A good "justification" of pure mathematics. Practicing mathematics satisfies an intellectual curiosity, it can be seen as making observations of a "mathematical reality", and mathematical theorems are "eternal". I agree with Hardy that pure math is like creative art with its aesthetics and so on, and I found the characterizations of applied mathematics and mathematical physics very good.

This book can be uplifting, or depressing, depending on the reader's state of mind. It encourages one to build up one's talents, but on the other hand it sends a message that only the most gifted can really make it. Hardy seems satisfied with his own life and proud of his profession, and he doesn't hide it. I didn't take it as arrogance.

About losing one's creativity: Is it really best to do mathematics in an early age, or is it just a myth? Perhaps it's true that the most revolutionary ideas are conceived by young mathematicians, but some of this claim is probably due to young people (without families) have more time to do math, and doing math should be intense, in order to achieve results.

Snow's foreword was a great, fun (in an old English way) introduction to Hardy as a person. The Apology was easier to appreciate after reading that. The Finnish translation wasn't so great. It was sloppy language, perhaps done in a hurry or without any professional ethics. ( )

It is a lovely little book, articulate, reasoned and opinionated. It is somewhat dated, since number theory is now central to the operation of the Web, whereas in Hardy’s time it was an area of mathematics he denotes as “real” mathematics and thus not useful. It is now “trivial” mathematics, in Hardy’s harsh division of the field. However, as an explanation of why one has a life in mathematics and what it might be like to be a mathematician, this book is remarkably effective.
It is not overtly autobiographical until the last section where with mathematical terseness he lays out his life in a few pages, but rather seeks to recreate the mathematical approach to work. He defends the world of mathematics that exists far beyond the applied mathematics that most people, even engineers and hard scientists, learn as a tool to practice their profession. This mathematics is more art than much painting or sculpture, since it is entirely a construct of the mind. It is beautiful to the trained eye and incomprehensible to anyone else.
There is a sorrowful tone that hangs over the entire book. This is especially true if the reader is wise enough to obtain a copy with the forward by CP Snow, who gives us a bit more detail on the man Hardy. Mathematicians, in general, do all their work when they are young and their minds are pliable and their egos intact. Hardy, when he writes the book, can no longer do math, and he grieves the loss as one would one’s manhood, since his solitary life had left him with little that he could identify as himself other than the creation of original work in mathematics. His anguish is apparent and he is inconsolable.

Life-changing. No, seriously. Hardy's brief monograph puts forth a spirited argument that mathematics is beautiful precisely because it is useless. (An argument that miraculously survives the subsequent utility of number theory, Hardy's own bailiwick, in computer encryption.) The abstraction away from personal human expression and basic human practicality gives math an Olympian clarity that makes a mathematical vocation–a career choice essentially guaranteed to be arduous and unrewarding–worth it for those lucky few who can manage to do it for real. Hardy was one, and his insider's description of the pursuit of a particularly austere variety of beauty is compelling. And beneath the heady ideas is the poignant subtext of a man past his prime, writing with passion about a life's work he no longer has the ability to pursue. C.P. Snow's extended biographical introduction (which is as much about Hardy's protégé Ramanujan, himself an intriguingly tragic figure) brings this personal angle to the forefront and makes it moving.

Mathematicians, scientists, and computer programmers are likely to find in Hardy's description of mathematical beauty a crisp expression of some of the deep motivations for their own work. Non-mathematicians will get a taste of why such a seemingly dry pursuit can be so compelling. And anyone interested in general questions of aesthetics will benefit from an encounter with a idea of beauty that does not automatically center itself around the Romantic notion of personal emotional expression. ( )

Hardy's own story is required reading for anyone seriously undertaking a life in hard creative fields: maths, science or arts. It is a cautionary tale against overt competitiveness, as he is a shining example of a person so insecure that his entire life is devoted to proving he is better than others.

From a young age, Hardy admits that even being good at school was to show that he was better than the other boys. Snow paints him as a bore who requires sycophants, with a lifelong fascination of literally ranking people.

Hardy himself implies his predicament:

`I still say to myself when I am depressed and find myself forced to listen to pompous and tiresome people, ``Well, I have done one thing you could never have done, and that is to have collaborated with Littlewood and Ramanujan on something like equal terms."'

Why does Hardy need to reinforce his superiority over pitiable interlocutors? If he is the self-proclaimed fifth best pure mathematician in the world (few would be qualified to deny him this), how could he be so insecure?

It is puzzling how such a genius never came to terms with his one-upmanship as the source of his own depression, especially since he was so honest about himself. To answer in part, we must accept that Hardy's younger days, his inner life as a mathematician was incredible. However, as he measured his own life against others he was destined for a sorry end. Perhaps he never saw the afflictions of old age coming, or believed that the sacrifice was somehow worth it.

Hardy's ideas on mathematical aesthetics, although genuine, are ingrained with his competitive affliction. He viewed mathematics as completely useless to the real world. His view that it is rarely genuine if one justifies his work to do good for others is refreshing, and a thought I'll always carry around with me whenever I meet anyone in a creative field. However, the definitiveness of this attitude now seems quaint, as clearly mathematics, even his abstract speciality of number theory, is now an integral part of modern day communications and cryptography.

As others have said, read Snow's forward second as it is completely inappropriate to be read before Hardy's own treatise.

Also note that the word `apology' is probably used in the title in its anachronistic meaning as a formally written justification, not necessarily as a statement of regret.

Although I have been scathing of Hardy, I am still immensely grateful to this character for having live such a unique life on the fringes of humanity. Few have gone so far in the inner-life and been so honest to themselves and the rest of us. ( )

Two Books In One!

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! ( )

Points of interest:
"I do not know an instance of a major mathematical advance initiated by a man past fifty."
Fame follows merit more closely in Maths than in most subjects.
Popularity of maths at a low level is shown by chess problems. "Chess-problems are the hymn-tunes of mathematics."
The object is to show that the main value of higher mathematics is aesthetic: "Beauty is the first test". Cogently and racily written: the author's conceitedness does not make him pompous. One questions the value of a form of beauty which can be appreciated by so few people, but the author's reply is that he is doing the thing at which he is best, and it is more valuable for him to do that well than something else indifferently.
(notes writen 1954)