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

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
Mathematics
Degrees
Economy
High
Unexpectedness
Great
Inevitability
Combined
Mathematical
Degree

More quotes by G. H. Hardy

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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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I was at my best at a little past forty, when I was a professor at Oxford.
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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.
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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.
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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).
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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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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.
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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.
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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.
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No one has yet discovered any warlike purpose to be served by the theory of numbers or relativity, and it seems unlikely that anyone will do so for many years.
G. H. Hardy
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The study of mathematics is, if an unprofitable, a perfectly harmless and innocent occupation.
G. H. Hardy
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There is always more in one of Ramanujan's formulae than meets the eye, as anyone who sets to work to verify those which look the easiest will soon discover. In some the interest lies very deep, in others comparatively near the surface but there is not one which is not curious and entertaining.
G. H. Hardy
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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
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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.
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The case for my life... is this: that I have added something to knowledge, and helped others to add more
G. H. Hardy
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The mathematician's patterns, like the painter's or the poet's, must be beautiful.
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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
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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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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.
G. H. Hardy
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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 at present at any rate, almost as useless as the theory of numbers.
G. H. Hardy