He also gave another reason for being what I suppose we should call "a good loser" — and which I found almost incredible: "I'm not the competitive type. I don't have the sportsman's mentality. I absolutely don't have the killer instinct. I never had it from the start." Kramnik explained to me that both his parents belonged to the world of the arts, his mother as a piano teacher and his father as a sculptor: "My father taught me chess when I was five, very much as part of my cultural education; and over the chessboard even when playing for the world championship I think of myself as an artist, as my parents were."

Kramnik brings to mind the French surrealist Marcel Duchamp, who played chess for France, and observed that "While not all artists are chess-players, all chess-players are artists." Certainly, Kramnik's best games have an extraordinary fusion of elegance and force, giving the impression that this is as well as chess could be played. Perhaps it is this, the desire to play the best possible chess, which makes him a tournament killer, even as he denies having any sporting instinct. In this sense, he is like the winner of multiple international piano competitions — a parallel he will have understood from observing his mother.

(There is perhaps another reason for Kramnik's inner serenity, something unusual among chess players at the highest level. He is quite a religious man, who married his French wife Marie-Laure in a Russian Orthodox Church in Paris. He told me that he himself had been "baptised in secret in the Soviet Union. It would have been trouble for my parents if it had been known. They could have lost their jobs.")

When I study the games of Vladimir Kramnik I feel a sense of genius, just as I do listening to the music of the greatest composers. Yet he dismisses this: "I'm no genius. And it's a myth that chess champions are geniuses, or even much more clever than the average person. Anyone could become a Grandmaster, if he studied hard enough." And what of the fact that as a 15-year-old he astonished people by being able to play 20 games simultaneously, without sight of any of the boards? "There are lots of things I'm useless at, an idiot in fact: I can't read maps at all."