There is no thing as a man who does not create mathematics and yet is a fine mathematics teacher. Textbooks, course material-these do not approach in importance the communication of what mathematics is really about, of where it is going, and of where it currently stands with respect to the specific branch of it being taught. What really matters is the communication of the spirit of mathematics. It is a spirit that is active rather than contemplative-a spirit of disciplined search for adventures of the intellect. Only as adventurer can really tell of adventures.

More important than innate disposition, objective experience, and environment is the subjective evaluation of these. Furthermore, this evaluation stands in a certain, often strange, relation to reality.

An educator's most important task, one might say his holy duty, is to see to it that no child is discouraged at school, and that a child who enters school already discouraged regains his self-confidence through his school and his teacher. This goes hand in hand with the vocation of the educator, for education is possible only with children who look hopefully and joyfully upon the future.

A lie would have no sense unless the truth were felt as dangerous.

My psychology belongs to everyone.

In the company of friends, writers can discuss their books, economists the state of the economy, lawyers their latest cases, and businessmen their latest acquisitions, but mathematicians cannot discuss their mathematics at all. And the more profound their work, the less understandable it is.

The style of life is a unity because it has grown out of the difficulties of early life and out of the striving for a goal.