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A Mathematician's Apology (Canto)

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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.

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...)

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.

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 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.

Godfrey Hardy was a great mathematician, and then some! His Apology is a discourse on the beauty of mathematics and, especially, of a life devouted to mathematical investigation. The author has, at the time of writing, passed his prime, and , being Hardy, does it no more. That's why it is moving, although, given the British love for understatement, this is really very subtle. The novelist C.P.Snow writes a brilliant introduction (actually larger that the Apology itself) on the figure of Hardy. You'll never forget either!

This is a classic defence of mathematics, that stresses the beauty and truth of pure mathematics -- its theorems being often of perfect elegance, and its truth having an exactness that other disciplines cannot equal. But the appeal of the book extends well beyond this. First, the way in which Hardy writes with complete honesty about what is most important to him is very moving, and he does so in a style that (like good mathematics) is a model of concise, plain and lucid expression; indeed I know no more perfect piece of writing in the language, (though this very perfection is a limitation). Secondly, the long biographical introduction by C.P. Snow is a vivid evocation of Cambridge academic life before the modern world began to impinge. Hardy's world combined intellectual preeminence, moral integrity, independence and frankness of judgement with an extraordinarily narrow social experience; it was a world where women had no place, and where emotions were kept jealously private. The modern reader will feel, at one and the same time, privileged to enter imaginatively into this environment and relieved that modern life is less constricted.

Hardy is amongst the important mathematicians of the 20th century. I read quite a few things about Hardy while I was reading Ramanujan's biography (by Robert Kanigel, another nice piece of work). Finally, I got a chance to read Hardy's writing himself. Though the overall theme of the book is sad in some sense, it makes for delightful reading. The book is easily accessible even to people who don't have a mathematical background, though I admit having a taste for math will only make the reading experience better. A must for the bookshelf of everyone who is interested in the lives of mathematicians (and their eccentricities :)

This short book with a biographical sketch by C. P. Snow is a superbly written explanation of what mathematicians
do and how they think. Hardy was a fascinating man then and he remains so today. His prose style is marvelous
and lucid. I have reread this book many times since I first discovered it in the 1960's. His essay is somewhat
melancholic in tone because he knew as he wrote this book that his fertile creative period was essentially ended.
As he remarks 'mathematics is a young man's game.' The biographical sketch by C. P. Snow is very illuminating
also in its portrayel of Hardy as a somewhat eccentric yet brilliant indivdual.

Hardy, in just a few short chapters, crafted a beautiful book that is nothing less than a devotional for mathematicians. Reading one chapter a day for the rest of my life would keep anyone in a state of mathematical bliss. In my own educational journey, Hardy gave me the feul for the fire to persist in my degree program. Every sentence of this short memoir is quotable, and I would recommend this book for anyone considering entering the field of math as well as anyone who feels stale in their choice of becoming a mathematician. In A Mathematician's Apology, Hardy clearly shows that he is the Knute Rockne of math.