A chess problem is simply an exercise in pure mathematics.

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

No mathematician should ever allow himself to forget that mathematics, more than any other art or science, is a young man's game

The case for my life... is this: that I have added something to knowledge, and helped others to add more

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

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.

[I was advised] to read Jordan's 'Cours d'analyse'; and I shall never forget the astonishment with which I read that remarkable work, the first inspiration for so many mathematicians of my generation, and learnt for the first time as I read it what mathematics really meant.