G.H. Hardy Quotes

#1. 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

#2. 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

#3. 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

#4. 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

#5. 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

#6. 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

#7. 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

#8. 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

#9. 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

#10. Chess problems are the hymn-tunes of mathematics.

G.H. Hardy

#11. 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

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

G.H. Hardy

#13. In [great mathematics] there is a very high degree of unexpectedness, combined with inevitability and economy.

G.H. Hardy

#14. I do not know an instance of a major mathematical advance initiated by a man past fifty

G.H. Hardy

#15. 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

#16. 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

#17. 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

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

G.H. Hardy

#19. 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

#20. [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

#21. 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

#22. 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

#23. The public does not need to be convinced that there is something in mathematics.

G.H. Hardy

#24. 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

#25. 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

#26. 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

#27. 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

#28. 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

#29. [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

#30. Good work is not done by 'humble' men

G.H. Hardy

#31. 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

#32. Exposition, criticism, appreciation, is work for second-rate minds. I

G.H. Hardy

#33. Young men should prove theorems, old men should write books.

G.H. Hardy

#34. 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

#35. Mathematics may, like poetry or music, "promote and sustain a lofty habit of mind."

G.H. Hardy

#36. 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

#37. 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

#38. 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

#39. The creative life [is] the only one for a serious man.

G.H. Hardy

#40. 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

#41. I am interested in mathematics only as a creative art.

G.H. Hardy

#42. 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

#43. 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

#44. Most people can do nothing at all well

G.H. Hardy

#45. 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

#46. All analysts spend half their time hunting through the literature for inequalities which they want to use and cannot prove.

G.H. Hardy

#47. 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

#48. 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

#49. As history proves abundantly, mathematical achievement, whatever its intrinsic worth, is the most enduring of all.

G.H. Hardy

#50. 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

#51. A mathematician, like a painter or a poet, is a maker of patterns.

G.H. Hardy

#52. Bombs are probably more merciful than bayonets

G.H. Hardy

#53. 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

#54. I was at my best at a little past forty, when I was a professor at Oxford.

G.H. Hardy

#55. Real mathematics must be justified as art if it can be justified at all.

G.H. Hardy

#56. 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

#57. Cricket is the only game where you are playing against eleven of the other side and ten of your own.

G.H. Hardy

#58. 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

#59. Sometimes one has to say difficult things, but one ought to say them as simply as one knows how.

G.H. Hardy

#60. 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

#61. 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

#62. The case for my life ... is this: that I have added something to knowledge, and helped others to add more

G.H. Hardy

#63. 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

#64. 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

#65. The study of mathematics is, if an unprofitable, a perfectly harmless and innocent occupation.

G.H. Hardy

#66. 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

#67. 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

#68. For any serious purpose, intelligence is a very minor gift.

G.H. Hardy

#69. 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

#70. No one should ever be bored. ... One can be horrified, or disgusted, but one can't be bored.

G.H. Hardy

#71. 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

#72. 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

#73. A chess problem is an exercise in pure mathematics.

G.H. Hardy