Reductio ad absurdum, which Euclid loved so much, is one of a mathematician's finest weapons. It is a far finer gambit than any chess play: a chess player may offer the sacrifice of a pawn or even a piece, but a mathematician offers the game.

The mathematician's patterns, like the painter's or the poet's, must be beautiful.

I propose to put forward an apology for mathematics; and I may be told that it needs none, since there are now few studies more generally recognized, for good reasons or bad, as profitable and praiseworthy.

Archimedes will be remembered when Aeschylus is forgotten, because languages die and mathematical ideas do not. "Immortality" may be a silly word, but probably a mathematician has the best chance of whatever it may mean.

It is not worth an intelligent man's time to be in the majority. By definition, there are already enough people to do that.

Real mathematics must be justified as art if it can be justified at all.

Exposition, criticism, appreciation, is work for second-rate minds.