Mathematician Quotes

Many errors, of a truth, consist merely in the application of the wrong names of things. For if a man says that the lines which are drawn from the centre of the circle to the circumference are not equal, he understands by the circle, at all events for the time, something else than mathematicians understand by it. ~ Baruch Spinoza

Indeed every mathematician knows that a proof has not been "understood" if one has done nothing more than verify step by step the correctness of the deductions of which it is composed and has not tried to gain a clear insight into the ideas which have led to the construction of this particular chain of deductions in preference to every other one. - Nicolas Bourbaki ~ Anonymous

Good mathematicians see analogies. Great mathematicians see analogies between analogies. ~ Stefan Banach

Mathematicians tend to prefer a worst-case analysis, a kind of paranoia that is especially understandable if you live in Israel! ~ Noga Alon

I'm not gay, but I don't think you have to be gay to have a gay hero. Growing up, Alan Turing was certainly mine. I'm also not the greatest mathematician of my generation. We have lots of biographical differences, but nonetheless, I always identified with him so much. ~ Graham Moore

Let no one read my principles who is not a mathematician," he famously declared (less famous is the fact that the principles he was referring to were his theories of how the aortic pulmonary valve worked). Ironically, he himself was a poor mathematician, often making simple mistakes. In one of his notes he counted up his growing library: "25 small books, 2 larger books, 16 still larger, 6 bound in vellum, 1 book with green chamois cover." This reckoning (with its charmingly haphazard system of classification) adds up to fifty, but Leonardo reached a different sum: "Total: 48," he confidently declared. ~ Ross King

On the question of whether mathematics was discovered or invented, Pythagoras and the Pythagoreans had no doubt-mathematics was real, immutable, omnipresent, and more sublime than anything that could conceivably emerge from the feeble human mind. The Pythagoreans literally embedded the universe into mathematics. In fact, to the Pythagoreans, God was not a mathematician-mathematics was God!

The importance of the Pythagorean philosophy lies not only in its actual, intrinsic value. By setting the stage, and to some extent the agenda, for the next generation of philosophers-Plato in particular-the Pythagoreans established a commanding position in Western thought. ~ Mario Livio

I think we need more math majors who don't become mathematicians. More math major doctors, more math major high school teachers, more math major CEOs, more math major senators. But we won't get there unless we dump the stereotype that math is only worthwhile for kid geniuses. ~ Jordan Ellenberg

For a long time the objects that mathematicians dealt with were mostly ill-defined; one believed one knew them, but one represented them with the senses and imagination; but one had but a rough picture and not a precise idea on which reasoning could take hold. ~ Henri Poincare

She is her odd self. The kiln has been fired. She is a person persnickity about keeping her house clean, but not above spitting on her desk to rub out a coffee stain. She will never be an athlete, or a mathematician, or a skinny person, or someone whose heart isn't snagged by the sight of fireflies on a summer night and the lilting cadence of a few good lines of poetry. ~ Elizabeth Berg

Turing was a quite brilliant mathematician, most famous for his work on breaking the German Enigma codes. It is no exaggeration to say that, without his outstanding contribution, the history of the Second World War could have been very different. ~ Gordon Brown

Exposition, criticism, appreciation, is work for second-rate minds. I ~ G.H. Hardy

If things are nice there is probably a good reason why they are nice: and if you do not know at least one reason for this good fortune, then you still have work to do. ~ Richard Askey

Dess shook her head. "Before he walked off, Rex said for you to wait. He said it's totally important you don't touch Angie until he comes back. and he said that if you were a pain about it, I get to hit you with that." She pointed to where the darkling had flung Flabbergasted Supernumerary Mathematician, its tip blackened by ichor and fire. "So, go ahead. ~ Scott Westerfeld

Mathematicians - for what they do - are really poorly rewarded. And it's a very competitive field, almost as bad as being a concert pianist. ~ Gian-Carlo Rota

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

Life is like mathematics,
with full of problems,
More you solve problems,
more you become expert,
Once you become expert,
you enjoy solving problems,
Once you enjoy solving problem,
you demand more problem of all type.
No matter wherever one goes,
there will be problems (opportunity)
One who loves to solve problems
is real mathematician. ~ V.B. Jadhav

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

We are concerned, not with the development of just one capacity, such as that of a mathematician, or a scientist, or a musician, but with the total development of the student as a human
being. ~ Jiddu Krishnamurti

In music, musicians must be able to read musical notes and have developed the skill to follow the music from their studies. This skill allows them to read new musical notes and be capable of hearing most or all of the sounds (melodies, harmonies, etc.) in their head without having to play the music piece. By analogy, in Mathematics, we believe a scientist, engineer or mathematician must be able to read and understand mathematical codes (e.g., Maple, Mathematica) in their head without having to execute the problem. ~ Inna K. Shingareva

The power of attaching an interest to the most trifling or painful pursuits, in which our whole attention and faculties are engaged, is one of the greatest happinesses of our nature. The common soldier mounts the breach with joy; the miser deliberately starves himself to death; the mathematician sets about extracting the cube-root with a feeling of enthusiasm; and the lawyer sheds tears of admiration over "Coke upon Littleton." It is the same through life. He who is not in some measure a pedant, though he maybe wise, cannot be a very happy man. ~ William Hazlitt

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

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

Mathematics is the cheapest science. Unlike physics or chemistry, it does not require any expensive equipment. All one needs for mathematics is a pencil and paper. ~ George Polya

Some mathematician has said that enjoyment lies in the search for truth, not in the finding it. ~ Leo Tolstoy

As for my father, I never knew whether he believed God was a mathematician but he certainly believed God could count and that only by picking up God's rhythms were we able to regain power and beauty. Unlike many Presbyterians, he often used the word beautiful. ~ Norman Maclean

Most programming languages are decidedly inferior to mathematical notation and are little used as tools of thought in ways that would be considered significant by, say, an applied mathematician. ~ Kenneth E. Iverson

A mathematician is always asking, "What assumptions are you making? And are they justified? ~ Jordan Ellenberg

Anatomists today would be hard put to identify the brain of a visual artist, a writer or a mathematician - but they would recognize the brain of a professional musician without moment's hesitation. ~ Oliver Sacks

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

It seems to me that the poet has only to perceive that which others do not perceive, to look deeper than others look. And the mathematician must do the same thing. ~ Sofia Kovalevskaya

A result once generally accepted by mathematicians is seldom retracted, and then only with great pangs.
The Nature of Mathematics ~ Max Black

The human race may well become extinct before the end of the century. Speaking as a mathematician, I should say the odds are about three to one against survival. ~ Bertrand Russell

Every mathematician worthy of the name has experienced ... the state of lucid exaltation in which one thought succeeds another as if miraculously ... this feeling may last for hours at a time, even for days. Once you have experienced it, you are eager to repeat it but unable to do it at will, unless perhaps by dogged work ... ~ Andre Weil

"I am not much of a mathematician," said the cigarette, "but I can add to a man's nervous troubles, I can subtract from his physical energy, I can multiply his aches and pains, I can divide his mental powers, I take interest from his work, and discount his chances for success." ~ David Starr Jordan

I think you can get better in mathematics on a school level, but when you're talking about being a mathematician, I think that's definitely a gift of genes or whatever, you know? Whatever your pool is. ~ John Hurt

It is well known that geometry presupposes not only the concept of space but also the first fundamental notions for constructions in space as given in advance. It only gives nominal definitions for them, while the essential means of determining them appear in the form of axioms. The relationship of these presumptions is left in the dark; one sees neither whether and in how far their connection is necessary, nor a priori whether it is possible. From Euclid to Legendre, to name the most renowned of modern writers on geometry, this darkness has been lifted neither by the mathematicians nor the philosophers who have laboured upon it. ~ Bernhard Riemann

Ohm (a distinguished mathematician, be it noted) brought into order a host of puzzling facts connecting electromotive force and electric current in conductors, which all previous electricians had only succeeded in loosely binding together qualitatively under some rather vague statements. Even as late as 20 years ago, "quantity" and "tension" were much used by men who did not fully appreciate Ohm's law. ~ Oliver Heaviside

If a mathematician wishes to disparage the work of one of his colleagues, say, A, the most effective method he finds for doing this is to ask where the results can be applied. The hard pressed man, with his back against the wall, finally unearths the researches of another mathematician B as the locus of the application of his own results. If next B is plagued with a similar question, he will refer to another mathematician C. After a few steps of this kind we find ourselves referred back to the researches of A, and in this way the chain closes. ~ Alfred Tarski

In the early part of the ninth century, Muhammad ibn Musa al-Khwarizmi, a mathematician working in Baghdad, wrote a seminal textbook in which he highlighted the usefulness of restoring a quantity being subtracted (like 2, above) by adding it to the other side of an equation. He called this process al-jabr (Arabic for "restoring"), which later morphed into "algebra." Then, long after his death, he hit the etymological jackpot again. His own name, al-Khwarizmi, lives on today in the word "algorithm. ~ Steven H. Strogatz

Naturally, the significant results that legitimize a mathematical theory take time to derive, and then even more time to be fully accepted, and of course throughout this time the Insanity-v.-Genius question remains undecided, probably even for the mathematician himself, so that he's developing his theory and cooking his proofs under conditions of enormous personal stress and doubt, and sometimes isn't even vindicated in his own lifetime, etc. ~ David Foster Wallace

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

No mathematician in the world would bother making these senseless distinctions: 2 1/2 is a "mixed number " while 5/2 is an "improper fraction." They're EQUAL for crying out loud. They are the exact same numbers and have the exact same properties. Who uses such words outside of fourth grade? ~ Paul Lockhart

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

I had the idea that it would be wonderful to be a physicist or a mathematician maybe 500 years ago around the time of Newton when there were really fundamental things just lying around to be discovered. ~ David Chalmers

Where there is matter, there is geometry. ~ Johannes Kepler

These estimates may well be enhanced by one from F. Klein (1849-1925), the leading German mathematician of the last quarter of the nineteenth century. 'Mathematics in general is fundamentally the science of self-evident things.' ... If mathematics is indeed the science of self-evident things, mathematicians are a phenomenally stupid lot to waste the tons of good paper they do in proving the fact. Mathematics is abstract and it is hard, and any assertion that it is simple is true only in a severely technical sense - that of the modern postulational method which, as a matter of fact, was exploited by Euclid. The assumptions from which mathematics starts are simple; the rest is not. ~ Eric Temple Bell

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

We have no knowledge, that is, no general principles drawn from the contemplation of particular facts, but what has been built up by pleasure, and exists in us by pleasure alone. The Man of Science, the Chemist and Mathematician, whatever difficulties and disgusts they may have had to struggle with, know and feel this. However painful may be the objects with which the Anatomist's knowledge is connected, he feels that his knowledge is pleasure; and where he has no pleasure he has no knowledge. ~ William Wordsworth

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

I have created a new universe from nothing. ~ Janos Bolyai

A mathematician is a device for turning coffee into theorems ~ Paul Erdos

The hardest thing in the world to understand is the income tax. ~ Albert Einstein

Our existence here, he says, is a case of "not we the accidental but we the expected." Mathematician Manfred Eigen wrote in 1971, "The evolution of life, if it is based on a derivable physical principle, must be considered an inevitable process. ~ Kevin Kelly

Mathematics has been called the science of the infinite. Indeed, the mathematician invents finite constructions by which questions are decided that by their very nature refer to the infinite. This is his glory. ~ Hermann Weyl

Who am I? Who am I?"
"You're Jude St. Francis. You are my oldest, dearest friend. You're the son of Harold Stein and Julia Altman. You're the friend of Malcolm Irvine, of Jean-Baptiste Marion, of Richard Goldfarb, of Andy Contractor, of Lucien Voigt, of Citizen van Straaten, of Rhodes Arrowsmith, of Elijah Kozma, of Phaedra de los Santos, of the Henry Youngs. You're a New Yorker. You live in SoHo. You volunteer for an arts organization; you volunteer for a food kitchen. You're a swimmer. You're a baker. You're a cook. You're a reader. You have a beautiful voice, though you never sing anymore. You're an excellent pianist. You're an art collector. You write me lovely messages when I'm away. You're patient. You're generous. You're the best listener I know. You're the smartest person I know, in every way. You're the bravest person I know, in every way. You're a lawyer. You're the chair of the litigation department at Rosen Pritchard and Klein. You love your job; you work hard at it. You're a mathematician. You're a logician. You've tried to teach me, again and again. You were treated horribly. You came out on the other end. You were always you."

"And who are you?"
"I'm Willem Ragnarsson. And I will never let you go. ~ Hanya Yanagihara

And when I go around and talk to schools, what I tell the kids are, first of all, you have to accept each other's differences. Some of you are going to be a crappy football player, some of you are going to be a great mathematician. Whatever it is, accept each other's differences and help prop each other up. ~ Vince Flynn

A mathematician will recognise Cauchy, Gauss, Jacobi or Helmholtz after reading a few pages, just as musicians recognise, from the first few bars, Mozart, Beethoven or Schubert. ~ Ludwig Boltzmann

A well-known mathematician once told me that the great thing about liking both math and sex was that he could do either one while thinking about the other. ~ Steven Landsburg

Geniuses of certain kinds - mathematicians, chess players, computer programmers - seem, if not mad, at least lacking in the social skills most easily identified with sanity. ~ James Gleick

Mathematicians grow very old; it is a healthy profession. The reason you live long is that you have pleasant thoughts. Math and physics are very pleasant things to do. ~ Dirk Jan Struik

Well, of
course one must have concentration. Courage. Self-control. That goes
without saying. But more important than these, one must have ... I
don't know how to say it. One must be both a mathematician and a
poet. As though poetry were a science; or mathematics an art. One
must have an affection for proportion to play Go at all well.Ah ... what Go is to philosophers
and warriors, chess is to accountants and merchants. ~ Trevanian

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

I still can't quite grasp what you are telling me. I find it impossible to believe that there would be such unreasoning feeling against harmless people."
Amaryl said bitterly, "That's because you've never had any occasion to interest yourself in such things. It can all pass right under your nose and you wouldn't smell a thing because it doesn't affect you."
Dors said, "Mr. Amaryl, Dr. Seldon is a mathematician like you and his head can sometimes be in the clouds. You must understand that. I am a historian, however. I know that it isn't unusual to have one group of people look down upon another group. There are peculiar and almost ritualistic hatreds that have no rational justification and that can have their serious historical influence. It's too bad."
Saying something is 'too bad' is easy. You say you disapprove, which makes you a nice person, and then you can go about your own business and not be interested anymore. It's a lot worse than 'too bad.' It's against everything decent and natural. We're all of us the same, yellow-hairs and black-hairs, tall and short, Easterners, Westerners, Southerners, and Outworlders. We're all of us, you and I and even the Emperor, descended from the people of Earth, aren't we? ~ Isaac Asimov

A totally new kind of education is needed in the world. The person who is born to be a poet is proving himself stupid in mathematics and the person who could have been a great mathematician is just cramming history and feeling lost. Everything is topsy-turvy because education is not according to your nature: it does not pay any respect to the individual. It forces everybody into a certain pattern. ~ Osho

In mathematics, if a pattern occurs, we can go on to ask, Why does it occur? What does it signify? And we can find answers to these questions. In fact, for every pattern that appears, a mathematician feels he ought to know why it appears. ~ W.W. Sawyer

This is a question too difficult for a mathematician. It should be asked of a philosopher(when asked about completing his income tax form) ~ Albert Einstein

Mathematics compares the most diverse phenomena and discovers the secret analogies that unite them. ~ Joseph Fourier

Even in the realm of pure mathematics, the mathematician may use any set of symbols he desires within any given region of space-time; he may even go so far as to maintain that any one set of symbols fits the scheme as well as any other, but to erect this method into a philosophy and confuse independence of any one special meaning with independence of all meaning is unjustified and unwarranted. ~ Fulton J. Sheen

It would be better for the true physics if there were no mathematicians on earth. ~ Daniel Bernoulli

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

We academic scientists move within a certain sphere, we can go on being useless up to a point, in the confidence that sooner or later some use will be found for our studies. The mathematician, of course, prides himself on being totally useless, but usually turns out to be the most useful of the lot. He finds the solution but he is not interested in what the problem is: sooner or later, someone will find the problem to which his solution is the answer. ~ John Desmond Bernal

In his book Opticks, Newton made it clear that he did not believe that the laws of nature by themselves were sufficient to explain the universe's existence-God was the creator and sustainer of all the atoms that make up the cosmic matter: "For it became him [God] who created them [the atoms] to set them in order. And if he did so, it's unphilosophical to seek for any other Origin of the World, or to pretend that it might arise out of a Chaos by the mere Laws of Nature." In other words, to Newton, God was a mathematician (among other things), not just as a figure of speech, but almost literally-the Creator God brought into existence a physical world that was governed by mathematical laws. ~ Mario Livio

No matter how correct a mathematical theorem may appear to be, one ought never to be satisfied that there was not something imperfect about it until it also gives the impression of being beautiful. ~ George Boole

Oh God, she could see it now - the police constable filling out a report: Mathematician drowned due to miscalculation. ~ Nina Rowan

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

You are an astronomer as well as a mathematician?"
He turned to face her, finally, half his face cast into shadowy light from the manor beyond. "You are a horticulturalist as well as an anatomist?"
She smiled. "We are surprising, aren't we?"
His lips twitched. "We are. ~ Sarah MacLean

It was this situation that led mathematician Chris Hauert and his colleagues to consider another possibility in an important evolutionary model published in Science in 2002. In Axelrod's study and in most previous theoretical models, individuals were forced to interact with each other. But what if they could choose not to interact? Rather than attempting to cooperate and risking being taken advantage of, a person could fend for herself. In other words, she could sever her connections to others in the network. Hauert called the people who adopt this strategy "loners."

Using some beautiful mathematics, Hauert and his colleagues showed that in a world full of loners it is easy for cooperation to evolve because there are no people to take advantage of the cooperators that appear. The loners fend for themselves, and the cooperators form networks with other cooperators. Soon, the cooperators take over the population because they always do better together than the loners. But once the world is full of cooperators, it is very easy for free riders to evolve and enjoy the fruits of cooperation without contributing (like parasites). As the free riders become the dominant type in the population, there is no one left for them to take advantage of; then, the loners once again take over -- because they want nothing to do, as it were, with those bastards. In short, cooperating can emerge because we can do more together than we can apart. But because of the free-rider problem, coop ~ Nicholas A. Christakis

She trained the girls in her Girl Scout troop to believe that they could be anything, and she went to lengths to prevent negative stereotypes of their race from shaping their internal views of themselves and other Negroes. It was difficult enough to rise above the silent reminders of Colored signs on the bathroom doors and cafeteria tables. But to be confronted with the prejudice so blatantly, there in that temple to intellectual excellence and rational thought, by something so mundane, so ridiculous, so universal as having to go to the bathroom...In the moment when the white women laughed at her, Mary had been demoted from professional mathematician to a second-class human being, reminded that she was a black girl whose piss wasn't good enough for the white pot. ~ Margot Lee Shetterly

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 astronomer, a physicist, and a mathematician (it is said) were holidaying in Scotland. Glancing from a train window, they observed a black sheep in the middle of a field. "How interesting," observed the astronomer, "all Scottish sheep are black!" To which the physicist responded, "No, no! Some Scottish sheep are black!" The mathematician gazed heavenward in supplication, and then intoned, "In Scotland there exists at least one field, containing at least one sheep, at least one side of which is black. ~ Simon Singh

Daniel Bernoulli: "Then this distinguished scholar informed me that the celebrated mathematician, Cramer, had developed a theory on the same subject several years before I produced my paper. Indeed I have found his theory so similar to mine that it seems miraculous that we independently reached sch close agreement on this sort of subject. ~ Persi Diaconis

Okay. So, Koturovic studied the structure of the brain and how much bio-electricity it put out and what frequencies that electricity was on. He moved to London and in 1877 he attended a lecture given by a mathematician named William Clifford who was one of the first people to propose the idea of other dimensions. He noticed - " "Wait," said Tim. "Other dimensions?" She nodded. "I looked him up. Clifford did a lot of work with concepts like curved space and there being more to the world than just the standard three dimensions. At least a fourth, mathematically speaking, and probably a fifth, sixth, seventh, and so on." Tim raised an eyebrow but said nothing else. ~ Peter Clines

A mathematician who is not also something of a poet will never be a complete mathematician. ~ Karl Weierstrass

Now, as Mandelbrot points out, ... Nature has played a joke on the mathematicians. The 19th-century mathematicians may not have been lacking in imagination, but Nature was not. The same pathological structures that the mathematicians invented to break loose from 19th-century naturalism turn out to be inherent in familiar objects all around us. ~ Freeman Dyson

I count Maxwell and Einstein, Eddington and Dirac, among "real" mathematicians. The great modern achievements of applied mathematics have been in relativity and quantum mechanics, and these subjects are at present at any rate, almost as "useless" as the theory of numbers. ~ G.H. Hardy

The brilliant British mathematician, eccentric, and computer pioneer Alan Turing came up with the following test: A computer can be said to be intelligent if it can (on average) fool a human into mistaking it for another human. The converse should be true. A human can be said to be unintelligent if we can replicate his speech by a computer, which we know is unintelligent, and fool a human into believing that it was written by a human. Can one produce a piece of work that can be largely mistaken for Derrida entirely randomly? ~ Nassim Nicholas Taleb

In an old joke, a physicist and a mathematician are asked what they would do if they needed to iron their pants, but although they are in possession of an iron, the electric outlet is in the adjacent room. Both answer that they would take the iron to the second room and plug it in there. Now they are asked what they would do if they were already in the room in which the outlet is located. They physicist answers that he would plug the iron into the outlet directly. The mathematician, on the other hand, says that he would take the iron to the room without the outlet, since that problem has already been solved. ~ Mario Livio

Every relationship of man to the infinite is religion, namely of a man in the full abundance of his humanity. Whenever a mathematician calculates infinity, that, to be sure, is not religion. Infinity conceived in this abundance is the Godhead. ~ Karl Wilhelm Friedrich Schlegel

Mathematics is a more powerful instrument of knowledge than any other that has been bequeathed to us by human agency. ~ Rene Descartes

A horse that can count to ten is a remarkable horse - not a remarkable mathematician. ~ Warren Buffett

Twentieth-century British mathematician G.H. Hardy also believed that the human function is to "discover or observe" mathematics rather than to invent it. In other words, the abstract landscape of mathematics was there, waiting for mathematical explorers to reveal it. ~ Mario Livio

Mathematical theories have sometimes been used to predict phenomena that were not confirmed until years later. For example, Maxwell's equations, named after physicist James Clerk Maxwell, predicted radio waves. Einstein's field equations suggested that gravity would bend light and that the universe is expanding. Physicist Paul Dirac once noted that the abstract mathematics we study now gives us a glimpse of physics in the future. In fact, his equations predicted the existence of antimatter, which was subsequently discovered. Similarly, mathematician Nikolai Lobachevsky said that "there is no branch of mathematics, however abstract, which may not someday be applied to the phenomena of the real world. ~ Clifford A. Pickover

Female physicists, astronomers and mathematicians are up against more than 2,000 years of convention that has long portrayed these fields as inherently male. ~ Margaret Wertheim

Abel has left mathematicians enough to keep them busy for five hundred years. ~ Charles Hermite

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

Nature and Nature's laws lay hid in night:
God said, Let Newton be! and all was light. ~ Alexander Pope

Q7. The total output of all the mathematicians who have ever lived, together with the output of all the human mathematicians of the next (say) thousand years is finite and could be contained in the memory banks of an appropriate computer. Surely this particular computer could, therefore, simulate this output and thus behave (externally) in the same way as a human mathematician-whatever the Godel argument might appear to tell us to the contrary?

While this is presumably true, it ignores the essential issue, which is how we (or computers) know which mathematical statements are true and which are false. (In any case, the mere storage of mathematical statements is something that could be achieved by a system much less sophisticated than a general purpose computer, e.g. photographically.) The way that the computer is being employed in Q7 totally ignores the critical issue of truth judgment. One could equally well envisage computers that contain nothing but lists of totally false mathematical 'theorems', or lists containing random jumbles of truths and falsehoods. How are we to tell which computer to trust? The arguments that I am trying to make here do not say that an effective simulation of the output of conscious human activity (here mathematics) is impossible, since purely by chance the computer might 'happen' to get it right-even without any understanding whatsoever. But the odds against this are absurdly enormous, and the issues that are being addressed here, namel ~ Roger Penrose

James Edward Oliver might have been one of the great mathematicians of his time had he not been absolutely wanting in the power of continuous work. ~ Simon Newcomb

The mathematical life of a mathematician is short. Work rarely improves after the age of twenty-five or thirty. If little has been accomplished by then, little will ever be accomplished. ~ Alfred Adler