A Mathematician's Apology (Canto)
by G.H. Hardy
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List Price: ££12.99
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Manufacturer: Cambridge University Press
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Average Customer Rating:  
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Binding: Paperback
Dewey Decimal Number: 510
EAN: 9780521427067
ISBN: 0521427061
Label: Cambridge University Press
Number Of Items: 1
Number Of Pages: 153
Publication Date: 1992-01-31
Publisher: Cambridge University Press
Studio: Cambridge University Press
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Spotlight customer reviews:
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Customer Rating: 
Summary: No need to apologize for this
Comment: "Exposition, criticism, appreciation, is work for second-rate minds." Already, in the first paragraph, G. H. Hardy is deploring the task of writing about mathematics in his characteristically forthright fashion. It's just as well that by the time we begin the Apology we have been softened up by C. P. Snow's excellent introduction and potted biography. Clearly, this first-rate book has attracted an altogether better class of reviewer, the self-effacing type not given to hissy fits on being reminded of their place in the intellectual pantheon.
"I had of course found at school, as every future mathematician does, that I could often do things much better than my teachers". Hardy's later achievements and his matter-of-fact style ensure that this is neither preening vanity nor a pompous boast. A professional mathematician might also agree that the "function of a mathematician is to do something" and not to talk about it. Mathematics as an active pursuit, being cleverer than your maths teacher - these count as revelations to ordinary mortals, even those of us who weren't too bad at maths. Then, and before any unsuspecting non-mathematician can run for cover, Hardy sets about proving "two of the famous theorems of Greek mathematics". There is really nothing to be scared of, even for the most equation-phobic humanities graduate. It's the ideas and the arguments that link them that matter, and they are not difficult to follow. In tracing the steps of Euclid and Pythagoras we are tracing patterns of thought that have lasted two thousand years, and we too can directly appreciate their beauty, and see for ourselves in a small way that a "mathematician, like a painter or a poet, is a maker of patterns."
Hardy does not take kindly to the commonplace idea "that an academic career is one sought mainly by cautious and unambitious persons who care primarily for comfort and security." While he is, unsurprisingly, motivated by "intellectual curiosity" and a "desire to know the truth", he also admits to "professional pride", "ambition" and a "desire for reputation". A lesser mind might have been tempted to feign guilt over such worldly traits, but Hardy has only a good word for ambition, the "noble passion". And his own noblest ambition? That "of leaving behind... something of permanent value". No dreams of heavenly bliss for this atheist.
Just when you might be thinking that all this talk of reputation and ambition must arise from an insufferable self-centredness, he declares that much of his best work was done in collaboration with two other mathematicians, Littlewood and Ramanujan, from very different backgrounds. Hardy's recognition of the unknown Indian was not inevitable: two other eminent Englishmen had returned the manuscripts without comment, on the assumption that Ramanujan was a crank. That too was Hardy's first impression, but he soon changed his mind and saw in Ramanujan a brilliant if untutored mathematical mind. It is a remarkable story by any standards, and has been recently staged as "A Disappearing Number" - a brilliant production in which a rather battered copy of this very edition gets a turn in the limelight.
What was a "melancholy experience" for Hardy (writing about mathematics) provides a rewarding experience for us. Graham Greene considered this the best account of what it is like to be a creative artist. I don't know if Greene is right, or if Hardy is right in his belief "that mathematical reality lies outside us," waiting to be discovered. I defer to their judgements but can better appreciate their conclusions after reading this book. C. P. Snow describes Hardy's "mocking horror of pretentiousness, self-righteous indignation, and the whole stately pantechnicon of the hypocritical virtues." More intriguing, given Hardy's hatred of God and all the pious nonsense carried out in God's name, and given that the spiritual side of human nature has been unthinkingly yoked to religious mumbo jumbo for far too long, is Snow's description of Hardy "as spiritually delicate" and "spiritually candid as few men are".
The dominant sense of "apology" implies a fault for which contrition is being expressed. Hardy's Apology is no craven exercise in self-abasement but a serious and vigorous justification of the intellectual and creative life, whether led by a mathematician or anyone else.
Customer Rating:
Summary: How maths used to be
Comment: Reading this book is like opening a time capsule - which is fun, up to a point. The academic world Hardy inhabited was largely swept away by the first world war, and this book is full of the feeling of that threatened world - one of Hardy's main aims is to show that a. "proper" mathematics is of no practical use, and that b. this is good news, partly because this makes it "purer" and hence better (in some unexplained way) partly because then it can't be blamed for killing people.
The idea that mathematicians should justify their incomes through the value of their work (either through actual income generation or through explaining how the universe works) seems not to occur to Hardy; it's hard to imagine any mathematician today making the uselessness of their subject the major theme of a book.
Unfortunately for Hardy, the very areas he singles out as being especially satisfyingly useless are key to modern code-breaking and secure financial transactions - in fact it's hard to think of any substantial area of mathematics that is "useless" in Hardy's sense.
Hardy's style is also very antiquated, involving a great deal of preparatory throat-clearing, unsupported value-judgments, meandering around the subject, and lengthy vagueness. To a modern reader it all seems a bit smug and fake.
On the other hand, the actual points that Hardy makes about the way mathematicians develop ideas, and the examples of explanations of the amazing way mathematical proof works, are good ones. And, as a look back at a vanished period of academic history, it's great. But as an introduction to how mathematicians work now, or the role of mathematical research, it has become a very weak book.
Customer Rating:
Summary: Hardy's Apology
Comment: I bought Hardy's biography almost 50 years ago, just before going up to university to read Maths. The gentle almost humourous tone of the book convinced me that the life of a mathematician was a potential source of pleasure. In fact I later moved to read Philosophy, for my interests grew to centre on Logic and Mathematical Foundations, but my current work on Infinity still finds me using Hardy's "Pure Mathematics", and I still occasionally read his "Apology" for the pure pleasure that this outstanding book provides.
Customer Rating:
Summary: Disappointing
Comment: I'm not sure I read the same book as the other reviewers. I'm fascinated by mathematics and have, for a long time, been meaning to read this book. Finally I have, and I have to say I was somewhat disappointed. C.P. Snow's foreword was an interesting potted biography of one of Britain's greatest 20th century mathematicians; but, the "apology" itself is overshadowed by its own introduction.
The first nine chapters are a clear indication - if any was needed - that intellectual brilliance is no talisman against small-mindedness. Maybe I'm being unfair but in those nine short chapters Hardy manages to denigrate most of humanity - "most people can do nothing at all well" - by which he means, nothing that he personally considers worthy. I'm not convinced we should readily accept the social opinions of a man who was born to privilege and spent his entire life in rarefied cloisters shielded from what the "most" in question would consider reality. A man who thought we should not go to war with Germany because of the caliber of its mathematicians and scientists. (?) There are many reasons why we shouldn't be at war with Iraq, for example, but that the region is the cradle of civilisation is not one of them.
From chapter ten onwards the book makes a change of direction and deals with the actual subject of mathematics and being a mathematician. This latter section of the book is a much more interesting (less infuriating) read but I still felt he dealt rather ineptly with the attempt to differentiate between "common and garden" mathematics and the truly profound and beautiful creative mathematics that he so clearly loves.
When you compare this book to say Marcus du Sautoy's "Music of the Primes" or Simon Singh's "Fermat's Last Theorem", both books which truly promote the essential character of mathematics, "A Mathematician's Apology" seems very pale.
Customer Rating:
Summary: Read it. Seriously.
Comment: This book is a facinating insight into the mind of one of the century's greatest mathematians. However, Hardy's ideas go far beyond this into the purpose of human endevour in general.
The best part of this book is the foreword by C.P Snow. This amounts to a lucid, if brief, biography of Hardy from a man who is brilliant in his own right.
If you have any kind of interest in the realities of mathematics, or the workings of genius, then this book is the place to start.
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