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The mathematician's patterns, like the painter's or the poet's, must be beautiful.

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
Painter
Patterns
Mathematics
Poet
Beautiful
Mathematician
Must
Mathematical
Like
Math

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All analysts spend half their time hunting through the literature for inequalities which they want to use and cannot prove.
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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 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.
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The public does not need to be convinced that there is something in mathematics.
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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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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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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.
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Good work is not done by 'humble' men
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Bombs are probably more merciful than bayonets
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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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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 and the youngest of all.
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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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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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... Philosophy proper is a subject, on the one hand so hopelessly obscure, on the other so astonishingly elementary, that there knowledge hardly counts.
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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.
G. H. Hardy
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In [great mathematics] there is a very high degree of unexpectedness, combined with inevitability and economy.
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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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Most people can do nothing at all well
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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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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