A Mathematician's Apology (Canto)

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

Product Description
G. H. Hardy was one of this century's finest mathematical thinkers, renowned among his contemporaries as a 'real mathematician ... the purest of the pure'. He was also, as C. P. Snow recounts in his Foreword, 'unorthodox, eccentric, radical, ready to talk about anything'. This 'apology', written in 1940 as his mathematical powers were declining, offers a brilliant and engaging account of mathematics as very much more than a science; when it was first published, Graham Greene hailed it alongside Henry James's notebooks as 'the best account of what it was like to be a creative artist'. C. P. Snow's Foreword gives sympathetic and witty insights into Hardy's life, with its rich store of anecdotes concerning his collaboration with the brilliant Indian mathematician Ramanujan, his aphorisms and idiosyncrasies, and his passion for cricket. This is a unique account of the fascination of mathematics and of one of its most compelling exponents in modern times.

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...)


One of my top 20. Somewhat depressing but oh so true.   July 7, 2006
Kersi Von Zerububbel (San Diego, CA USA)
23 out of 24 found this review helpful

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.


A unique book, should be read by everybody   December 8, 2000
10 out of 11 found this review helpful

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.


This is the book to read.   August 25, 2000
5 out of 5 found this review helpful

This is the book that made me stop and think. As a result of this book I have decided to become a math major. When you have a book written as beautifully as this by a man as brilliant as G.H. Hardy, there is no possible way that it couldn't influence your life. Through Hardy's prose, you can see the writer, in his aged brilliance, his deep eyes reflecting on his days as the brightest in Europe. This is an immensely powerful book and is worth reading several times. Of all the books that I have ever read, this is the single pinnacle- the only book that changed my life.