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Home > Dictionary of Science Quotations > Scientist Names Index H > G. H. Hardy Quotes

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G. H. Hardy
(7 Feb 1877 - 1 Dec 1947)

English pure mathematician who made leading contributions in analysis and number theory.


Science Quotes by G. H. Hardy (35 quotes)

Godfrey Harold Hardy quote “Languages die and mathematical ideas do not.”
background by Tom_Brown 6117, CC by 2.0 (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
'A Mathematician's Apology', in James Roy Newman, The World of Mathematics (2000), 2029.
Science quotes on:  |  Beautiful (16)  |  Chess (13)  |  Essential (41)  |  Important (20)  |  Ingenious (4)  |  Intricate (6)  |  Mathematics (367)  |  Original (13)  |  Problem (180)  |  Serious (13)  |  Surprise (19)  |  Trivial (14)  |  Unimportant (2)

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
In A Mathematician’s Apology (1940, reprint with Foreward by C.P. Snow 1992), 84.
Science quotes on:  |  Mathematician (110)

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
In A Mathematician's Apology (1940, reprint with Foreward by C.P. Snow 1992), 113.
Science quotes on:  |  Science (875)

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
In A Mathematician's Apology (1940, reprint with Foreward by C.P. Snow 1992), 81.
Science quotes on:  |  Aeschylus (3)  |  Archimedes (13)  |  Mathematics (367)

As history proves abundantly, mathematical achievement, whatever its intrinsic worth, is the most enduring of all.
— G. H. Hardy
In A Mathematician’s Apology (1940, 1967), 80.
Science quotes on:  |  Achievement (73)  |  Enduring (5)  |  History (156)  |  Intrinsic (7)  |  Mathematics (367)  |  Proof (136)  |  Worth (30)

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
Quoted in G. H. Hardy, A Mathematician's Apology (1940, 1992), 81.
Science quotes on:  |  Clever (4)  |  College (15)  |  Fellow (6)  |  Greek (17)

Beauty is the first test: there is no permanent place in the world for ugly mathematics.
— G. H. Hardy
In A Mathematician’s Apology (1940, reprint with Foreward by C.P. Snow 1992), 85.
Science quotes on:  |  Mathematics (367)

Chess problems are the hymn-tunes of mathematics.
— G. H. Hardy
'A Mathematician's Apology', in James Roy Newman, The World of Mathematics (2000), 2028.
Science quotes on:  |  Chess (13)  |  Mathematics (367)  |  Problem (180)  |  Tune (3)

Good work is no done by “humble” men. It is one of the first duties of a professor, for example, in any subject, to exaggerate a little both the importance of his subject and his own importance in it. A man who is always asking “Is what I do worth while?” and “Am I the right person to do it?” will always be ineffective himself and a discouragement to others. He must shut his eyes a little and think a little more of his subject and himself than they deserve. This is not too difficult: it is harder not to make his subject and himself ridiculous by shutting his eyes too tightly.
— G. H. Hardy
In A Mathematician’s Apology (1940, 1967), 66.
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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
In A Mathematician’s Apology (1940, 1967), 81.
Science quotes on:  |  Greek (17)  |  Language (71)  |  Literature (33)  |  Mathematician (110)  |  Mathematics (367)  |  Modern (44)  |  Permanent (5)  |  Real (28)  |  Understanding (231)

I am interested in mathematics only as a creative art.
— G. H. Hardy
In A Mathematician’s Apology (1940, reprint with Foreward by C.P. Snow 1992), 115.
Science quotes on:  |  Mathematics (367)

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 the notes of our observations.
— G. H. Hardy
In A Mathematician's Apology (1940, reprint with Foreward by C.P. Snow 1992), 113.
Science quotes on:  |  Mathematics (367)  |  Theorem (34)

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
In A Mathematician's Apology (1940, reprint with Foreward by C.P. Snow 1992), 144.
Science quotes on:  |  Mathematician (110)

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
A Mathematician's Apology (1940), 90-1.
Science quotes on:  |  Mathematics (367)  |  Usefulness (54)

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. [The things I have added to knowledge do not differ from] the creations of the other artists, great or small, who have left some kind of memorial beind them.
— G. H. Hardy
Concluding remarks in A Mathmatician's Apology (1940, 2012), 150-151.
Science quotes on:  |  Biography (199)  |  History Of Science (34)

I remember once going to see him when he was lying 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
Quoted in G.H. Hardy, Ramanujan; Twelve Lectures on Subjects Suggested by his Life and Work (1940, reprint 1999), 12.
Science quotes on:  |  Cube (9)  |  Number (90)  |  Srinivasa Ramanujan (10)

I was at my best at a little past forty, when I was a professor at Oxford.
— G. H. Hardy
In A Mathematician’s Apology (1940, reprint with Foreward by C.P. Snow 1992), 148.
Science quotes on:  |  Biography (199)

I wrote a great deal during the next ten [early] years,but very little of any importance; there are not more than four or five papers which I can still remember with some satisfaction.
— G. H. Hardy
In A Mathematician’s Apology (1940, reprint with Foreward by C.P. Snow 1992), 147.
Science quotes on:  |  Publication (75)

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
In A Mathematician’s Apology (1940, 1967), 80.
Science quotes on:  |  Ambition (18)  |  Curiosity (52)  |  Dominant (6)  |  Gratification (8)  |  Incentive (4)  |  Intellect (99)  |  Mathematician (110)  |  Pride (21)  |  Profession (26)  |  Research (360)

In [great mathematics] there is a very high degree of unexpectedness, combined with inevitability and economy.
— G. H. Hardy
In A Mathematician’s Apology (1940, reprint with Foreward by C.P. Snow 1992), 113.
Science quotes on:  |  Mathematics (367)

It is a melancholy experience for a professional mathematician to find him 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 men who make for the men who explain. Exposition, criticism, appreciation, is work for second-rate minds.
— G. H. Hardy
In A Mathematician's Apology (1940, reprint with Foreward by C.P. Snow 1992), 61 (Hardy's opening lines after Snow's foreward).
Science quotes on:  |  Mathematician (110)

It is not worth a first class man’s time to express a majority opinion. By definition, there are already enough people to do that.
— G. H. Hardy
Quoted in the foreward to A Mathematician's Apology (1941, reprint with Foreward by C.P. Snow 1992), 46.
Science quotes on:  |  Opinion (81)

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
In A Mathematician’s Apology (1941, reprint with Foreward by C.P. Snow 1992), 150.
Science quotes on:  |  Discovery (360)  |  Mathematics (367)

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
In A Mathematician's Apology (1941, reprint with Foreward by C.P. Snow 1992), 70-71.
Science quotes on:  |  Niels Henrik Abel (9)  |  Age (60)  |  Évariste Galois (3)  |  Mathematician (110)  |  Srinivasa Ramanujan (10)  |  Youth (32)

No mathematician should ever allow himself to forget that mathematics, more than any other art or science, is a young man's game.
— G. H. Hardy
A Mathematician's Apology (1940), 10.

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
In A Mathematician's Apology (1940, reprint with Foreward by C.P. Snow 1992), 94.
Science quotes on:  |  Euclid (24)  |  Mathematics (367)

The fact is that there are few more “popular” subjects than mathematics. 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 may 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
In A Mathematician's Apology (1940, reprint with Foreward by C.P. Snow 1992), 86.
Science quotes on:  |  Fear (53)  |  Mathematics (367)  |  Music (26)

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
In A Mathematician's Apology (1940, reprint with Foreward by C.P. Snow 1992), 85.
Science quotes on:  |  Mathematics (367)

The study of mathematics is, if an unprofitable, a perfectly harmless and innocent occupation.
— G. H. Hardy
From Inaugural Lecture, Oxford (1920). Recalled in A Mathematician’s Apology (1940, 1967), 74.
Science quotes on:  |  Harmless (4)  |  Innocent (2)  |  Mathematics (367)  |  Occupation (28)  |  Perfectly (2)  |  Study (157)

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
From Inaugural Lecture, Oxford (1920). Recalled in A Mathematician’s Apology (1940, 1967), 76.
Science quotes on:  |  Beyond (19)  |  Certain (14)  |  Character (39)  |  Geometry (68)  |  Interest (82)  |  Majority (17)  |  Mathematician (110)  |  Permanence (10)  |  Power (103)  |  Production (72)  |  Small (35)  |  Theorem (34)  |  Utterly (4)  |  Vast (20)  |  Verse (7)

Young men should prove theorems, old men should write books.
— G. H. Hardy
Quoted by Freeman Dyson as the answer from G.H. Hardy about the book An Introduction to the Theory of Numbers. Dyson, while at Cambridge, had asked him why “he spent so much time and effort writing that marvellous book when he might be doing serious mathematics.” In Freeman Dyson 'A Walk Through Ramanujan's Garden', Lecture by Dyson at Ramanujan Centenary Conference (2 Jun 1987). Collected in Selected Papers of Freeman Dyson with Commentary (1996), 189. Also as quoted in 'Mathematician, Physicist, and Writer.' Interview (Jun 1990) with Donald J. Albers, The College Mathematics Journal (Jan 1994), 25, No. 1, 4.
Science quotes on:  |  Old Age (17)  |  Theorem (34)  |  Youth (32)

[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
In A Mathematician’s Apology (1940, reprint with Foreward by C.P. Snow 1992), 23.
Science quotes on:  |  Mathematician (110)

[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
In A Mathematician's Apology (), Note.
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[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
In A Mathematician’s Apology (1940, reprint with Foreward by C.P. Snow 1992), 134.
Science quotes on:  |  Mathematics (367)

[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
In A Mathematician's Apology (1940, reprint with Foreward by C.P. Snow 1992), 63-64.
Science quotes on:  |  Astronomy (105)  |  Atomic Physics (4)  |  Albert Einstein (174)  |  Mathematics (367)



Quotes by others about G. H. Hardy (6)

[Godfrey H. Hardy] personified the popular idea of the absent-minded professor. But those who formed the idea that he was merely an absent-minded professor would receive a shock in conversation, where he displayed amazing vitality on every subject under the sun. ... He was interested in the game of chess, but was frankly puzzled by something in its nature which seemed to come into conflict with his mathematical principles.
The Times
In 'Prof. G. H. Hardy: A Mathematician of Genius,' Obituary The Times.
Science quotes on:  |  Chess (13)  |  Obituary (9)

Littlewood, on Hardy's own estimate, is the finest mathematician he has ever known. He was the man most likely to storm and smash a really deep and formidable problem; there was no one else who could command such a combination of insight, technique and power. (1943)
In Béla Bollobás, Littlewood's Miscellany (1986), Foreward, 22.
Science quotes on:  |  Biography (199)  |  Deep (17)  |  Insight (28)  |  Mathematician (110)  |  Power (103)  |  Problem (180)  |  Proof (136)  |  Technique (13)

I do not think that G. H. Hardy was talking nonsense when he insisted that the mathematician was discovering rather than creating, nor was it wholly nonsense for Kepler to exult that he was thinking God's thoughts after him. The world for me is a necessary system, and in the degree to which the thinker can surrender his thought to that system and follow it, he is in a sense participating in that which is timeless or eternal.
'Reply to Lewis Edwin Hahn', The Philosophy of Brand Blanshard (1980), 901.
Science quotes on:  |  Discovery (360)  |  Johannes Kepler (43)  |  Mathematician (110)  |  Nonsense (13)  |  Thought (170)

Replying to G. H. Hardy's suggestion that the number of a taxi (1729) was “dull”: No, it is a very interesting number; it is the smallest number expressible as a sum of two cubes in two different ways, the two ways being 13 + 123 and 93 + 103.
Proceedings of the London Mathematical Society (26 May 1921).
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Plenty of mathematicians, Hardy knew, could follow a step-by-step discursus unflaggingly—yet counted for nothing beside Ramanujan. Years later, he would contrive an informal scale of natural mathematical ability on which he assigned himself a 25 and Littlewood a 30. To David Hilbert, the most eminent mathematician of the day, he assigned an 80. To Ramanujan he gave 100.
In The Man who Knew Infinity: A Life of the Genius Ramanujan (1975), 226.
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One day at Fenner's (the university cricket ground at Cambridge), just before the last war, G. H. Hardy and I were talking about Einstein. Hardy had met him several times, and I had recently returned from visiting him. Hardy was saying that in his lifetime there had only been two men in the world, in all the fields of human achievement, science, literature, politics, anything you like, who qualified for the Bradman class. For those not familiar with cricket, or with Hardy's personal idiom, I ought to mention that “the Bradman class” denoted the highest kind of excellence: it would include Shakespeare, Tolstoi, Newton, Archimedes, and maybe a dozen others. Well, said Hardy, there had only been two additions in his lifetime. One was Lenin and the other Einstein.
Variety of Men (1966), 87.
Science quotes on:  |  Achievement (73)  |  Addition (12)  |  Archimedes (13)  |  Cricket (5)  |  Albert Einstein (174)  |  Excellence (18)  |  Field (69)  |  Human (168)  |  Idiom (3)  |  Lenin_Vladimir (2)  |  Lifetime (10)  |  Literature (33)  |  Sir Isaac Newton (176)  |  Personal (16)  |  Politics (52)  |  Science (875)  |  William Shakespeare (63)  |  Count Leo Tolstoy (6)  |  Visit (4)


See also:
  • todayinsci icon 7 Feb - short biography, births, deaths and events on date of Hardy's birth.
  • todayinsci icon Godfrey Harold Hardy - context of quote Languages die and mathematical ideas do not - Medium image (500 x 350 px)
  • todayinsci icon Godfrey Harold Hardy - context of quote Languages die and mathematical ideas do not - Large image (800 x 600 px)
  • todayinsci icon Godfrey Harold Hardy - context of quote Young men should prove theorems, old men should write books. - Medium image (500 x 350 px)
  • todayinsci icon Godfrey Harold Hardy - context of quote Young men should prove theorems, old men should write books. - Large image (800 x 600 px)
  • book icon A Mathematician's Apology, by G. H. Hardy. - book suggestion.

Carl Sagan Thumbnail In science it often happens that scientists say, 'You know that's a really good argument; my position is mistaken,' and then they would actually change their minds and you never hear that old view from them again. They really do it. It doesn't happen as often as it should, because scientists are human and change is sometimes painful. But it happens every day. I cannot recall the last time something like that happened in politics or religion. (1987) -- Carl Sagan
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