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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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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
Mathematical
Degree
Mathematics
Degrees
Economy
High
Unexpectedness
Great
Inevitability
Combined

More quotes by G. H. Hardy

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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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The case for my life... is this: that I have added something to knowledge, and helped others to add more
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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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Exposition, criticism, appreciation, is work for second-rate minds.
G. H. Hardy
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Most people can do nothing at all well
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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.
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A chess problem is simply an exercise in pure mathematics.
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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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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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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 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.
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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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... 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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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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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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The public does not need to be convinced that there is something in mathematics.
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.
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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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Cricket is the only game where you are playing against eleven of the other side and ten of your own.
G. H. Hardy