Real mathematics must be justified as art if it can be justified at all.

... Philosophy proper is a subject, on the one hand so hopelessly obscure, on the other so astonishingly elementary, that there knowledge hardly counts.

Sometimes one has to say difficult things, but one ought to say them as simply as one knows how.

As history proves abundantly, mathematical achievement, whatever its intrinsic worth, is the most enduring of all.

No one has yet discovered any warlike purpose to be served by the theory of numbers or relativity, and it seems unlikely that anyone will do so for many years.

I was at my best at a little past forty, when I was a professor at Oxford.

The fact is there are few more popular subjects than mathematics. Most people have some appreciation of mathematics, just as most people can enjoy a pleasant tune.