Back Cover Blurb
- G. H. Hardy was one of the twentieth century’s finest mathematical thinkers, renowned among his contemporaries as ‘a real mathematician... the purest of the pure’.
- This 'apology’, written poignantly 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 is 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 academic life as well as his passion for cricket.
- '... 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
Canto, CUP, 2006 Reprint
"Hardy (G.H.) - A Mathematician's Apology"
Source: Hardy (G.H.) - A Mathematician's Apology
"Snow (C.P.) - A Mathematician's Apology - Forward"
Source: Hardy (G.H.) - A Mathematician's Apology
- It was a perfectly ordinary night at Christ’s high table, except that Hardy was dining as a guest. He had just returned to Cambridge as Sadleirian professor, and I had heard something of him from young Cambridge mathematicians. They were delighted to have him back: he was a real mathematician, they said, not like those Diracs and Bohrs the physicists were always talking about: he was the purest of the pure. He was also unorthodox, eccentric, radical, ready to talk about anything. This was 1931, and the phrase was not yet in English use, but in later days they would have said that in some indefinable way he had star quality.
- So, from lower down the table, I kept studying him. He was then in his early fifties: his hair was already grey, above skin so deeply sunburnt that it stayed a kind of Red Indian bronze. His face was beautiful — high cheek bones, thin nose, spiritual and austere but capable of dissolving into convulsions of internal gamin-like amusement. He had opaque brown eyes, bright as a bird’s — a kind of eye not uncommon among those with a gift for conceptual thought. Cambridge at that time was full of unusual and distinguished faces — but even then, I thought that night, Hardy’s stood out.
- I do not remember what he was wearing. It may easily have been a sports coat and grey flannels under his gown. Like Einstein, he dressed to please himself: though, unlike Einstein, he diversified his casual clothing by a taste for expensive silk shirts.
- As we sat round the combination-room table, drinking wine after dinner, someone said that Hardy wanted to talk to me about cricket. I had been elected only a year before, but Christ’s was then a small college, and the pastimes of even the junior fellows were soon identified. I was taken to sit by him. I was not introduced. He was, as I later discovered, shy and self-conscious in all formal actions, and had a dread of introductions. He just put his head down as it were in a butt of acknowledgment, and without any preamble whatever began:
- ‘You’re supposed to know something about cricket, aren’t you?’ Yes, I said, I knew a bit.
- Immediately he began to put me through a moderately stiff viva. Did I play? What sort of performer was I? I half-guessed that he had a horror of persons, then prevalent in academic society, who devotedly studied the literature but had never played the game. I trotted out my credentials, such as they were. He appeared to find the reply partially reassuring, and went on to more tactical questions. Whom should I have chosen as captain for the last test match a year before (in 1930)? If the selectors had decided that Snow was the man to save England, what would have been my strategy and tactics? (‘You are allowed to act, if you are sufficiently modest, as non-playing captain.’) And so on, oblivious to the rest of the table. He was quite absorbed.
- As I had plenty of opportunities to realize in the future, Hardy had no faith in intuitions or impressions, his own or anyone else’s. The only way to assess someone’s knowledge, in Hardy’s view, was to examine him. That went for mathematics, literature, philosophy, politics, anything you like. If the man had bluffed and then wilted under the questions, that was his lookout. First things came first, in that brilliant and concentrated mind.
- That night in the combination-room, it was necessary to discover whether I should be tolerable as a cricket companion. Nothing else mattered. In the end he smiled with immense charm, with child-like openness, and said that Fenner's (the university cricket ground) next season might be bearable after all, with the prospect of some reasonable conversation.
- Thus, just as I owed my acquaintanceship with Lloyd George to his passion for phrenology, I owed my friendship with Hardy to having wasted a disproportionate amount of my youth on cricket. I don’t know what the moral is. But it was a major piece of luck for me. This was intellectually the most valuable friendship of my life. His mind, as I have just mentioned, was brilliant and concentrated: so much so that by his side anyone else’s seemed a little muddy, a little pedestrian and confused. He wasn’t a great genius, as Einstein and Rutherford were. He said, with his usual clarity, that if the word meant anything he was not a genius at all. At his best, he said, he was for a short time the fifth best pure mathematician in the world. Since his character was as beautiful and candid as his mind, he always made the point that his friend and collaborator Littlewood was an appreciably more powerful mathematician than he was, and that his protege Ramanujan really had natural genius in the sense (though not to the extent, and nothing like so effectively) that the greatest mathematicians had it.
- People sometimes thought he was under-rating himself, when he spoke of these friends. It is true that he was magnanimous, as far from envy as a man can be: but I think one mistakes his quality if one doesn’t accept his judgment. I prefer to believe in his own statement in A Mathematician's Apology, at the same time so proud and so humble: 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.”’
Text Colour Conventions (see disclaimer)
- Blue: Text by me; © Theo Todman, 2020
- Mauve: Text by correspondent(s) or other author(s); © the author(s)