Science does not aim at establishing immutable truths and eternal dogmas; its aim is to approach the truth by successive approximations, without claiming that at any stage final and complete accuracy has been achieved.

All religions are both harmful and untrue.

An atheist, like a Christian, holds that we can know whether or not there is a God. The Christian holds that we can know there is a God; the atheist, that we can know there is not. The Agnostic suspends judgment, saying that there are not sufficient grounds either for affirmation or for denial. At the same time, an Agnostic may hold that the existence of God, though not impossible, is very improbable; he may even hold it so improbable that it is not worth considering in practice. In that case, he is not far removed from atheism.

Men fear thought as they fear nothing else on earth - more than ruin, more even than death.

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.

Insight, untested and unsupported, is an uncertain guarantee of the truth.

Suppose atomic bombs had reduced the population of the world to one brother and sister; should they let the human race die out?