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G. H. Hardy

36 quotes

“If I knew I was going to die today, I think I should still want to hear the cricket scores.”
G. H. Hardy (1877–1947) said by 1947 at the latest wikiquote, CC BY-SA 4.0 source
Recorded in: Quoted in The Joy of Cricket (ed. John Bright-Holmes, 1984)
“If I could prove by logic that you would die in five minutes, I should be sorry you were going to die, but my sorrow would be very much mitigated by pleasure in the proof.”
G. H. Hardy (1877–1947) first seen 1909 wikiquote, CC BY-SA 4.0 source
Recorded in: Quoted by Bertrand Russell, Logical and Philosophical Papers, 1909–13, Routledge, 1992, p. xxix.
“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.”
G. H. Hardy (1877–1947) said by 1947 at the latest wikiquote, CC BY-SA 4.0 source
“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.”
G. H. Hardy (1877–1947) said by 1947 at the latest wikiquote, CC BY-SA 4.0 source
“… 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 (1877–1947) said by 1947 at the latest wikiquote, CC BY-SA 4.0 source
“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 (1877–1947) said by 1947 at the latest wikiquote, CC BY-SA 4.0 source
“No mathematician should... allow himself to forget that mathematics, more than any other art or science, is a young man's game. ...Newton gave up mathematics at fifty; ...by the time he was forty ...his great creative days were over. His greatest ideas.., fluxions and the law of gravitation, came... about 1666, when he was twenty four... He made big discoveries until... nearly forty (the 'elliptic orbit' at thirty-seven), but after that he did little but polish and perfect.”
G. H. Hardy (1877–1947) said by 1947 at the latest wikiquote, CC BY-SA 4.0 source
“Galois died at twenty-one, Abel at twenty-seven, Ramanujan at thirty-three, Riemann at forty. There have been men who have done great work a good deal later; Gauss's great memoir on differential geometry was published when he was fifty (though he had had the fundamental ideas ten years before). I do not know an instance of a major mathematical advance initiated by a man past fifty. If a man of mature age loses interest in and abandons mathematics, the loss is not likely to be very serious either for mathematics or for himself.”
G. H. Hardy (1877–1947) said by 1947 at the latest wikiquote, CC BY-SA 4.0 source
“[L]ater records of mathematicians... are not... encouraging. ...There is no instance ...of a first rate mathematician abandoning mathematics and attaining first-rate distinction in any other field. ...Every young mathematician of real talent whom I have known has been faithful to mathematics.., not from lack of ambition but from abundance of it; they have all recognized that there... lay the road to a life of any distinction.”
G. H. Hardy (1877–1947) said by 1947 at the latest wikiquote, CC BY-SA 4.0 source
“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 (1877–1947) said by 1947 at the latest wikiquote, CC BY-SA 4.0 source
“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 (1877–1947) said by 1947 at the latest wikiquote, CC BY-SA 4.0 source
“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, as Housman insisted, 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 (1877–1947) said by 1947 at the latest wikiquote, CC BY-SA 4.0 source
“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 (1877–1947) said by 1947 at the latest wikiquote, CC BY-SA 4.0 source
“Chess problems are the hymn-tunes of mathematics.”
G. H. Hardy (1877–1947) said by 1947 at the latest wikiquote, CC BY-SA 4.0 source
“, which Euclid loved so much, is one of a mathematician's finest weapons. It is a far finer than any chess gambit: a chess player may offer the sacrifice of a pawn or even a piece, but a mathematician offers the game.”
G. H. Hardy (1877–1947) said by 1947 at the latest wikiquote, CC BY-SA 4.0 source
“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 is something essential lacking. Chess problems are unimportant. 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 better.”
G. H. Hardy (1877–1947) said by 1947 at the latest wikiquote, CC BY-SA 4.0 source
“I am interested in mathematics only as a creative art.”
G. H. Hardy (1877–1947) said by 1947 at the latest wikiquote, CC BY-SA 4.0 source
“It is... astonishing how little practical value scientific knowledge has for ordinary men, how dull and commonplace such of it as has value is, and how its value seems almost to vary inversely to its reputed utility. ...We live either by or on other people's professional knowledge.”
G. H. Hardy (1877–1947) said by 1947 at the latest wikiquote, CC BY-SA 4.0 source
“[A] good deal of elementary mathematics... 'elementary' in the sense in which professional mathematicians use it... [e.g.,] knowledge of the differential and integral calculus—has considerable practical utility. These... are... rather dull... the parts which have least aesthetic value. The 'real' mathematics of the 'real' mathematicians... of Fermat and Euler and Gauss and Abel and Riemann, is almost wholly 'useless' (...as true of 'applied' as of 'pure' mathematics). It is not possible to justify the life of any genuine professional mathematician on the ground of... 'utility'...”
G. H. Hardy (1877–1947) said by 1947 at the latest wikiquote, CC BY-SA 4.0 source
“[S]cience works for evil as well as for good (...particularly ...in time of war); and... mathematicians may be justified in rejoicing that there is one science... their own, whose ...remoteness from ordinary human activities should keep it gentle and clean.”
G. H. Hardy (1877–1947) said by 1947 at the latest wikiquote, CC BY-SA 4.0 source
“It is... natural to suppose that there is a great difference in utility between 'pure' and 'applied' mathematics. This is a delusion...”
G. H. Hardy (1877–1947) said by 1947 at the latest wikiquote, CC BY-SA 4.0 source
“A man who could give a convincing account of mathematical reality would have solved very many of the most difficult problems of metaphysics. If he could include physical reality in his account, he would have solved them all.”
G. H. Hardy (1877–1947) said by 1947 at the latest wikiquote, CC BY-SA 4.0 source
“[M]athematical reality lies outside us ...our function is to discover or observe it, and ...the theorems ...we prove, and ...describe grandiloquently as our 'creations', are simply our notes of our observations. This view has been held, in one form or another, by many philosophers of high reputation from Plato onwards [...]”
G. H. Hardy (1877–1947) said by 1947 at the latest wikiquote, CC BY-SA 4.0 source
“There is the science of pure geometry, in which there are many geometries, , , non-Euclidean geometry... [etc.]. Each... is a , a pattern of ideas... judged by the interest and beauty of... pattern. It is a map or picture, the... product of many hands, a partial and imperfect copy (yet exact so far as it extends) of a section of mathematical reality. But... there is one thing... of which pure geometries are not pictures, and that is the spatio-temporal reality of the physical world. ...[T]hey cannot be, since earthquakes and eclipses are not mathematical concepts.”
G. H. Hardy (1877–1947) said by 1947 at the latest wikiquote, CC BY-SA 4.0 source
“[T]here is no mathematician so pure that he feels no interest at all in the physical world; but, in so far as he succumbs to this temptation, he will be abandoning his purely mathematical position.”
G. H. Hardy (1877–1947) said by 1947 at the latest wikiquote, CC BY-SA 4.0 source
“...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 (1877–1947) said by 1947 at the latest wikiquote, CC BY-SA 4.0 source
“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 so, because mathematical reality is built that way.”
G. H. Hardy (1877–1947) said by 1947 at the latest wikiquote, CC BY-SA 4.0 source
“[[Pure mathematics|[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 through pure mathematics.”
G. H. Hardy (1877–1947) said by 1947 at the latest wikiquote, CC BY-SA 4.0 source
“[T]he trivial mathematics is, on the whole, useful, and... the real mathematics, on the whole, is not...”
G. H. Hardy (1877–1947) said by 1947 at the latest wikiquote, CC BY-SA 4.0 source
“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 (1877–1947) said by 1947 at the latest wikiquote, CC BY-SA 4.0 source
“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 (1877–1947) said by 1947 at the latest wikiquote, CC BY-SA 4.0 source
“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 (1877–1947) said by 1947 at the latest wikiquote, CC BY-SA 4.0 source
“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. (pg 28)”
G. H. Hardy (1877–1947) said by 1947 at the latest wikiquote, CC BY-SA 4.0 source
“It is never worth a first-class man's time to express a majority opinion. By definition, there are plenty of others to do that. (pg 46)”
G. H. Hardy (1877–1947) said by 1947 at the latest wikiquote, CC BY-SA 4.0 source
“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.”
G. H. Hardy (1877–1947) first seen 1922 wikiquote, CC BY-SA 4.0 source
Recorded in: The Theory of Numbers," Nature (Sep 16, 1922) Vol. 110 p. 381
“The play is independent of the pages on which it is printed, and 'pure geometries' are independent of lecture rooms, [rough blackboard drawings] or of any other detail of the physical world. This is the point of view of a pure mathematician. Applied mathematicians, mathematical physicists... take a different view... preoccupied with the physical world itself, which also has its structure or pattern. ...We may be able to trace a ...resemblance between the two sets of relations, and then the pure geometry will become interesting to physicists; it will give us ...a map which 'fits the facts' ...The geometer offers ...a whole set of maps from which to choose.”
G. H. Hardy (1877–1947) said by 1947 at the latest wikiquote, CC BY-SA 4.0 source