The only worthwhile achievements of man are those which are socially useful.

Our modern states are preparing for war without even knowing the future enemy.

The educator must believe in the potential power of his pupil, and he must employ all his art in seeking to bring his pupil to experience this power.

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.

We cannot say that if a child is badly nourished he will become a criminal. We must see what conclusion the child has drawn.

Death is really a great blessing for humanity, without it there could be no real progress. People who lived for ever would not only hamper and discourage the young, but they would themselves lack sufficient stimulus to be creative.

The goal of the human soul is conquest, perfection, security, superiority.