It is one of the triumphs of human wit ... to conquer by humility and submissiveness ... to make oneself small in order to appear great ... such ... are often the expedients of the neurotic.

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

Courage is not an ability one either possess or lacks. Courage is the willingness to engage in a risk-taking behavior regardless of whether the consequences are unknown or possibly adverse. We are capable of courageous behavior provided we are willing to engage in it. Given that life offers few guarantees, all living requires risk-taking.

To be a human being means to possess a feeling of inferiority which constantly presses towards its own conquest. The greater the feeling of inferiority that has been experienced, the more powerful is the urge for conquest and the more violent the emotional agitation.

The mathematical life of a mathematician is short. Work rarely improves after the age of twenty-five or thirty. If little has been accomplished by then, little will ever be accomplished.

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.

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.