Overcoming difficulties leads to courage, self-respect, and knowing yourself.

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.

What is courage? Courage is the willingness to risk failure...There is only one danger I find in life, and that, indeed, is a real one. You may take too many precautions.

A simple rule in dealing with those who are hard to get along with is to remember that this person is striving to assert his superiority; and you must deal with him from that point of view.

What do you first do when you learn to swim? You make mistakes, do you not? And what happens? You make other mistakes, and when you have made all the mistakes you possibly can without drowning - and some of them many times over - what do you find? That you can swim? Well - life is just the same as learning to swim! Do not be afraid of making mistakes, for there is no other way of learning how to live!

There is a law that man should love his neighbor as himself. In a few hundred years it should be as natural to mankind as breathing or the upright gait; but if he does not learn it he must perish.

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