Theorem And Proof Quotes & Sayings

I carried this problem around in my head basically the whole time. I would wake up with it first thing in the morning, I would be thinking about it all day, and I would be thinking about it when I went to sleep. Without distraction I would have the same thing going round and round in my mind.
(Recalling the degree of focus and determination that eventually yielded the proof of Fermat's Last Theorem.) — Andrew John Wiles

The proof of Fermat's Last Theorem underscores how stable mathematics is through the centuries - how mathematics is one of humanity's long continuous conversations with itself. — Barry Mazur

Been stuck in airports, terrorized; sent to meetings, hypnotized; overexposed, commercialized. Handle me with care. — George Harrison

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. — Christopher Zeeman

Here are the basic principles of Constructivism as practiced by Kronecker and codified by J.H. Poincare and L.E.J. Brouwer and other major figures in Intuitionism: (1) Any mathematical statement or theorem that is more complicated or abstract than plain old integer-style arithmetic must be explicitly derived (i.e. 'constructed') from integer arithmetic via a finite number of purely deductive steps. (2) The only valid proofs in math are constructive ones, with the adjective here meaning that the proof provides a method for finding (i.e., 'constructing') whatever mathematical entities it's concerned with. — David Foster Wallace

There's nothing cure or funny or lovable about being cheap. It's a total turn-off. — Douglas Coupland

Why not do as much as you can, and learn as much as you can about each process? — Cam Gigandet

There are no proofs. There are only agreements — Paul W. Silver

Science in its everyday practice is much closer to art than to philosophy. When I look at Godel's proof of his undecidability theorem, I do not see a philosophical argument. The proof is a soaring piece of architecture, as unique and as lovely as Chartres Cathedral. Godel took Hilbert's formalized axioms of mathematics as his building blocks and built out of them a lofty structure of ideas into which he could finally insert his undecidable arithmetical statement as the keystone of the arch. The proof is a great work of art. It is a construction, not a reduction. It destroyed Hilbert's dream of reducing all mathematics to a few equations, and replaced it with a greater dream of mathematics as an endlessly growing realm of ideas. Godel proved that in mathematics the whole is always greater than the sum of the parts. Every formalization of mathematics raises questions that reach beyond the limits of the formalism into unexplored territory. — Freeman Dyson

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

It is an unfortunate fact that proofs can be very misleading. Proofs exist to establish once and for all, according to very high standards, that certain mathematical statements are irrefutable facts. What is unfortunate about this is that a proof, in spite of the fact that it is perfectly correct, does not in any way have to be enlightening. Thus, mathematicians, and mathematics students, are faced with two problems: the generation of proofs, and the generation of internal enlightenment. To understand a theorem requires enlightenment. If one has enlightenment, one knows in one's soul why a particular theorem must be true. — Herbert S. Gaskill

She wanted to tell him so much, on the tarmac, the day he left. The world is run by brutal men and the surest proof is their armies. If they ask you to stand still, you should dance. If they ask you to burn the flag, wave it. If they ask you to murder, re-create. Theorem, anti-theorem, corollary, anti-corollary. Underline it twice. It's all there in the numbers. Listen to your mother. Listen to me, Joshua. Look me in the eyes. I have something to tell you. — Colum McCann

In 1931, Kurt Godel proved in his famous second incompleteness theorem that there could be no finitary proof of the consistency of arithmetic. He had killed Hilbert's program with a single stroke.

So should you be worried that all of mathematics might collapse tomorrow afternoon? For what it's worth, I'm not. I do believe in infinite sets, and I find the proofs of consistency that use infinite sets to be convincing enough to let me sleep at night. — Jordan Ellenberg

That story is proof of the theorem that then as today in Chicago, the mysterious equation of whiskey plus music equals what can only be called happiness. — Sarah Vowell

You'll often see posts about people beating the CAP theorem. They haven't. What they have done is create a system where some capabilities are CP, and some are AP. The mathematical proof behind the CAP theorem holds. Despite many attempts at school, I've learned that you don't beat math. — Sam Newman

I passed by General Zia's tomb and knew that I never would have become Muslim if I was raised in this country [Pakistan]. As a rebellious American adolescent, I had chosen Islam because it was the religion of Malcolm X, a language of resistance against unjust power. But in Pakistan, Islam was the unjust power, or at least part of what kept the machine running. Pakistan's Islam was guilty of everything for which I had rebelled against Reagen-Falwaell Christianity of America. — Michael Muhammad Knight

Any good theorem should have several proofs, the more the better — Michael Atiyah

[...] provability is a weaker notion than truth — Douglas R. Hofstadter

Nothing is more exhilarating than philistine vulgarity. — Vladimir Nabokov

This skipping is another important point. It should be done whenever a proof seems too hard or whenever a theorem or a whole paragraph does not appeal to the reader. In most cases he will be able to go on and later he may return to the parts which he skipped. — Emil Artin

A felicitous but unproved conjecture may be of much more consequence for mathematics than the proof of many a respectable theorem. — Atle Selberg

The goal of a definition is to introduce a mathematical object. The goal of a theorem is to state some of its properties, or interrelations between various objects. The goal of a proof is to make such a statement convincing by presenting a reasoning subdivided into small steps each of which is justified as an "elementary" convincing argument. — Yuri Manin

In any event, Socrates' proof of prenatal immortality is that one of Meno's uneducated slave boys actually comes up with the Pythagorean theorem without ever having studied geometry! Therefore, he must be remembering it. You recall that theorem: in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. Huh? We can barely remember that from tenth grade, let alone from before we were born. — Thomas Cathcart

Reality bites. Micron underlines that despite the market run-up recently, there's still no confidence about growth and earnings. — David Thwaites

Occasionally, I get a letter from someone who is in "contact" with extraterrestrials. I am invited to "ask them anything." And so over the years I've prepared a little list of questions. The extraterrestrials are very advanced, remember. So I ask things like, "Please provide a short proof of Fermat's Last Theorem." Or the Goldbach Conjecture. And then I have to explain what these are, because extraterrestrials will not call it Fermat's Last Theorem. So I write out the simple equation with the exponents. I never get an answer. On the other hand, if I ask something like "Should we be good?" I almost always get an answer. — Carl Sagan

But you can't prove God exists. And isn't that what all science is ultimately about? Proving theories about the universe?"
"Provability is not truth, Caro. Godel's incompleteness theorem tells us that, if we didn't already know it intuitively, which we do. — Anna Jarzab

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. — Martin Gardner