I was at my best at a little past forty, when I was a professor at Oxford.

All analysts spend half their time hunting through the literature for inequalities which they want to use and cannot prove.

A mathematician, like a painter or a poet, is a maker of patterns.

A chess problem is simply an exercise in pure mathematics.

[Regarding mathematics,] there are now few studies more generally recognized, for good reasons or bad, as profitable and praiseworthy. This may be true; indeed it is probable, since the sensational triumphs of Einstein, that stellar astronomy and atomic physics are the only sciences which stand higher in popular estimation.

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.

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