So has biology reasserted itself? Last weekend the extraordinary Hungarian Judit Polgar, by a yawning chasm far and away the strongest woman chess player in history, was knocked out of the game's World Cup. Yet Judit, now a 35-year-old mother of two, had got as far as the quarter-final round of the world championship eliminating tournament in the sub-arctic Russian city of Khanty-Mansiysk, beating a series of her male rivals in matches of increasing tension and difficulty. Finally, on Sunday, her epic run was halted by the reigning Russian chess champion, Peter Svidler.
As with more physical competitions, such as athletics or football, chess is divided into male and female events. Judit Polgar, however, has been unique in refusing to take any part in the latter. There would simply be little point, so large is the gulf between her and other women. Thus she told the British magazine Chess in August, when asked if she might enter the Women's World Championship: "I have never competed for it and wasn't really interested."
Judit is also unique in being the result of an educational experiment. Her father, the psychologist Laszlo Polgar, had a theory that what we call genius is in fact merely a form of learned behaviour, rather than any innate gift. He proposed to prove this, supported by his wife Clara, with any children that they had. Chess, which is widely thought to be a touchstone of the intellect, would be the conduit; and because they then produced three girls, the experiment would be especially telling, since there had never been any acknowledged female chess geniuses.
As Judit puts it: "Practically from the moment of my birth, I became involved in an educational experiment. Even before I came into the world, my parents had already decided: I would be a chess player." Lazlo Polgar appeared to prove his point: as a result of his intensive home coaching, all three of his daughters achieved remarkable playing strength at an early age – and Judit, the third daughter, beat Bobby Fischer's record to become, at 15 years and four months, the youngest person ever to attain the title of international grandmaster.
I visited the Polgars' home in Budapest, in the middle of this "experiment", when Judit was 11 years old. When I asked to play a game of chess against her, she insisted that she would only do so without sight of the board or pieces. So I stared at her ponytails, while this little girl called out the moves which demolished my position. When I then challenged her to a game of table-tennis, she annihilated me at that too, a defeat all the more humiliating because her head barely rose above the height of the table. She was, and is, a ferocious competitor, a psychological attribute that is quite separate from purely intellectual ability. As the former US chess champion Joel Benjamin reported after playing her: "It was all-out war for five hours. I was totally exhausted. She absolutely has a killer instinct."
It may in part be this, rather than what is sometimes called "genius", which has separated the girls from the boys, and made the latter much more successful at chess (Judit is the only woman who has even got into the official list of the world's top 100: at her peak she was ranked eighth in the world). The "killer instinct" described by Benjamin is something which most parents tend not to welcome in their daughters, but would positively encourage in a son. Then there is the biological element: chess at the very highest level might seem a purely mental struggle, but in fact it is physically draining: imagine doing five hours of degree-level exams every day for weeks on end, year after year, and you begin to get the point. Thus one of the world's strongest women players, Alexandra Kosteniuk, in explaining the apparently extraordinary dearth of top-level females, wrote, in some exasperation: "It's almost impossible to explain to non-chess players how physically demanding the game is, and how hard, physically and psychologically, it is to compete in world-championship level competition."
So, the weaker sex? There is, of course, a different explanation, put by Judit's sister Szofia, who gave up the game in 2002 at the age of 28. "It was not that chess was too much for me," she said, "but that it was not enough." By this she meant that she wanted a life that allowed her to be a good mother, and to have hobbies and pastimes – in other words to enjoy a whole world entirely unconnected to the black and white struggle over 64 squares.
To some extent that has also been Judit's experience. Six years ago she started a family, and her world chess ranking dropped dramatically. As she recently explained in words which will be painfully familiar to any working mother: "Very shortly after Oliver [her first child] was born I was playing in the world championship ... I wanted to have everything, and it wasn't really possible. I thought I could manage it but 23 months later my daughter Hanna was born and then everything really kind of fell apart ... Obviously I can't blame my kids for the fact that I fell from number 10 to number 50 on the world rating list ... but in every sport, you have to work a lot, you have to focus 100 per cent. But when doing the right thing in family matters, you mathematically have less time."
This helps to explain what Judit told somewhat startled chess correspondents at the press conference in Khanty-Mansiysk in the immediate aftermath of her elimination from the World Cup. While regretting her loss to Peter Svidler, she said that "on the other hand, my elimination is great because I can finally get home to my family, to be with my husband and kids". When a male politician accompanies his resignation statement with the classic observation that he wants to spend more time with his family, everyone knows that this is a convenient untruth. Yet when Judit said that, her face lit up with a genuine smile.
It made me all the sadder that she had lost, if only because it brought home how much she had sacrificed to get as far as she did.