A Mathematician's Apology (Canto) [Paperback]

 

 

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This is a delightful read. The foreword by C.P. Snow takes up approximately one-third of the book, and is effectively a short biography of Hardy. It follows his life from late Victorian public school, to Trinity at Cambridge, then to New College Oxford, and then back to Cambridge. His initial decision to go to Cambridge came after reading “A Fellow of Trinity” by “Alan St Aubyn” – this is apparently not one of the world’s greatest works of literature, but I just have to read it now to see what was in it that could inspire him so strongly!
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!

"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.

This is a good book for people intersted in mathematics, no prior knowledge needed! It discusses how mathematics is important in the everyday world. I would recommend this book especially to mathematics students (or prospective ones) as wider reading. It is interesting to see how in Hardy's time, less than sixty years ago, areas of mathematics that had no obvious use and were studied purely for their beauty have become the centre of importance in the computer and internet technology of today and the future with important applications and areas of research.

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3.0 out of 5 stars Very approachable for non-mathematicians
This essay by one of the great pure mathematicians is rightly famous, but not for the right reasons. Read more

Published 23 months ago by D. R. Cantrell

5.0 out of 5 stars Mathematicians apology
I had read that Hardy's apology was very good value and, my goodness, it is. Hardy's uncompromising attitude to success and his delightfuland precise use of English make this a... Read more

Published on 7 Feb 2010 by Carrolean

3.0 out of 5 stars How maths used to be
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... Read more

Published on 24 Nov 2008 by Dr. Mike Goldsmith

5.0 out of 5 stars Hardy's Apology
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... Read more

Published on 23 July 2008 by conan fitz elis

3.0 out of 5 stars Disappointing
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. Read more

Published on 26 Mar 2008 by Kevin Roche

5.0 out of 5 stars Read it. Seriously.
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... Read more

Published on 4 Feb 2008 by Promethean Fate

5.0 out of 5 stars a reviewer's apology
I believe that the two biggest compliments a math author can get are first to have Graham Greene write: "the best account of what it was like to be a creative artist". Read more

Published on 23 Oct 2005 by Palle E T Jorgensen

4.0 out of 5 stars A fascinating book, but doesn't Hardy contradict himself?
There is, I believe, a non sequitur in Hardy's justification of his chosen life as a mathematician, which seems surprising from a mathematician of his class. Read more

Published on 14 Sep 2004 by Robert Saunders

5.0 out of 5 stars Classic text: required reading for all mathematicians
Quite simply: if you are 'doing' mathematics, or if you are about to embark on a course of study in mathematics or the philosophy of mathematics, then you must read this... Read more

Published on 25 Jun 2003 by S. Powell

5.0 out of 5 stars An inspirational text from a legendary mathematician
This is simply a superb book, and I am not sure that any review I write will really do this classic text justice. Read more

Published on 14 May 2001

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