A man who sets out to justify his existence and his activities has to distinguish two different questions. The first is whether the work which he does is worth doing; and the second is why he does it (whatever its value may be).

I wrote a great deal during the next ten [early] years,but very little of any importance; there are not more than four or five papers which I can still remember with some satisfaction.

The mathematician is in much more direct contact with reality. ... [Whereas] the physicist's reality, whatever it may be, has few or none of the attributes which common sense ascribes instinctively to reality. A chair may be a collection of whirling electrons.

Sometimes one has to say difficult things, but one ought to say them as simply as one knows how.

As Littlewood said to me once [of the ancient Greeks], they are not clever school boys or "scholarship candidates," but "Fellows of another college."

Reductio ad absurdum, which Euclid loved so much, is one of a mathematician's finest weapons. It is a far finer gambit than any chess play: a chess player may offer the sacrifice of a pawn or even a piece, but a mathematician offers the game.

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