Theorems Quotes

We are on the verge: Today our program proved Fermat's next-to-last theorem.

Thus, be it understood, to demonstrate a theorem, it is neither necessary nor even advantageous to know what it means.

The Limbaugh Theorem was not about me giving me credit for something. It was simply sharing with you when the light went off.

I have found a very great number of exceedingly beautiful theorems.

There are three signs of senility. The first sign is that a man forgets his theorems. The second sign is that he forgets to zip up. The third sign is that he forgets to zip down.

The story does what no theorem can quite do. It may not be "like real life" in the superficial sense: but it sets before us an image of what reality may well be like at some more central region.

A proven theorem of game theory states that every game with complete information possesses a saddle point and therefore a solution.

All theorems have three names: a French name, a German name, and a Russian name, each nationality having claimed to discover it first. Once in a while there's an English name, too, but it's always Newton.

Young men should prove theorems, old men should write books.

If all sentient beings in the universe disappeared, there would remain a sense in which mathematical objects and theorems would continue to exist even though there would be no one around to write or talk about them. Huge prime numbers would continue to be prime, even if no one had proved them prime.

Math does come easily to me, but I was always much more interested in what theorems imply about the world than in proving them.

A theorem is a proposition which is a strict logical consequence of certain definitions and other propositions.

Less depends upon the choice of words than upon this, that their introduction shall be justified by pregnant theorems.

Phyllis explained to him, trying to give of her deeper self, 'Don't you find it so beautiful, math? Like an endless sheet of gold chains, each link locked into the one before it, the theorems and functions, one thing making the next inevitable. It's music, hanging there in the middle of space, meaning nothing but itself, and so moving...'

How many theorems in geometry which have seemed at first impracticable are in time successfully worked out!

Mathematics is not a deductive science - that's a cliché. When you try to prove a theorem, you don't just list the hypotheses, and then start to reason. What you do is trial and error, experimentation, guesswork.

Theorems often tell us complex truths about the simple things, but only rarely tell us simple truths about the complex ones. To believe otherwise is wishful thinking or "mathematics envy."

The fundamental laws of the universe which correspond to the two fundamental theorems of the mechanical theory of heat. 1. The energy of the universe is constant. 2. The entropy of the universe tends to a maximum.

The great poem and the deep theorem are new to every reader, and yet are his own experiences, because he himself recreates them.

The development of mathematics towards greater precision has led, as is well known, to the formalization of large tracts of it, so that one can prove any theorem using nothing but a few mechanical rules.

We decided that 'trivial' means 'proved'. So we joked with the mathematicians: We have a new theorem- that mathematicians can prove only trivial theorems, because every theorem that's proved is trivial.

Now, one of my beliefs, one of my theorems that I have evolved over the years is that when it comes to Democrats and the media they will always tell us who they fear. And all we have to do to learn that is look at who they're trying to damage and/or destroy.

One way of looking at Impossibility Theorem is that we proposed some criteria for what a good system should be: what is it you want from a voting system, and impose some conditions. And then ask: can you have a voting system that guarantees that?

Do people believe in human rights because such rights actually exist, like mathematical truths, sitting on a cosmic shelf next to the Pythagorean theorem just waiting to be discovered by Platonic reasoners? Or do people feel revulsion and sympathy when they read accounts of torture, and then invent a story about universal rights to help justify their feelings?

One geometry cannot be more true than another; it can only be more convenient.

Carnal embrace is sexual congress, which is the insertion of the male genital organ into the female genital organ for purposes of procreation and pleasure. Fermat’s last theorem, by contrast, asserts that when x, y and z are whole numbers each raised to power of n, the sum of the first two can never equal the third when n is greater than 2.

I have a basic theorem as to how I do my jokes. Growing up, I knew when to cross the line and when not to cross the line. It's the same with my comedy. I know what my audience will take and how much they won't take. I can't give you a formula for it. It's my own personal formula inside my head. Somebody else's might be different.

Gradually, at various points in our childhoods, we discover different forms of conviction. There's the rock-hard certainty of personal experience ("I put my finger in the fire and it hurt,"), which is probably the earliest kind we learn. Then there's the logically convincing, which we probably come to first through maths, in the context of Pythagoras's theorem or something similar, and which, if we first encounter it at exactly the right moment, bursts on our minds like sunrise with the whole universe playing a great chord of C Major.

The Mean Value Theorem is the midwife of calculus - not very important or glamorous by itself, but often helping to deliver other theorems that are of major significance.

A mathematician is a device for turning coffee into theorems.

The Open Source theorem says that if you give away source code, innovation will occur. Certainly, Unix was done this way... However, the corollary states that the innovation will occur elsewhere. No matter how many people you hire. So the only way to get close to the state of the art is to give the people who are going to be doing the innovative things the means to do it. That's why we had built-in source code with Unix. Open source is tapping the energy that's out there.

There was a seminar for advanced students in Zürich that I was teaching and von Neumann was in the class. I came to a certain theorem, and I said it is not proved and it may be difficult. Von Neumann didn't say anything but after five minutes he raised his hand. When I called on him he went to the blackboard and proceeded to write down the proof. After that I was afraid of von Neumann.

God has the Big Book, the beautiful proofs of mathematical theorems are listed here.

Our offense is like the pythagorean theorem: There is no answer!

The theory that gravitational attraction is inversely proportional to the square of the distance leads by remorseless logic to the conclusion that the path of a planet should be an ellipse .... It is this logical thinking that is the real meat of the physical sciences. The social scientist keeps the skin and throws away the meat.... His theorems no more follow from his postulates than the hunches of a horse player follow logically from the latest racing news. The result is guesswork clad in long flowing robes of gobbledygook.

An axiomatic system establishes a reverberating relationship between what a mathematician assumes (the axioms) and what he or she can derive (the theorems). In the best of circumstances, the relationship is clear enough so that the mathematician can submit his or her reasoning to an informal checklist, passing from step to step with the easy confidence the steps are small enough so that he cannot be embarrassed nor she tripped up.

The scientist has to take 95 per cent of his subject on trust. He has to because he can't possibly do all the experiments, therefore he has to take on trust the experiments all his colleagues and predecessors have done. Whereas a mathematician doesn't have to take anything on trust. Any theorem that's proved, he doesn't believe it, really, until he goes through the proof himself, and therefore he knows his whole subject from scratch. He's absolutely 100 per cent certain of it. And that gives him an extraordinary conviction of certainty, and an arrogance that scientists don't have.

Heaven is angered by my arrogance; my proof [of the four-color theorem] is also defective.

I compare arithmetic with a tree that unfolds upwards in a multitude of techniques and theorems while the root drives into the depths.

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.

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.

Paul Erdos has a theory that God has a book containing all the theorems of mathematics with their absolutely most beautiful proofs, and when he wants to express particular appreciation of a proof he exclaims, "This is from the book!"

The principle is so perfectly general that no particular application of it is possible.

He knew by heart every last minute crack on its surface. He had made maps of the ceiling and gone exploring on them; rivers, islands, and continents. He had made guessing games of it and discovered hidden objects; faces, birds, and fishes. He made mathematical calculations of it and rediscovered his childhood; theorems, angles, and triangles. There was practically nothing else he could do but look at it. He hated the sight of it.

The analysis of variance is not a mathematical theorem, but rather a convenient method of arranging the arithmetic.

In many cases a dull proof can be supplemented by a geometric analogue so simple and beautiful that the truth of a theorem is almost seen at a glance.

Papers should include more side remarks, open questions, and such. Very often, these are more interesting than the theorems actually proved. Alas, most people are afraid to admit that they don't know the answer to some question, and as a consequence they refrain from mentioning the question, even if it is a very natural one. What a pity! As for myself, I enjoy saying 'I do not know'.

There is a theorem that colloquially translates, You cannot comb the hair on a bowling ball. ... Clearly, none of these mathematicians had Afros, because to comb an Afro is to pick it straight away from the scalp. If bowling balls had Afros, then yes, they could be combed without violation of mathematical theorems.

Men propound mathematical theorems in besieged cities, conduct metaphysical arguments in condemned cells, make jokes on the scaffold, discuss a new poem while advancing to the walls of Quebec, and comb their hair at Thermopylae. This is not panache; it is our nature.

A dozen more questions occurred to me. Not to mention twenty-two possible solutions to each one, sixteen resulting hypotheses and counter-theorems, eight abstract speculations, a quadrilateral equation, two axioms, and a limerick. That's raw intelligence for you.