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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

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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
Thinking
Minds
Built
Rather
Another
Reality
Shaped
Mind
Prime
Way
Mathematical
Think
Logic

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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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... Philosophy proper is a subject, on the one hand so hopelessly obscure, on the other so astonishingly elementary, that there knowledge hardly counts.
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In [great mathematics] there is a very high degree of unexpectedness, combined with inevitability and economy.
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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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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.
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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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Sometimes one has to say difficult things, but one ought to say them as simply as one knows how.
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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.
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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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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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Exposition, criticism, appreciation, is work for second-rate minds.
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Asked if he believes in one G-d, a mathematician answered: Yes, up to isomorphism.
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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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The public does not need to be convinced that there is something in mathematics.
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For my part, it is difficult for me to say what I owe to Ramanujan - his originality has been a constant source of suggestion to me ever since I knew him, and his death is one of the worst blows I have ever had.
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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 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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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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I do not know an instance of a major mathematical advance initiated by a man past fifty
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The study of mathematics is, if an unprofitable, a perfectly harmless and innocent occupation.
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