出版社: Cambridge University Press
出版年: 1992131
页数: 153
定价: USD 21.00
装帧: Paperback
丛书: Canto Classics
ISBN: 9780521427067
内容简介 · · · · · ·
G. H. Hardy was one of this century's finest mathematical thinkers, renowned among his contemporaries as a 'real mathematician ... the purest of the pure'. He was also, as C. P. Snow recounts in his Foreword, 'unorthodox, eccentric, radical, ready to talk about anything'. This 'apology', written in 1940 as his mathematical powers were declining, offers a brilliant and engaging ...
G. H. Hardy was one of this century's finest mathematical thinkers, renowned among his contemporaries as a 'real mathematician ... the purest of the pure'. He was also, as C. P. Snow recounts in his Foreword, 'unorthodox, eccentric, radical, ready to talk about anything'. This 'apology', written in 1940 as his mathematical powers were declining, offers a brilliant and engaging account of mathematics as very much more than a science; when it was first published, Graham Greene hailed it alongside Henry James's notebooks as 'the best account of what it was like to be a creative artist'. C. P. Snow's Foreword gives sympathetic and witty insights into Hardy's life, with its rich store of anecdotes concerning his collaboration with the brilliant Indian mathematician Ramanujan, his aphorisms and idiosyncrasies, and his passion for cricket. This is a unique account of the fascination of mathematics and of one of its most compelling exponents in modern times.
作者简介 · · · · · ·
A Mathematician's Apology is a profoundly sad book, the memoir of a man who has reached the end of his ambition, who can no longer effectively practice the art that has consumed him since he was a boy. But at the same time, it is a joyful celebration of the subjectand a stern lecture to those who would sully it by dilettantism or attempts to make it merely useful. "The mathem...
A Mathematician's Apology is a profoundly sad book, the memoir of a man who has reached the end of his ambition, who can no longer effectively practice the art that has consumed him since he was a boy. But at the same time, it is a joyful celebration of the subjectand a stern lecture to those who would sully it by dilettantism or attempts to make it merely useful. "The mathematician's patterns," G.H. Hardy declares, "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."
Hardy was, in his own words, "for a short time the fifth best pure mathematician in the world" and knew full well that "no mathematician should ever allow himself to forget that mathematics, more than any other art or science, is a young man's game." In a long biographical foreword to Apology, C.P. Snow (now best known for The Two Cultures) offers invaluable background and a context for his friend's occasionally brusque tone: "His life remained the life of a brilliant young man until he was old; so did his spirit: his games, his interests, kept the lightness of a young don's. And, like many men who keep a young man's interests into their sixties, his last years were the darker for it." Reading Snow's recollections of Hardy's Cambridge University years only makes Apology more poignant. Hardy was popular, a terrific conversationalist, and a notoriously good cricket player.
When summer came, it was taken for granted that we should meet at the cricket ground.... He used to walk round the cinderpath with a long, loping, clumpingfooted stride (he was a slight spare man, physically active even in his late fifties, still playing real tennis), head down, hair, tie, sweaters, papers all flowing, a figure that caught everyone's eyes. "There goes a Greek poet, I'll be bound," once said some cheerful farmer as Hardy passed the scoreboard.
G.H. Hardy's elegant 1940 memoir has provided generations of mathematicians with pithy quotes and examples for their office walls, and plenty of inspiration to either be great or find something else to do. He is a worthy mentor, a man who understood deeply and profoundly the rewards and losses of true devotion. Therese Littleton
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a. The value of pure mathematics lies in the eternity of its beauty b. The significance of mathematics consists of generality and depths c. Curiosity, pride, and ambition are the incentives to research d. The work of mathematicians is to observe the mathema... (展开)> 更多书评 34篇

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感谢刘晴同学提供1967年C. P. Snow序言本扫描版 1 I write about mathematics because, like any other mathematician who has passed sixty, I have no longer the freshness of mind, the energy, or the patience to carry on effectively with my proper job. 2 A metaphysician, says Bradley, will be told that 'metaphysical knowledge is wholly impossible', or that 'even if possible to a certain degree, it is p...20141029 22:31 2人喜欢
感谢刘晴同学提供1967年C. P. Snow序言本扫描版 1 I write about mathematics because, like any other mathematician who has passed sixty, I have no longer the freshness of mind, the energy, or the patience to carry on effectively with my proper job. 2 A metaphysician, says Bradley, will be told that 'metaphysical knowledge is wholly impossible', or that 'even if possible to a certain degree, it is practically no knowledge worth the name'. 'The same problems,' he will hear, 'the same disputes, the same sheer failure. Why not abandon it and come out? Is there nothing else worth your labour?' There is no one so stupid as to use this sort of language about mathematics. The mass of mathematical truth is obvious and imposing; its practical applications, the bridges and steamengines and dynamos, obtrude themselves on the dullest imagination.... All this is in its way very comforting to mathematicians, but it is hardly possible for a genuine mathematician to be content with it. Good work is not 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. 3 'I do what I do because it is the one and only thing that I can do at all well....' 4 No mathematician should ever allow himself to forget that mathematics, more than any other art or science, is a young man's game. 5 Is mathematics 'unprofitable'? In some ways, plainly, it is not; for example, it gives great pleasure to quite a large number of people. I was using the word, however, in a narrower senseis mathematics 'useful', directly useful, as other sciences such as chemistry and physiology are? This is not an altogether easy or uncontroversial question, and I shall ultimately say No, though some mathematicians, and most outsiders, would no doubt say Yes. 7 A man's first duty, a young man's at any rate, is to be ambitious. A physiologist may indeed be glad to remember that his work will benefit mankind, but the motives which provide the force and the inspiration for it are indistinguishable from those of a classical scholar or a mathematician. There are many highly respectable motives which may lead men to prosecute research, but three which are much more important than the rest. The first (without which the rest must come to nothing) is intellectual curiosity, desire to know the truth. Then, professional pride, anxiety to be satisfied with one's performance, the shame that overcomes any selfrespecting craftsman when his work is unworthy of his talent. Finally, ambition, desire for reputation, and the position, even the power or the money, which it brings. 按：此处可与George Orwell《我为何写作》参照 10 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. It may be very hard to define mathematical beauty, but that is just as true of beauty of any kindwe may not know quite what we mean by a beautiful poem, but that does not prevent us from recognizing one when we read it. 15 A significant mathematical idea, a serious mathematical theorem, should be 'general' in some such sense as this. The idea should be one which is a constituent in many mathematical constructs, which is used in the proof of theorems of many different kinds. The theorem should be one which, even if stated originally (like Pythagoras's theorem) in a quite special form, is capable of considerable extension and is typical of a whole class of theorems of its kind. The relations revealed by the proof should be such as connect many different mathematical ideas. All this is very vague, and subject to many reservations. 16 It is quite common, for example, for an astronomer or a physicist to claim that he has found a 'mathematical proof' that the physical universe must behave in a particular way. All such claims, if interpreted literally, are strictly nonsense. It cannot be possible to prove mathematically that there will be an eclipse tomorrow,because eclipses, and other physical phenomena, do not form part of the abstract world of mathematics; and this, I suppose, all astronomers would admit when pressed, however many eclipses they may have predicted correctly. We do not choose our friends because they embody all the pleasant qualities of humanity, but because they are the people that they are. And so in mathematics; a property common to too many objects can hardly be very excitng, and mathematical ideas also become dim unless they have plenty of individuality. 21 But here I must deal with a misconception. It is sometimes suggested that pure mathematicians glory in the usefulness of their work, and make it a boast that it has no practical applications. The imputation is usually based on an incautious saying attributed to Gauss, to the effect that, if mathematics is the queen of the sciences, then the theory of numbers is, because of its supreme usefulness, the queen of mathematicsI have never been able to find an exact quotation. I am sure that Gauss's saying (if indeed it be his) has been rather crudely misinterpreted. If the theory of numbers could be employed for any practical and obviously honourable purpose, if it could be turned directly to the furtherance of human happiness or the relief of human suffering, as physiology and even chemistry can, then surely neither Gauss nor any other mathematician would have been so foolish as to decry or regret such applications. But science works for evil as well as for good (and particularly, of course, in time of war); and both Gauss and lesser mathematicians may be justified in rejoicing that there is one science at any rate, and that their own, whose very remoteness from ordinary human activities should keep it gentle and clean. 按：许多人把Hardy对应用（在非常窄的意义下）的漠不关心误解为鄙视。比如下面这段话（Reuben Hersh, What is Mathematics, Really?, Oxford University Press, Criteria for a philosophy of mathematics in Part One）就带着打Hardy脸的口气说道： G. H. Hardy "famously" boasted: "(按出自《自白》28节)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." Nevertheless, the HardyWeinberg law of genetics is better known than his profound contributions to analytic number theory. What's worse, cryptology is making number theory applicable. Hardy's contribution to that pure field may yet be useful. 但说Hardy以纯数学为傲倒是不假。 23 The room in which I am lecturing is part of the physical world, and has itself a certain pattern....Suppose now that a violent dynamo, or a massive gravitating body, is introduced into the room. Then the physicists tell us that the geometry of the room is changed, its whole physcial pattern slightly but definitely distorted. Do the theorems which I have proved become false? Surely it would be nonsense to suppose that the proofs of them which I have given are affected in any way. The geometer offers to the physicist a whole set of maps from which to choose. 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. I may add that even a pure mathematician may find his appreciation of this geometry quickened, since there is no mathematician so pure that he feels no interest at all in the physical world; but, in so far as he succumbs to this tempatation, he will be abandoning his purely mathematical position. 27 It may be objected that my concept of 'utility' has been too narrow, that I have define it in terms of 'happiness' or 'comfort' only, and have ignored the general 'social' effects of mathematics on which recent writers, with very different sympathies, have laid so much stress. Thus Whitehead (who has been a mathematician) speaks of 'the tremendous effort of mathematical knowledge on the lives of men, on their daily avocations, on the organization of society';... I cannot really believe that all this eloquence will do much to comfort mathematicians. The language of both writers is violently exaggerated, and both of them ignore very obvious distinctions.... It is not lack of understanding or of sympathy which is the trouble in Whitehead's cases; but he forgets, in his enthusiasm, distinctions with which he is quite familiar. The mathematics which has this 'tremendous effect' on the 'daily avocations of men' and on 'the organization of society' is not the Whitehead but the Hogben mathematics. The mathematics which can be used 'for ordinary purposes by ordinary men' is negligible, and that which can be used by economists or sociologists hardly rises to 'scholarship standard'. The Whitehead mathematics may affect astronomy or physics profoundly, philosophy very appreciablyhigh thinking of one kind is always likely to affect high thinking of anotherbut it has extremely little effect on anything else. Its 'tremendous effects' have been, not on men generally, but on men like Whitehead himself. 按：Whitehead的观点以及Kline在Mathematics in Western Culture里表达的观点，正是Hardy之前所云的，对学科重要性的必要的夸张。
回应 20141029 22:31 
C.P. Snow Nevertheless, he had to live with an overdelicate nature. He seems to have been born with three skins too few. Unlike Einstein, who had to subjugate his powerful ego in the study of the external world before he could attain his moral stature, Hardy had to strengthen an ego which wasn't much protected. This at times in later life made him selfassertive (as Einstein never was) when...
20130327 11:16 1人喜欢


C.P. Snow Nevertheless, he had to live with an overdelicate nature. He seems to have been born with three skins too few. Unlike Einstein, who had to subjugate his powerful ego in the study of the external world before he could attain his moral stature, Hardy had to strengthen an ego which wasn't much protected. This at times in later life made him selfassertive (as Einstein never was) when...
20130327 11:16 1人喜欢

好养活 (Till then I walk alone.)
So, from lower down the table, I kept studying him. He was then in his fifties: his hair was already grey, above skin so deeply sunburnt that it stayed a kind of Red Indian bronze. His face was beautiful  high cheek bones,, thin nose, spiritual and austere but capable of dissolving into convulsions of internal gaminlike amusement. He had opaque brown eyes, bright as a bird’s  a kind of eyes...20190615 18:17

好养活 (Till then I walk alone.)
There is something else, though, at which he was clearly superior to Einstein or Rutherford or any other great genius: and that is at turning any work of the intellect, major or mine or sheer play, into a work of art. It was that gift above all, I think, which made him, almost without realising it, purvey such intellectual delight. When A Mathematician’s Apology was first published, Graham Gre...20190622 03:34

窜 (You ignorant fuck//)
I shall assume that I am writing for readers who are full, or have in the past been full, of a proper spirit of ambition. A man's first duty, a young man's at any rate, is to be ambitious. 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 ... (5回应)20121105 21:38


好养活 (Till then I walk alone.)
The second minor upset of his undergraduate years was professional. Almost since the time of Newton, and all through the nineteenth century, Cambridge had been dominated by the examination for the old Mathematical Tripos. The English have always had more faith in competitive examinations than any other people (except perhaps the Imperial Chinese): … 正准备吐槽“我大天朝！！！”的呢。。😂HHHH...20190624 20:21

好养活 (Till then I walk alone.)
There is something else, though, at which he was clearly superior to Einstein or Rutherford or any other great genius: and that is at turning any work of the intellect, major or mine or sheer play, into a work of art. It was that gift above all, I think, which made him, almost without realising it, purvey such intellectual delight. When A Mathematician’s Apology was first published, Graham Gre...20190622 03:34
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3 有用 shuzhuo 20110910
1）数学是一流的，谈论数学的学问是二流的，正如文学之于文学批评。2）纯粹数学是真正的数学，应用数学是trivial的。3）对纯粹数学的辩护是美学的，而非实用的。至少纯粹数学是最无害的。4）其实最好的辩护是：如果再年轻一次，还是选择做数学家。5）老了就做不了数学了，数学是创造性的，而非沉思，属于年轻人。
0 有用 狗打肉包子 20110316
虽然聪明绝顶，但这家伙的理性之中却暗藏着难以控制的武断。数学家对于他的事业也是用情至深的。
1 有用 壞人 20111010
差不多每句話都是我想說的啊，太偉大了。以後需要談論有關的東西，引用就好了，因為我不可能比Hardy說得更好。
0 有用 MorningBlue 20110907
创造力枯竭之后的无尽哀伤。
0 有用 [已注销] 20101224
我学数学因为它美
0 有用 ice 20201129
There are many highly respected motives which may lead men to prosecute research, but three which are much more important to the rest. The first (without which the rest must come to nothing) is INTELL... There are many highly respected motives which may lead men to prosecute research, but three which are much more important to the rest. The first (without which the rest must come to nothing) is INTELLECTUAL CURIOSITY, DESIRE TO KNOW THE TRUTH !!! (展开)
0 有用 不是凯西 20200727
陈老师看的
0 有用 珈琲貓少女 20200720
📍圖書館 7/20/20
0 有用 普通麻瓜 20200522
第一句话简直是我写各种soi时内心的咆哮：）
0 有用 放下手机 20200406
Hardy was born in 1877; he's older than the Queen's father King George. 最近在看crown非常可以联想到what kind of victorian household must Hardy be in. This book was a secret fantasy of mine. i now mark it read an... Hardy was born in 1877; he's older than the Queen's father King George. 最近在看crown非常可以联想到what kind of victorian household must Hardy be in. This book was a secret fantasy of mine. i now mark it read and put it away because i am now on the road to my real fortune and destiny. (展开)