G. H. Hardy Quotes
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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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Beauty is the first test: there is no permanent place in the world for ugly mathematics.
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[Regarding mathematics,] there are now few studies more generally recognized, for good reasons or bad, as profitable and praiseworthy. This may be true; indeed it is probable, since the sensational triumphs of Einstein, that stellar astronomy and atomic physics are the only sciences which stand higher in popular estimation.
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It is not worth an intelligent man's time to be in the majority. By definition, there are already enough people to do that.
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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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A mathematician, like a painter or poet, is a maker of patterns. If his patterns are more permanent than theirs, it is because they are made with ideas.
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No discovery of mine has made, or is likely to make, directly or indirectly, for good or ill, the least difference to the amenity of the world.
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I am interested in mathematics only as a creative art.
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There is no scorn more profound, or on the whole more justifiable, than that of the men who make for the men who explain. Exposition, criticism, appreciation, is work for second-rate minds.
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A mathematician, like a painter or a poet, is a maker of patterns. If his patterns are more permanent than theirs, it is because they are made with ideas.
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Young men should prove theorems, old men should write books.
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I wrote a great deal... but very little of any importance; there are not more than four of five papers which I can still remember with some satisfaction.
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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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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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... 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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Archimedes will be remembered when Aeschylus is forgotten, because languages die and mathematical ideas do not.
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I still say to myself when I am depressed and find myself forced to listen to pompous and tiresome people 'Well, I have done one thing you could never have done, and that is to have collaborated with Littlewood and Ramanujan on something like equal terms.'
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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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Chess problems are the hymn-tunes of mathematics.
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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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In [great mathematics] there is a very high degree of unexpectedness, combined with inevitability and economy.
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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, because mathematical reality is built that way.
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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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If a man has any genuine talent, he should be ready to make almost any sacrifice in order to cultivate it to the full.