Sublime

There are two things at any rate which seem essential, a certain generality and a certain depth; but neither quality is easy to define at all precisely. A significant mathematical idea, a serious mathematical theorem, should be ‘general’ in some such sense as this. The idea should be one which is a constituent in many mathematical constructs, which

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

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. I am not thinking of the ‘practical’ consequences of mathematics. I have to return to that point later: at present I will say only that if a chess problem is, in the crude sense, ‘useless’,