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

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….

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

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

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"..

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..

Good work is not done by 'humble' men.

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….

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

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

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

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….

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 ….

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….

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

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

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….

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 ….

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….

What we do may be small, but it has a certain character of permanence; and to have produced anything of the slightest permanent interest, whether it ….