G. H. Hardy Quotes

75 quotes in 1090 categories

• 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… Ambition
• [Regarding mathematics,] there are now few studies more generally recognized, for good reasons or bad, as profitable and praiseworthy. This may be true; indeed it… Astronomy
• A chess problem is genuine mathematics, but it is in some way "trivial" mathematics. However, ingenious and intricate, however original and surprising the moves, there… Ambiguous
• 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… Accentuate
• 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… Amenity
• 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… Aeschylus
• As history proves abundantly, mathematical achievement, whatever its intrinsic worth, is the most enduring of all. Abundantly
• Chess problems are the hymn-tunes of mathematics. Chess
• 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… First Spoke
• I am interested in mathematics only as a creative art. Art
• 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… Believe
• 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… All
• In [great mathematics] there is a very high degree of unexpectedness, combined with inevitability and economy. Combined
• 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:… Absurdum
• 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… Beautiful
• The study of mathematics is, if an unprofitable, a perfectly harmless and innocent occupation. Harmless
• [P]ure mathematics is on the whole distinctly more useful than applied. For what is useful above all is technique, and mathematical technique is taught mainly… All
• As Littlewood said to me once [of the ancient Greeks], they are not clever school boys or "scholarship candidates," but "Fellows of another college." Ancient
• 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… Built
• Real mathematics must be justified as art if it can be justified at all. All

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