G. H. Hardy Quotes About Mathematics

Quotes about: Mathematics

• 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

• 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

• 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

• 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

• 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

• 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)

• 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)

• A mathematician, like a painter or poet, is a maker of patterns. If his patterns are more permanent than theirs, it is because they are made with ideas.

  G. H. Hardy

  Education, Math, Unique

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

• In [great mathematics] there is a very high degree of unexpectedness, combined with inevitability and economy.

  G. H. Hardy

  Degrees, Economy, Mathematics

  G. H. Hardy (2012). “A Mathematician's Apology”, p.113, Cambridge University Press

• 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

• 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

• Reductio ad absurdum, which Euclid loved so much, is one of a mathematician's finest weapons. It is a far finer gambit than any chess play: a chess player may offer the sacrifice of a pawn or even a piece, but a mathematician offers the game.

  G. H. Hardy

  Love, Sacrifice, Math

  G. H. Hardy, C. P. Snow (2012). “A Mathematician's Apology”, p.94, Cambridge University Press

• The mathematician's patterns, like the painter's or the poet's, must be beautiful.

  G. H. Hardy

  Beautiful, Math, Patterns

  A Mathematician's Apology ch. 10 (1940)

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

  G. H. Hardy

  Exercise, Chess, Problem

  "A Mathematician's Apology".

• 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

• 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

  Sensual, Technique, Taught

  "A Mathematician's Apology". Book by G. H. Hardy, 1941.

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

  G. H. Hardy

  Book, Writing, Math

• 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

• 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

• 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

• The Babylonian and Assyrian civilizations have perished; Hammurabi, Sargon and Nebuchadnezzar are empty names; yet Babylonian mathematics is still interesting, and the Babylonian scale of 60 is still used in Astronomy.

  G. H. Hardy

  Science, Civilization, Names

• 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

• 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

• If a man is in any sense a real mathematician, then it is a hundred to one that his mathematics will be far better than anything else he can do, and that he would be silly if he surrendered any decent opportunity of exercising his one talent in order to do undistinguished work in other fields. Such a sacrifice could be justified only by economic necessity of age.

  G. H. Hardy

  Real, Silly, Sacrifice

  "A Mathematician's Apology".

• 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

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