Theorems are not to mathematics what successful courses are to a meal.

Theorems are fun especially when you are the prover, but then the pleasure fades. What keeps us going are the unsolved problems.

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.

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.

In 1975, ... [speaking with Shiing Shen Chern], I told him I had finally learned ... the beauty of fiber-bundle theory and the profound Chern-Weil theorem. I said I found it amazing that gauge fields are exactly connections on fiber bundles, which the mathematicians developed without reference to the physical world. I added, "this is both thrilling and puzzling, since you mathematicians dreamed up these concepts out of nowhere." He immediately protested: "No, no. These concepts were not dreamed up. They were natural and real."

For what is important when we give children a theorem to use is not that they should memorize it. What matters most is that by growing up with a few very powerful theorems one comes to appreciate how certain ideas can be used as tools to think with over a lifetime. One learns to enjoy and to respect the power of powerful ideas. One learns that the most powerful idea of all is the idea of powerful ideas.

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.

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.

Murphy's Law, that brash proletarian restatement of Godel's Theorem.

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.

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.

To insure the adoration of a theorem for any length of time, faith is not enough, a police force is needed as well.

One cannot really argue with a mathematical theorem.

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

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

There is no answer to the Pythagorean theorem. Well, there is an answer, but by the time you figure it out, I got 40 points, 10 rebounds and then we're planning for the parade.

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.

The Three Theorems of Psychohistorical Quantitivity: The population under scrutiny is oblivious to the existence of the science of Psychohistory. The time periods dealt with are in the region of 3 generations. The population must be in the billions (±75 billions) for a statistical probability to have a psychohistorical validity.

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.

The paraphrase of Gödel's Theorem says that for any record player, there are records which it cannot play because they will cause its indirect self-destruction.

The missing piece in his stomach hurt so much-and eventually he stopped thinking about the Theorem and wondered only how something that isn't there can hurt you.

You can learn to find unknowns in equations, draw equidistant lines and demonstrate theorems, but in real life there's nothing to position, calculate, or guess.

Imagine a life-form whose brainpower is to ours as ours is to a chimpanzee’s. To such a species, our highest mental achievements would be trivial. Their toddlers, instead of learning their ABCs on Sesame Street, would learn multivariable calculus on Boolean Boulevard. Our most complex theorems, our deepest philosophies, the cherished works of our most creative artists, would be projects their schoolkids bring home for Mom and Dad to display on the refrigerator door.

And I believe that the Binomial Theorem and a Bach Fugue are, in the long run, more important than all the battles of history.

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

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