The Mathematician Quotes & Sayings

The mathematician, carried along on his flood of symbols, dealing apparently with purely formal truths, may still reach results of endless importance for our description of the physical universe. — Karl Pearson

The appearance of Professor Benjamin Peirce, whose long gray hair, straggling grizzled beard and unusually bright eyes sparkling under a soft felt hat, as he walked briskly but rather ungracefully across the college yard, fitted very well with the opinion current among us that we were looking upon a real live genius, who had a touch of the prophet in his make-up. — William Elwood Byerly

What is the difference between a mathematician and a philosopher?

A mathematician uses a pencil, paper, and a wastebasket.
The philosopher needs only the pencil and paper. — Matthew Rave

Archimedes will be remembered when Aeschylus is forgotten, because languages die and mathematical ideas do not. "Immortality" may be a silly word, but probably a mathematician has the best chance of whatever it may mean. — G.H. Hardy

It is the mark of an educated mind to expect that amount of exactness which the nature of the particular subject admits. It is equally unreasonable to accept merely probable conclusions from a mathematician and to demand strict demonstration from an orator. — Aristotle.

I am genuinely sorry for scientists of the younger generation who never knew Fisher personally. So long as you avoided a handful of subjects like inverse probability that would turn Fisher in the briefest possible moment from extreme urbanity into a boiling cauldron of wrath, you got by with little worse than a thick head from the port which he, like the Cambridge mathematician J. E. Littlewood, loved to drink in the evening. And on the credit side you gained a cherished memory of English spoken in a Shakespearean style and delivered in the manner of a Spanish grandee. — Fred Hoyle

Let me tell you how at one time the famous mathematician Euclid became a physician. It was during a vacation, which I spent in Prague as I most always did, when I was attacked by an illness never before experienced, which manifested itself in chilliness and painful weariness of the whole body. In order to ease my condition I took up Euclid's Elements and read for the first time his doctrine of ratio, which I found treated there in a manner entirely new to me. The ingenuity displayed in Euclid's presentation filled me with such vivid pleasure, that forthwith I felt as well as ever. — Bernard Bolzano

When it was first proposed to establish laboratories at Cambridge, Todhunter, the mathematician, objected that it was unnecessary for students to see experiments performed, since the results could be vouched for by their teachers, all of them of the highest character, and many of them clergymen of the Church of England. — Bertrand Russell

The master-economist must possess a rare combination of gifts ... He must be mathematician, historian, statesman, philosopher - in some degree. He must understand symbols and speak in words. He must contemplate the particular, in terms of the general, and touch abstract and concrete in the same flight of thought. He must study the present in the light of the past for the purposes of the future. No part of man's nature or his institutions must be entirely outside his regard. He must be purposeful and disinterested in a simultaneous mood, as aloof and incorruptible as an artist, yet sometimes as near to earth as a politician. — John Maynard Keynes

No mathematician of equal stature has risen from our generation ... Hilbert was singularly free from national and racial prejudices; in all public questions, be they political, social or spiritual, he stood forever on the side of freedom. — Hermann Weyl

I am exclusively occupied with the problem of gravitation and hope with the help of a local mathematician friend [Marcel Grossman] to overcome all the difficulties. One thing is certain, however, that never in life have I been quite so tormented. A great respect for mathematics has been instilled within me, the subtler aspects of which, in my stupidity, I regarded until now as pure luxury. — Albert Einstein

The mathematician uses an indirect definition of congruence, making use of the fact that the axiom of parallels together with an additional condition can replace the definition of congruence. — Hans Reichenbach

As time goes on, it becomes increasingly evident that the rules which the mathematician finds interesting are the same as those which Nature has chosen. — Paul Dirac

The computer was, to the best of my feelings about the subject, not thinking like a mathematician, and it was much more successful, because it was thinking not like a mathematician. — Kenneth Appel

The calculus of probabilities, when confined within just limits, ought to interest, in an equal degree, the mathematician, the experimentalist, and the statesman. — Francois Arago

Yes, sir. The mathematician Archimedes is related to have discovered the principle of displacement quite suddenly one morning, while in his bath.' 'Well, there you are. And I don't suppose he was such a devil of a chap. Compared with you, I mean.' 'A gifted man, I believe, sir. It has been a matter of general regret that he was subsequently killed by a common soldier.' 'Too bad. Still, all flesh is as grass, what? — P.G. Wodehouse

The practical man demands an appearance of reality at least. Always dealing in the concrete, he regards mathematical terms not as symbols or thought but as images of reality. A system acceptable to the mathematician because of its inner consistency may appear to the practical man to be full of contradictions because of the incomplete manner in which it represents reality. — Tobias Dantzig

All abilities are paid for with disabilities. perfect health may entail the heavy toll of bovine stupidity. insight into one area involves blind spots in another. i could not have done what i have done as a writer had i been a gifted mathematician or physicist.
honesty wrung out of him by pain, he cried out with a loud voice. — William S. Burroughs

Each electron wants the whole of three-dimensional space for its waves; so Schrodinger generously allows three dimensions for each of them. For two electrons he requires a six-dimensional sub-aether. He then successfully applies his method on the same lines as before. I think you will see now that Schrodinger has given us what seemed to be a comprehensible physical picture only to snatch it away again. His sub-aether does not exist in physical space; it is in a 'configuration space' imagined by the mathematician for the purpose of solving his problems, and imagined afresh with different numbers of dimensions according to the problem proposed. It was only an accident that in the earliest problems considered the configuration space had a close correspondence with physical space, suggesting some degree of objective reality of the waves. Schrodinger's wave mechanics is not a physical theory but a dodge - and a very good dodge too. — Arthur Stanley Eddington

Wormholes were first introduced to the public over a century ago in a book written by an Oxford mathematician. Perhaps realizing that adults might frown on the idea of multiply connected spaces, he wrote the book under a pseudonym and wrote it for children. His name was Charles Dodgson, his pseudonym was Lewis Carroll, and the book was Through The Looking Glass. — Michio Kaku

Mathematics is not a contemplative but a creative subject; no one can draw much consolation from it when he has lost the power or the desire to create; and that is apt to happen to a mathematician rather soon. It is a pity, but in that case he does not matter a great deal anyhow, and it would be silly to bother about him. — G.H. Hardy

The mathematician's patterns, like the painter's or the poet's must be beautiful; the ideas like the colours or the words, must fit together in a harmonious way. Beauty is the first test: there is no permanent place in the world for ugly mathematics. — G.H. Hardy

I have written a book called 'In the Wonderland of Numbers.' It's about a young girl, Neha, who is very poor in mathematics, but in a series of illusory experiences, she becomes a great mathematician. — Shakuntala Devi

The union of the mathematician with the poet, fervor with measure, passion with correctness, this surely is the ideal. — William James

It is indubitable that a 50-year-old mathematician knows the mathematics he learned at 20 or 30, but has only notions, often rather vague, of the mathematics of his epoch, i.e. the period of time when he is 50. — Jean Dieudonne

An Engineer rounds numbers based on the system behaviour and a Mathematician or a Schoolkid does it based on a pedagogical rule. — Ibrahim Ibrahim

The physicists say that I am a mathematician, and the mathematicians say that I am a physicist. I am a completely isolated man and though everybody knows me, there are very few people who really know me. — Albert Einstein

The simplicity of the law by which the celestial bodies move, and the relations of their masses and distances, permit analysis to follow their motions up to a certain point; and in order to determine the state of the system of these great bodies in past or future centuries, it suffices for the mathematician that their position and their velocity be given by observation for any moment in time. — Pierre-Simon Laplace

The world of being is unchangeable, rigid, exact, delightful to the mathematician, the logician, the builder of metaphysical systems, and all who love perfection more than life. The world of existence is fleeting, vague, without sharp boundaries, without any clear plan or arrangement, but it contains all thoughts and feelings, all the data of sense, and all physical objects, everything that can do either good or harm, everything that makes any difference to the value of life and the world. According to our temperaments, we shall prefer the contemplation of the one or of the other. — Bertrand Russell

What is this frog and mouse battle among the mathematicians? — Albert Einstein

Was it not the great philosopher and mathematician Leibnitz who said that the more knowledge advances the more it becomes possible to condense it into little books? — J. Arthur Thomson

To the average mathematician who merely wants to know his work is securely based, the most appealing choice is to avoid difficulties by means of Hilbert's program. Here one regards mathematics as a formal game and one is only concerned with the question of consistency ... The Realist position is probably the one which most mathematicians would prefer to take. It is not until he becomes aware of some of the difficulties in set theory that he would even begin to question it. If these difficulties particularly upset him, he will rush to the shelter of Formalism, while his normal position will be somewhere between the two, trying to enjoy the best of two worlds. — Paul Cohen

Archimedes was a mathematician," blurted Ethan from the back of the room. "And he was Greek. And he invented things." Ethan was the sort of student who was always keeping score
if he couldn't be the first to declare his knowledge of something, he would make certain you understood that he'd known it already. One day he would be declared the winner, and there would be a Smartest Boy trophy and a parade. — Adam Rex

To Goethe again we owe the profound saying: "the mathematician is only complete insofar as he feels within himself the beauty of the true. — Oswald Spengler

It is a pleasant surprise to him (the pure mathematician) and an added problem if he finds that the arts can use his calculations, or that the senses can verify them, much as if a composer found that sailors could heave better when singing his songs. — George Santayana

Marya pinned out her childhood like a butterfly. She considered it the way a mathematician considers an equation. — Catherynne M Valente

The numbers may be said to rule the whole world of quantity, and the four rules of arithmetic may be regarded as the complete equipment of the mathematician. — James C. Maxwell

I began to research the concept of dimensionality from the point of view of quality, and not just quantity, as a mathematician might do. Taking my clues from the theosophical use made of the Vedantic levels of reality, I identified the western notion of Energy (as someting which is effecatious by means of motion), with the idea of Time. The more comprehensive dimension 'eternity' I defined as a form of energy which is efficacious without motion. In this manner I began to establish the qualities of dimensions and open out the seemingly monolithic concept of energy. — Paul Laffoley

Isolated, so-called "pretty theorems" have even less value in the eyes of a modern mathematician than the discovery of a new "pretty flower" has to the scientific botanist, though the layman finds in these the chief charm of the respective sciences. — Hermann Hankel

A scientist worthy of his name, about all a mathematician, experiences in his work the same impression as an artist; his pleasure is as great and of the same nature. — Henri Poincare

I think you mother has Asperger's," Georgie had said to Neal.
"They didn't get Asperger's int he '50s."
"I'm just saying maybe she's on the the spectrum."
"She's just a math teacher. — Rainbow Rowell

A mathematician would hardly call a correspondence between the set of 64 triples of four units and a set of twenty other units, "universal", while such correspondence is, probably, the most fundamental general feature of life on Earth. — Mikhail Leonidovich Gromov

The mathematician lives long and lives young; the wings of his soul do not early drop off, nor do its pores become clogged with the earthy particles blown from the dusty highways of vulgar life. — James Joseph Sylvester

The calendar is intolerable to all wisdom, the horror of all astronomy, and a laughing stock from a mathematician's point of view. — Roger Bacon

I am not enough of a mathematician to be able to judge either the well-foundedness or the limits of relativity in physics. — Pierre Teilhard De Chardin

In various ways, methods of approaching the mathematician's ideal were sought, and the resulting suggestions were the source of much that was mistaken in metaphysics and theory of knowledge. — Bertrand Russell

This Excellent Mathematician having given us, in the Transactions of February last, an account of the cause, which induced him to think upon Reflecting Telescopes, instead of Refracting ones, hath thereupon presented the curious world with an Essay of what may be performed by such Telescopes; by which it is found, that Telescopical Tubes may be considerably shortened without prejudice to their magnifiying effect. On his invention of the catadioptrical telescope, as he communicated to the Royal Society. — Isaac Newton

Professor Weyl,* the mathematician, gave an excellent definition of symmetry, which is that a thing is symmetrical if there is something that you can do to it so that after you have finished doing it it looks the same as it did before. That is the sense in which we say that the laws of physics are symmetrical; that there are things we can do to the physical laws, or to our way of representing the physical laws, which make no difference, and leave everything unchanged in its effects. It is this aspect of physical laws that is going to concern us in this lecture. — Richard Feynman

I forget if it was the Mathematician of Alexandria who said that geometry is beauty laid bare or the Father of Relativity who made the claim for physics," Darger said. "She is, in either case, ravishing. — Michael Swanwick

For it is the mark of an educated man to look for precision in each class of things just so far as the nature of the subject admits; it is evidently equally foolish to accept probable reasoning from a mathematician and to demand from a rhetorician scientific proofs. — Aristotle.

It is the invaluable merit of the great Basle mathematician Leonard Euler, to have freed the analytical calculus from all geometric bounds, and thus to have established analysis as an independent science, which from his time on has maintained an unchallenged leadership in the field of mathematics. — Thomas Reid

The spectacular thing about Johnny [von Neumann] was not his power as a mathematician, which was great, or his insight and his clarity, but his rapidity; he was very, very fast. And like the modern computer, which no longer bothers to retrieve the logarithm of 11 from its memory (but, instead, computes the logarithm of 11 each time it is needed), Johnny didn't bother to remember things. He computed them. You asked him a question, and if he didn't know the answer, he thought for three seconds and would produce and answer. — Paul R. Halmos

A philosopher/mathematician named Bertrand Russell who lived and died in the same century as Gass once wrote: "Language serves not only to express thought but to make possible thoughts which could not exist without it." Here is the essence of mankind's creative genius: not the edifices of civilization nor the bang-flash weapons which can end it, but the words which fertilize new concepts like spermatazoa attacking an ovum. — Dan Simmons

But Einstein was not the best mathematician around, and others, undeterred by neither the difficulty of the equations nor the war that was ravaging Europe (this was 1916), were able to find solutions. Some of the most important solutions ever found - those that describe the gravitational fields of stars and black holes - were written down by a German officer named Karl Schwarzchild as he lay dying in a field hospital of a skin disease he had picked up in the trenches. — Lee Smolin

It is a melancholy experience for a professional mathematician to find himself writing about mathematics. The function of a mathematician is to do something, to prove new theorems, to add to mathematics, and not to talk about what he or other mathematicians have done. Statesmen despise publicists, painters despise art-critics, and physiologists, physicists, or mathematicians have usually similar feelings: there is no scorn more profound, or on the whole more justifiable, than that of the men who make for the men who explain. Exposition, criticism, appreciation, is work for second-rate minds. — G.H. Hardy

An old French mathematician said: A mathematical theory is not to be considered complete until you have made it so clear that you can explain it to the first man whom you meet on the street. This clearness and ease of comprehension, here insisted on for a mathematical theory, I should still more demand for a mathematical problem if it is to be perfect; for what is clear and easily comprehended attracts, the complicated repels us. — David Hilbert

However great a man's fear of life, suicide remains the courageous act, the clear-headed act of a mathematician. The suicide has judged by the laws of chance - so many odds against one that to live will be more miserable than to die. His sense of mathematics is greater than his sense of survival. But think how a sense of survival must clamor to be heard at the last moment, what excuses it must present of a totally unscientific nature. — Graham Greene

The desire to explore thus marks out the mathematician. This is one of the forces making for the growth of mathematics. The mathematician enjoys what he already knows; he is eager for more knowledge. — W.W. Sawyer

Logic is the hygiene the mathematician practices to keep his ideas healthy and strong. — Hermann Weyl

To Plato, God was a mathematician. To Kepler, too, and to Biehl and Fredhoj. I do not believe it was a coincidence that their main subjects were biology and mathematics. A purpose behind them, the purpose that steered both them and the school, had caused them to align their own fates as closely as possible with God. — Peter Hoeg

Two of the most famous Baghdadi scholars, the philosopher Al-Kindi and the mathematician Al-Khawarizmi, were certainly the most influential in transmitting Hindu numerals to the Muslim world. Both wrote books on the subject during al-Ma'mun's reign, and it was their work that was translated into Latin and transmitted to the West, thus introducing Europeans to the decimal system, which was known in the Middle Ages only as Arabic numerals. But it would be many centuries before it was widely accepted in Europe. One reason for this was sociological: decimal numbers were considered for a long time as symbols of the evil Muslim foe. — Jim Al-Khalili

On completing my degree, I started a Ph.D. in statistics, although I knew very little about the topic. My supervisor was Professor Harry Pitt, who was an excellent pure mathematician and probabilist. — Clive Granger

The traditional mathematician recognizes and appreciates mathematical elegance when he sees it. I propose to go one step further, and to consider elegance an essential ingredient of mathematics: if it is clumsy, it is not mathematics. — Edsger Dijkstra

What is a look of absolute fear? Popescu asked. The doctor belched a few times, shifted in his chair, and answered that it was a kind of look of mercy, but empty, as if all that were left of mercy, after a mysterious voyage, was the skin, as if mercy were a skin of water, say, in the hands of a Tatar horseman who gallops away over the steppe and dwindles untile he vanishes, and then the horseman returns, or the ghost of the horseman returns, or his shadow, or the idea of him, and he has the skin, empty of water now, because he drank it all during his trip, or he and his horse drank it, and the skin is empty now, it's a normal skin, an empty skin, because after all the abnormal thing is a skin swollen with water, but this skin swollen with water, this hideous skin swollen with water doesn't arouse fear, doesn't awaken it, much less isolate it, but the empty skin does, and that was what he saw in the mathematician's face, absolute fear. — Roberto Bolano

One may be an excellent pianist, mathematician, gardener, or scientist and still be cranky and jealous, but in the West one can be considered a great moralist and yet not live by one's moral principles. We must simply recall here the Buddhist requirement that a person and his or her teachings be compatible. Ethics is not like any ordinary science. It must arise from the deepest understanding of human qualities, and such understanding comes only when one undertakes the journey of discovery personally. An ethic that is built exclusively on intellectual ideas and that is not buttressed at every point by virtue, genuine wisdom, and compassion has no solid foundation. — Matthieu Ricard

The whole thing that makes a mathematician's life worthwhile is that he gets the grudging admiration of three or four colleagues. — Donald Knuth

I heard about this man who fell into a pit, and while he was down there several people came by and offered their opinions. The Pharisee said, "You deserve to be in the pit." The Catholic said, "You need to suffer while you're in the pit." The Baptist said, "If you'd been saved, you wouldn't have fallen into the pit." The charismatic said, "Just confess I'm not in the pit." The mathematician said, "Let me calculate how you fell into the pit." The IRS agent said, "Have you paid taxes on that pit?" The optimist said, "Things could be worse." The pessimist said, "Things will get worse. — Joel Osteen

My favourite fellow of the Royal Society is the Reverend Thomas Bayes, an obscure 18th-century Kent clergyman and a brilliant mathematician who devised a complex equation known as the Bayes theorem, which can be used to work out probability distributions. It had no practical application in his lifetime, but today, thanks to computers, is routinely used in the modelling of climate change, astrophysics and stock-market analysis. — Bill Bryson

Had you or I been born at the Bay of Soldania, possibly our Thoughts, and Notions, had not exceeded those brutish ones of the Hotentots that inhabit there: And had the Virginia King Apochancana, been educated in England, he had, perhaps been as knowing a Divine, and as good a Mathematician as any in it. The difference between him, and a more improved English-man, lying barely in this, That the exercise of his Facilities was bounded within the Ways, Modes, and Notions of his own Country, and never directed to any other or farther Enquiries. — John Locke

Most writers on the subject seem to agree that the typical working mathematician is a Platonist on weekdays and a formalist on Sundays. — Philip J. Davis

By analyzing data from Greenwich Observatory in the period 1836-1953, John A. Eddy [Harvard-Smithsonian Center for Astrophysics and High Altitude Observatory in Boulder] and Aram A. Boornazian [mathematician with S. Ross and Co. in Boston] have found evidence that the sun has been contracting about 0.1% per century during that time, corresponding to a shrinkage rate of about 5 feet per hour. And digging deep into historical records, Eddy has found 400-year-old eclipse observations that are consistent with such a shrinkage. — Jonathan Sarfati

Some of the greatest mathematical minds of all ages, from Pythagoras and Euclid in ancient Greece, through the medieval Italian mathematician Leonardo of Pisa and the Renaissance astronomer Johannes Kepler, to present-day scientific figures such as Oxford physicist Roger Penrose, have spent endless hours over this simple ratio and its properties. But the fascination with the Golden Ratio is not confined just to mathematicians. Biologists, artists, musicians, historians, architects, psychologists, and even mystics have pondered and debated the basis of its ubiquity and appeal. In fact, it is probably fair to say that the Golden Ratio has inspired thinkers of all disciplines like no other number in the history of mathematics. — Mario Livio

... That little narrative is an example of the mathematician's art: asking simple and elegant questions about our imaginary creations, and crafting satisfying and beautiful explanations. There is really nothing else quite like this realm of pure idea; it's fascinating, it's fun, and it's free! — Paul Lockhart

Rigour is to the mathematician what morality is to men. — Andre Weil

A hundred years after his death, a statue of Lavoisier was erected in Paris and much admired until someone pointed out that it looked nothing like him. Under questioning the sculptor admitted that he had used the head of the mathematician and philosopher the Marquis de Condorcet - apparently he had a spare - in the hope that no one would notice or, having noticed, would care. In the second regard he was correct. The statue of Lavoisier-cum- Condorcet was allowed to remain in place for another half century until the Second World War when, one morning, it was taken away and melted down for scrap. — Bill Bryson

The Canadian-Australian mathematician Norman Wildberger has posted an essay arguing that real numbers are a joke. — Max Tegmark

A mathematician of the first rank, Laplace quickly revealed himself as only a mediocre administrator; from his first work we saw that we had been deceived. Laplace saw no question from its true point of view; he sought subtleties everywhere; had only doubtful ideas, and finally carried the spirit of the infinitely small into administration. — Napoleon Bonaparte

A single inattention may lose a chess game, whereas a single successful approach to a problem, among many which have been relegated to the wastebasket, will make a mathematician's reputation. — Norbert Wiener

Reductio ad absurdum, which Euclid loved so much, is one of a mathematician's finest weapons. It is a far finer gambit than any chess play: a chess player may offer the sacrifice of a pawn or even a piece, but a mathematician offers the game. — G.H. Hardy

This cognitive illusion was first noted in 1968 by the mathematician William Feller in his classic textbook on probability: "To the untrained eye, randomness appears as regularity or tendency to cluster."33 Here are a few examples of the cluster illusion. The — Steven Pinker

[John Wheeler] rejuvenated general relativity; he made it an experimental subject and took it away from the mathematicians — Freeman Dyson

The mathematician of to-day admits that he can neither square the circle, duplicate the cube or trisect the angle. May not our mechanicians, in like manner, be ultimately forced to admit that aerial flight is one of that great class of problems with which men can never cope ... I do not claim that this is a necessary conclusion from any past experience. But I do think that success must await progress of a different kind from that of invention. — Simon Newcomb

Statistically, it would seem improbable that any mathematician or scientist, at the age of 66, would be able through continued research efforts, to add much to his or her previous achievements. However I am still making the effort and it is conceivable that with the gap period of about 25 years of partially deluded thinking providing a sort of vacation my situation may be atypical. Thus I have hopes of being able to achieve something of value through my current studies or with any new ideas that come in the future. — John Forbes Nash

Always preoccupied with his profound researches, the great Newton showed in the ordinary-affairs of life an absence of mind which has become proverbial. It is related that one day, wishing to find the number of seconds necessary for the boiling of an egg, he perceived, after waiting a minute, that he held the egg in his hand, and had placed his seconds watch (an instrument of great value on account of its mathematical precision) to boil!
This absence of mind reminds one of the mathematician Ampere, who one day, as he was going to his course of lectures, noticed a little pebble on the road; he picked it up, and examined with admiration the mottled veins. All at once the lecture which he ought to be attending to returned to his mind; he drew out his watch; perceiving that the hour approached, he hastily doubled his pace, carefully placed the pebble in his pocket, and threw his watch over the parapet of the Pont des Arts. — Camille Flammarion

Mathematical knowledge is not-as all Cambridge men are surely aware-the result of any special gift. It is merely the development of those conceptions of form and number which every human being possesses; and any person of average intellect can make himself a fair mathematician if he will only pay continuous attention; in plain English, think enough about the subject. — Charles Kingsley

She hesitated slightly. "I've seen what was called telekinesis with dice - but I'm no mathematician and I could not testify that what I saw was telekinesis." "Hell's bells, you wouldn't testify that the sun had risen if the day was cloudy. — Robert A. Heinlein

The life of a mathematician is dominated by an insatiable curiosity, a desire bordering on passion to solve the problems he is studying. — Jean Dieudonne

But unlike most physicists, Marcus eventually learned Lorenz's lesson, that a deterministic system can produce much more than just periodic behavior. He knew to look for wild disorder, and he knew that islands of structure could appear within the disorder. So he brought to the problem of the Great Red Spot an understanding that a complex system can give rise to turbulence and coherence at the same time. He could work within an emerging discipline that was creating its own tradition of using the computer as an experimental tool. And he was willing to think of himself as a new kind of scientist: not primarily an astronomer, not a fluid dynamicist, not an applied mathematician, but a specialist in chaos. — James Gleick

Think of a "discovery" as an act that moves the arrival of information from a later point in time to an earlier time. The discovery's value does not equal the value of the information discovered but rather the value of having the information available earlier than it otherwise would have been. A scientist or a mathematician may show great skill by being the first to find a solution that has eluded many others; yet if the problem would soon have been solved anyway, then the work probably has not much benefited the world [unless having a solution even slightly sooner is immensely valuable or enables further important and urgent work]. — Nick Bostrom

In 1862, the Scottish mathematician James Clerk Maxwell developed a set of fundamental equations that unified electricity and magnetism. On his deathbed, he coughed up a strange sort of confession, declaring that "something within him" discovered the famous equations, not he. He admitted he had no idea how ideas actually came to him - they simply came to him. William Blake related a similar experience, reporting of his long narrative poem Milton: "I have written this poem from immediate dictation twelve or sometimes twenty lines at a time without premeditation and even against my will." Johann Wolfgang von Goethe claimed to have written his novella The Sorrows of Young Werther with practically no conscious input, as though he were holding a pen that moved on its own. — David Eagleman

Perhaps ... some day the precision of the data will be brought so far that the mathematician will be able to calculate at his desk the outcome of any chemical combination, in the same way, so to speak, as he calculates the motions of celestial bodies. — Antoine Lavoisier

A considreable portion of my high school trigonometry course was devoted to the solution of oblique triangles ... I have still not had an excuse for using my talents for solving oblique triangles. If a professional mathematician never uses these dull techniques in a highly varied career, why must all high school students devote several weeks to the subject? — John G. Kemeny

The mathematician requires tact and good taste at every step of his work, and he has to learn to trust to his own instinct to distinguish between what is really worthy of his efforts and what is not. — James Whitbread Lee Glaisher

A mathematician tells you that the wall of warped space prevents the Moon from flying out of its orbit yet can't tell you why an astronaut can go back and forth across that same space. — Bill Gaede

One of the chief duties of the mathematician in acting as an advisor ... is to discourage ... from expecting too much from mathematics. — Norbert Wiener

Alas he had forgotten, he said, that she was a novelist as well as a mathematician. What a disappointment for the Parisian that he was neither. Merely a scholar, and a man. — Alice Munro

I do not remember having felt, as a boy, any passion for mathematics, and such notions as I may have had of the career of a mathematician were far from noble. I thought of mathematics in terms of examinations and scholarships: I wanted to beat other boys, and this seemed to be the way in which I could do so most decisively. — G.H. Hardy

Mathematicians also make terrible salesmen. Physicists can discover the same thing as a mathematician and say 'We've discovered a great new law of nature. Give us a billion dollars.' And if it doesn't change the world, then they say, 'There's an even deeper thing. Give us another billion dollars.' — Gian-Carlo Rota

Carl Friedrich Gauss, often rated the greatest mathematician of all time, played the market. On a salary of 1,000 thalers a year, Euler left an estate of 170,587 thalers in cash and securities. Nothing is known of Gauss's investment methods. — William Poundstone

I was, from early on, interested in science. And my parents were very obliging about that. My father used to take me to the museum of natural history, and I knew much more scientific stuff early on. From the time I was 11 or 12, I wanted to be a mathematician. — Whitfield Diffie