A Quote by George Polya

The result of the mathematician's creative work is demonstrative reasoning, a proof; but the proof is discovered by plausible reasoning, by guessing.

George Polya

Quote Topics

Creative Creative Work Discovered Guessing Mathematician Plausible Proof Reasoning Result Work

Quote Author

George Polya
Hungarian - Mathematician
December 13, 1887 - September 7, 1985

It is evidently equally foolish to accept probable reasoning from a mathematician and to demand from a rhetorician demonstrative proofs.

Aristotle

My proof convinces the ignorant, and the wise man's proof convinces me. But he whose reasoning falls between wisdom and ignorance, I neither can convince him, nor can he convince me.

Khalil Gibran

A proof is a proof. What kind of a proof? It's a proof. A proof is a proof. And when you have a good proof, it's because it's proven.

Jean Chretien

I mean the word proof not in the sense of the lawyers, who set two half proofs equal to a whole one, but in the sense of a mathematician, where half proof = 0, and it is demanded for proof that every doubt becomes impossible.

Carl Friedrich Gauss

The great mathematician fully, almost ruthlessly, exploits the domain of permissible reasoning and skirts the impermissible. That his recklessness does not lead him into a morass of contradictions is a miracle in itself: certainly it is hard to believe that our reasoning power was brought, by Darwin's process of natural selection, to the perfection which it seems to possess.

Eugene Wigner

The deep paradox uncovered by AI research: the only way to deal efficiently with very complex problems is to move away from pure logic.... Most of the time, reaching the right decision requires little reasoning.... Expert systems are, thus, not about reasoning: they are about knowing.... Reasoning takes time, so we try to do it as seldom as possible. Instead we store the results of our reasoning for later reference.

Daniel Crevier

We live in an age of technology and science that demands proof, and yet we desire mystery. But when God gives us mystery, we seek to destroy it by gross indifference or childish reasoning.

Mother Angelica

I would call the attention of the reader to the difference between "reason" and "reasoning." Reason is a light, reasoning a process. Reason is a faculty, reasoning an exercise of that faculty. Reasoning proceeds from one truth to another by means of argumentation. This generally involves the whole mind in labor and complexity. But reason does not exist merely in order to engage in reasoning. The process is a means to an end. The true fulfillment of reason as a faculty is found when it can embrace the truth simply and without labor in the light of single intuition.

Thomas Merton

A proof only becomes a proof after the social act of "accepting it as a proof".

Yuri Manin

What God declares the believing heart confesses without the need of further proof. Indeed, to seek proof is to admit doubt, and to obtain proof is to render faith superfluous.

Aiden Wilson Tozer

Proof is boring. Proof is tiresome. Proof is an irrelevance. People would far rather be handed an easy lie than search for a difficult truth, especially if it suits their own purposes.