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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 subject--and 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, clumping-footed 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 score-board.

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 -- Dieser Text bezieht sich auf eine andere Ausgabe: Taschenbuch .


'A classic tale of retrospection considering wider, powerful themes in mathematics.' Mathematics Today

'Hardy provides an amazing insight into the mind of the mathematician.' Marcus du Sautoy, The Week

'Hardy provides an amazing insight into the mind of the mathematician.' Marcus du Sautoy, Waitrose Weekend Magazine

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Beautiful 18. Juni 2012
Von UL - Veröffentlicht auf Amazon.com
Format: Taschenbuch
This is one of the best books I have read in a while. The foreword by C.P. Snow was a perfect start. Hardy has done a marvellous job of explaning his point of view about Mathematics, the impact the subject has on every day life and his own reasons to get into the study of this very challanging subject. One could say that Hardy was a little pompous and self-congratulatory but if what he says is read in context, the reader will realize that, as Snow points out in the foreword, Hardy had a broken heart when he was writing this book. He was at the end of his creative 'boom' and was wary of the fact that he was no longer the same agile mind that was needed to perform real mathematical miracles.
Brilliant book and one that should be read by everyone ..... regardless of how they feel about mathematics because more than about math, this book is about how life is the great equalizer and how we will all one day be humbled by our aging neurons and weakening muscles .... regardless of how much prodigous talent we may possess.
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"A passionate lament for creative powers that used to be and that will never come again" 31. August 2013
Von Jordan Bell - Veröffentlicht auf Amazon.com
Format: Taschenbuch
I strongly disagree with Hardy's opening statement that "there is no scorn more profound, or on the whole more justifiable, than that of the men who make for the men who explain." It is indeed easier to write uninspired but passable explanation or criticism than it is to write uninspired but passable mathematics, and excellent exposition is also easier to do than excellent mathematics. But good exposition is both more useful for the discipline of mathematics and harder to do than uninspired but passable mathematics.

Although I disagree with what Hardy thinks is important and also his belief that people who are able to be excellent in one field are unlikely to be able to be excellent in another field, he expounds his ideas clearly and beautifully and I was glad to read them. And Hardy has made a serious though brief attempt at making precise ideas mathematicians have about what important and good mathematics is, which are usually avoided by saying that one knows quality when one sees it. In section 11, Hardy says "We may say, roughly, that a mathematical idea is 'significant' if it can be connected, in a natural and illuminating way, with a large complex of other mathematical ideas." In sections 15-17 he talks about "generality" and "depth" of mathematical ideas. In section 18 he presents three qualities of good mathematics: unexpectedness, inevitability, and economy.

Hardy makes a point that I don't think I've read before and with which I strongly agree: "the most 'useful' subjects are quite commonly just those which it is most useless for most of us to learn." (For example, there is huge social benefit from having good sewers, but sewer design is probably not something that should be a mandatory course to get a high school diploma.) This in fact leads to a good argument about why pure mathematics, about prime numbers and irrationals for example, is more useful to teach than applied mathematics.

Someone wanting to know about Hardy's mathematical development would need more than this book. (It's been a while since I've read it, but Kanigel's biography of Ramanujan is probably the next place to look for biographical information about Hardy.) When did Hardy first learn a proof? What material did he learn at Cranleigh and Winchester and then at Cambridge? Snow just tells us that at Winchester he was in a class of one, but not what that class covered. I would like to know what material he had worked through before reading Jordan's Cours d'analyse; once he starts to read the Cours d'analyse he can properly called a mathematician, although not yet a productive researcher. The historian who wants to know about Hardy's Cambridge studies at least is told when he took the Tripos if they want to know the specific material that he mastered before becoming a researcher.
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Good But Not Great 14. August 2014
Von David Milliern - Veröffentlicht auf Amazon.com
Format: Taschenbuch
“A Mathematician’s Apology” is a slightly better than decent read, but it certainly isn’t great. Probably the two most interesting aspects of the book are the philosophical forays and Hardy’s own psychology. As an apology for mathematics, it’s one the verge of sorry. It really is more of a mathematicians’ apology than an apology for mathematics. Moreover, it is more of an apology for a mathematician, videlicet, Hardy, than it is a mathematicians’ apology, thus the psychological remark. It is very difficult to make this aspect of the text more obvious, unless one were to have a relatively close friend, such as C.P. Snow, write a pseudo-psychoanalytic preface, as the publisher has. Some aspects of the text are downright bizarre, which may make it all the more interesting to some readers. For instance, the terms in which Hardy wants to talk about “utility,” in relation to mathematics’ utility, will induce some amount of thought, though, I am sure, many will find some such oddities in Hardy’s views not worth expression. Rather unfortunately, I think the text is a bit too short for Hardy to have effectively communicated the value and veracity of the distinctions he tries to draw. Nonetheless, there is some merit to what he says, on the basis of what he does say.

I think the disappointment for me has been the Victorian and Edwardian British mentality of Hardy’s apology: doing mathematics for the sake of distinction, as tradition affords, is a horribly weak point to make. Perhaps it is this mentality that leads him to an elitist sounding lamentation that resurfaces throughout, not to mention is bitter sadness in, at, and with life. How such sociological considerations fit with his strong Platonism is beyond me (e.g., he refers to the Platonic position on mathematics “realism,” as opposed to “idealism”). Claiming that mathematicians are more in touch with reality than physicists requires quite a bit more discussion than Hardy gives.

All these frustrations considered, there are some really beautiful points that he makes, and I think it is more those beautiful nuggets than anything that have garner the book such acclaim. Ultimately, if I could, I would rate the book a 3.7 or 3.8 stars, because it certainly is one of those books I’d recommend to someone of sufficient interest in math, philosophy of math, scientific biographies, psychology in science, etc. I did experience a considerable amount of pleasure in reading it in some places within the text, but there were certainly stretches where the psychological pathology and the rants were a bit much. It is certainly suitable for high school students, especially the advanced ones, for college students, and at-large intellectuals. I wish, however, it weren’t in the Great Books of the Western World. I definitely think it doesn’t deserve to be.
False dichotomy but worth reading 6. Dezember 2014
Von Ed Battistella - Veröffentlicht auf Amazon.com
Format: Taschenbuch
A friend loaned me a copy of G. H. Hardy’s “A Mathematcian;s Apology” which focuses on the creative aspect of mathematical proofs. After a 60-page biographical essay/forward by C. P. Snow, the bulk of the slim volume (page 61-151) is Hardy’s ruminations on the creative aesthetic of mathematics—an apology in the older sense of a defense of a choice (i.e., the apology of Socrates). It’s hard not to be charmed by a book that begins with the (ironic?) line that “Exposition, criticisms, appreciation is work for second-rate minds,” dissing not but readers but himself as well. Feeling past his prime and concerned about the military uses of applied math, Hardy sets out to defend pure math versus applied. It’s a false dichotomy, I think, (and makes me think of C. P. Snow’s later two cultures false dichotomy), but Hardy’s apology turns out to be a discourse on the idea of being committed to a discipline—math, linguistics, criticism, physics, anthropology, you name it (or as one of my old professors put it, the value of having a perspective and theory with which to analyze the world). There is some math (Pythagoras’s proof of the irrationality of the square root of 2, etc.), but not enough to give anyone a headache. For me though, the real value of Hardy’s essay is that the seriousness of intellectual work lies is the ideas that it connects, not in immediate applications, making it wortha read by any academic.
Snow is terrific! 19. September 2014
Von James R C Baker - Veröffentlicht auf Amazon.com
Format: Taschenbuch
I think that the creative process that G. H. Hardy describes is illustrative and the introduction by Dr. C. P. Snow is terrific!
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