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A science or an art may be said to be useful if its development increases, even indirectly, the material well-being and comfort of men, it promotes happiness, using that word in a crude and commonplace way.
G. H. Hardy
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G. H. Hardy
Age: 70 †
Born: 1877
Born: February 7
Died: 1947
Died: December 1
Academic
Mathematician
University Teacher
Cranleigh
Surrey
G. H. Hardy
Godfrey Harold Hardy
Godfrey·Harold·Hardy
Godfrey Harold
Well
Comfort
Crude
Even
Development
Commonplace
Way
Word
Increases
Men
Happiness
Useful
Science
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Art
Material
May
Increase
Indirectly
Wells
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Promotes
More quotes by 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 simply the notes of our observations.
G. H. Hardy
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.
G. H. Hardy
The mathematician is in much more direct contact with reality. ... [Whereas] the physicist's reality, whatever it may be, has few or none of the attributes which common sense ascribes instinctively to reality. A chair may be a collection of whirling electrons.
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.
G. H. Hardy
I do not know an instance of a major mathematical advance initiated by a man past fifty
G. H. Hardy
The study of mathematics is, if an unprofitable, a perfectly harmless and innocent occupation.
G. H. Hardy
For my part, it is difficult for me to say what I owe to Ramanujan - his originality has been a constant source of suggestion to me ever since I knew him, and his death is one of the worst blows I have ever had.
G. H. Hardy
Bradman is a whole class above any batsman who has ever lived: if Archimedes, Newton and Gauss remain in the Hobbs class, I have to admit the possibility of a class above them, which I find difficult to imagine. They had better be moved from now on into the Bradman class.
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 soon. It is a pity, but in that case he does not matter a great deal anyhow, and it would be silly to bother about him.
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 any genuine talent, he should be ready to make almost any sacrifice in order to cultivate it to the full.
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
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.
G. H. Hardy
I propose to put forward an apology for mathematics and I may be told that it needs none, since there are now few studies more generally recognized, for good reasons or bad, as profitable and praiseworthy.
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 still have been to increase the average length of life.
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.
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.
G. H. Hardy
In [great mathematics] there is a very high degree of unexpectedness, combined with inevitability and economy.
G. H. Hardy
... Philosophy proper is a subject, on the one hand so hopelessly obscure, on the other so astonishingly elementary, that there knowledge hardly counts.
G. H. Hardy
Sometimes one has to say difficult things, but one ought to say them as simply as one knows how.
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.
G. H. Hardy