A chess problem is simply an exercise in pure mathematics.

The "seriousness" of a mathematical theorem lies, not in its practical consequences, which are usually negligible, but in the significance of the mathematical ideas which it connects.

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

Perhaps five or even ten per cent of men can do something rather well. It is a tiny minority who can do anything really well, and the number of men who can do two things well is negligible. If a man has any genuine talent, he should be ready to make almost any sacrifice in order to cultivate it to the full.

In [great mathematics] there is a very high degree of unexpectedness, combined with inevitability and economy.

I am interested in mathematics only as a creative art.

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