G. H. Hardy

Born: February 7, 1877

Die: December 1, 1947

Occupation: Mathematician

Quotes of G. H. Hardy

G. H. Hardy

As Littlewood said to me once [of the ancient Greeks], they are not clever school boys or "scholarship candidates," but "Fellows of another college."

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G. H. Hardy

317 is a prime, not because we think so, or because our minds are shaped in one way rather than another, but because it is so, because mathematical reality is built that way.

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G. H. Hardy

A chess problem is an exercise in pure mathematics.

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G. H. Hardy

I count Maxwell and Einstein, Eddington and Dirac, among "real" mathematicians. The great modern achievements of applied mathematics have been in relativity and quantum mechanics, and these subjects are...

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G. H. Hardy

If a man is in any sense a real mathematician, then it is a hundred to one that his mathematics will be far better than anything else he can do, and that it would be silly if he surrendered any decent...

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G. H. Hardy

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

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G. H. Hardy

It is hardly possible to maintain seriously that the evil done by science is not altogether outweighed by the good. For example, if ten million lives were lost in every war, the net effect of science would...

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G. H. Hardy

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 twenty-one, Abel at twenty-seven, Ramanujan at thirty-three,...

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G. H. Hardy

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

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G. H. Hardy

Good work is no done by "humble" men. It is one of the first duties of a professor, for example, in any subject, to exaggerate a little both the importance of his subject and his own importance in it....

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G. H. Hardy

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

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G. H. Hardy

Most people have some appreciation of mathematics, just as most people can enjoy a pleasant tune; and there are probably more people really interested in mathematics than in music. Appearances suggest...

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G. H. Hardy

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

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G. H. Hardy

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.

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G. H. Hardy

In these days of conflict between ancient and modern studies, there must surely be something to be said for a study which did not begin with Pythagoras, and will not end with Einstein, but is the oldest...

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G. H. Hardy

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...

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G. H. Hardy

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

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G. H. Hardy

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...

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G. H. Hardy

Most people are so frightened of the name of mathematics that they are ready, quite unaffectedly, to exaggerate their own mathematical stupidity.

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G. H. Hardy

It is a melancholy experience for a professional mathematician to find himself writing about mathematics. The function of a mathematician is to do something, to prove new theorems, to add to mathematics,...

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G. H. Hardy

Cricket is the only game where you are playing against eleven of the other side and ten of your own.

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G. H. Hardy

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

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G. H. Hardy

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

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G. H. Hardy

Bombs are probably more merciful than bayonets

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G. H. Hardy

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

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G. H. Hardy

Mathematics is not a contemplative but a creative subject; no one can draw much consolation from it when he has lost the power or the desire to create; and that is apt to happen to a mathematician rather...

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G. H. Hardy

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 to me rather a dull one, and that I hoped it was not...

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G. H. Hardy

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.

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G. H. Hardy

If intellectual curiosity, professional pride, and ambition are the dominant incentives to research, then assuredly no one has a fairer chance of gratifying them than a mathematician.

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G. H. Hardy

Exposition, criticism, appreciation, is work for second-rate minds.

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G. H. Hardy

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

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G. H. Hardy

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

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G. H. Hardy

[Regarding mathematics,] there are now few studies more generally recognized, for good reasons or bad, as profitable and praiseworthy. This may be true; indeed it is probable, since the sensational triumphs...

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G. H. Hardy

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.

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G. H. Hardy

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.

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G. H. Hardy

A chess problem is genuine mathematics, but it is in some way "trivial" mathematics. However, ingenious and intricate, however original and surprising the moves, there is something essential lacking. Chess...

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G. H. Hardy

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...

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G. H. Hardy

As history proves abundantly, mathematical achievement, whatever its intrinsic worth, is the most enduring of all.

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G. H. Hardy

Chess problems are the hymn-tunes of mathematics.

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G. H. Hardy

Greek mathematics is the real thing. The Greeks first spoke a language which modern mathematicians can understand... So Greek mathematics is 'permanent', more permanent even than Greek literature.

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G. H. Hardy

I am interested in mathematics only as a creative art.

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G. H. Hardy

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...

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G. H. Hardy

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 difference to the amenity of the world... Judged by all practical...

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G. H. Hardy

In [great mathematics] there is a very high degree of unexpectedness, combined with inevitability and economy.

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G. H. Hardy

Reductio ad absurdum, which Euclid loved so much, is one of a mathematician's finest weapons. It is a far finer gambit than any chess play: a chess player may offer the sacrifice of a pawn or even a piece,...

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G. H. Hardy

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 harmonious way. Beauty is the first test: there is no permanent...

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G. H. Hardy

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

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G. H. Hardy

[P]ure 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.

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G. H. Hardy

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

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