None of our beliefs are quite true; all have at least a penumbra of vagueness and error.

Education ought to foster the wish for truth, not the conviction that some particular creed is the truth.

Although it is a gloomy view to suppose that life will die out, sometimes when I contemplate the things that people do with their lives I think it is almost a consolation

Calculating machines do sums better than even the cleverest people… As arithmetic has grown easier, it has come to be less respected.

It has become a commonplace that aggressiveness also often has its roots in fear. I am inclined to think that this theory has been pushed too far. [...] The type of aggressiveness that is the outcome of timidity is not, I think, that which inspires great leaders; the great leaders, I should say, have an exceptional self-confidence which is not only on the surface, but penetrates deep into the subconscious.

All that passes for knowledge can be arranged in a hierarchy of degrees of certainty, with arithmetic and the facts of perception at the top.

The solution of the difficulties which formerly surrounded the mathematical infinite is probably the greatest achievement of which our age has to boast.