Quotes from G. H. Hardy

The creative life was the only one for a serious man.

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

I do not know an instance of a major mathematical advance initiated by a man past fifty

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

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.

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

I wrote a great deal during the next ten [early] years,but very little of any importance; there are not more than four or five papers which I can still remember with some satisfaction.

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

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

Pure mathematics is on the whole distinctly more useful than applied. For what is useful above all is technique, and mathematical technique is taught mainly through pure mathematics.

The case for my life... is this: that I have added something to knowledge, and helped others to add more

A science is said to be useful if its development tends to accentuate the existing inequalities in the distribution of wealth, or more directly promotes the destruction of human life.

A mathematician, like a painter or a poet, is a maker of patterns. If his patterns are more permanent than theirs, it is because they are made with ideas.

There is no scorn more profound, or on the whole more justifiable, than that of the men who make for the men who explain. Exposition, criticism, appreciation, is work for second-rate minds.

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

Archimedes will be remembered when Aeschylus is forgotten, because languages die and mathematical ideas do not.

I am interested in mathematics only as a creative art.

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

Imaginary' universes are so much more beautiful than this stupidly constructed 'real' one; and most of the finest products of an applied mathematician's fancy must be rejected, as soon as they have been created, for the brutal but sufficient reason that they do not fit the facts.

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 be a copy of verses or a geometrical theorem, is to have done something utterly beyond the powers of the vast majority of men.

We may say, roughly, that a mathematical idea is 'significant' if it can be connected, in a natural and illuminating way, with a large complex of other mathematical ideas. Thus a serious mathematical theorem, a theorem which connects significant ideas, is likely to lead to important advances in mathematics itself and even in other sciences.

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

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

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.