G. H. Hardy Quotes

57 Sourced Quotes

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
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
It is not worth an intelligent man's time to be in the majority. By definition, there are already enough people to do that.

G. H. Hardy
A science or an art may be said to be "useful" if its development increases, even indirectly, the material well-being and comfort of men, it promotes happiness, using that word in a crude and commonplace way.

G. H. Hardy
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
The primes are the raw material out of which we have to build arithmetic, and Euclid's theorem assures us that we have plenty of material for the task.

G. H. Hardy
I will say only that if a chess problem is, in the crude sense, 'useless', then that is equally true of most of the best mathematics; that very little of mathematics is useful practically, and that the little [that is] is comparatively dull.

G. H. Hardy
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.

G. H. Hardy
I have myself always thought of a mathematician as in the first instance an observer, a man who gazes at a distant range of mountains and notes down his observations. His object is simply to distinguish clearly and notify to others as many different peaks as he can.

G. H. Hardy
When the world is mad, a mathematician may find in mathematics an incomparable anodyne. For mathematics is, of all the arts and sciences, the most austere and the most remote, and a mathematician should be of all men the one who can most easily take refuge where, as Bertrand Russell says, "one at least of our nobler impulses can best escape from the dreary exile of the actual world."

G. H. Hardy
We may say, roughly, that a mathematical idea is "significant" if it can be connected, in a natural and illuminating way, with a large complex of other mathematical ideas.

G. H. Hardy
Mathematical fame, if you have the cash to pay for it, is one of the soundest and steadiest of investments.

G. H. Hardy
I propose to put forward an apology for mathematics; and I may be told that it needs none, since there are now few studies more generally recognized, for good reasons or bad, as profitable and praiseworthy.

G. H. Hardy
A man who sets out to justify his existence and his activities has to distinguish two different questions. The first is whether the work which he does is worth doing; and the second is why he does it (whatever its value may be).

G. H. Hardy
If a man is in any sense a real mathematician, then it is a hundred to one that his mathematics will be far better than anything else he can do, and that it would be silly if he surrendered any decent opportunity of exercising his one talent in order to do undistinguished work in other fields. Such a sacrifice could be justified only by economic necessity of age.

G. H. Hardy
There is, strictly, no such thing as mathematical proof; that we can::: do nothing but point; that proofs are what Littlewood and I call gas, rhetorical flourishes designed to affect psychology, pictures on the board in the lectures, devices to stimulate the imagination of pupils.

G. H. Hardy
Sometimes one has to say difficult things, but one ought to say them as simply as one knows how.

G. H. Hardy
As history proves abundantly, mathematical achievement, whatever its intrinsic worth, is the most enduring of all.

G. H. Hardy
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
I do not remember having felt, as a boy, any passion for mathematics, and such notions as I may have had of the career of a mathematician were far from noble. I thought of mathematics in terms of examinations and scholarships: I wanted to beat other boys, and this seemed to be the way in which I could do so most decisively.

G. H. Hardy
I do not know an instance of a major mathematical advance initiated by a man past fifty

G. H. Hardy
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
Young men should prove theorems, old men should write books.

G. H. Hardy
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
A mathematical proof should resemble a simple and clear-cut constellation, not a scattered cluster in the Milky Way.

G. H. Hardy