The English mathematician G. H. Hardy is now remembered less for his own mathematical contributions than for his support of Ramanujan and for a book written toward the end of his life, *A Mathematician’s Apology*. In the *Apology* he sets out one of the orthodox doctrines of pure mathematics: the book is a classic because, whether Hardy is right or wrong, he puts his case with great clarity.

In one of the most famous passages, Hardy discusses whether “real” mathematics — by which he means non-trivial pure mathematics — does any harm in the world.

Real mathematics has no effects on war. No one has yet discovered any warlike purpose to be served by the theory of numbers or relativity, and it seems very unlikely that anyone will do so for many years.

This was written in 1940, when — presumably unknown to Hardy — Bletchley Park was already in existence, and the Manhattan Project, with its devastating demonstration of mass–energy equivalence, was only a few years away. Hardy’s friend C. P. Snow described the *Apology* as “a book of haunting sadness” for other reasons, but this irony has outlived them all.

(DP)

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