A Mathematician's Apology

An ageing mathematician, not particularly famous but well respected in his dwindling professional community, gives a lecture to justify the life he led and his devotion to pure mathematics. While some of his thoughts and their exposition deserve attention, I would like to focus on one point that is fundamentally wrong. The author claims that mathematics in its high form is inherently useless and therefore absolutely harmless. One might be willing to agree to some extent when thinking about Poincaré's conjecture or Ferma's great theorem. Yet the author labels Einstein a mathematician and gives quantum mechanics as an example of useless mathematics. It took only 5 years from the time of the lecture for a byproduct of this 'useless show more mathematics' to wipe out populations of Hiroshima and Nagasaki. A hundred years later will anyone survive the side effects of this harmless math as we approach the Great Filter moment? show less

Why is the mathematician apologizing? Because although he became an Oxford don and left something permanent in the field of pure mathematics, he did nothing to improve the life of others. It was a selfish life because he loved the creative process and was fortunate enough that it brought him the other measures of success. The book was worth reading again to get another glimpse of his logical mind at work in what is more a justification than an apology.

Although he uses some "simple" math examples to illustrate a point, it is not necessary to understand them precisely (nor need you apologize for skipping them).

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 show more 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. show less

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, show more 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! show less

Very nicely written, but not very inspiring. It seems to me that Hardy was completely wrong in asserting that much of his Mathis is useless. Many of the ideas he wrote off are now fundamental to the modern world. Eg engineers creating digital filters need to be able to integrate around "poles" in the complex domain.

A Mathematician's Apology has been on my mental reading list for a long time and, like many titles on that mental list, I cannot understand how I didn't read it before. The edition contains a 50 page Foreword by C.P. Snow followed by the 90 page book by Hardy (actually, adjusting for different font sizes, the two parts are probably about equal in length). I read the book first so that I could think about it on its own terms and the Foreword afterwords. Both of them are outstanding and I would recommend reading them in that same reverse order.

Hardy wrote A Mathematician's Apology in the twilight of his career when he no longer was a creative, productive mathematician--and one of the many apologies in the book is the very notion of show more writing about what mathematics rather than actually doing mathematics. He conveys an enormous love and wonder for the discipline, illustrates it with sketches of some proofs, reflects back on his own work and his partnerships with Ramanujan and Littlewood, and discusses the purpose or lack thereof for mathematics. The book itself beautifully conveys the creativity and beauty of mathematics and the process and drive that leads people to do it.

C.P. Snow's Foreword is a mini-biography of Hardy, the almost novelistic story of Snow's friendship with Hardy (which begins and ends with discussions of cricket, starting when they met in the dining hall at Cambridge and ending on Hardy's deathbed), and a critical appreciation of A Mathematician's Apology. show less

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 show more 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. show less