Math 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

Besides it is an error to believe that rigour is the enemy of simplicity. On the contrary we find it confirmed by numerous examples that the rigorous method is at the same time the simpler and the more easily comprehended. The very effort for rigor forces us to find out simpler methods of proof. — David Hilbert

Mathematical proofs, like diamonds, are hard and clear, and will be touched with nothing but strict reasoning. — John Locke

Proof is an idol before which the mathematician tortures himself. — Arthur Eddington

Be honest: did you actually read [the above geometric proof]? Of course not. Who would want to?
The effect of such a production being made over something so simple is to make people doubt their own intuition. Calling into question the obvious by insisting that it be 'rigorously proved' ... is to say to a student 'Your feelings and ideas are suspect. You need to think and speak our way. — Paul Lockhart

From now on whenever I read a math book, I'm going to try to figure out by myself how everything was done, before looking at the solution. Even if I don't figure it out, I think I'll be able to see the beauty of a proof then. — Donald E. Knuth

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

In law, we talk about a beautiful summation, or a beautiful judgment: and what we mean by that, of course, is the loveliness of not only its logic but its expression. And similarly, in math, when we talk about a beautiful proof, what we're recognizing is the simplicity of the proof, its ... elementalness, I suppose: its inevitability. — Hanya Yanagihara

My love for math eventually became a passion. I went to math camp when I was fourteen and came home clutching a Rubik's Cube to my chest. Math provided a neat refuge from the messiness of the real world. It marched forward, its field of knowledge expanding relentlessly, proof by proof. And — Cathy O'Neil

Someone has remarked that 'An ideal math talk should have one proof and one joke and they should not be the same'. — Ronald Graham

A consistency proof for [any] system ... can be carried out only by means of modes of inference that are not formalized in the system ... itself. — Kurt Godel

A math lecture without a proof is like a movie without a love scene. This talk has two proofs. — Hendrik Lenstra

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

Sophie Germain proved to the world that even a woman can accomplish something in the most rigorous and abstract of sciences and for that reason would well have deserved an honorary degree. — Carl Friedrich Gauss

By the end of an intense four years at UCLA, I had co-authored a new math proof, which the media, in fact, loved. As it turned out, math itself blazed my entry back into the spotlight and consequently into wonderful acting jobs like 'The West Wing' and others. You just never know, do you? — Danica McKellar

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

There was, I think, a feeling that the best science was that done in the simplest way. In experimental work, as in mathematics, there was 'style' and a result obtained with simple equipment was more elegant than one obtained with complicated apparatus, just as a mathematical proof derived neatly was better than one involving laborious calculations. Rutherford's first disintegration experiment, and Chadwick's discovery of the neutron had a 'style' that is different from that of experiments made with giant accelerators. — John Ashworth Ratcliffe

We often hear that mathematics consists mainly of 'proving theorems.' Is a writer's job mainly that of 'writing sentences? — Gian-Carlo Rota

Human beings are more or less formulas. Pun intended. We are not any one thing that is mathematically provable. We are more or less than we are anything. We are more or less kind, or more or less not. More or less selfish, happy, wise, lonely. — Adi Alsaid