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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.

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
Science
Generally
May
Reasons
Mathematics
Praiseworthy
Reason
None
Propose
Needs
Forward
Profitable
Good
Told
Apology
Study
Studies
Since
Recognized

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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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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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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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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In [great mathematics] there is a very high degree of unexpectedness, combined with inevitability and economy.
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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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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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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.
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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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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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Most people can do nothing at all well
G. H. Hardy
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The case for my life... is this: that I have added something to knowledge, and helped others to add more
G. H. Hardy
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Bombs are probably more merciful than bayonets
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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The mathematician's patterns, like the painter's or the poet's, must be beautiful.
G. H. Hardy
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A mathematician, like a painter or a poet, is a maker of patterns.
G. H. Hardy
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Good work is not done by 'humble' men
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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 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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Young men should prove theorems, old men should write books.
G. H. Hardy