The Metropolitan Club, on Fifth Avenue at 60th street, is a palazzo in the mighty Manhattan style. Damn the expense. That's what J.P. Morgan is supposed to have said when he commissioned Stanford White, the city's most flamboyant architect, to build him a private gentleman's club in 1894. Inside, on a Monday evening in late January, only a few members drifted over the red, monogrammed carpets, but it was still early, only a little after seven. This, however, is when Marilyn vos Savant likes to show up.

Savant, who has the world's highest recorded IQ, is fond of dancing. She took it up seriously a few years ago with her husband, Robert Jarvik, the inventor of the Jarvik artificial heart, and they get to the club about once a month. If they arrive early enough, they can have the dance floor to themselves. And so it proved that Monday. The room was largely empty, the band were playing “Anything Goes” and once a happy, though quivering, old man was led from the floor by his partner, Savant and Jarvik could foxtrot wherever they pleased. A slim, prosperous couple in their sixties, they moved easily: she with a simple precision, he with the odd heel-tap, a bit of dash. After a time, though, as the floor filled up and became a carousel of perfectly tailored, carefully moving couples, they came back to their table. “It's a social scene,” said Savant, who is 62, with a smile. “But it's not our social scene. Let me just say that.” A few minutes later, when a serious-looking man happened to make a goofy swish right in front of them, Savant and Jarvik caught each other's eye and couldn't help laughing. Not long afterwards, they took a taxi home, to their midtown penthouse. “We usually dance more, a lot more,” said Savant as they are leaving. It is only 8.30pm. “And then we go back to the office.”

Savant – the surname is real, it was her mother's maiden name – has had a unique claim to fame since the mid-1980s. It was then, almost 30 years after she took a test as a schoolgirl in downtown St Louis, Missouri, that her IQ came to light. In 1985, Guinness World Records accepted that she had answered every question correctly on an adult Stanford-Binet IQ test at the age of just 10, a result that gave her a corresponding mental age of 22 years and 11 months, and an unearthly IQ of 228.