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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.

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
May
Increase
Indirectly
Wells
Materials
Promotes
Well
Comfort
Crude
Even
Development
Commonplace
Way
Word
Increases
Men
Happiness
Useful
Science
Using
Art
Material

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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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Chess problems are the hymn-tunes of mathematics.
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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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... 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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All analysts spend half their time hunting through the literature for inequalities which they want to use and cannot prove.
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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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Sometimes one has to say difficult things, but one ought to say them as simply as one knows how.
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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 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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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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Archimedes will be remembered when Aeschylus is forgotten, because languages die and mathematical ideas do not. Immortality may be a silly word, but probably a mathematician has the best chance of whatever it may mean.
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Asked if he believes in one G-d, a mathematician answered: Yes, up to isomorphism.
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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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The mathematician's patterns, like the painter's or the poet's, must be beautiful.
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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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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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A chess problem is simply an exercise in pure mathematics.
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The public does not need to be convinced that there is something in mathematics.
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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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