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.

Am I really a good mathematician?

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

I have said that science is impossible without faith. ... Inductive logic, the logic of Bacon, is rather something on which we can act than something which we can prove, and to act on it is a supreme assertion of faith ... Science is a way of life which can only fluorish when men are free to have faith.

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

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.

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.