If an opinion contrary to your own makes you angry, that is a sign that you are subsciously aware of having no good reason for thinking as you do. [...] The most savage controversies are those about matters as to which there is no good evidence either way. Persecution is used in theology, not in arithmetic, because in arithmetic there is knowledge, but in theology there is only opinion. So whenever you find yourself getting angry about a difference of opinion, be on your guard; you will probably find, on examination, that your belief is going beyond what the evidence warrants.

Both in thought and in feeling, even though time be real, to realise the unimportance of time is the gate of wisdom.

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.

Too little liberty brings stagnation, and too much brings chaos.

Fear is the main source of superstition, and one of the main sources of cruelty. To conquer fear is the beginning of wisdom.

These illustrations suggest four general maxims[...]. The first is: remember that your motives are not always as altruistic as they seem to yourself. The second is: don't over-estimate your own merits. The third is: don't expect others to take as much interest in you as you do yourself. And the fourth is: don't imagine that most people give enough thought to you to have any special desire to persecute you.

In all affairs it's a healthy thing now and then to hang a question mark on the things you have long taken for granted.