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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.

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
Useful
Technique
Mathematics
Pure
Distinctly
Taught
Sensual
Whole
Mainly
Applied
Mathematical

More quotes by G. H. Hardy

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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.
G. H. Hardy
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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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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.
G. H. Hardy
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Young men should prove theorems, old men should write books.
G. H. Hardy
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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.
G. H. Hardy
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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.
G. H. Hardy
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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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Good work is not done by 'humble' men
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.
G. H. Hardy
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I was at my best at a little past forty, when I was a professor at Oxford.
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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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.
G. H. Hardy
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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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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.
G. H. Hardy
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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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Perhaps five or even ten per cent of men can do something rather well. It is a tiny minority who can do anything really well, and the number of men who can do two things well is negligible. If a man has any genuine talent, he should be ready to make almost any sacrifice in order to cultivate it to the full.
G. H. Hardy
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In [great mathematics] there is a very high degree of unexpectedness, combined with inevitability and economy.
G. H. Hardy
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The mathematician's patterns, like the painter's or the poet's, must be beautiful.
G. H. Hardy
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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
G. H. Hardy
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Exposition, criticism, appreciation, is work for second-rate minds.
G. H. Hardy