience of man, there vanishes as well a religious emotion, a poetic mood, which gives depth to the adventure of humanity. By day, space is one with the earth and with man - it is his sun that is shining, his clouds that are floating past; at night, space is his no more. When the great earth, abandoning day, rolls up the deeps of the heavens and the universe, a new door opens for the human spirit, and there are few so clownish that some awareness of the mystery of being does not touch them as they gaze. For a moment of night we have a glimpse of ourselves and of our world islanded in its stream of stars - pilgrims of mortality, voyaging between horizons across eternal seas of space and time. Fugitive though the instant be, the spirit of man is, during it, ennobled by a genuine moment of emotional dignity, and poetry makes its own both the human spirit and experience.
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Let it be understood that the University is a preparatory school: it is life that gives you the “finals”—not college.
Aphorism in The Philistine (Dec 1904), 20, No. 1, 30.
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Life is a thin narrowness of taken-for-granted, a plank over a canyon in a fog. There is something under our feet, the taken-for-granted. A table is a table, food is food, we are we—because we don’t question these things. And science is the enemy because it is the questioner. Faith saves our souls alive by giving us a universe of the taken-for-granted.
From a 1923 journal entry. As quoted in The Ghost in the Little House, ch. 7, by William V. Holtz (1993).
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Many of life’s failures are people who did not realize how close they were to success when they gave up.
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Mathematics associates new mental images with ... physical abstractions; these images are almost tangible to the trained mind but are far removed from those that are given directly by life and physical experience. For example, a mathematician represents the motion of planets of the solar system by a flow line of an incompressible fluid in a 54-dimensional phase space, whose volume is given by the Liouville measure
Mathematics and Physics (1981), Foreward. Reprinted in Mathematics as Metaphor: Selected Essays of Yuri I. Manin (2007), 90.
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Mathematics gives the young man a clear idea of demonstration and habituates him to form long trains of thought and reasoning methodically connected and sustained by the final certainty of the result; and it has the further advantage, from a purely moral point of view, of inspiring an absolute and fanatical respect for truth. In addition to all this, mathematics, and chiefly algebra and infinitesimal calculus, excite to a high degree the conception of the signs and symbols—necessary instruments to extend the power and reach of the human mind by summarizing an aggregate of relations in a condensed form and in a kind of mechanical way. These auxiliaries are of special value in mathematics because they are there adequate to their definitions, a characteristic which they do not possess to the same degree in the physical and mathematical [natural?] sciences.
There are, in fact, a mass of mental and moral faculties that can be put in full play only by instruction in mathematics; and they would be made still more available if the teaching was directed so as to leave free play to the personal work of the student.
In 'Science as an Instrument of Education', Popular Science Monthly (1897), 253.
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Mathematics in its pure form, as arithmetic, algebra, geometry, and the applications of the analytic method, as well as mathematics applied to matter and force, or statics and dynamics, furnishes the peculiar study that gives to us, whether as children or as men, the command of nature in this its quantitative aspect; mathematics furnishes the instrument, the tool of thought, which we wield in this realm.
In Psychologic Foundations of Education (1898), 325.
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Mathematics is the art of giving the same name to different things.
Henri Poincaré and George Bruce Halsted (trans.) The Foundations of Science: Science and Hypothesis (1921), 375.
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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.
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Medicine sometimes snatches away health, sometimes gives it.
From 'Tristia' (9 A.D.), 2, 269. As quoted in Latin, cited and translated to English in W. Gurney Benham (ed.), A Book of Quotations, Proverbs and Household Words (1907), 527. From the original Latin, “Eripit interdum, modo de medicina saluterem”. Also translated as, “Medicine sometimes brings health, sometimes removes it,” in Ovid and A.D. Melville (trans.), Sorrows of an exile: Tristia (1992), 33.
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My own emotional feeling is that life has a purpose—ultimately, I’d guess that purpose it has is the purpose that we’ve given it and not a purpose that come out of any cosmic design.
Alan Guth
As quoted in Michio Kaku, Parallel Worlds: A Journey Through Creation, Higher Dimensions, and the Future of the Cosmos (2006), 359.
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No more impressive warning can be given to those who would confine knowledge and research to what is apparently useful, than the reflection that conic sections were studied for eighteen hundred years merely as an abstract science, without regard to any utility other than to satisfy the craving for knowledge on the part of mathematicians, and that then at the end of this long period of abstract study, they were found to be the necessary key with which to attain the knowledge of the most important laws of nature.
In Introduction to Mathematics (1911), 136-137.
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No person was ever honored for what he received; honor has been the reward for what he gave.
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Nobody, certainly, will deny that the idea of the existence of an omnipotent, just, and omnibeneficent personal God is able to accord man solace, help, and guidance; also, by virtue of its simplicity it is accessible to the most undeveloped mind. But, on the other hand, there are decisive weaknesses attached to this idea in its elf, which have been painfully felt since the beginning of history. That is, if this being is omnipotent, then every occurrence, including every human action, every human thought, and every human feeling and aspiration is also His work; how is it possible to think of holding men responsible for their deeds and thoughts before such an almighty Being? In giving out punishment and rewards He would to a certain extent be passing judgment on Himself. How can this be combined with the goodness and righteousness ascribed to Him?
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Now do you not see that the eye embraces the beauty of the whole world? It counsels and corrects all the arts of mankind... it is the prince of mathematics, and the sciences founded on it are absolutely certain. It has measured the distances and sizes of the stars it has discovered the elements and their location... it has given birth to architecture and to perspective and to the divine art of painting.
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Old and new put their stamp to everything in Nature. The snowflake that is now falling is marked by both. The present moment gives the motion and the color of the flake, Antiquity its form and properties. All things wear a lustre which is the gift of the present, and a tarnish of time.
Epigraph for chapter 'Quotation and Originality', in Letters and Social Aims (1875, 1917), 175.
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One evening at a Joint Summer Research Congerence in the early 1990’s Nicholai Reshetikhin and I [David Yetter] button-holed Flato, and explained at length Shum’s coherence theorem and the role of categories in “quantum knot invariants”. Flato was persistently dismissive of categories as a “mere language”. I retired for the evening, leaving Reshetikhin and Flato to the discussion. At the next morning’s session, Flato tapped me on the shoulder, and, giving a thumbs-up sign, whispered, “Hey! Viva les categories! These new ones, the braided monoidal ones.”
In David N. Yetter, Functorial Knot Theory: Categories of Tangles, Coherence, Categorical Deformations, and Topological Invariants (2001), 8. Yetter writes this personal anecdote is given as a narrative in his own words. Presumable the phrases in quotation marks are based on recollection when written years later.
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One should guard against inculcating a young man with the idea that success is the aim of life, for a successful man normally receives from his peers an incomparably greater portion than the services he has been able to render them deserve. The value of a man resides in what he gives and not in what he is capable of receiving. The most important motive for study at school, at the university, and in life is the pleasure of working and thereby obtaining results which will serve the community. The most important task for our educators is to awaken and encourage these psychological forces in a young man {or woman}. Such a basis alone can lead to the joy of possessing one of the most precious assets in the world - knowledge or artistic skill.
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One summer night, out on a flat headland, all but surrounded by the waters of the bay, the horizons were remote and distant rims on the edge of space. Millions of stars blazed in darkness, and on the far shore a few lights burned in cottages. Otherwise there was no reminder of human life. My companion and I were alone with the stars: the misty river of the Milky Way flowing across the sky, the patterns of the constellations standing out bright and clear, a blazing planet low on the horizon. It occurred to me that if this were a sight that could be seen only once in a century, this little headland would be thronged with spectators. But it can be seen many scores of nights in any year, and so the lights burned in the cottages and the inhabitants probably gave not a thought to the beauty overhead; and because they could see it almost any night, perhaps they never will.
In The Sense of Wonder (1956), as condensed in Reader’s Digest (1986), 129, 174.
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Orthodoxy can be as stubborn in science as in religion. I do not know how to shake it except by vigorous imagination that inspires unconventional work and contains within itself an elevated potential for inspired error. As the great Italian economist Vilfredo Pareto wrote: ‘Give me a fruitful error any time, full of seeds, bursting with its own corrections. You can keep your sterile truth for yourself.’ Not to mention a man named Thomas Henry Huxley who, when not in the throes of grief or the wars of parson hunting, argued that ‘irrationally held truths may be more harmful than reasoned errors.’
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Our Professor, which doth have tenure,
Feared be thy name.
Thy sets partition,
Thy maps commute,
In groups as in vector spaces.
Give us this day our daily notation,
And forgive us our obtuseness,
As we forgive tutors who cannot help us.
Lead us not into Lye rings,
But deliver us from eigenvalues,
For thine is the logic, the notation, and the accent,
That confuses us forever.
Amen.
Anonymous
'Algebra Prayer' by an unnamed University of Toronto mathematics student. On the Department of Mathematics, University of Toronto web site.
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Peace means creative giving, making a contribution to the betterment of our own people and to the betterment of people throughout the world. And who better understands that than the men and women of American agriculture?
'Remarks to Farm Leaders Participating in the “Salute to Agriculture”' (7 May 1971), Public Papers of the Presidents of the United States: Richard M. Nixon (1972), 627.
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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.
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Psychoanalysis has changed American psychiatry from a diagnostic to a therapeutic science, not because so many patients are cured by the psychoanalytic technique, but because of the new understanding of psychiatric patients it has given us and the new and different concepts of illness and health.
News summaries 29 Apr 56
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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.
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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.
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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 cannot determine origin, and so cannot determine destiny. As it presents only a sectional view of creation, it gives only a sectional view of everything in creation.
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Science gives us knowledge, but only philosophy can give us wisdom.
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Science gives us the grounds of premises from which religious truths are to be inferred; but it does not set about inferring them, much less does it reach the inference; that is not its province. It brings before us phenomena, and it leaves us, if we will, to call them works of design, wisdom, or benevolence; and further still, if we will, to proceed to confess an Intelligent Creator. We have to take its facts, and to give them a meaning, and to draw our own conclusions from them. First comes Knowledge, then a view, then reasoning, then belief. This is why Science has so little of a religious tendency; deductions have no power of persuasion. The heart is commonly reached, not through the reason, but through the imagination, by means of direct impressions, by the testimony of facts and events, by history, by description. Persons influence us, voices melt us, looks subdue us, deeds inflame us. Many a man will live and die upon a dogma; no man will be a martyr for a conclusion.
Letter collected in Tamworth Reading Room: Letters on an Address Delivered by Sir Robert Peel, Bart., M.P. on the Establishment of a Reading Room at Tamworth (1841), 32. Excerpted in John Henry Newman, An Essay in Aid of a Grammar of Assent (1870), 89 & 94 footnote.
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Science is not illusion. But it would be an illusion to suppose that we could get anywhere else what it cannot give us.
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Science is properly more scrupulous than dogma. Dogma gives a charter to mistake, but the very breath of science is a contest with mistake, and must keep the conscience alive.
In Middlemarch: A Study of Provincial Life (1873), 255.
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Secondly, the study of mathematics would show them the necessity there is in reasoning, to separate all the distinct ideas, and to see the habitudes that all those concerned in the present inquiry have to one another, and to lay by those which relate not to the proposition in hand, and wholly to leave them out of the reckoning. This is that which, in other respects besides quantity is absolutely requisite to just reasoning, though in them it is not so easily observed and so carefully practised. In those parts of knowledge where it is thought demonstration has nothing to do, men reason as it were in a lump; and if upon a summary and confused view, or upon a partial consideration, they can raise the appearance of a probability, they usually rest content; especially if it be in a dispute where every little straw is laid hold on, and everything that can but be drawn in any way to give color to the argument is advanced with ostentation. But that mind is not in a posture to find truth that does not distinctly take all the parts asunder, and, omitting what is not at all to the point, draws a conclusion from the result of all the particulars which in any way influence it.
In Conduct of the Understanding, Sect. 7.
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Since natural selection demands only adequacy, elegance of design is not relevant; any combination of behavioural adjustment, physiological regulation, or anatomical accommodation that allows survival and reproduction may be favoured by selection. Since all animals are caught in a phylogenetic trap by the nature of past evolutionary adjustments, it is to be expected that a given environmental challenge will be met in a variety of ways by different animals. The delineation of the patterns of the accommodations of diverse types of organisms to the environment contributes much of the fascination of ecologically relevant physiology.
In 'The roles of physiology and behaviour in the maintenance of homeostasis in the desert environment.', Symposia of the Society for Experimental Biology (1964), 11.
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Since you are now studying geometry and trigonometry, I will give you a problem. A ship sails the ocean. It left Boston with a cargo of wool. It grosses 200 tons. It is bound for Le Havre. The mainmast is broken, the cabin boy is on deck, there are 12 passengers aboard, the wind is blowing East-North-East, the clock points to a quarter past three in the afternoon. It is the month of May. How old is the captain?
Letter (14 Aug 1853) to Louise Colet. As quote and cited in Robert A. Nowlan, Masters of Mathematics: The Problems They Solved, Why These Are Important, and What You Should Know about Them (2017), 271.
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So many people today–and even professional scientists–seem to me like someone who has seen thousands of trees but has never seen a forest . A knowledge of the historic and philosophical background gives that kind of independence from prejudices of his generation from which most scientists are suffering. This independence created by philosophical insight is–in my opinion–the mark of distinction between a mere artisan or specialist and a real seeker after truth.
…...
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Someone who had begun to read geometry with Euclid, when he had learned the first proposition, asked Euclid, “But what shall I get by learning these things?” whereupon Euclid called his slave and said, “Give him three-pence, since he must make gain out of what he learns.”
As quoted in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath's Quotation-Book (1914), 152-153, citing Stobaeus, Edition Wachsmuth (1884), Ecl. II.
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Space travel is at the frontier of my profession. It is going to be accomplished and I want to be in on it. There is also an element of simple duty involved. I am convinced that I have something to give this project.
As he wrote in an article for Life (14 Sep 1959), 38.
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Standing beside each other, we feasted our eyes. Above us the cerulean sky deepened to an inky black as the remnants of the atmosphere gave way to the depths of space. The mighty Himalaya were now a sparkling relief map spread out before us and garnished with a gleaming lattice work of swirling glaciers. Even Cho Oyu, Lhotse and Makalu, all 8,000-meter giants, were dwarfed. To the east and west, Kanchenjunga and Shishapangma, two more great sentinels of the Himalaya, stood crystal clear over 100 kilometers away. To the north were the burnished plains of Tibet, and to the south the majestic peaks and lush foothills of Nepal. We stood on the crown jewel of the earth, the curved horizon spinning endlessly around us.
Jo Gambi
…...
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Such explosives [atomic bombs] in men’s hands, while their moral and intellectual status is declining, is about as useful as giving out firearms to all inmates of a gaol and then saying that you hope ‘this will ensure peace’.
From Letter (No. 102) to Christopher Tolkien (9 Aug 1945). In Humphrey Carpenter (ed.) assisted by Christopher Tolkien, The Letters of J.R.R. Tolkien (1995, 2014), 116, Letter No. 102.
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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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Talent gives out what it has taken in ; genius, what has risen from its unsounded wells of living thought.
In 'Genius', Wellman’s Miscellany (Dec 1871), 4, No. 6, 203.
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Technique and ability alone do not get you to the top; it is the willpower that is the most important. This willpower you cannot buy with money or be given by others...it rises from your heart.
…...
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That form of popular science which merely recites the results of investigations, which merely communicates useful knowledge, is from this standpoint bad science, or no science at all. … Apply this test to every work professing to give a popular account of any branch of science. If any such work gives a description of phenomena that appeals to his imagination rather than to his reason, then it is bad science.
From The Grammar of Science (1892), 12.
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That mathematics “do not cultivate the power of generalization,”; … will be admitted by no person of competent knowledge, except in a very qualified sense. The generalizations of mathematics, are, no doubt, a different thing from the generalizations of physical science; but in the difficulty of seizing them, and the mental tension they require, they are no contemptible preparation for the most arduous efforts of the scientific mind. Even the fundamental notions of the higher mathematics, from those of the differential calculus upwards are products of a very high abstraction. … To perceive the mathematical laws common to the results of many mathematical operations, even in so simple a case as that of the binomial theorem, involves a vigorous exercise of the same faculty which gave us Kepler’s laws, and rose through those laws to the theory of universal gravitation. Every process of what has been called Universal Geometry—the great creation of Descartes and his successors, in which a single train of reasoning solves whole classes of problems at once, and others common to large groups of them—is a practical lesson in the management of wide generalizations, and abstraction of the points of agreement from those of difference among objects of great and confusing diversity, to which the purely inductive sciences cannot furnish many superior. Even so elementary an operation as that of abstracting from the particular configuration of the triangles or other figures, and the relative situation of the particular lines or points, in the diagram which aids the apprehension of a common geometrical demonstration, is a very useful, and far from being always an easy, exercise of the faculty of generalization so strangely imagined to have no place or part in the processes of mathematics.
In An Examination of Sir William Hamilton’s Philosophy (1878), 612-13.
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The aid which we feel impelled to give to the helpless is mainly an incidental result of the instinct of sympathy, which was originally acquired as part of the social instincts, but subsequently rendered, in the manner previously indicated, more tender and more widely diffused. Nor could we check our sympathy, even at the urging of hard reason, without deterioration in the noblest part of our nature.
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The aim of poetry is to give a high and voluptuous plausibility to what is palpably not true. I offer the Twenty-third Psalm as an example: ‘The Lord is my shepherd: I shall not want.’ It is immensely esteemed by the inmates of almshouses, and by gentlemen waiting to be hanged. I have to limit my own reading of it, avoiding soft and yielding moods, for I too, in my way, am a gentleman waiting to be hanged, as you are.
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The ancients devoted a lifetime to the study of arithmetic; it required days to extract a square root or to multiply two numbers together. Is there any harm in skipping all that, in letting the school boy learn multiplication sums, and in starting his more abstract reasoning at a more advanced point? Where would be the harm in letting the boy assume the truth of many propositions of the first four books of Euclid, letting him assume their truth partly by faith, partly by trial? Giving him the whole fifth book of Euclid by simple algebra? Letting him assume the sixth as axiomatic? Letting him, in fact, begin his severer studies where he is now in the habit of leaving off? We do much less orthodox things. Every here and there in one’s mathematical studies one makes exceedingly large assumptions, because the methodical study would be ridiculous even in the eyes of the most pedantic of teachers. I can imagine a whole year devoted to the philosophical study of many things that a student now takes in his stride without trouble. The present method of training the mind of a mathematical teacher causes it to strain at gnats and to swallow camels. Such gnats are most of the propositions of the sixth book of Euclid; propositions generally about incommensurables; the use of arithmetic in geometry; the parallelogram of forces, etc., decimals.
In Teaching of Mathematics (1904), 12.
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The astronomers said, ‘Give us matter and a little motion and we will construct the universe. It is not enough that we should have matter, we must also have a single impulse, one shove to launch the mass and generate the harmony of the centrifugal and centripetal forces.’ ... There is no end to the consequences of the act. That famous aboriginal push propagates itself through all the balls of the system, and through every atom of every ball.
From essay, 'Nature', collected in Ralph Waldo Emerson and J.E. Cabot (ed.), Emerson's Complete Works: Essays, Second Series (1884), Vol. 3, 176-177.
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The attitude of the intellectual community toward America is shaped not by the creative few but by the many who for one reason or another cannot transmute their dissatisfaction into a creative impulse, and cannot acquire a sense of uniqueness and of growth by developing and expressing their capacities and talents. There is nothing in contemporary America that can cure or alleviate their chronic frustration. They want power, lordship, and opportunities for imposing action. Even if we should banish poverty from the land, lift up the Negro to true equality, withdraw from Vietnam, and give half of the national income as foreign aid, they will still see America as an air-conditioned nightmare unfit for them to live in.
In 'Some Thoughts on the Present', The Temper of Our Time (1967), 107.
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The belief that mathematics, because it is abstract, because it is static and cold and gray, is detached from life, is a mistaken belief. Mathematics, even in its purest and most abstract estate, is not detached from life. It is just the ideal handling of the problems of life, as sculpture may idealize a human figure or as poetry or painting may idealize a figure or a scene. Mathematics is precisely the ideal handling of the problems of life, and the central ideas of the science, the great concepts about which its stately doctrines have been built up, are precisely the chief ideas with which life must always deal and which, as it tumbles and rolls about them through time and space, give it its interests and problems, and its order and rationality. That such is the case a few indications will suffice to show. The mathematical concepts of constant and variable are represented familiarly in life by the notions of fixedness and change. The concept of equation or that of an equational system, imposing restriction upon variability, is matched in life by the concept of natural and spiritual law, giving order to what were else chaotic change and providing partial freedom in lieu of none at all. What is known in mathematics under the name of limit is everywhere present in life in the guise of some ideal, some excellence high-dwelling among the rocks, an “ever flying perfect” as Emerson calls it, unto which we may approximate nearer and nearer, but which we can never quite attain, save in aspiration. The supreme concept of functionality finds its correlate in life in the all-pervasive sense of interdependence and mutual determination among the elements of the world. What is known in mathematics as transformation—that is, lawful transfer of attention, serving to match in orderly fashion the things of one system with those of another—is conceived in life as a process of transmutation by which, in the flux of the world, the content of the present has come out of the past and in its turn, in ceasing to be, gives birth to its successor, as the boy is father to the man and as things, in general, become what they are not. The mathematical concept of invariance and that of infinitude, especially the imposing doctrines that explain their meanings and bear their names—What are they but mathematicizations of that which has ever been the chief of life’s hopes and dreams, of that which has ever been the object of its deepest passion and of its dominant enterprise, I mean the finding of the worth that abides, the finding of permanence in the midst of change, and the discovery of a presence, in what has seemed to be a finite world, of being that is infinite? It is needless further to multiply examples of a correlation that is so abounding and complete as indeed to suggest a doubt whether it be juster to view mathematics as the abstract idealization of life than to regard life as the concrete realization of mathematics.
In 'The Humanization of Teaching of Mathematics', Science, New Series, 35, 645-46.
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The best education will not immunize a person against corruption by power. The best education does not automatically make people compassionate. We know this more clearly than any preceding generation. Our time has seen the best-educated society, situated in the heart of the most civilized part of the world, give birth to the most murderously vengeful government in history.
In Before the Sabbath (1979), 40-41.
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The custom of giving patients appointments weeks in advance, during which time their illness may become seriously aggravated, seems to me to fall short of the ideal doctor-patient relationship.
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The difference between the impossible and the possible lies in not giving up.
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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.
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The greatest joy in life is to accomplish. It is the getting, not the having. It is the giving, not the keeping.
From Cameron Prize Lecture (1928), delivered before the University of Edinburgh. As quoted and cited in Editorial Section, 'Sir Frederick Banting', Canadian Public Health Journal (May 1941), 32, No. 5, 266.
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The heart may give a lesson to the head,
And Learning wiser grow without his books.
In Hialmer Day Gould, New Practical Spelling (1905), 14.
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The highest principles for our aspirations and judgments are given to us in the Jewish-Christian religious tradition. It is a very high goal which, with our weak powers, we can reach only very inadequately, but which gives a sure foundation to our aspirations and valuations.
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The kind of lecture which I have been so kindly invited to give, and which now appears in book form, gives one a rare opportunity to allow the bees in one's bonnet to buzz even more noisily than usual.
From Assumption and Myth in Physical Theory (1967), v.
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The long-range trend toward federal regulation, which found its beginnings in the Interstate Commerce Act of 1887 and the Sherman Act of 1890, which was quickened by a large number of measures in the Progressive era, and which has found its consummation in our time, was thus at first the response of a predominantly individualistic public to the uncontrolled and starkly original collectivism of big business. In America the growth of the national state and its regulative power has never been accepted with complacency by any large part of the middle-class public, which has not relaxed its suspicion of authority, and which even now gives repeated evidence of its intense dislike of statism. In our time this growth has been possible only under the stress of great national emergencies, domestic or military, and even then only in the face of continuous resistance from a substantial part of the public. In the Progressive era it was possible only because of widespread and urgent fear of business consolidation and private business authority. Since it has become common in recent years for ideologists of the extreme right to portray the growth of statism as the result of a sinister conspiracy of collectivists inspired by foreign ideologies, it is perhaps worth emphasizing that the first important steps toward the modern organization of society were taken by arch-individualists—the tycoons of the Gilded Age—and that the primitive beginning of modern statism was largely the work of men who were trying to save what they could of the eminently native Yankee values of individualism and enterprise.
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The most important human endeavor is the striving for morality in our actions. Our inner balance and even our very existence depend on it. Only morality in our actions can give beauty and dignity to life.
In a letter to a minister in Brooklyn, N.Y. (20 Nov 1950), first paragraph, as quoted in Helen Dukas and Banesh Hoffmann (eds.), Albert Einstein: The Human Side (1979, 1981), 95.
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The negative cautions of science are never popular. If the experimentalist would not commit himself, the social philosopher, the preacher, and the pedagogue tried the harder to give a short-cut answer.
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The night spread out of the east in a great flood, quenching the red sunlight in a single minute. We wriggled by breathless degrees deep into our sleeping bags. Our sole thought was of comfort; we were not alive to the beauty or the grandeur of our position; we did not reflect on the splendor of our elevation. A regret I shall always have is that I did not muster up the energy to spend a minute or two stargazing. One peep I did make between the tent flaps into the night, and I remember dimly an appalling wealth of stars, not pale and remote as they appear when viewed through the moisture-laden air of lower levels, but brilliant points of electric blue fire standing out almost stereoscopically. It was a sight an astronomer would have given much to see, and here were we lying dully in our sleeping bags concerned only with the importance of keeping warm and comfortable.
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The number of mathematical students … would be much augmented if those who hold the highest rank in science would condescend to give more effective assistance in clearing the elements of the difficulties which they present.
In Study and Difficulties of Mathematics (1902), Preface.
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The prevailing trend in modern physics is thus much against any sort of view giving primacy to ... undivided wholeness of flowing movement. Indeed, those aspects of relativity theory and quantum theory which do suggest the need for such a view tend to be de-emphasized and in fact hardly noticed by most physicists, because they are regarded largely as features of the mathematical calculus and not as indications of the real nature of things.
Wholeness and the Implicate Order? (1981), 14.
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The realization that our small planet is only one of many worlds gives mankind the perspective it needs to realize sooner that our own world belongs to all of its creatures, that the Moon landing marks the end of our childhood as a race and the beginning of a newer and better civilization.
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The reasoning of mathematicians is founded on certain and infallible principles. Every word they use conveys a determinate idea, and by accurate definitions they excite the same ideas in the mind of the reader that were in the mind of the writer. When they have defined the terms they intend to make use of, they premise a few axioms, or self-evident principles, that every one must assent to as soon as proposed. They then take for granted certain postulates, that no one can deny them, such as, that a right line may be drawn from any given point to another, and from these plain, simple principles they have raised most astonishing speculations, and proved the extent of the human mind to be more spacious and capacious than any other science.
In Diary, Works (1850), Vol. 2, 21.
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The scientist is not a person who gives the right answers, he’s one who asks the right questions.
Translation of the original French, “Le savant n’est pas l’homme qui fournit les vraies réponses; c’est luis qui pose les vraies questions,” in Mythologiques, Vol. 1, Le Cru et le Cuit (1964), 15. As seen in various books, with no credit to a translator, for example, in What a Piece of Work is Man!: Camp's Unfamiliar Quotations (1989), 283. Also translated as “The scientific mind does not so much provide the right answers as ask the right questions.”
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The simplest schoolboy is now familiar with facts for which Archimedes would have sacrificed his life. What would we not give to make it possible for us to steal a look at a book that will serve primary schools in a hundred years?
In Souvenirs d’Enfance et de Jeunesse (1846), Preface, 13. From the original French, “Le simple écolier sait maintenant des vérités pour lesquelles Archimède eût sacrifié sa vie. Que ne donnerions-nous pas pour qu’il nous fût possible de jeter un coup d’œil furtif sur tel livre qui servira aux écoles primaires dans cent ans?”
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The so-called Marxian dialectic is simply an effort by third-rate men to give an air of profundity to balderdash. Christianity has gone the same way. There are some sound ideas in it, but its advocates always add a lot of preposterous nonsense. The result is theology.
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The spirit of science is not to prejudge, but to give any honest query a fair shake.
In How People Change (1975), 86.
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The sun gives spirit and life to the plants and the earth nourishes them with moisture.
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The world itself looks cleaner and so much more beautiful. Maybe we can make it that way - the way God intended it to be - by giving everybody that new perspective from out in space.
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There are few enough people with sufficient independence to see the weaknesses and follies of their contemporaries and remain themselves untouched by them. And these isolated few usually soon lose their zeal for putting things to rights when they have come face to face with human obduracy. Only to a tiny minority is it given to fascinate their generation by subtle humour and grace and to hold the mirror up to it by the impersonal agency of art. To-day I salute with sincere emotion the supreme master of this method, who has delighted–and educated–us all.
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There is a curious illusion today that nature is both wise and good. The awful truth is that nature is a bitch from the human point of view I care about the whooping crane a little. I would even give $10 to save the whooping crane. The whooping crane doesn’t give a damn about me.
From paper presented at Laramie College of Commerce and Industry, University of Wyoming, 'Energy and the Environment' (Jan 1976), 12, as quoted in Kenneth Ewart Boulding and Richard P. Beilock (ed.), Illustrating Economics: Beasts, Ballads and Aphorisms (1980, 2009), 153.
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There is no failure for the man who realizes his power, who never knows when he is beaten; there is no failure for the determined endeavor; the unconquerable will. There is no failure for the man who gets up every time he falls, who rebounds like a rubber ball, who persist when everyone else gives up, who pushes on when everyone else turns back.
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There is the immense sea of energy ... a multidimensional implicate order, ... the entire universe of matter as we generally observe it is to be treated as a comparatively small pattern of excitation. This excitation pattern is relatively autonomous and gives rise to approximately recurrent, stable separable projections into a three-dimensional explicate order of manifestation, which is more or less equivalent to that of space as we commonly experience it.
Wholeness and the Implicate Order? (1981), 192.
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There will always be a psychological problem in the peasant’s soul: no one is born a Communist. In the Soviet Union farmers look in the barn for “their” horses even after they have given them to the collective.
As quoted in Editorial, 'The High Cost of Marx on the Farm', Life (23 Nov 1962), 38.
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This topic brings me to that worst outcrop of the herd nature, the military system, which I abhor. That a man can take pleasure in marching in formation to the strains of a band is enough to make me despise him. He has only been given his big brain by mistake; a backbone was all he needed. This plague-spot of civilisation ought to be abolished with all possible speed. Heroism by order, senseless violence, and all the pestilent nonsense that goes by the name of patriotism–how I hate them! War seems to me a mean, contemptible thing: I would rather be hacked in pieces than take part in such an abominable business.
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To every man is given the key to the gates of heaven; the same key opens the gates of hell.
Buddhist
Quoted in Kim Lim (ed.), 1,001 Pearls of Spiritual Wisdom: Words to Enrich, Inspire, and Guide Your Life (2014), 238
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To fulfill a dream, to be allowed to sweat over lonely labor, to be given a chance to create, are the meat and potatoes of life. The money is the gravy.
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To make “beauty” the objects of the æsthetic emotion, we must give to the word an over-strict and unfamiliar definition.
In Art (1913), 14.
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To say that mind is a product or function of protoplasm, or of its molecular changes, is to use words to which we can attach no clear conception. You cannot have, in the whole, what does not exist in any of the parts; and those who argue thus should put forth a definite conception of matter, with clearly enunciated properties, and show, that the necessary result of a certain complex arrangement of the elements or atoms of that matter, will be the production of self-consciousness. There is no escape from this dilemma—either all matter is conscious, or consciousness is something distinct from matter, and in the latter case, its presence in material forms is a proof of the existence of conscious beings, outside of, and independent of, what we term matter. The foregoing considerations lead us to the very important conclusion, that matter is essentially force, and nothing but force; that matter, as popularly understood, does not exist, and is, in fact, philosophically inconceivable. When we touch matter, we only really experience sensations of resistance, implying repulsive force; and no other sense can give us such apparently solid proofs of the reality of matter, as touch does. This conclusion, if kept constantly present in the mind, will be found to have a most important bearing on almost every high scientific and philosophical problem, and especially on such as relate to our own conscious existence.
In 'The Limits of Natural Selection as Applied to Man', last chapter of Contributions to the Theory of Natural Selection (1870), 365-366.
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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 understand [our cosmological roots]...is to give voice to the silent stars. Stand under the stars and say what you like to them. Praise them or blame them, question them, pray to them, wish upon them. The universe will not answer. But it will have spoken.
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True science investigates and brings to human perception such truths and such knowledge as the people of a given time and society consider most important. Art transmits these truths from the region of perception to the region of emotion.
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Vision - It reaches beyond the thing that is, into the conception of what can be. Imagination gives you the picture. Vision gives you the impulse to make the picture your own.
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Vision, in my view, is the cause of the greatest benefit to us, inasmuch as none of the accounts now given concerning the Universe would ever have been given if men had not seen the stars or the sun or the heavens. But as it is, the vision of day and night and of months and circling years has created the art of number and has given us not only the notion of Time but also means of research into the nature of the Universe. From these we have procured Philosophy in all its range, than which no greater boon ever has come or will come, by divine bestowal, unto the race of mortals.
Plato
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We believe in the possibility of a theory which is able to give a complete description of reality, the laws of which establish relations between the things themselves and not merely between their probabilities ... God does not play dice.
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We have genuflected before the god of science only to find that it has given us the atomic bomb, producing fears and anxieties that science can never mitigate.
In Strength to Love (1963).
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We know very little, and yet it is astonishing that we know so much, and still more astonishing that so little knowledge can give us so much power.
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We seem to have a compulsion these days to bury time capsules in order to give those people living in the next century or so some idea of what we are like.
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What humanity owes to personalities like Buddha, Moses, and Jesus ranks for me higher than all the achievements of the enquiring and constructive mind. What these blessed men have given us we must guard and try to keep alive with all our strength if humanity is not to lose its dignity, the security of its existence, and its joy in living.
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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 I give form to in daylight is only one per cent of what I have seen in darkness.
As quoted, without citation, on the mcescher.com website.
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Whatever answers faith gives.. .such answers always give an infinite meaning to the finite existence of man; a meaning that is not destroyed by suffering, deprivation or death. This means only in faith can we find the meaning and possibility of life.
Quoted in Kim Lim (ed.), 1,001 Pearls of Spiritual Wisdom: Words to Enrich, Inspire, and Guide Your Life (2014), 19
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Whatever you can teach him from the nature of things themselves, do not teach him by words. Leave him to himself to see, hear, find, stumble, rise again, and be mistaken. Give no words when action or deed is possible. What he can do for himself, let him do.
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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.
In Proceedings of London Royal Society (1895), 58, 23-24.
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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.
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When we seek a textbook case for the proper operation of science, the correction of certain error offers far more promise than the establishment of probable truth. Confirmed hunches, of course, are more upbeat than discredited hypotheses. Since the worst traditions of ‘popular’ writing falsely equate instruction with sweetness and light, our promotional literature abounds with insipid tales in the heroic mode, although tough stories of disappointment and loss give deeper insight into a methodology that the celebrated philosopher Karl Popper once labeled as ‘conjecture and refutation.’
…...
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Whether or not it draws on new scientific research, technology is a branch of moral philosophy, not of Science. It aims at prudent goods for the comnonweal and to provide efficient means for these goods … philosopher, a technician should be able to criticize the programs given him (or her) to implement.
In 'Can Technology Be Humane?', New York Review of Books (20 Nov 1969),
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With the key of the secret he marches faster
From strength to strength, and for night brings day,
While classes or tribes too weak to master
The flowing conditions of life, give way.
From poem 'Rex' from one of his Poetry Notebooks, used as epigraph to 'Education', The Works of Ralph Waldo Emerson: Vol X: Lectures and Biographical Sketches (1883), 123.
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Would you have a man reason well, you must use him to it betimes; exercise his mind in observing the connection between ideas, and following them in train. Nothing does this better than mathematics, which therefore, I think should be taught to all who have the time and opportunity, not so much to make them mathematicians, as to make them reasonable creatures; for though we all call ourselves so, because we are born to it if we please, yet we may truly say that nature gives us but the seeds of it, and we are carried no farther than industry and application have carried us.
In Conduct of the Understanding, Sect. 6.
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You do what you can for as long as you can, and when you finally can’t, you do the next best thing. You back up but you don’t give up.
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You find FACTS as things given; I get them only by a long process of excavating (so to say), and so regard them as the very antipodes of things given.
In Letter, collected in Adolf Meyer and Edward Bradford Titchener, Defining American Psychology: The Correspondence Between Adolf Meyer and Edward Bradford Titchener (1990), 259.
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You must not give the world what it asks for, but what it needs.
…...
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[The famous attack of Sir William Hamilton on the tendency of mathematical studies] affords the most express evidence of those fatal lacunae in the circle of his knowledge, which unfitted him for taking a comprehensive or even an accurate view of the processes of the human mind in the establishment of truth. If there is any pre-requisite which all must see to be indispensable in one who attempts to give laws to the human intellect, it is a thorough acquaintance with the modes by which human intellect has proceeded, in the case where, by universal acknowledgment, grounded on subsequent direct verification, it has succeeded in ascertaining the greatest number of important and recondite truths. This requisite Sir W. Hamilton had not, in any tolerable degree, fulfilled. Even of pure mathematics he apparently knew little but the rudiments. Of mathematics as applied to investigating the laws of physical nature; of the mode in which the properties of number, extension, and figure, are made instrumental to the ascertainment of truths other than arithmetical or geometrical—it is too much to say that he had even a superficial knowledge: there is not a line in his works which shows him to have had any knowledge at all.
In Examination of Sir William Hamilton's Philosophy (1878), 607.
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[The National Academy of Sciences] would be unable to give a unanimous decision if asked whether the sun would rise tomorrow.
In David M. Rorvik, 'Ecology’s Angry Lobbyist: Dr. Paul Ehrlich Argues That the Chief Cause of Pollution Is Overpopulation', Look (21 Apr 1970). As quoted and cited in Columbia World of Quotations (1966).
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[The] complex pattern of the misallocation of credit for scientific work must quite evidently be described as “the Matthew effect,” for, as will be remembered, the Gospel According to St. Matthew puts it this way: For unto every one that hath shall be given, and he shall have abundance: but from him that hath not shall be taken away even that which he hath. Put in less stately language, the Matthew effect consists of the accruing of greater increments of recognition for particular scientific contributions to scientists of considerable repute and the withholding of such recognition from scientists who have not yet made their mark.
'The Matthew Effect in Science', Science (1968), 159, 58.
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“She can't do sums a bit!” the Queens said together, with great emphasis.
“Can you do sums?” Alice said, turning suddenly on the White Queen, for she didn't like being found fault with so much.
The Queen gasped and shut her eyes. “I can do Addition, if you give me time-but I can do Subtraction, under any circumstances!”
Through the Looking Glass and What Alice Found There (1871, 1897), 191.
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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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- 90 -
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- 80 -
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- 70 -
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- 60 -
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- 50 -
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- 40 -
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- 30 -
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- 20 -
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- 10 -
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