G. H. Hardy: Quotes about mathematics

G. H. Hardy was British mathematician. Explore interesting quotes on mathematics.

G. H. Hardy: 40 quotes23 likes

“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.”

"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.”

G. H. Hardy book A Mathematician's Apology

A Mathematician's Apology (1941)

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

G. H. Hardy book A Mathematician's Apology

Source: 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.”

G. H. Hardy book 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.”

G. H. Hardy book A Mathematician's Apology

A Mathematician's Apology (1941)

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

G. H. Hardy book 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.”

G. H. Hardy book 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.”

Source: 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.”

G. H. Hardy book A Mathematician's Apology

A Mathematician's Apology (1941)