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The best mathematics is serious as well as beautiful—‘important’ if you like, but the word is very ambiguous, and ‘serious’ expresses what I mean much...more

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...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, because mathematical re...more

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

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It (proof by contradiction) is a far finer gambit than any chess gambit: a chess player may offer the sacrifice of a pawn or even a piece, but a mathe...more

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The ‘seriousness’ of a mathematical theorem lies, not in its practical consequences, which are usually negligible, but in the significance of the math...more

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[I was advised] to read Jordan's 'Cours d'analyse'; and I shall never forget the astonishment with which I read that remarkable work, the first inspir...more

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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 live...more

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

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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 w...more

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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 harm...more

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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-...more

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[Regarding mathematics,] there are now few studies more generally recognized, for good reasons or bad, as profitable and praiseworthy. This may be tru...more

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Archimedes will be remembered when Aeschylus is forgotten, because languages die and mathematical ideas do not. “Immortality” may be a silly word, but...more

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Most people have some appreciation of mathematics, just as most people can enjoy a pleasant tune; and there are probably more people really interested...more

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It seems that mathematical ideas are arranged somehow in strata, the ideas in each stratum being linked by a complex of relations both among themselve...more