We have modified our environment so radically that we must now modify ourselves to exist in this new environment.

Any use of a human being in which less is demanded of him and less is attributed to him than his full status is a degradation and a waste.

The advantage is that mathematics is a field in which one's blunders tend to show very clearly and can be corrected or erased with a stroke of the pencil.

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

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

The Advantage is that mathematics is a field in which one's blunders tend to show very clearly and can be corrected or erased with a stroke of the pencil. It 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. A single inattention may lose a chess game, whereas a single successful approach to a problem, among many which have been relegated to the wastebasket, will make a mathematician's reputation.

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