Famous Quotes & Sayings

G.H. Hardy Quotes & Sayings

Enjoy the top 89 famous quotes, sayings and quotations by G.H. Hardy.

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Famous Quotes By G.H. Hardy

G.H. Hardy Quotes 352296

For my part, it is difficult for me to say what I owe to Ramanujan - his originality has been a constant source of suggestion to me ever since I knew him, and his death is one of the worst blows I have ever had. — G.H. Hardy

G.H. Hardy Quotes 1357994

Real mathematics must be justified as art if it can be justified at all. — G.H. Hardy

G.H. Hardy Quotes 364278

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

G.H. Hardy Quotes 564030

A month's intelligent instruction in the theory of numbes ought to be twice as instructive, twice as useful, and at least 10 times as entertaining as the same amount of 'calculus for engineers'. — G.H. Hardy

G.H. Hardy Quotes 1462177

The geometer offers to the physicist a whole set of maps from which to choose. One map, perhaps, will fit the facts better than others, and then the geometry which provides that particular map will be the geometry most important for applied mathematics. — G.H. Hardy

G.H. Hardy Quotes 621018

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

G.H. Hardy Quotes 2096572

I was at my best at a little past forty, when I was a professor at Oxford. — G.H. Hardy

G.H. Hardy Quotes 1479092

Mathematics may, like poetry or music, "promote and sustain a lofty habit of mind." — G.H. Hardy

G.H. Hardy Quotes 608866

The Babylonian and Assyrian civilizations have perished; Hammurabi, Sargon and Nebuchadnezzar are empty names; yet Babylonian mathematics is still interesting, and the Babylonian scale of 60 is still used in Astronomy. — G.H. Hardy

G.H. Hardy Quotes 942974

In these days of conflict between ancient and modern studies, there must surely be something to be said for a study which did not begin with Pythagoras, and will not end with Einstein, but is the oldest and the youngest of all. — G.H. Hardy

G.H. Hardy Quotes 229878

Bombs are probably more merciful than bayonets — G.H. Hardy

G.H. Hardy Quotes 2207734

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

G.H. Hardy Quotes 2077175

No one should ever be bored. ... One can be horrified, or disgusted, but one can't be bored. — G.H. Hardy

G.H. Hardy Quotes 1822465

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

G.H. Hardy Quotes 1099538

A science is said to be useful if its development tends to accentuate the existing inequalities in the distribution of wealth, or more directly promotes the destruction of human life. — G.H. Hardy

G.H. Hardy Quotes 1540411

[Regarding mathematics,] there are now few studies more generally recognized, for good reasons or bad, as profitable and praiseworthy. This may be true; indeed it is probable, since the sensational triumphs of Einstein, that stellar astronomy and atomic physics are the only sciences which stand higher in popular estimation. — G.H. Hardy

G.H. Hardy Quotes 2060523

Cricket is the only game where you are playing against eleven of the other side and ten of your own. — G.H. Hardy

G.H. Hardy Quotes 214647

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

G.H. Hardy Quotes 1256003

All analysts spend half their time hunting through the literature for inequalities which they want to use and cannot prove. — G.H. Hardy

G.H. Hardy Quotes 2199336

If I had a statue on a column in London, would I prefer the columns to be so high that the statue was invisible, or low enough for the features to be recognizable? I would choose the first alternative, Dr Snow, presumably, the second. — G.H. Hardy

G.H. Hardy Quotes 141660

Poetry is more valuable than cricket, but Bradman would be a fool if he sacrificed his cricket in order to write second-rate minor poetry (and I suppose that it is unlikely that he could do better). — G.H. Hardy

G.H. Hardy Quotes 1971731

It is rather 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. — G.H. Hardy

G.H. Hardy Quotes 1733336

The mathematician is in much more direct contact with reality ... [Whereas] the physicist's reality, whatever it may be, has few or none of the attributes which common sense ascribes instinctively to reality. A chair may be a collection of whirling electrons. — G.H. Hardy

G.H. Hardy Quotes 1434339

Greek mathematics is the real thing. The Greeks first spoke a language which modern mathematicians can understand ... So Greek mathematics is 'permanent', more permanent even than Greek literature. — G.H. Hardy

G.H. Hardy Quotes 896919

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

G.H. Hardy Quotes 2042657

No mathematician should ever allow him to forget that mathematics, more than any other art or science, is a young man's game. ... 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 later; ... [but] I do not know of a single instance of a major mathematical advance initiated by a man past fifty. ... A mathematician may still be competent enough at sixty, but it is useless to expect him to have original ideas. — G.H. Hardy

G.H. Hardy Quotes 2122506

There is always more in one of Ramanujan's formulae than meets the eye, as anyone who sets to work to verify those which look the easiest will soon discover. In some the interest lies very deep, in others comparatively near the surface; but there is not one which is not curious and entertaining. — G.H. Hardy

G.H. Hardy Quotes 165148

The study of mathematics is, if an unprofitable, a perfectly harmless and innocent occupation. — G.H. Hardy

G.H. Hardy Quotes 1098438

I count Maxwell and Einstein, Eddington and Dirac, among "real" mathematicians. The great modern achievements of applied mathematics have been in relativity and quantum mechanics, and these subjects are at present at any rate, almost as "useless" as the theory of numbers. — G.H. Hardy

G.H. Hardy Quotes 498896

I am interested in mathematics only as a creative art. — G.H. Hardy

G.H. Hardy Quotes 731325

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

G.H. Hardy Quotes 1899924

A mathematician ... has no material to work with but ideas, and so his patterns are likely to last longer, since ideas wear less with time than words. — G.H. Hardy

G.H. Hardy Quotes 523085

A mathematician, like a painter or 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

G.H. Hardy Quotes 1532871

Most people can do nothing at all well — G.H. Hardy

G.H. Hardy Quotes 260383

Mathematics is not a contemplative but a creative subject; no one can draw much consolation from it when he has lost the power or the desire to create; and that is apt to happen to a mathematician rather soon. It is a pity, but in that case he does not matter a great deal anyhow, and it would be silly to bother about him. — G.H. Hardy

G.H. Hardy Quotes 181290

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

G.H. Hardy Quotes 110439

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

G.H. Hardy Quotes 1053613

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

G.H. Hardy Quotes 962890

I wrote a great deal ... but very little of any importance; there are not more than four of five papers which I can still remember with some satisfaction. — G.H. Hardy

G.H. Hardy Quotes 1664268

A person's first duty, a young person's at any rate, is to be ambitious, and the noblest ambition is that of leaving behind something of permanent value. — G.H. Hardy

G.H. Hardy Quotes 2100045

There is no scorn more profound, or on the whole more justifiable, than that of the men who make for the men who explain. — G.H. Hardy

G.H. Hardy Quotes 2269420

The public does not need to be convinced that there is something in mathematics. — G.H. Hardy

G.H. Hardy Quotes 2270979

I remember once going to see him [Ramanujan] when he was lying ill at Putney. I had ridden in taxi-cab No. 1729, and remarked that the number seemed to me rather a dull one, and that I hoped it was not an unfavourable omen. "No," he replied, "it is a very interesting number; it is the smallest number expressible as a sum of two cubes in two different ways." — G.H. Hardy

G.H. Hardy Quotes 2004917

If intellectual curiosity, professional pride, and ambition are the dominant incentives to research, then assuredly no one has a fairer chance of gratifying them than a mathematician. — G.H. Hardy

G.H. Hardy Quotes 1981932

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

G.H. Hardy Quotes 1974080

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

G.H. Hardy Quotes 2180769

Good work is not done by 'humble' men — G.H. Hardy

G.H. Hardy Quotes 1603859

[I was advised] to read Jordan's 'Cours d'analyse'; and I shall never forget the astonishment with which I read that remarkable work, the first inspiration for so many mathematicians of my generation, and learnt for the first time as I read it what mathematics really meant. — G.H. Hardy

G.H. Hardy Quotes 1853950

It seems that mathematical ideas are arranged somehow in strata, the ideas in each stratum being linked by a complex of relations both among themselves and with those above and below. The lower the stratum, the deeper (and in general more difficult) the idea. Thus the idea of an 'irrational' is deeper than that of an integer; and Pythagoras's theorem is, for that reason, deeper than Euclid's. — G.H. Hardy

G.H. Hardy Quotes 2165496

The theory of numbers, more than any other branch of mathematics, began by being an experimental science. Its most famous theorems have all been conjectured, sometimes a hundred years or more before they were proved; and they have been suggested by the evidence of a mass of computations. — G.H. Hardy

G.H. Hardy Quotes 2145710

Philosophy proper is a subject, on the one hand so hopelessly obscure, on the other so astonishingly elementary, that there knowledge hardly counts. — G.H. Hardy

G.H. Hardy Quotes 1930667

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

G.H. Hardy Quotes 1753477

Imaginary' universes are so much more beautiful than this stupidly constructed 'real' one; and most of the finest products of an applied mathematician's fancy must be rejected, as soon as they have been created, for the brutal but sufficient reason that they do not fit the facts. — G.H. Hardy

G.H. Hardy Quotes 2101590

We must guard against a fallacy common among apologists of science, the fallacy of supposing that the men whose work most benefits humanity are thinking much of that while they do it, that physiologists, for example, have particularly noble souls. — G.H. Hardy

G.H. Hardy Quotes 2090591

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

G.H. Hardy Quotes 1894768

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

G.H. Hardy Quotes 455741

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

G.H. Hardy Quotes 675370

They [formulae 1.10 - 1.12 of Ramanujan] must be true because, if they were not true, no one would have had the imagination to invent them. — G.H. Hardy

G.H. Hardy Quotes 674081

What we do may be small, but it has a certain character of permanence; and to have produced anything of the slightest permanent interest, whether it be a copy of verses or a geometrical theorem, is to have done something utterly beyond the powers of the vast majority of men. — G.H. Hardy

G.H. Hardy Quotes 647820

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

G.H. Hardy Quotes 642130

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

G.H. Hardy Quotes 607223

I can remember Bertrand Russell telling me of a horrible dream. He was in the top floor of the University Library, about A.D. 2100. A library assistant was going round the shelves carrying an enormous bucket, taking down books, glancing at them, restoring them to the shelves or dumping them into the bucket. At last he came to three large volumes which Russell could recognize as the last surviving copy of Principia Mathematica. He took down one of the volumes, turned over a few pages, seemed puzzled for a moment by the curious symbolism, closed the volume, balanced it in his hand and hesitated.... — G.H. Hardy

G.H. Hardy Quotes 597310

[It] is hardly possible to maintain seriously that the evil done by science is not altogether outweighed by the good. For example, if ten million lives were lost in every war, the net effect of science would still have been to increase the average length of life. — G.H. Hardy

G.H. Hardy Quotes 538180

It is a melancholy experience for a professional mathematician to find himself writing about mathematics. The function of a mathematician is to do something, to prove new theorems, to add to mathematics, and not to talk about what he or other mathematicians have done. Statesmen despise publicists, painters despise art-critics, and physiologists, physicists, or mathematicians have usually similar feelings: 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

G.H. Hardy Quotes 521076

The play is independent of the pages on which it is printed, and 'pure geometries' are independent of lecture rooms, or of any other detail of the physical world. — G.H. Hardy

G.H. Hardy Quotes 682221

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

G.H. Hardy Quotes 356968

Chess problems are the hymn-tunes of mathematics. — G.H. Hardy

G.H. Hardy Quotes 322225

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

G.H. Hardy Quotes 269626

Asked if he believes in one G-d, a mathematician answered: "Yes, up to isomorphism". — G.H. Hardy

G.H. Hardy Quotes 254270

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

G.H. Hardy Quotes 177365

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

G.H. Hardy Quotes 142801

A chess problem is an exercise in pure mathematics. — G.H. Hardy

G.H. Hardy Quotes 110928

The 'seriousness' of a mathematical theorem lies, not in its practical consequences, which are usually negligible, but in the significance of the mathematical ideas which it connects. 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. Thus a serious mathematical theorem, a theorem which connects significant ideas, is likely to lead to important advances in mathematics itself and even in other sciences. — G.H. Hardy

G.H. Hardy Quotes 1404072

The fact is there are few more popular subjects than mathematics. Most people have some appreciation of mathematics, just as most people can enjoy a pleasant tune. — G.H. Hardy

G.H. Hardy Quotes 764131

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

G.H. Hardy Quotes 809318

Most people have some appreciation of mathematics, just as most people can enjoy a pleasant tune; and there are probably more people really interested in mathematics than in music. Appearances suggest the contrary, but there are easy explanations. Music can be used to stimulate mass emotion, while mathematics cannot; and musical incapacity is recognized (no doubt rightly) as mildly discreditable, whereas most people are so frightened of the name of mathematics that they are ready, quite unaffectedly, to exaggerate their own mathematical stupidity — G.H. Hardy

G.H. Hardy Quotes 859020

For any serious purpose, intelligence is a very minor gift. — G.H. Hardy

G.H. Hardy Quotes 873433

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

G.H. Hardy Quotes 912051

The case for my life ... is this: that I have added something to knowledge, and helped others to add more — G.H. Hardy

G.H. Hardy Quotes 937245

Immortality is often ridiculous or cruel: few of us would have chosen to be Og or Ananias or Gallio. Even in mathematics, history sometimes plays strange tricks; Rolle figures in the textbooks of elementary calculus as if he had been a mathematician like Newton; Farey is immortal because he failed to understand a theorem which Haros had proved perfectly fourteen years before; the names of five worthy Norwegians still stand in Abel's Life, just for one act of conscientious imbecility, dutifully performed at the expense of their country's greatest man. But on the whole the history of science is fair, and this is particularly true in mathematics. No other subject has such clear-cut or unanimously accepted standards, and the men who are remembered are almost always the men who merit it. Mathematical fame, if you have the cash to pay for it, is one of the soundest and steadiest of investments. — G.H. Hardy

G.H. Hardy Quotes 1054215

Exposition, criticism, appreciation, is work for second-rate minds. I — G.H. Hardy

G.H. Hardy Quotes 1075518

I have never done anything 'useful'. 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 ... Judged by all practical standards, the value of my mathematical life is nil; and outside mathematics it is trivial anyhow. I have just one chance of escaping a verdict of complete triviality, that I may be judged to have created something worth creating. And that I have created something is undeniable: the question is about its value. — G.H. Hardy

G.H. Hardy Quotes 1159038

As Littlewood said to me once [of the ancient Greeks], they are not clever school boys or 'scholarship candidates,' but 'Fellows of another college. — G.H. Hardy

G.H. Hardy Quotes 1168006

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

G.H. Hardy Quotes 1174261

The creative life [is] the only one for a serious man. — G.H. Hardy

G.H. Hardy Quotes 1190779

A mathematician, like a painter or a poet, is a maker of patterns. — G.H. Hardy

G.H. Hardy Quotes 1247869

The function of a mathematician is to do something, to prove new theorems, to add to mathematics, and not to talk about what he or other mathematicians have done. — G.H. Hardy

G.H. Hardy Quotes 1284875

In [great mathematics] there is a very high degree of unexpectedness, combined with inevitability and economy. — G.H. Hardy

G.H. Hardy Quotes 1357782

I believe that mathematical reality lies outside us, that our function is to discover or observe it, and that the theorems which we prove, and which we 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, and I shall use the language which is natural to a man who holds it. — G.H. Hardy