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

The study of mathematics is, if an unprofitable, a perfectly harmless and innocent occupation.

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.

I have never done anything 'useful'. No discovery of mine has made, or is likely to make, directly or indirectly, for good or ill, the least difference to the amenity of the world... Judged by all practical standards, the value of my mathematical life is nil; and outside mathematics it is trivial anyhow. I have just one chance of escaping a verdict of complete triviality, that I may be judged to have created something worth creating. And that I have created something is undeniable: the question is about its value.

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

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

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