Below are a few of G. H. Hardy’s thoughts and sayings. Beauty is the first test: there is no permanent place in the world for ugly mathematics.”, “The Greeks were the first mathematicians who are still ‘real’ to us to-day. Archimedes will be remembered when Aeschylus is forgotten, because languages die and mathematical ideas do not. They had better be moved from now on into the Bradman class. mathematician’s life? I should not think it worth while to apologize for my subject if I regarded myself as one of its failures. To take a simple illustration at a comparatively humble level, the average age of election to the Royal Society is lowest in mathematics. He made big discoveries until he was nearly forty (the 'elliptic orbit' at thirty-seven), but after that he did little but polish and perfect. Philosophy proper is a subject, on the one hand so hopelessly obscure, on the other so astonishingly elementary, that there knowledge hardly counts. Hardy Description : A Mathematician's Apology is the famous essay by British mathematician G. H. Hardy. But on the whole the history of science is fair, and this is particularly true in mathematics. If his patterns are more permanent than theirs, it is because they are made with ideas. Be the first to learn about new releases! But I should say at once that my defense of mathematics will be a defense of myself, and that my apology is bound to be to some extent egotistical. 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. But I should say at once that my defence of mathematics will be a defence of myself, and that my apology is bound to be to some extent egotistical. Welcome back. 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. 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. Error rating book. 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. 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. ... For what is useful above all is technique, and mathematical technique is taught mainly through pure mathematics.”, “I still say to myself when I am depressed, and find myself forced to listen to pompous and tiresome people, 'Well, I have done one thing you could never have done, and that is to have collaborated with both Littlewood and Ramanujan on something like equal terms.”, “A MAN who sets out to justify his existence and his activities has to distinguish two different questions. Most people are so frightened of the name of mathematics that they are ready, quite unaffectedly, to exaggerate their own mathematical stupidity. And my answers will be, for the most part, such as are expected from a mathematician: I think that it is worth while, that there is ample justification. A Mathematician's Apology Quotes by G.H. I “A mathematician, like a painter or poet, is a maker of patterns. [...] 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.”, “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.”, “The Greeks were the first mathematicians who are still ‘real’ to us to-day. It is a melancholy experience for a professional mathematician to find himself writing about mathematics. For what is useful above all is technique, and mathematical technique is taught mainly through pure mathematics. Newton gave up mathematics at fifty, and had lost his enthusiasm long before; he had recognized no doubt by the time he was forty that his greatest creative days were over. Reductio ad absurdum, which Euclid loved so much, is one of a mathematician's finest weapons. Appearances suggest the contrary, but there are easy explanations. Beauty is the first test: there is no permanent place in the world for ugly mathematics. ― G.H. No one foresaw the applications of matrices and groups and other purely mathematical theories to modern physics, and it may be that some of the 'highbrow' applied mathematics will become 'useful' in as unexpected a way; but the evidence so far points to the conclusion that, in one subject as in the other, it is what is commonplace and dull that counts for practical life.”, “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.”. Good work is no done by "humble" men. Hardy, A Mathematician's Apology. But I should say at once that my defense of mathematics will be a defense of myself, and that my apology is bound to be to some extent egotistical. 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”, “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. 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. 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.”, “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.”, “The geometer offers to the physicist a whole set of maps from which to choose. 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. Firstly, at age 62, Hardy felt the approach of old age (he had survived a heart attack in 1939) and the decline of his mathematical creativity and skills. No one should ever be bored. 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.”, “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”, “Chess problems are the hymn-tunes of mathematics.”, “One rather curious conclusion emerges, that pure mathematics is on the whole distinctly more useful than applied. 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.”, “Real mathematics must be justified as art if it can be justified at all.”, “Archimedes will be remembered when Aeschylus is forgotten, because languages die and mathematical ideas do not. So Greek mathematics is ‘permanent’, more permanent even than Greek literature. Goodreads helps you follow your favorite authors. Mathematical fame, if you have the cash to pay for it, is one of the soundest and steadiest of investments.”, “It (proof by contradiction) is a far finer gambit than any chess gambit: a chess player may offer the sacrifice of a pawn or even a piece, but a mathematician offers the game.”, “[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.”, “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. 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.