On Proofs II

"The folly of mistaking a paradox for a discovery, a metaphor for a proof, a torrent of verbiage for a spring of capital truths, and oneself for an oracle, is inborn in us." (Paul Valéry, "Introduction to the Method of Leonardo da Vinci", 1895)

"It is by logic that we prove, but by intuition that we discover." (Henri Poincaré, “Science and Method”, 1908)

"Symbols, formulae and proofs have another hypnotic effect. Because they are not immediately understood, they, like certain jokes, are suspected of holding in some sort of magic embrace the secret of the universe, or at least some of its more hidden parts." (Scott Buchanan, “Poetry and Mathematics”, 1975)

"Heuristic reasoning is good in itself. What is bad is to mix up heuristic reasoning with rigorous proof. What is worse is to sell heuristic reasoning for rigorous proof." (George Pólya,  "How to Solve It", 1973)

"A proof only becomes a proof after the social act of ‘accepting it as a proof’." (Yu I Manin, "A Course in Mathematical Logic", 1977)

"A proof in science does more than eliminate doubt. It eliminates inconsistencies and provides the underlying logical basis of the statement." (Edward Teller, “The Pursuit of Simplicity”, 1981)

"A proof only becomes a proof after the social act of 'accepting it as a proof'" (Yuri I Manin, "Provable and Unprovable", 1982)

"A math lecture without a proof is like a movie without a love scene." (Hendrik Lenstra, 2002)

“The more powerful the mathematical tools used to prove a result, the shorter that proof might be expected to be […]” (Julian Havil, “Nonplussed!”, 2007