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.

Am I really a good mathematician?

It is possible to believe in progress as a fact without believing in progress as an ethical principle; but in the catechism of many Americans, the one goes with the other.

A painter like Picasso, who runs through many periods and phases, ends up by saying all those things which are on the tip of the tongue of the age to say, and finally sterilizes the originality of his contemporaries and juniors.

The modern physicist is a quantum theorist on Monday, Wednesday, and Friday, and a student of gravitational relativity on Tuesday, Thursday, and Saturday. On Sunday, he is praying... that someone will find the reconciliation between the two views.

Progress imposes not only new possibilities for the future but new restrictions.

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.