Mathematics is not a contemplative but a creative subject; no one can draw much consolation from it when he has lost the power or the desire to create; and that is apt to happen to a mathematician rather soon. It is a pity, but in that case he does not matter a great deal anyhow, and it would be silly to bother about him.

A chess problem is simply an exercise in pure mathematics.

If a man is in any sense a real mathematician, then it is a hundred to one that his mathematics will be far better than anything else he can do, and that he would be silly if he surrendered any decent opportunity of exercising his one talent in order to do undistinguished work in other fields. Such a sacrifice could be justified only by economic necessity of age.

Young men should prove theorems, old men should write books.

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

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

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