“Proof is the idol before whom the pure mathematician tortures himself.”

— Arthur Stanley Eddington

Source: The Nature of the Physical World (1928), Ch. 15 Science and Mysticism

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Arthur Stanley Eddington 105

British astrophysicist 1882–1944

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“I am obliged to interpolate some remarks on a very difficult subject: proof and its importance in mathematics. All physicists, and a good many quite respectable mathematicians, are contemptuous about proof. I have heard Professor Eddington, for example, maintain that proof, as pure mathematicians understand it, is really quite uninteresting and unimportant, and that no one who is really certain that he has found something good should waste his time looking for proof.”

G. H. Hardy (1877–1947) British mathematician

Source: Ramanujan (1940), Ch. I : The Indian mathematician Ramanujan.

“The simplicity of Bell's proof opens it to everyone, not just physicists and mathematicians.”

Nick Herbert (1936) American physicist

Source: Quantum Reality - Beyond The New Physics, Chapter 12, Bell's Interconnectedness Theorem, p. 215

“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 ½ proof = 0, and it is demanded for proof that every doubt becomes impossible.”

Carl Friedrich Gauss (1777–1855) German mathematician and physical scientist

In a letter to Heinrich Wilhelm Matthias Olbers (14 May 1826), defending Chevalier d'Angos against presumption of guilt (by Johann Franz Encke and others), of having falsely claimed to have discovered a comet in 1784; as quoted in Calculus Gems (1992) by George F. Simmons

“A mathematician is a person who can find analogies between theorems; a better mathematician is one who can see analogies between proofs and the best mathematician can notice analogies between theories. One can imagine that the ultimate mathematician is one who can see analogies between analogies.”

Stefan Banach (1892–1945) Polish &Ukrainian mathematician

[Beata Randrianantoanina, Narcisse Randrianantoanina, Banach Spaces and Their Applications in Analysis: Proceedings of the International Conference at Miami University, May 22-27, 2006, in Honor of Nigel Kalton's 60th Birthday, http://books.google.com/books?id=1GiwqU-gB_kC&pg=PR5, 2007, Walter de Gruyter, 978-3-11-019449-4, 5]

“A mathematician, then, will be defined in what follows as someone who has published the proof of at least one non-trivial theorem.”

Jean Dieudonné

Mathematics and Mathematicians (1992); published in Is Mathematics Inevitable? A Miscellany (2008), edited by Underwood Dudley, p. 3. ISBN 0883855666

“The result of the mathematician's creative work is demonstrative reasoning, a proof; but the proof is discovered by plausible reasoning, by guessing. If the learning of mathematics reflects to any degree the invention of mathematics, it must have a place for guessing, for plausible inference.”

George Pólya (1887–1985) Hungarian mathematician

Induction and Analogy in Mathematics (1954)

“The Love of Allah for the human being is that He Himself gives proof of Himself, not revealing Himself to anything that is not He.”

Mansur Al-Hallaj (858–922) Persian mystic, revolutionary writer and teacher of Sufism

As quoted in "Husayn ibn Mansur al-Hallaj" at Sidi Muhammad Press http://www.sufimaster.org/teachings/husayn.htm
Context: Love is in the pleasure of possession, but in the Love of Allah there is no pleasure of possession, because the stations of the Reality are wonderment, the cancelling of the debt which is owed, and the blinding of vision. The Love of the human being for God is a reverence which penetrates the very depths of his being, and which is not permitted to be given except to Allah alone. The Love of Allah for the human being is that He Himself gives proof of Himself, not revealing Himself to anything that is not He.

“The pure religious consciousness lies in a region which is forever beyond all proof or disproof.”

Walter Terence Stace (1886–1967) British civil servant, educator and philosopher.

p. 136

“I don't believe Fermat had a proof. I think he fooled himself into thinking he had a proof.”

Andrew Wiles (1953) British mathematician

Nova Interview

“It is not proof that I sought. I, of all men, know that proof is but a fallacy invented by man to justify to himself and his fellows his own crass lust and folly.”

William Faulkner (1897–1962) American writer

The Judge
"Beyond" (1933)

“Proof is the idol before whom the pure mathematician tortures himself.”

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Arthur Stanley Eddington 105

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