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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).

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
First
Whatever
Justify
Different
Values
Questions
Work
Whether
Activity
Men
Science
Value
Two
Worth
Doe
Second
Distinguish
May
Differences
Activities
Firsts
Existence
Sets

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The mathematician's patterns, like the painter's or the poet's, must be beautiful.
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A chess problem is simply an exercise in pure mathematics.
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The fact is there are few more popular subjects than mathematics. Most people have some appreciation of mathematics, just as most people can enjoy a pleasant tune.
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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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Bombs are probably more merciful than bayonets
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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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I was at my best at a little past forty, when I was a professor at Oxford.
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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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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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In [great mathematics] there is a very high degree of unexpectedness, combined with inevitability and economy.
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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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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.
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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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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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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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All analysts spend half their time hunting through the literature for inequalities which they want to use and cannot prove.
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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 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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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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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.
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