a mathematician's apology quotes


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. 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.
No mathematician should ever allow himself to forget that mathematics, more than any other art or science, is a young man's game. 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'. 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. He must shut his eyes a little and think a little more of his subject and himself than they deserve. Besides his works, his essay on aesthetics of mathematics ‘A Mathematicians Apology’ is one of the best visions for a mathematician written in the layman’s language. 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. 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. 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. Goodreads helps you follow your favorite authors. Just a moment while we sign you in to your Goodreads account. Mathematical fame, if you have the cash to pay for it, is one of the soundest and steadiest of investments.”, “The Greeks were the first mathematicians who are still ‘real’ to us to-day. “A mathematician, like a painter or poet, is a maker of patterns. “The beauty of a mathematical theorem depends a great deal on its seriousness, as even in poetry the beauty of a line may depend to some extent on the significance of the ideas which it contains.”, “A mathematical proof should resemble a simple and clear-cut constellation, not a scattered cluster in the Milky Way.”, “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).”, “Ambition is a noble passion which may legitimately take many forms; there was something noble in the ambitions of Attila or Napoleon; but the noblest ambition is that of leaving behind something of permanent value.”, “The seriousness of a theorem, of course, does not lie in its consequences, which are merely the evidence for its seriousness.”, “[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.”, “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. mathematician’s life? For what is useful above all is technique, and mathematical technique is taught mainly through pure mathematics. If his patterns are more permanent than theirs, it is because they are made with ideas. The public does not need to be convinced that there is something in mathematics. It is a melancholy experience for a professional mathematician to find himself writing about mathematics. 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. Mathematics is the purest of the arts, as well as the most misunderstood. “It is not worth an intelligent man's time to be in the majority. Just a moment while we sign you in to your Goodreads account. My answers will be, for the most part, such as are expected from a mathematician: I think that it is worthwhile, that there is ample justification. … A mathematician may still be competent enough at sixty, but it is useless to expect him to have original ideas.”, “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. A man who is always asking "Is what I do worth while?" 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.”, “There is no scorn more profound, or on the whole more justifiable, than that of the men who make for the men who explain.”, “What is the proper justification of a mathematician’s life? 'A Mathematician's Apology', in James Roy Newman, The World of Mathematics (2000), 2029. If his patterns are more permanent than theirs, it is because they are made with ideas.”, “Reductio ad absurdum, which Euclid loved so much, is one of a mathematician's finest weapons. A Mathematicians Apology Item Preview remove-circle ... My favourite quotes: (a) "I am interested in mathematics only as a creative art." 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.
This view has been held, in one form or another, by many philosophers of high reputation from Plato onwards, and I shall use the language which is natural to a man who holds it.”, “A mathematician, like a painter or a poet, is a maker of patterns. To take a simple illustration at a comparatively humble level, the average age of election to the Royal Society is lowest in mathematics. Even in mathematics, history sometimes plays strange tricks; Rolle figures in the textbooks of elementary calculus as if he had been a mathematician like Newton; Farey is immortal because he failed to understand a theorem which Haros had proved perfectly fourteen years before; the names of five worthy Norwegians still stand in Abel’s Life, just for one act of conscientious imbecility, dutifully performed at the expense of their country’s greatest man. (b) "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 … But on the whole the history of science is fair, and this is particularly true in mathematics. The creative life [is] the only one for a serious man. So Greek mathematics is ‘permanent’, more permanent even than Greek literature. Such a sacrifice could be justified only by economic necessity of age. My answers will be, for the most part, such as are expected from a mathematician: I think that it is worthwhile, that there is ample justification. Young men should prove theorems, old men should write books. 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. 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. 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. “It is not worth an intelligent man's time to be in the majority. All analysts spend half their time hunting through the literature for inequalities which they want to use and cannot prove. I should not think it worth while to apologize for my subject if I regarded myself as one of its failures. Appearances suggest the contrary, but there are easy explanations. So let me try to explain what mathematics is, and what mathematicians do. 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. will always be ineffective himself and a discouragement to others. His greatest idea of all, fluxions and the law of gravitation, came to him about 1666 , when he was twentyfour—'in those days I was in the prime of my age for invention, and minded mathematics and philosophy more than at any time since'.

and "Am I the right person to do it?" We can naturally find much more striking illustrations.

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