G. H. Hardy Quotes

Quotes about:

• 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.

  G. H. Hardy

  Lying, Believe, Science

  G. H. Hardy (1992). “A Mathematician's Apology”, p.123, Cambridge University Press

  150 Copy quote

• The mathematician's patterns, like the painter's or the poet's must be beautiful; the ideas, like the colours or the words must fit together in a harmonious way. Beauty is the first test: there is no permanent place in the world for ugly mathematics.

  G. H. Hardy

  Beauty, Beautiful, Math

  A Mathematician's Apology ch. 10 (1940)

  13 Copy quote

• Exposition, criticism, appreciation, is work for second-rate minds.

  G. H. Hardy

  Appreciation, Mind, Criticism

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

  8 Copy quote

• 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

  Knowledge, Intelligent, Men

  46 Copy quote

• A mathematician, like a painter or a poet, is a maker of patterns.

  G. H. Hardy

  Math, Patterns, Original Ideas

  G. H. Hardy (2012). “A Mathematician's Apology”, p.84, Cambridge University Press

  32 Copy quote

• A person’s first duty, a young person’s at any rate, is to be ambitious, and the noblest ambition is that of leaving behind something of permanent value.

  G. H. Hardy

  Ambition, Leaving, Ambitious

  8 Copy quote

• For any serious purpose, intelligence is a very minor gift.

  G. H. Hardy

  Science, Purpose, Serious

  G. H. Hardy (2012). “A Mathematician's Apology”, p.46, Cambridge University Press

  6 Copy quote

• I have never done anything 'useful'. 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... Judged by all practical standards, the value of my mathematical life is nil; and outside mathematics it is trivial anyhow. I have just one chance of escaping a verdict of complete triviality, that I may be judged to have created something worth creating. And that I have created something is undeniable: the question is about its value.

  G. H. Hardy

  Differences, Creating, Escaping

  27 Copy quote

• Good work is not done by 'humble' men

  G. H. Hardy

  Humble, Men, Done

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

  6 Copy quote

• 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

  Sorry, Sorrow, Would Be

  19 Copy quote

• Beauty is the first test: there is no permanent place in the world for ugly mathematics.

  G. H. Hardy

  Beauty, Math, Apology

  A Mathematician's Apology ch. 10 (1940)

  37 Copy quote

• 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

  Lying, Ideas, Mathematics

  G. H. Hardy, C. P. Snow (2012). “A Mathematician's Apology”, p.89, Cambridge University Press

  5 Copy quote

• I remember once going to see him [Ramanujan] when he was lying ill at Putney. I had ridden in taxi-cab No. 1729, and remarked that the number seemed to me rather a dull one, and that I hoped it was not an unfavourable omen. "No," he replied, "it is a very interesting number; it is the smallest number expressible as a sum of two cubes in two different ways."

  G. H. Hardy

  Lying, Two, Numbers

  39 Copy quote

• Mathematics may, like poetry or music, "promote and sustain a lofty habit of mind."

  G. H. Hardy

  Science, Mind, May

  G. H. Hardy, C. P. Snow (2012). “A Mathematician's Apology”, p.116, Cambridge University Press

  5 Copy quote

• Young men should prove theorems, old men should write books.

  G. H. Hardy

  Book, Writing, Math

  11 Copy quote

• 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

  4 Copy quote

• I am interested in mathematics only as a creative art.

  G. H. Hardy

  Art, Creativity, Creative

  G. H. Hardy, C. P. Snow (2012). “A Mathematician's Apology”, p.115, Cambridge University Press

  54 Copy quote

• 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

  Sacrifice, Men, Order

  G. H. Hardy (2012). “A Mathematician's Apology”, p.68, Cambridge University Press

  26 Copy quote

• 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

  4 Copy quote

• 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.

  G. H. Hardy

  Silly, Mean, Math

  A Mathematician's Apology ch. 8 (1940)

  23 Copy quote

• Sometimes one has to say difficult things, but one ought to say them as simply as one knows how.

  G. H. Hardy

  Knowledge, Science, Simplicity

  G. H. Hardy (2012). “A Mathematician's Apology”, p.47, Cambridge University Press

  19 Copy quote

• Most people can do nothing at all well

  G. H. Hardy

  People, Wells, Can Do

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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

  8 Copy quote

• 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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• Real mathematics must be justified as art if it can be justified at all.

  G. H. Hardy

  Art, Real, Justified

  G. H. Hardy, C. P. Snow (2012). “A Mathematician's Apology”, p.139, Cambridge University Press

  19 Copy quote

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