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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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 ...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10A 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.15A 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.16It 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.21But 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。23The 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.27It 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 he had to take a moral stand. On the other hand, it gave him his introspective insight and beautiful candour, so that he could speak of himself with absolute simplicity (as Einstein never could). His behaviour was often different, bizarrely so, from ours: but it came to seem a kind of superstructure set upon a nature which wasn't all that different from our own, except that it was more delicate, less paddd, finernerved. Hardy: ``Cricket is the only game where you are playing against eleven of the other side and then of your own.'' That is why A Mathematician's Apology is, read with the textual attention it deserves, a book of haunting sadness. Yes, it is witty and sharp with intellectual high spirits; yes ,the crystalline clarity and candour are still there; yes, it is the testament of a creative artist. But it is also, in an understated stoical fashion, a passionate lament for creative powers that used to be and that will never come again. I know nothing like it in the language: partly because most people with the literary gift to express such a lament don't come to feel it: it is very rare for a writer to realize, with the finality of truth, that he is absolutely finished. 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. Exposition, criticism, appreciation, is work of secondrate minds. Good work is not done by ``humble'' men. It is one of the first duties of 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?'' 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. 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. A.E. Housman: Smooth Between Sea and Land Here on the level sand, Between the sea and land, What shall I build or write Against the fall of night? Tell me of runes to grave That hold the bursting wave, Or bastions to design For longer date than mine. 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. As Housman insisted, the importance of ideas in poetry is habitually exaggerated: ``I cannot satisfy myself that there are any such things as poetical ideas. Poetry is not the thing said but a way of saying it.'' Chess problems are the hymntunes of mathematics. It (reductio ad absurdum) is a far finer gambit than any chess gambit: a chess player may offer the sacrifice of apawn or even a piece, but a mathematician offers the game. Mathematics may, like poetry or music, ``promote and sustain a lofty habit of mind'', and so increase the happiness of mathematicians and even of other people; but to defend it on that ground would be merely to elaborate what I have said already. 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 interestat all in the physical world; but, in so far as he succumbs to this temptation, he will be abandoning his purely mathemtical position. One rather curious conclusion emerges, that pure mathematics is on the whole distinctly more useful than applied. A pure mathematician seems to have the advantage on the practical as well as on the aesthetic side. For what is useful above all is technique, and mathematical technique is taught mainly through pure mathematics. ``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.
回应 20130327 11:16 
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
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。。😂HHHHHHHOTZ
回应 20190624 20:21

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 he had to take a moral stand. On the other hand, it gave him his introspective insight and beautiful candour, so that he could speak of himself with absolute simplicity (as Einstein never could). His behaviour was often different, bizarrely so, from ours: but it came to seem a kind of superstructure set upon a nature which wasn't all that different from our own, except that it was more delicate, less paddd, finernerved. Hardy: ``Cricket is the only game where you are playing against eleven of the other side and then of your own.'' That is why A Mathematician's Apology is, read with the textual attention it deserves, a book of haunting sadness. Yes, it is witty and sharp with intellectual high spirits; yes ,the crystalline clarity and candour are still there; yes, it is the testament of a creative artist. But it is also, in an understated stoical fashion, a passionate lament for creative powers that used to be and that will never come again. I know nothing like it in the language: partly because most people with the literary gift to express such a lament don't come to feel it: it is very rare for a writer to realize, with the finality of truth, that he is absolutely finished. 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. Exposition, criticism, appreciation, is work of secondrate minds. Good work is not done by ``humble'' men. It is one of the first duties of 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?'' 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. 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. A.E. Housman: Smooth Between Sea and Land Here on the level sand, Between the sea and land, What shall I build or write Against the fall of night? Tell me of runes to grave That hold the bursting wave, Or bastions to design For longer date than mine. 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. As Housman insisted, the importance of ideas in poetry is habitually exaggerated: ``I cannot satisfy myself that there are any such things as poetical ideas. Poetry is not the thing said but a way of saying it.'' Chess problems are the hymntunes of mathematics. It (reductio ad absurdum) is a far finer gambit than any chess gambit: a chess player may offer the sacrifice of apawn or even a piece, but a mathematician offers the game. Mathematics may, like poetry or music, ``promote and sustain a lofty habit of mind'', and so increase the happiness of mathematicians and even of other people; but to defend it on that ground would be merely to elaborate what I have said already. 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 interestat all in the physical world; but, in so far as he succumbs to this temptation, he will be abandoning his purely mathemtical position. One rather curious conclusion emerges, that pure mathematics is on the whole distinctly more useful than applied. A pure mathematician seems to have the advantage on the practical as well as on the aesthetic side. For what is useful above all is technique, and mathematical technique is taught mainly through pure mathematics. ``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.
回应 20130327 11:16 
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
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 not uncommon among those with a gift for conceptual thought. Cambridge at that time was full of unusual and distinguished faces  but even then, I thought that night, Hardy’s stood out.
1931, Christ's high table. A sketch of an outstanding mathematician...
PS. "Cambridge at that time was full of unusual and distinguished faces"，所以这会儿不是了么LOL（顺便想了想Oxford。Hmmmm
P10
I do not remember what he was wearing. It may easily have been a sports coat and grey flannels under his gown. Like Einstein, he dressed to please himself: though, unlike Einstein, he diversified his casual clothing by a taste for expensive silk shirts.
Very English 233333
回应 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
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 Greene in a review wrote that along with Henry James’s notebooks, this was the best account of what it was like to be a creative artist.
1. A work of art!
2. Greene...贵圈真小。。
回应 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 val... (5回应)20121105 21:38
King Gillette 发明了现代刮胡刀。William Willett，彩色玻璃设计师。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 value Here, on the level sand, Between the sea and land, What shall I build or write Against the fall of night? Tell me of runes to grave That hold the bursting wave, Or bastions to design, For longer date than mine. Ambition has been the driving force behind nearly all the best work of the world. In particular, practically all substantial contributions to human happiness have been made by ambitious men. To make two famous examples, were not Lister and Pasteur ambitous?Or, on a humbler level, King Gillette and William Willet; and who in recent times have contributed more to human comfort than they?
Married Couple, 1915 Leaded Stained Glass Window designed and fabricated by William WillePhysiology provides particularly good examples, just because it is so obviously a 'beneficial' study. We must guard against a fallacy common among aplogist 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. 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 form those of a classical scholar or mathematician.
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
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。。😂HHHHHHHOTZ
回应 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
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 Greene in a review wrote that along with Henry James’s notebooks, this was the best account of what it was like to be a creative artist.
1. A work of art!
2. Greene...贵圈真小。。
回应 20190622 03:34 
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
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 not uncommon among those with a gift for conceptual thought. Cambridge at that time was full of unusual and distinguished faces  but even then, I thought that night, Hardy’s stood out.
1931, Christ's high table. A sketch of an outstanding mathematician...
PS. "Cambridge at that time was full of unusual and distinguished faces"，所以这会儿不是了么LOL（顺便想了想Oxford。Hmmmm
P10
I do not remember what he was wearing. It may easily have been a sports coat and grey flannels under his gown. Like Einstein, he dressed to please himself: though, unlike Einstein, he diversified his casual clothing by a taste for expensive silk shirts.
Very English 233333
回应 20190615 18:17
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谁读这本书?
二手市场
订阅关于A Mathematician's Apology的评论:
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0 有用 lovepooh 20110910
来生，请赐予我数学的天赋，让我安心自在的驰骋在“无用”的数学想象里
0 有用 chase.hong 20130912
老头在最后一段写得很感人，一个富有逻辑，自省，优雅的人
0 有用 rhine 20110323
为什么要学数学？数学的实际意义在哪里？数学的永恒不朽和普遍意义（permanence, immortality,generality）区别于其他科学学科。应用数学或可有所实用，但纯数学的价值在哪里？
1 有用 刘德维希 20141006
连夜看完了，哈代文笔相当不错，读起来舒服又快活。
0 有用 小刺客 20101217
哈代好自负
0 有用 等风信子再开花 20190720
Hardy说工程师不会用到比50847478，哪知几十年后密码学就运用到了大数分解之难；Hardy说chess涉及的问题是trivial的，哪知几十年之后对于计算复杂度问题的研究养活了一帮子人。人无法脱离他所处的时代的印记，如Hardy举了被时代抛弃的论据，而他的论点仍然是有效的，如果把elementary math的范畴放宽一点。// Hardy对useless和harmless的论证是最有趣的... Hardy说工程师不会用到比50847478，哪知几十年后密码学就运用到了大数分解之难；Hardy说chess涉及的问题是trivial的，哪知几十年之后对于计算复杂度问题的研究养活了一帮子人。人无法脱离他所处的时代的印记，如Hardy举了被时代抛弃的论据，而他的论点仍然是有效的，如果把elementary math的范畴放宽一点。// Hardy对useless和harmless的论证是最有趣的，pure mathematics是useless的，而比mathematical physics更接近reality，这里哈代定义了physical reality和mathematical reality。//数学无用，自嘲也是自我辩解吧。//be ambitious (展开)
0 有用 好养活 20190625
A creative art in every sense.
0 有用 假装在伦敦 20190324
十年前看的了有点忘了讲啥了..
0 有用 蓬头稚子 20190207
自大又聪明之人的精妙的文字，不管支持／反对，一个prospective mathematician总该花五个小时想想这本书
0 有用 milandroid 20180825
小册子是老早看完了 只不过(太懒?)整理不出思绪 没辙直接把笔记润色一下吧 milandroid.com/rawnoteshardyapology/