A mathematician, then, will be defined in what follows as someone who has published the proof of at least one non-trivial theorem.
--
Mathematics and Mathematicians (1992); published in Is Mathematics Inevitable? A Miscellany (2008), edited by Underwood Dudley, p. 3. ISBN 0883855666Jean Dieudonne
» Jean Dieudonne - all quotes »
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 ? proof = 0, and it is demanded for proof that every doubt becomes impossible.
Carl Friedrich Gauss
As a boy of six I could understand the proof of a mathematical theorem more readily than that meat had to be cut with one's knife, not one's fork.
Ferdinand Eisenstein
In many cases a dull proof can be supplemented by a geometric analogue so simple and beautiful that the truth of a theorem is almost seen at a glance.
Martin Gardner
Proof is the idol before whom the pure mathematician tortures himself.
Arthur Stanley Eddington
The totality of all alephs cannot be conceived as a determinate, well-defined, and also a finished set. This is the punctum saliens, and I venture to say that this completely certain theorem, provable rigorously from the definition of the totality of all alephs, is the most important and noblest theorem of set theory. One must only understand the expression "finished" correctly. I say of a set that it can be thought of as finished (and call such a set, if it contains infinitely many elements, "transfinite" or "suprafinite") if it is possible without contradiction (as can be done with finite sets) to think of all its elements as existing together, and to to think of the set itself as a compounded thing for itself; or (in other words) if it is possible to imagine the set as actually existing with the totality of its elements.
Georg Cantor
Dieudonne, Jean
DiFranco, Ani
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