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A Mathematician's Apology (Canto) Paperback – January 31, 1992

ISBN-13: 978-0521427067 ISBN-10: 0521427061 Edition: Reprint
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Editorial Reviews

Amazon.com Review

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


'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

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Product Details

  • Series: Canto
  • Paperback: 153 pages
  • Publisher: Cambridge University Press; Reprint edition (January 31, 1992)
  • Language: English
  • ISBN-10: 0521427061
  • ISBN-13: 978-0521427067
  • Product Dimensions: 5.4 x 0.5 x 8.5 inches
  • Shipping Weight: 12 ounces
  • Average Customer Review: 4.0 out of 5 stars  See all reviews (50 customer reviews)
  • Amazon Best Sellers Rank: #313,112 in Books (See Top 100 in Books)

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Most Helpful Customer Reviews

44 of 47 people found the following review helpful By James R. Mccall on May 14, 2001
Format: Paperback
I confess to a weakness for the Oxbridge culture of the early 20th century, so I'm a pushover for something like this. I'm not personally familiar with Hardy's work (my studies, such as they were, were in computability, provability, and the like), but it's enchanting to think of him sitting down with Housman or Russell at lunch and disputing or joking, so much shared tacit knowledge at the table.
The long foreward by C. P. Snow makes the subsequent text richer and more sad than it would otherwise be. Still, the most important point is made by Hardy: mathematics is a serious creative art, and is worth doing for that reason. Moreover, you should move heaven and earth to develop your abilities if you have the talent, and not bother with it otherwise.
More generally, Hardy places great value on the doing of something - anything! - supremely well, and has little interest in the lot of most people, which is to muddle through in their arbitrary careers. And there's the rub. Like a great athlete, a great mathematician is finished rather early. Yet he must contrive to live long after his powers have deserted him. Athletes often go to seed when their playing days are over, where less well-endowed people might remain physically active into old age. Hardy lost his math "legs" and never got over it. And here he's weighing in on Housman's side in the perennial problem of getting old: better to slip betimes away.
Anyway, it's a darn good read, and short, at that. And we must remember that it was written in those dark days when Germany was rolling over Europe. Can we blame Hardy for taking solace in the fact that his beloved number theory seemed to have no applications to war? (These days, of course, prime factorization methods constitute a strategic advantage...)
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39 of 42 people found the following review helpful By Kersi Von Zerububbel VINE VOICE on July 7, 2006
Format: Paperback Verified Purchase
This short book has long been one of my favorites. Hardy's philosophical musings may depress some but they ring so very true. Hardy is quite honest about life, art, mathematics, and his failing abilities. For example, his statement, that a very small minority of us are really good at what we do may sound depressing today. But the fact is true.

I can recall when words such as super, excellent, awesome etc. were used judiciously and very rarely to describe truly significant achievement. Today, doing one's job, albeit poorly, is described as excellent.

What I most like about Hardy's book is it's honesty and respect for the reader. A suggestion. Read the book proper BEFORE wading through C.P. Snow's forward. After about the second read tackle the forward.

A must have.
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51 of 57 people found the following review helpful By Charles Ashbacher HALL OF FAMETOP 500 REVIEWERVINE VOICE on February 18, 2001
Format: Paperback
Every discipline has a list of items that must be read if one is to be considered educated in that field. There is no doubt that this book should be required reading for any degree in mathematics. Most of the soul of mathematics is contained in the 91 pages of the `Apology' (the first 58 pages consists of the foreword by Snow). Written in his later years when Hardy knew his mathematical powers were failing, this is a superb exposition by a brilliant, eccentric personality. He not only captures the grandeur of mathematical discovery, but also clearly articulates the feelings of a man who knows that his time has passed. First published in 1940, the twin messages are timeless.
Clearly distinguishing between the real mathematician and the puzzle solver, Hardy is exceptional in declaring what the real beauty of mathematics is. Among all the beautiful things that exist, the percentage of individuals that can truly appreciate an elegant theorem is among the smallest. However, anyone who can read this work and not see at least some of the poetic qualities of mathematics has a blind spot in their soul. One of the masterpieces of literature, this book can be understood and appreciated by anyone with an eye for the beautiful things that life has to offer.

Published in Journal of Recreational Mathematics, reprinted with permission.
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11 of 12 people found the following review helpful By A Customer on December 8, 2000
Format: Paperback
Hardy was a man that comes along rarely in life, and this book is an even rarer portrait of how men like him think. As a mathematician, Hardy was excellent, his collaboration produced much fruitful work, and he is perhaps most renowned for discovering the young protege Ramanujan. But this book is not really about his work, but about his views on life, and mathematics, as a whole. Considering how little people in American society know about mathematics and its practitioners, this book, which is emminently readable, will give all people a unique view of what some mathematicians think like. The book is short, but interesting from first page to last. Hardy was past his mathematical prime when he wrote this book, but this book probably is his most influencial he ever wrote.
The introduction by C.P. Snow is more like a short biography about Hardy, and it's about the same length as Hardy's actual text. It gives us insights into what one of Hardy's friends thought of him, and it also frames the life Hardy was living in as he wrote this book.
Hardy's opinions are strong, and undoubtedly every reader will disagree here and there with him. But he shows the reader some of the gems of mathematics, and perhaps the reader will be able to appreciate those even without formal mathematical training. He also talks about war and what he thinks of it. Whatever the reader thinks about Hardy's opinions, this book gives us the opportunity to glimpse into the mind of an artist - one different than the usual meaning attached to the word, but one nonetheless - and experience a part of human life not experienced by many - the wonders of mathematics.
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