G.H. Hardy 1992. A Mathematician’s Apology. With a foreword by C.P. Snow Campbridge: Campbridge University Press, 153 pp.

A defense of pure mathematics. But Oxford and Cambridge don G.H. Hardy is so apologetic about it all that he devotes first part of his esay to a defense of having to go to the bother of making a defense. The central assertion is that mathematics is either simple, dull, unimaginative and useful (applied maths, undergraduate maths), or else it is beautiful, creative pure mathematics. Hardy claims this latter mathematics to be useless, including of no military consequence. But the first edition was published in 1940 - before the Bletchley Park team of mathematicians broke the German Enigma Code. And before the Manhattan Project. Also the recent 100-plus page proof of Fermat’s Last Theorem would surely violate Hardy’s rule that great mathematics is simple and elegant?

There are a few aphorisms scattered through the text, but none that I have remembered. There is at least one thing in this essay where Hardy would probably find himself in agreement with mathematicians and philosophers from Plato to Tegmark: mathematics is apart from the physical universe. We discover it, we do not create it.

The foreword by C.P. Snow paints a revealing picture of his eccentric and pathologically shy friend, who by his own admission was only a bit brilliant and stated that for a short time he was probably about the fifth best pure mathematician alive. Lots of modern mathematicians cite this book in various contexts but perhaps they are being a bit polite?