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“Mathematicians have constructed a very large number of different systems of geometry, Euclidean or non-Euclidean, of one, two, three, or any number of dimensions. All these systems are of complete and equal validity. They embody the results of mathematicians' observations of their reality, a reality far more intense and far more rigid than the dubious and elusive reality of physics. The old-fashioned geometry of Euclid, the entertaining seven-point geometry of Veblen, the space-times of Minkowski and Einstein, are all absolutely and equally real. …There may be three dimensions in this room and five next door. As a professional mathematician, I have no idea; I can only ask some competent physicist to instruct me in the facts.
The function of a mathematician, then, is simply to observe the facts about his own intricate system of reality, that astonishingly beautiful complex of logical relations which forms the subject-matter of his science, as if he were an explorer looking at a distant range of mountains, and to record the results of his observations in a series of maps, each of which is a branch of pure mathematics. …Among them there perhaps none quite so fascinating, with quite the astonishing contrasts of sharp outline and shade, as that which constitutes the theory of numbers.”

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G. H. Hardy

"The Theory of Numbers," Nature (Sep 16, 1922) Vol. 110 https://books.google.com/books?id=1bMzAQAAMAAJ p. 381

“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.”

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G. H. Hardy buch A Mathematician's Apology

A Mathematician's Apology (1941)

“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.”

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G. H. Hardy buch A Mathematician's Apology

A Mathematician's Apology (1941)

“I am interested in mathematics only as a creative art.”

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G. H. Hardy buch A Mathematician's Apology

Quelle: A Mathematician's Apology (1941)

“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.”

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G. H. Hardy buch A Mathematician's Apology

A Mathematician's Apology (1941)

“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 reality is built that way.”

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G. H. Hardy buch A Mathematician's Apology

A Mathematician's Apology (1941)

“…there is probably less difference between the positions of a mathematician and of a physicist than is generally supposed, […] the mathematician is in much more direct contact with reality. This may seem a paradox, since it is the physicist who deals with the subject-matter usually described as ‘real’, but […] [a physicist] is trying to correlate the incoherent body of crude fact confronting him with some definite and orderly scheme of abstract relations, the kind of scheme he can borrow only from mathematics.”

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G. H. Hardy buch A Mathematician's Apology

A Mathematician's Apology (1941)

“Bradman is a whole class above any batsman who has ever lived: if Archimedes, Newton and Gauss remain in the Hobbs class, I have to admit the possibility of a class above them, which I find difficult to imagine. They had better be moved from now on into the Bradman class.”

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G. H. Hardy buch A Mathematician's Apology

Quoted by C. P. Snow in his introduction to reprints of the book.
A Mathematician's Apology (1941)

“… there is no scorn more profound, or on the whole more justifiable, than that of the men who make for the men who explain. Exposition, criticism, appreciation, is work for second-rate minds.”

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G. H. Hardy buch A Mathematician's Apology

A Mathematician's Apology (1941)

“A painter makes patterns with shapes and colours, a poet with words. A painting may embody an ‘idea’, but the idea is usually commonplace and unimportant. In poetry, ideas count for a good deal more; but, […] the importance of ideas in poetry is habitually exaggerated: '… Poetry is not the thing said but a way of saying it.' [In poetry, ] the poverty of the ideas seems hardly to affect the beauty of the verbal pattern.”

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G. H. Hardy buch A Mathematician's Apology

A Mathematician's Apology (1941)

“Chess problems are the hymn-tunes of mathematics.”

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G. H. Hardy buch A Mathematician's Apology

A Mathematician's Apology (1941)

“No one has yet discovered any warlike purpose to be served by the theory of numbers or relativity, and it seems unlikely that anyone will do so for many years.”

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G. H. Hardy buch A Mathematician's Apology

A Mathematician's Apology (1941)

“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.”

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G. H. Hardy buch A Mathematician's Apology

A Mathematician's Apology (1941)

“I still say to myself when I am depressed and find myself forced to listen to pompous and tiresome people "Well, I have done one thing you could never have done, and that is to have collaborated with Littlewood and Ramanujan on something like equal terms."”

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G. H. Hardy buch A Mathematician's Apology

A Mathematician's Apology (1941)

“If a man has any genuine talent, he should be ready to make almost any sacrifice in order to cultivate it to the full.”

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G. H. Hardy buch A Mathematician's Apology

A Mathematician's Apology (1941)

“I am obliged to interpolate some remarks on a very difficult subject: proof and its importance in mathematics. All physicists, and a good many quite respectable mathematicians, are contemptuous about proof. I have heard Professor Eddington, for example, maintain that proof, as pure mathematicians understand it, is really quite uninteresting and unimportant, and that no one who is really certain that he has found something good should waste his time looking for proof.”

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G. H. Hardy

Quelle: Ramanujan (1940), Ch. I : The Indian mathematician Ramanujan.

“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.”

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G. H. Hardy buch A Mathematician's Apology

A Mathematician's Apology (1941)

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

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G. H. Hardy buch A Mathematician's Apology

A Mathematician's Apology (1941)

“He could remember the idiosyncrasies of numbers in an almost uncanny way. It was Littlewood who said that every positive integer was one of Ramanujan's personal friends. I remember once going to see him when he was ill at Putney. I had ridden in taxi cab number 1729 and remarked that the number seemed to me rather a dull one, and that I hoped it was not an unfavorable omen. "No," he replied, "it is a very interesting number; it is the smallest number expressible as the sum of two cubes in two different ways."”

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G. H. Hardy

Quelle: Ramanujan (1940), Ch. I : The Indian mathematician Ramanujan.

“If I knew I was going to die today, I think I should still want to hear the cricket scores.”

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G. H. Hardy

Quelle: Quoted in The Joy of Cricket (ed. John Bright-Holmes, 1984)

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