G. H. Hardy Quotes
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Most people are so frightened of the name of mathematics that they are ready, quite unaffectedly, to exaggerate their own mathematical stupidity.
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I do not know an instance of a major mathematical advance initiated by a man past fifty
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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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[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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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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I am interested in mathematics only as a creative art.
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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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In [great mathematics] there is a very high degree of unexpectedness, combined with inevitability and economy.
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Good work is no done by "humble" men. It is one of the first duties of a professor, for example, in any subject, to exaggerate a little both the importance of his subject and his own importance in it. A man who is always asking "Is what I do worth while?" and "Am I the right person to do it?" will always be ineffective himself and a discouragement to others. He must shut his eyes a little and think a little more of his subject and himself than they deserve. This is not too difficult: it is harder not to make his subject and himself ridiculous by shutting his eyes too tightly.
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A chess problem is genuine mathematics, but it is in some way "trivial" mathematics. However, ingenious and intricate, however original and surprising the moves, there is something essential lacking. Chess problems are unimportant. The best mathematics is serious as well as beautiful-"important" if you like, but the word is very ambiguous, and "serious" expresses what I mean much better.
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The mathematician's patterns, like the painter's or the poet's, must be beautiful.
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When the world is mad, a mathematician may find in mathematics an incomparable anodyne. For mathematics is, of all the arts and sciences, the most austere and the most remote, and a mathematician should be of all men the one who can most easily take refuge where, as Bertrand Russell says, "one at least of our nobler impulses can best escape from the dreary exile of the actual world."
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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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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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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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Beauty is the first test: there is no permanent place in the world for ugly mathematics.
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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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... 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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If I could prove by logic that you would die in five minutes, I should be sorry you were going to die, but my sorrow would be very much mitigated by pleasure in the proof.
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The public does not need to be convinced that there is something in 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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[I was advised] to read Jordan's 'Cours d'analyse'; and I shall never forget the astonishment with which I read that remarkable work, the first inspiration for so many mathematicians of my generation, and learnt for the first time as I read it what mathematics really meant.
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For any serious purpose, intelligence is a very minor gift.
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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.
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It is rather astonishing how little practical value scientific knowledge has for ordinary men, how dull and commonplace such of it as has value is, and how its value seems almost to vary inversely to its reputed utility.
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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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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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Good work is not done by 'humble' men
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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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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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