A Quote by Kenneth Appel

Without computers we will be stuck only proving theorems that have short proofs.

Kenneth Appel

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Computers Only Proving Short Stuck Theorems Will Without

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Kenneth Appel
October 8, 1932 - April 19, 2013

It is a matter for considerable regret that Fermat, who cultivated the theory of numbers with so much success, did not leave us with the proofs of the theorems he discovered. In truth, Messrs Euler and Lagrange, who have not disdained this kind of research, have proved most of these theorems, and have even substituted extensive theories for the isolated propositions of Fermat. But there are several proofs which have resisted their efforts.

Adrien-Marie Legendre

If only I had the Theorems! Then I should find the proofs easily enough.

Bernhard Riemann

That's the problem with false proofs of true theorems; it's not easy to produce a counterexample.

Jeffrey Shallit

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

Paul Erdos

It is the facts that matter, not the proofs. Physics can progress without the proofs, but we can't go on without the facts ... if the facts are right, then the proofs are a matter of playing around with the algebra correctly.

Richard P. Feynman

To many, mathematics is a collection of theorems. For me, mathematics is a collection of examples; a theorem is a statement about a collection of examples and the purpose of proving theorems is to classify and explain the examples.

John B. Conway

Mystery is an inescapable ingredient of mathematics. Mathematics is full of unanswered questions, which far outnumber known theorems and results. It's the nature of mathematics to pose more problems than it can solve. Indeed, mathematics itself may be built on small islands of truth comprising the pieces of mathematics that can be validated by relatively short proofs. All else is speculation.

Ivars Peterson

I think that mathematics can benefit by acknowledging that the creation of good models is just as important as proving deep theorems.

David Mumford

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

Antony Garrett Lisi

We often hear that mathematics consists mainly of "proving theorems." Is a writer's job mainly that of "writing sentences?"

Gian-Carlo Rota

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!"

Ross Honsberger

Mathematics does not grow through a monotonous increase of the number of indubitably established theorems but through the incessant improvement of guesses by speculation and criticism, by the logic of proofs and refutations.

Imre Lakatos

Computer assisted proofs are getting better and better and computers will play a bigger and bigger role in the future.

Enrico Bombieri

When a patient says he feels stuck and confused, and through good intentions he struggles to become loose and clear, he only remains chronically trapped in the mire of his own stubbornness. If instead he will go with where he is, only then is there hope. If he will let himself get deeply into the experience of being stuck, only then will he reclaim that part of himself that is holding him. Only if he will give up trying to control his thinking, and let himself sink into his confusion, only then will things become clear. (64)

Sheldon B. Kopp

I claim that this bookless library is a dream, a hallucination of on-line addicts; network neophytes, and library-automation insiders...Instead, I suspect computers will deviously chew away at libraries from the inside. They'll eat up book budgets and require librarians that are more comfortable with computers than with children and scholars. Libraries will become adept at supplying the public with fast, low-quality information. The result won't be a library without books--it'll be a library without value.

Clifford Stoll

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.

William Thurston

A Quote by Kenneth Appel

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