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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.

G. H. Hardy

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G. H. Hardy
Age: 70 †
Born: 1877
Born: February 7
Died: 1947
Died: December 1
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Cranleigh
Surrey
G. H. Hardy
Godfrey Harold Hardy
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Godfrey Harold
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Lying
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Observe
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Theorems
Outside
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Observations
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Simply
Discover
Observing

More quotes by G. H. Hardy

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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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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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Asked if he believes in one G-d, a mathematician answered: Yes, up to isomorphism.
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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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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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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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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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The public does not need to be convinced that there is something in mathematics.
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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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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.
G. H. Hardy
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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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It is not worth an intelligent man's time to be in the majority. By definition, there are already enough people to do that.
G. H. Hardy
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I do not know an instance of a major mathematical advance initiated by a man past fifty
G. H. Hardy
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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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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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All analysts spend half their time hunting through the literature for inequalities which they want to use and cannot prove.
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Good work is not done by 'humble' men
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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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Sometimes one has to say difficult things, but one ought to say them as simply as one knows how.
G. H. Hardy
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Young men should prove theorems, old men should write books.
G. H. Hardy