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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
Degrees
Economy
High
Unexpectedness
Great
Inevitability
Combined
Mathematical
Degree
Mathematics

More quotes by 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.
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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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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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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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I was at my best at a little past forty, when I was a professor at Oxford.
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Asked if he believes in one G-d, a mathematician answered: Yes, up to isomorphism.
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Most people can do nothing at all well
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Young men should prove theorems, old men should write books.
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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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The case for my life... is this: that I have added something to knowledge, and helped others to add more
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The study of mathematics is, if an unprofitable, a perfectly harmless and innocent occupation.
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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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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
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Bombs are probably more merciful than bayonets
G. H. Hardy
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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.
G. H. Hardy
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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.
G. H. Hardy
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A chess problem is simply an exercise in pure mathematics.
G. H. Hardy
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Good work is not done by 'humble' men
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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.
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The public does not need to be convinced that there is something in mathematics.
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