"A mathematician offers the game"

Karr's memoir book also includes a superb list of memoirs (she stars the ones that are exceptional as books as well as personal histories - I find a high degree of congruence between her tastes and my own). One that I hadn't read and immediately obtained and devoured was G. H. Hardy's heartbreaking A Mathematician's Apology, which comes with a wonderful introductory essay by C. P. Snow.

Snow on Hardy: "His life remained the life of a brilliant young man until he was old: so did his spirit: his games, his interests, kept the lightness of a young don’s. And, like many men who keep a young man’s interests into their sixties, his last years were the darker for it." And this striking description of the relationships Hardy had with a handful of young men over the years:

These were intense affections, absorbing, non-physical but exalted. The one I knew about was for a young man whose nature was as spiritually delicate as his own. I believe, though I only picked this up from chance remarks, that the same was true of the others. To many people of my generation, such relationships would seem either unsatisfactory or impossible. They were neither the one nor the other; and unless one takes them for granted, one doesn’t begin to undertand the temperament of men like Hardy (they are rare, but not as rare as white rhinoceroses), nor the Cambridge society of his time. He didn’t get the satisfactions that most of us can’t help finding: but he knew himself unusually well, and that didn’t make him unhappy. His inner life was his own, and very rich. The sadness came at the end.

The charm of Hardy's style of thought: “The proof is by reduction ad absurdum, and reduction ad absurdum, which Euclid loved so much, is one of a mathematician’s finest weapons. It is a far finer gambit than any chess gambit: a chess player may offer the sacrifice of a pawn or even a piece, but a mathematician offers the game.”

Here is Hardy on the morality of mathematics:

... there is one purpose at any rate which the real mathematics may serve in war. When the world is mad, a mathematician may find in mathematics an incomparable anodyne. For mathematics is, of all the arts and sciences, the most austere and the most remote, and a mathematician should be of all men the one who can most easily take refuge where, as Bertrand Russell says, ‘one at least of our nobler impulses can best escape from the dreary exile of the actual world’. It is a pity it should be necessary to make one very serious reservation—he must not be too old. Mathematics is not a contemplative but a creative subject; no one can draw much consolation from it when he has lost the power or the desire to create; and that is apt to happen to a mathematician rather soon. It is a pity, but in that case he does not matter a great deal anyhow, and it would be silly to bother about him.