G. H. Hardy Quotes - Page 2

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• No mathematician should ever allow him to forget that mathematics, more than any other art or science, is a young man's game. ... Galois died at twenty-one, Abel at twenty-seven, Ramanujan at thirty-three, Riemann at forty. There have been men who have done great work later; ... [but] I do not know of a single instance of a major mathematical advance initiated by a man past fifty. ... A mathematician may still be competent enough at sixty, but it is useless to expect him to have original ideas.

  G. H. Hardy

  Art, Science, Past

  61 Copy quote

• All analysts spend half their time hunting through the literature for inequalities which they want to use and cannot prove.

  G. H. Hardy

  Math, Hunting, Use

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• Mathematics is not a contemplative but a creative subject.

  G. H. Hardy

  Creative, Mathematics, Contemplative

  G. H. Hardy (2012). “A Mathematician's Apology”, p.143, Cambridge University Press

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• The study of mathematics is, if an unprofitable, a perfectly harmless and innocent occupation.

  G. H. Hardy

  Science, Occupation, Study

  G. H. Hardy, C. P. Snow (2012). “A Mathematician's Apology”, p.74, Cambridge University Press

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• Most people are so frightened of the name of mathematics that they are ready, quite unaffectedly, to exaggerate their own mathematical stupidity.

  G. H. Hardy

  Math, Names, People

  G. H. Hardy (1992). “A Mathematician's Apology”, p.86, Cambridge University Press

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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

  War, Science, Average

  G. H. Hardy (2012). “A Mathematician's Apology”, p.152, Cambridge University Press

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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.

  G. H. Hardy

  Science, Study, Conflict

  G. H. Hardy (2012). “A Mathematician's Apology”, p.76, Cambridge University Press

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• Bombs are probably more merciful than bayonets

  G. H. Hardy

  Bayonets, Bombs, Merciful

  G. H. Hardy (2012). “A Mathematician's Apology”, p.142, Cambridge University Press

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• Greek mathematics is the real thing. The Greeks first spoke a language which modern mathematicians can understand... So Greek mathematics is 'permanent', more permanent even than Greek literature.

  G. H. Hardy

  Real, Science, Understanding

  G. H. Hardy, C. P. Snow (2012). “A Mathematician's Apology”, p.81, Cambridge University Press

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• Asked if he believes in one G-d, a mathematician answered: "Yes, up to isomorphism".

  G. H. Hardy

  Believe, Mathematician, Ifs

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• I was at my best at a little past forty, when I was a professor at Oxford.

  G. H. Hardy

  Science, Past, Oxford

  G. H. Hardy (2012). “A Mathematician's Apology”, p.148, Cambridge University Press

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• The public does not need to be convinced that there is something in mathematics.

  G. H. Hardy

  Doe, Needs, Mathematics

  G. H. Hardy, C. P. Snow (2012). “A Mathematician's Apology”, p.64, Cambridge University Press

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• There is no scorn more profound, or on the whole more justifiable, than that of the men who make for the men who explain.

  G. H. Hardy

  Men, Profound, He Man

  G. H. Hardy (2012). “A Mathematician's Apology”, p.61, Cambridge University Press

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• No one should ever be bored. … One can be horrified, or disgusted, but one can’t be bored.

  G. H. Hardy

  Bored, Boring, Should

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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).

  G. H. Hardy

  Science, Men, Two

  G. H. Hardy (2012). “A Mathematician's Apology”, p.66, Cambridge University Press

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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.

  G. H. Hardy

  Character, Science, Men

  G. H. Hardy (2012). “A Mathematician's Apology”, p.76, Cambridge University Press

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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

  Philosophy, Hands, Obscure

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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

  Real, Science, Numbers

  57 Copy quote

• Chess problems are the hymn-tunes of mathematics.

  G. H. Hardy

  Science, Hymns, Tunes

  G. H. Hardy (2012). “A Mathematician's Apology”, p.87, Cambridge University Press

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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

  Add, Life Is, Cases

  G. H. Hardy (2012). “A Mathematician's Apology”, p.151, Cambridge University Press

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• Good work is no done by "humble" men. It is one of the first duties of a professor, for example, in any subject, to exaggerate a little both the importance of his subject and his own importance in it. A man who is always asking "Is what I do worth while?" and "Am I the right person to do it?" will always be ineffective himself and a discouragement to others. He must shut his eyes a little and think a little more of his subject and himself than they deserve. This is not too difficult: it is harder not to make his subject and himself ridiculous by shutting his eyes too tightly.

  G. H. Hardy

  Eye, Hard Work, Humble

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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

  Art, Science, Men

  19 Copy quote

• If intellectual curiosity, professional pride, and ambition are the dominant incentives to research, then assuredly no one has a fairer chance of gratifying them than a mathematician.

  G. H. Hardy

  Ambition, Pride, Science

  G. H. Hardy, C. P. Snow (2012). “A Mathematician's Apology”, p.80, Cambridge University Press

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• No discovery of mine has made, or is likely to make, directly or indirectly, for good or ill, the least difference to the amenity of the world.

  G. H. Hardy

  Science, Discovery, Differences

  G. H. Hardy (2012). “A Mathematician's Apology”, p.150, Cambridge University Press

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• A chess problem is simply an exercise in pure mathematics.

  G. H. Hardy

  Exercise, Chess, Problem

  "A Mathematician's Apology".

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