A chess problem is genuine mathematics, but it is in some way "trivial" mathematics. However, ingenious and intricate, however original and surprising the moves, there is something essential lacking. Chess problems are unimportant. The best mathematics is serious as well as beautiful-"important" if you like, but the word is very ambiguous, and "serious" expresses what I mean much better.

As history proves abundantly, mathematical achievement, whatever its intrinsic worth, is the most enduring of all.

There is no scorn more profound, or on the whole more justifiable, than that of the men who make for the men who explain.

Asked if he believes in one G-d, a mathematician answered: "Yes, up to isomorphism".

A science is said to be useful if its development tends to accentuate the existing inequalities in the distribution of wealth, or more directly promotes the destruction of human life.

Mathematics is not a contemplative but a creative subject.

A man who sets out to justify his existence and his activities has to distinguish two different questions. The first is whether the work which he does is worth doing; and the second is why he does it (whatever its value may be).