Top 312 Mathematicians Quotes & Sayings - Page 4

Thus the good christian should beware of mathematicians and all those who make false prophecies, however much they may in fact speak the truth; lest, being in league with the devil, they may deceive errant souls into making common cause.

In the broad light of day mathematicians check their equations and their proofs, leaving no stone unturned in their search for rigour. But, at night, under the full moon, they dream, they float among the stars and wonder at the miracle of the heavens. They are inspired. Without dreams there is no art, no mathematics, no life.

After preliminary work by a number of other distinguished mathematicians and economists, game theory as a systematic theory started with von Neumann and Morgenstern's book, 'Theory of Games and Economic Behavior,' published in 1944.

True education seeks to make men and women not only good mathematicians, proficient linguists, profound scientists, or brilliant literary lights, but also honest men and women with virtue, temperance, and brotherly love.

Have you noticed that the astronomers and mathematicians are much the most cheerful people of the lot? I suppose that perpetually contemplating things on so vast a scale makes them feel either that it doesn't matter a hoot anyway, or that anything so large and elaborate must have some sense in it somewhere.

Two centuries ago Carl Friedrich Gauss, one of the greatest mathematicians and a founder of number theory, described his brainchild as "the queen of mathematics." Queens are regal, but they are also largely decorative, and this nuance was not lost on Gauss.

By keenly confronting the enigmas that surround us, and by considering and analyzing the observations that I had made, I ended up in the domain of mathematics. Although I am absolutely without training in the exact sciences, I often seem to have more in common with mathematicians than with my fellow artists.

Oh these mathematicians make me tired! When you ask them to work out a sum they take a piece of paper, cover it with rows of A's, B's, and X's and Y's ... scatter a mess of flyspecks over them, and then give you an answer that's all wrong!

[I was advised] to read Jordan's 'Cours d'analyse'; and I shall never forget the astonishment with which I read that remarkable work, the first inspiration for so many mathematicians of my generation, and learnt for the first time as I read it what mathematics really meant.

Nobody defines it as something women shouldn't be doing. In a way, there are more mathematicians, more doctors, more scientists in India than there are in this country. We even had a woman head of state, and that's something the United States has yet to catch up with.

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.

The work of mathematicians on 'pure' problems has often yielded ideas that have waited to be rediscovered by physicists. The work of Euclid, Apollonius and Archimedes on ellipses would be used centuries later by Kepler for his theory of planetary motion.

Physicists are more like avant-garde composers, willing to bend traditional rules... Mathematicians are more like classical composers.

Greek mathematics is the real thing. The Greeks first spoke a language which modern mathematicians can understand... So Greek mathematics is 'permanent', more permanent even than Greek literature.

I never got a pass mark in math... Just imagine - mathematicians now use my prints to illustrate their books. Funny me consorting with all these learned folks, as though I were their long lost brother. I guess they are unaware of the fact that I am ignorant about the whole thing.

...nature seems very conversant with the rules of pure mathematics, as our own mathematicians have formulated them in their studies, out of their own inner consciousness and without drawing to any appreciable extent on their experience of the outer world.

[Adams] supposed that, except musicians, everyone thought Beethoven a bore, as every one except mathematicians thought mathematics a bore.

Should I not be proud, when for twenty years I have had to admit to myself that the great Newton and all the mathematicians and noble calculators along with him were involved in a decisive error with respect to the doctrine of color, and that I among millions was the only one who knew what was right in this great subject of nature?

Mathematicians enjoy thinking about the simplest possible things, and the simplest possible things are imaginary.

The product of mathematics is clarity and understanding. Not theorems, by themselves. ... In short, mathematics only exists in a living community of mathematicians that spreads understanding and breathes life into ideas both old and new.

The existence of these patterns [fractals] challenges us to study forms that Euclid leaves aside as being formless, to investigate the morphology of the amorphous. Mathematicians have disdained this challenge, however, and have increasingly chosen to flee from nature by devising theories unrelated to anything we can see or feel.

I worked in a number of high schools in New York, and I wound up at Stuyvesant High School, which is known nationally for producing brilliant scientists and mathematicians, but I had writing classes. I thought I was teaching. They thought I was teaching, but I was learning.

The truth has never been of any real value to any human being - it is a symbol for mathematicians and philosophers to pursue. In human relations kindness and lies are worth a thousand truths.

A lot of boys in my poker circle are mathematicians who play on probability. I don't have that kind of brain, so I rely on instinct. But I recently found out that poker and cards in general go way back in my family gene pool.

Among mathematicians, even in those days, the reputation of being a good Glass Bead Game player meant a great deal; it was equivalent to being a very good mathematician.

(Space programs are) a force operating on educational pipelines that stimulate the formation of scientists, technologists, engineers and mathematicians... They're the ones that make tomorrow come. The foundations of economies... issue forth from investments we make in science and technology.

People tend to think that mathematicians always work in sterile conditions, sitting around and staring at the screen of a computer, or at a ceiling, in a pristine office. But in fact, some of the best ideas come when you least expect them, possibly through annoying industrial noise.

It may be appropriate to quote a statement of Poincare, who said (partly in jest no doubt) that there must be something mysterious about the normal law since mathematicians think it is a law of nature whereas physicists are convinced that it is a mathematical theorem.

A dead tree, cut into planks and read from one end to the other, is a kind of line graph, with dates down one side and height along the other, as if trees, like mathematicians, had found a way of turning time into form.

Mathematicians are always playing tricks on each other. They're always pulling jokes on each other.

Mathematicians do not study objects, but relations among objects; they are indifferent to the replacement of objects by others as long the relations don't change. Matter is not important, only form interests them.

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.

Another advantage of a mathematical statement is that it is so definite that it might be definitely wrong; and if it is found to be wrong, there is a plenteous choice of amendments ready in the mathematicians' stock of formulae. Some verbal statements have not this merit; they are so vague that they could hardly be wrong, and are correspondingly useless.

The Internet gives you access to a lot of material, and it's fun to sit and read. I go to something like Wikipedia and look at different topics... I find the subject fascinating. I like to read about concepts and mathematicians.

Land surveyors can spend as much time reading legislation, bylaws, and engineering documents as we spend in front of an instrument in the field or calculating coordinates for a subdivision. We are mathematicians, historians, project managers, advocates, engineers, and even chainsaw operators!

Physicists and mathematicians regularly invade other fields but other fields do not invade theirs so we can see which fields are hardest for very talented people.

Our next-door neighbour taught physics at Hampton University. Our church abounded with mathematicians. Supersonics experts held leadership positions in my mother's sorority, and electrical engineers sat on the board of my parents' college alumni associations.

If there should chance to be any mathematicians who, ignorant in mathematics yet pretending to skill in that science, should dare, upon the authority of some passage of Scripture wrested to their purpose, to condemn and censure my hypothesis, I value them not, and scorn their inconsiderate judgement. De Revolutionibus Coelestibus

Elegance? It may seem odd to non-scientists, but there is an aesthetic in software as there is in every other area of intellectual endeavour. Truly great programmers are like great poets or great mathematicians - they can achieve in a few lines what lesser mortals can only approach in three volumes

A Noah's Ark of mathematicians, their lives, loves, hard times, and madnesses, Loving and Hating Mathematics shows our community with all its warts as well as its triumphs. I especially liked the chapter on much-hated school mathematics, 'Almost All Children Left Behind.'

The bottom line for mathematicians is that the architecture has to be right. In all the mathematics that I did, the essential point was to find the right architecture. It's like building a bridge. Once the main lines of the structure are right, then the details miraculously fit. The problem is the overall design.

Mathematicians stand on each others' shoulders and computer scientists stand on each others' toes.

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.

When I first began studying prices, it wasn't a topic that mathematicians were working on. Purely by accident, I saw a set of data on price changes presented in a lecture and realized they behaved similarly to the geometric models I was already studying.

Today, you have neuroscientists working on a genetic, behavioural or cognitive level, and then you have informaticians, chemists and mathematicians. They all have their own understanding of how the brain functions and is structured. How do you get them all around the same table?

The only reason psychology students don't have to do more and harder mathematics than physics students is because the mathematicians haven't yet discovered ways of dealing with problems as hard as those in psychology.

In the company of friends, writers can discuss their books, economists the state of the economy, lawyers their latest cases, and businessmen their latest acquisitions, but mathematicians cannot discuss their mathematics at all. And the more profound their work, the less understandable it is.

"Do you know," the Devil confided, "not even the best mathematicians on other planets - all far ahead of yours - have solved it? Why, there is a chap on Saturn - he looks something like a mushroom on stilts - who solves partial differential equations mentally; and even he's given up."

A typical mathematician does not actively try to be useful. Individual mathematicians are motivated primarily by a subtle mixture of ambition and intellectual curiosity, and not by a wish to benefit society, nevertheless, mathematics as a whole does benefit society.

Oh yes, children often commit murders. And quite clever ones, too. Some murderers, particularly the distinguished ones who are going to make great names for themselves, start amazingly early.... Like mathematicians and musicians. Poets develop later.

Poincaré [was] the last man to take practically all mathematics, pure and applied, as his province. ... Few mathematicians have had the breadth of philosophic vision that Poincaré had, and none in his superior in the gift of clear exposition.

Mathematicians have a certain type of mind, and climbers have a certain type of mind, because climbing poses these incredibly interesting problems for them.

Mathematicians do not deal in objects, but in relations between objects; thus, they are free to replace some objects by others so long as the relations remain unchanged. Content to them is irrelevant: they are interested in form only.

So in the end it wasn't Gödel, it wasn't Turing, and it wasn't my results that are making mathematics go into an experimental mathematics direction, in a quasi-empirical direction. The reason why mathematicians are changing their working habits is the computer. I think that this is an excellent joke!

The discovery in 1846 of the planet Neptune was a dramatic and spectacular achievement of mathematical astronomy. The very existence of this new member of the solar system, and its exact location, were demonstrated with pencil and paper; there was left to observers only the routine task of pointing their telescopes at the spot the mathematicians had marked.

Games are among the most interesting creations of the human mind, and the analysis of their structure is full of adventure and surprises. Unfortunately there is never a lack of mathematicians for the job of transforming delectable ingredients into a dish that tastes like a damp blanket.

In fact, the answer to the question "What is mathematics?" has changed several times during the course of history... It was only in the last twenty years or so that a definition of mathematics emerged on which most mathematicians agree: mathematics is the science of patterns.

But as no two (theoreticians) agree on this (skin friction) or any other subject, some not agreeing today with what they wrote a year ago, I think we might put down all their results, add them together, and then divide by the number of mathematicians, and thus find the average coefficient of error. (1908)

Instruction tables will have to be made up by mathematicians with computing experience and perhaps a certain puzzle-solving ability. There need be no real danger of it ever becoming a drudge, for any processes that are quite mechanical may be turned over to the machine itself.

I am persuaded that this method [for calculating the volume of a sphere] will be of no little service to mathematics. For I foresee that once it is understood and established, it will be used to discover other theorems which have not yet occurred to me, by other mathematicians, now living or yet unborn.