A Mathematician's Apology Hardcover – 1 Sep 1967
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'Generations of readers, both in and out of mathematics, have read Apology as one of the most eloquent descriptions in our language of the pleasure and power of mathematical invention.' The New Yorker
'Great mathematicians rarely write about themselves or about their work, and few of them would have the literary gift to compose an essay of such charm, candour and insight … a manifesto for mathematics itself.' The Guardian
'Hardy's book is carefully reasoned, beautifully written and very stimulating; … it can profitably be read by anyone.' New Scientist
'A beautiful book written by a leading mathematician of the time.' BBC Focus --This text refers to an out of print or unavailable edition of this title.
Top customer reviews
"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.
CP Snow paints a delightful picture of the life of an honest, eccentric, and intellectually gifted man – a life revolving around academia in general, mathematics, cricket, radical ideas and some superb eccentricities. Hardy was suspicious of all things mechanical – “If you fancy yourself at the telephone, there is one in the other room”. This book is worth reading for the foreword alone.
Hardy’s work then follows, written in a series of short, pithy chapters, a bit too long to be called aphorisms, but each almost stands alone in placing an argument, crafted in step-by-step fashion, as you would expect of a mathematician. Now, maybe my interpretation of Hardy’s words is different to others, but for me, although he concentrates on the rights or wrongs of devoting one’s life to pure mathematics, discussing how “worthwhile” mathematics is as a profession, I think you can read this as an argument on the merits or otherwise of any human endeavour. He basically concludes that it is far better to exercise to the full whatever talent one has, than do undistinguished work in other fields. There’s more depth to it than that of course, all very readable, and an interesting set of views for those faced with an awkward crossroads in life!
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