G. H. Hardy Quotes and Sayings  Page 1
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“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 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 
“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 
“I am interested in mathematics only as a creative art.”
 G. H. Hardy 
“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 twentyone, Abel at twentyseven, Ramanujan at thirtythree, 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 
“[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 
“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 
“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 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 
“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 
“Real mathematics must be justified as art if it can be justified at all.”
 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 
“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 
“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 
“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 
“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 
“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 
“A science or an art may be said to be "useful" if its development increases, even indirectly, the material wellbeing and comfort of men, it promotes happiness, using that word in a crude and commonplace way.”
 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 
“The creative life [is] the only one for a serious man.”
 G. H. Hardy 
“I was at my best at a little past forty, when I was a professor at Oxford.”
 G. H. Hardy 
“The study of mathematics is, if an unprofitable, a perfectly harmless and innocent occupation.”
 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 
“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 
“Young men should prove theorems, old men should write books.”
 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 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 
“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 
“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