I propose to put forward an apology for mathematics; and I may be told that it needs none, since there are now few studies more generally recognized, for good reasons or bad, as profitable and praiseworthy.

All analysts spend half their time hunting through the literature for inequalities which they want to use and cannot prove.

Greek mathematics is the real thing. The Greeks first spoke a language which modern mathematicians can understand... So Greek mathematics is 'permanent', more permanent even than Greek literature.

Bombs are probably more merciful than bayonets

It is not worth an intelligent man's time to be in the majority. By definition, there are already enough people to do that.

I remember once going to see him [Ramanujan] when he was lying ill at Putney. I had ridden in taxi-cab No. 1729, and remarked that the number seemed to me rather a dull one, and that I hoped it was not an unfavourable omen. "No," he replied, "it is a very interesting number; it is the smallest number expressible as a sum of two cubes in two different ways."

No mathematician should ever allow himself to forget that mathematics, more than any other art or science, is a young man's game