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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
Mathematical
Useful
Technique
Mathematics
Pure
Distinctly
Taught
Sensual
Whole
Mainly
Applied
More quotes by G. H. Hardy
Exposition, criticism, appreciation, is work for second-rate minds.
G. H. Hardy
The public does not need to be convinced that there is something in mathematics.
G. H. Hardy
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
I was at my best at a little past forty, when I was a professor at Oxford.
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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.
G. H. Hardy
Cricket is the only game where you are playing against eleven of the other side and ten of your own.
G. H. Hardy
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
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
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
317 is a prime, not because we think so, or because our minds are shaped in one way rather than another, but because it is so, because mathematical reality is built that way.
G. H. Hardy
Sometimes one has to say difficult things, but one ought to say them as simply as one knows how.
G. H. Hardy
All analysts spend half their time hunting through the literature for inequalities which they want to use and cannot prove.
G. H. Hardy
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
... 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
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.
G. H. Hardy
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
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
No one has yet discovered any warlike purpose to be served by the theory of numbers or relativity, and it seems unlikely that anyone will do so for many years.
G. H. Hardy
Asked if he believes in one G-d, a mathematician answered: Yes, up to isomorphism.
G. H. Hardy
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).
G. H. Hardy