There is no scorn more profound, or on the whole more justifiable, than that of the men who make for the men who explain.

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

Mathematics may, like poetry or music, "promote and sustain a lofty habit of mind."

The primes are the raw material out of which we have to build arithmetic, and Euclid's theorem assures us that we have plenty of material for the task.

A person’s first duty, a young person’s at any rate, is to be ambitious, and the noblest ambition is that of leaving behind something of permanent value.

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

A mathematician ... has no material to work with but ideas, and so his patterns are likely to last longer, since ideas wear less with time than words.