Quotes from book
A Mathematician's Apology

A Mathematician's Apology
G. H. Hardy

A Mathematician's Apology is a 1940 essay by British mathematician G. H. Hardy. It concerns the aesthetics of mathematics with some personal content, and gives the layman an insight into the mind of a working mathematician.

G. H. Hardy photo

“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 book A Mathematician's Apology

A Mathematician's Apology (1941)

G. H. Hardy photo

“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 book A Mathematician's Apology

A Mathematician's Apology (1941)

G. H. Hardy photo

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

G. H. Hardy book A Mathematician's Apology

Source: A Mathematician's Apology (1941)

G. H. Hardy photo

“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.”

G. H. Hardy book A Mathematician's Apology

A Mathematician's Apology (1941)

G. H. Hardy photo

“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.”

G. H. Hardy book A Mathematician's Apology

A Mathematician's Apology (1941)

G. H. Hardy photo

“…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.”

G. H. Hardy book A Mathematician's Apology

A Mathematician's Apology (1941)

G. H. Hardy photo

“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.”

G. H. Hardy book A Mathematician's Apology

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

G. H. Hardy photo

“… 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.”

G. H. Hardy book A Mathematician's Apology

A Mathematician's Apology (1941)

G. H. Hardy photo

“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.”

G. H. Hardy book A Mathematician's Apology

A Mathematician's Apology (1941)

G. H. Hardy photo

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

G. H. Hardy book A Mathematician's Apology

A Mathematician's Apology (1941)

G. H. Hardy photo

“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.”

G. H. Hardy book A Mathematician's Apology

A Mathematician's Apology (1941)

G. H. Hardy photo

“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 book A Mathematician's Apology

A Mathematician's Apology (1941)

G. H. Hardy photo

“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."”

G. H. Hardy book A Mathematician's Apology

A Mathematician's Apology (1941)

G. H. Hardy photo

“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 book A Mathematician's Apology

A Mathematician's Apology (1941)

G. H. Hardy photo

“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.”

G. H. Hardy book A Mathematician's Apology

A Mathematician's Apology (1941)

G. H. Hardy photo

“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 book A Mathematician's Apology

A Mathematician's Apology (1941)

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