Extreme hopes are born of extreme misery, and in such a world hopes could only be irrational.

Neither acquiescence in skepticism nor acquiescence in dogma is what education should produce.

But as the work proceeded I was continually reminded of the fable about the elephant and the tortoise. Having constructed an elephant upon which the mathematical world could rest, I found the elephant tottering, and proceeded to construct a tortoise to keep the elephant from falling. But the tortoise was not more secure than the elephant, and after some twenty years of very arduous toil, I came to the conclusion that there was nothing more that I could do in the way of making mathematical knowledge indubitable.

I believe in using words, not fists. I believe in my outrage knowing people are living in boxes on the street. I believe in honesty. I believe in a good time. I believe in good food. I believe in sex.

There are certain things that our age needs, and certain things that it should avoid. It needs compassion and a wish that mankind should be happy; it needs the desire for knowledge and the determination to eschew pleasant myths; it needs, above all, courageous hope and the impulse to creativeness.

There is something feeble, and a little contemptible, about a man who cannot face the perils of life without the help of comfortable myths. Almost inevitably some part of him is aware that they are myths and that he believes them only because they are comforting. But he dare not face this thought, and he therefore cannot carry his own reflection to any logical conclusion.

The fundamental defect of fathers, in our competitive society, is that they want their children to be a credit to them. We all feel instinctively, that our children's success reflect glory upon ourselves, while their failures make us feel shame. Unfortunately, the successes which cause us to swell with pride are often of an undesirable kind.... Neither happiness nor virtue, but worldly success, is what the average father desires for his children.