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.

3 is prime, 5 is prime, 7 is prime, 9 is a paradox; as is a paradox why the number 1 is not prime if it has no other divisors besides himself.

That the world is in a bad shape is undeniable, but there is not the faintest reason in history to suppose that Christianity offers a way out.

We know that the exercise of virtue should be its own reward, and it seems to follow that the enduring of it on the part of the patient should be its own punishment.

It is not my prayer and humility that you cause things to go as you wish, but by acquiring a knowledge of natural laws.

Gradually, ... the aspect of science as knowledge is being thrust into the background by the aspect of science as the power of manipulating nature. It is because science gives us the power of manipulating nature that it has more social importance than art. Science as the pursuit of truth is the equal, but not the superior, of art. Science as a technique, though it may have little intrinsic value, has a practical importance to which art cannot aspire.

There is no excuse for deceiving children. And when, as must happen in conventional families, they find that their parents have lied, they lose confidence in them and feel justified in lying to them.