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 va….

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

The mathematician's patterns, like the painter's or the poet's must be beautiful; the ideas, like the colours or the words must fit together in a har….

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 ….

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

Young men should prove theorems, old men should write books..

For any serious purpose, intelligence is a very minor gift..

Beauty is the first test: there is no permanent place in the world for ugly mathematics..

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

Asked if he believes in one G-d, a mathematician answered: "Yes, up to isomorphism"..

No mathematician should ever allow him to forget that mathematics, more than any other art or science, is a young man's game. ... Galois died at twen….

They [formulae 1.10 - 1.12 of Ramanujan] must be true because, if they were not true, no one would have had the imagination to invent them..

I have never done anything 'useful'. No discovery of mine has made, or is likely to make, directly or indirectly, for good or ill, the least differen….

Good work is not done by 'humble' men.

When the world is mad, a mathematician may find in mathematics an incomparable anodyne. For mathematics is, of all the arts and sciences, the most au….

The study of mathematics is, if an unprofitable, a perfectly harmless and innocent occupation..

I believe that mathematical reality lies outside us, that our function is to discover or observe it, and that the theorems which we prove, and which ….

I am interested in mathematics only as a creative art..

Archimedes will be remembered when Aeschylus is forgotten, because languages die and mathematical ideas do not. "Immortality" may be a silly word, bu….

A mathematician, like a painter or a poet, is a maker of patterns..

Perhaps five or even ten per cent of men can do something rather well. It is a tiny minority who can do anything really well, and the number of men w….