One of the chief duties of the mathematician in acting as an advisor ... is to discourage ... from expecting too much from mathematics.

In a very real sense, we are shipwrecked passengers on a doomed planet. Yet, even in a shipwreck, human decencies and human values do not necessarily vanish, and we must make the most of them. We shall go down, but let it be in a manner to which we may look forward as worthy of our dignity.

I have said that the modern man, and especially the modern American, however much 'know-how' he may have, has very little 'know-what'

What most experimenters take for granted before they begin their experiments is infinitely more interesting than any results to which their experiments lead.

The simplest type of breakdown exhibits itself as an oscillation in a goal-seeking process which appears only when that process is actively invoked.

Progress imposes not only new possibilities for the future but new restrictions. It seems almost as if progress itself and our fight against the increase of entropy intrinsically must end in the downhill path from which we are trying to escape.

Mathematics is a field which has often been compared with chess, but differs from the latter in that it is only one's best moments that count and not one's worst.