There is one quality more important than know-how.... This is know-how by which we determine not only how to accomplish our purposes, but what our purposes are to be.

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.

Any useful logic must concern itself with Ideas with a fringe of vagueness and a Truth that is a matter of degree.

It is easy to make a simple machine which will run toward the light or run away from it, and if such machines also contain lights of their own, a number of them together will show complicated forms of social behavior.

Science is a way of life which can only flourish when men are free to have faith.

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 more we get out of the world the less we leave, and in the long run we shall have to pay our debts at a time that may be very inconvenient for our own survival.