G. H. Hardy Quotes

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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.

  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)

  12 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 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

• 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

• 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

• 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

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• 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

• 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

• 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

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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.

  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

• 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

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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.

  G. H. Hardy

  Sacrifice, Men, Order

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

  26 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

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• 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

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

  G. H. Hardy

  Book, Writing, Math

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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

• 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

• When the world is mad, a mathematician may find in mathematics an incomparable anodyne. For mathematics is, of all the arts and sciences, the most austere and the most remote, and a mathematician should be of all men the one who can most easily take refuge where, as Bertrand Russell says, "one at least of our nobler impulses can best escape from the dreary exile of the actual world."

  G. H. Hardy

  Art, Science, Men

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

  20 Copy quote

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

  G. H. Hardy

  Believe, Mathematician, Ifs

  22 Copy quote

• They [formulae 1.10 - 1.12 of Ramanujan] must be true because, if they were not true, no one would have had the imagination to invent them.

  G. H. Hardy

  Imagination, Ramanujan, Being True

  31 Copy quote

• 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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