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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
Great
Inevitability
Combined
Mathematical
Degree
Mathematics
Degrees
Economy
High
Unexpectedness

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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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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.
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A chess problem is simply an exercise in pure mathematics.
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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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Exposition, criticism, appreciation, is work for second-rate minds.
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The mathematician's patterns, like the painter's or the poet's, must be beautiful.
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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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I wrote a great deal during the next ten [early] years,but very little of any importance there are not more than four or five papers which I can still remember with some satisfaction.
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The study of mathematics is, if an unprofitable, a perfectly harmless and innocent occupation.
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The public does not need to be convinced that there is something in mathematics.
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A month's intelligent instruction in the theory of numbes ought to be twice as instructive, twice as useful, and at least 10 times as entertaining as the same amount of 'calculus for engineers'.
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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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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.
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Good work is not done by 'humble' men
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Sometimes one has to say difficult things, but one ought to say them as simply as one knows how.
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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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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.
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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.
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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.
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The seriousness of a mathematical theorem lies, not in its practical consequences, which are usually negligible, but in the significance of the mathematical ideas which it connects.
G. H. Hardy