G. H. Hardy Quotes

Good work is not done by ‘humble’ men

If I could prove by logic that you would die in five minutes, I should be sorry you were going to die, but my sorrow would be very much mitigated by pleasure in the proof.

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.

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

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.

Archimedes will be remembered when Aeschylus is forgotten, because languages die and mathematical ideas do not. “Immortality” may be a silly word, but probably a mathematician has the best chance of whatever it may mean.

I am interested in mathematics only as a creative art.

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

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 who can do two things well is negligible. If a man has any genuine talent, he should be ready to make almost any sacrifice in order to cultivate it to the full.

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

No discovery of mine has made, or is likely to make, directly or indirectly, for good or ill, the least difference to the amenity of the world.

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.

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

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 we describe grandiloquently as our “creations,” are simply the notes of our observations.

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

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.

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

Real mathematics must be justified as art if it can be justified at all.

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

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.

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

A man who sets out to justify his existence and his activities has to distinguish two different questions. The first is whether the work which he does is worth doing; and the second is why he does it (whatever its value may be).