77+ G. H. Hardy Quotes On Ramanujan, Mathematical Analysis. And Majority

G. H. Hardy was a British mathematician who made major contributions to number theory, analysis, and mathematical biology. He is best known for his 1940 essay, A Mathematician's Apology, which defended the pure mathematics he worked on and argued against the utilitarian view of mathematics. He also wrote the influential textbook A Course of Pure Mathematics. Following is our collection on famous quotes by G. H. Hardy on ramanujan, mathematical analysis., majority.

Top 10 G. H. Hardy Quotes

1. In [great mathematics] there is a very high degree of unexpectedness, combined with inevitability and economy.
2. I am interested in mathematics only as a creative art.
3. It is not worth an intelligent man's time to be in the majority. By definition, there are already enough people to do that.
4. Beauty is the first test: there is no permanent place in the world for ugly mathematics.
5. A mathematician, like a painter or a poet, is a maker of patterns.
6. The mathematician's patterns, like the painter's or the poet's, must be beautiful.
7. Most people are so frightened of the name of mathematics that they are ready, quite unaffectedly, to exaggerate their own mathematical stupidity.
8. 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.
9. Mathematics is not a contemplative but a creative subject.
10. 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 Short Quotes

• Young men should prove theorems, old men should write books.
• I was at my best at a little past forty, when I was a professor at Oxford.
• Exposition, criticism, appreciation, is work for second-rate minds.
• The creative life was the only one for a serious man.
• Good work is not done by 'humble' men
• Sometimes one has to say difficult things, but one ought to say them as simply as one knows how.
• A chess problem is simply an exercise in pure mathematics.
• For any serious purpose, intelligence is a very minor gift.
• I do not know an instance of a major mathematical advance initiated by a man past fifty
• Bombs are probably more merciful than bayonets

G. H. Hardy Quotes About Ramanujan

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

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

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 Famous Quotes And Sayings

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

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

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

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

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

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

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

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

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 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

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

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

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

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

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

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

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. — G. H. Hardy

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

[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

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

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

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

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

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

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

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

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

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

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

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

... 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

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

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

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

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

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 he 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

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

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

Perhaps five or even ten per cent of men can do something rather well. It is a tiny minority who can do anything really well, and the number of men who can do two things well is negligible. 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

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

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

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 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

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

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

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

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

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

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

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

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

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

[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

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

Life Lessons by G. H. Hardy

G. H. Hardy was a British mathematician who made significant contributions to the field of number theory. He was also a mentor and colleague of the Indian mathematician Srinivasa Ramanujan. His work serves as an example of the importance of collaboration and mentorship in mathematics, as well as the value of pursuing difficult problems with dedication and perseverance. His famous quote, "It is not worth doing something unless you do it with all your heart" is a reminder to strive for excellence in everything we do.