A good mathematical joke is better, and better mathematics, than a dozen mediocre papers.

The infinitely competent can be uncreative.

In passing, I firmly believe that research should be offset by a certain amount of teaching, if only as a change from the agony of research. The trouble, however, I freely admit, is that in practice you get either no teaching, or else far too much.

I constantly meet people who are doubtful, generally without due reason, about their potential capacity [as mathematicians]. The first test is whether you got anything out of geometry. To have disliked or failed to get on with other [mathematical] subjects need mean nothing; much drill and drudgery is unavoidable before they can get started, and bad teaching can make them unintelligible even to a born mathematician.

The surprising thing about this paper is that a man who could write it would.

A good mathematical joke is better, and better mathematics, than a dozen mediocre papers.

I've been giving this lecture to first-year classes for over twenty-five years. You'd think they would begin to understand it by now.