Will Gompertz is a happily married and apparently sane father of four with a prestigious position at the centre of the British art world. By rights he should be sunning himself somewhere luxurious, reflecting on another successful year for Tate galleries, where he is director of media.

Instead he has given up his summer holiday and, starting today, is risking his reputation and mental wellbeing by performing a solo comedy show in one of the most unforgiving, competitive bearpits in the entertainment world — the Edinburgh Fringe.

Why would anyone in his position do that? “I’m really looking forward to it,” he said yesterday, managing to sound breezily convincing. “It’s an absolute privilege to be here. What’s so fantastic about the festival is that anybody can take part. It’s like being on a tiny stage at Glastonbury or part of the tubby mass of humanity following the elite runners round the London marathon.”

The build-up to Edinburgh Festival month has been grim, marred by construction work on a tramline that cuts the city in half, predictions of low spending by audiences and a binmen’s strike that has led to piles of rubbish mounting up in the streets.

But the mood in Edinburgh has transformed in recent days. Ticket sales are 20 per cent up on 2007, the Fringe’s best ever year. A total of 2,098 shows from 60 countries are taking part in the festival, with Gompertz one of 979 acts making their Fringe debut. Some 265 venues are lined up, including an island in the Firth of Forth, a London bus, a fudge shop and a public lavatory.

Double Art History with Mr Gompertz is staged in a classroom. The set-up is that the audience are pupils facing a history of art exam and Gompertz is a supply teacher standing in for their hopeless regular teacher, who has suffered a nervous breakdown.

In just under an hour he promises to unpack more than 100 years of modern and contemporary art history and theory into a narrative sufficiently digestible for the audience to pass an actual brief exam at the end.

In Fringe publicity parlance it’s “27 art movement ‘isms in 55 minutes, plus a lot of antics and humour, a bit of theatre and some drawing”.

“The point is not to convince people of what they should and should not like,” Gompertz said. “The excitement about art is that you can make your own mind up but what people struggle with is why some things are art. I want to show them.”

Along the way audiences will discover Primitivism, Orphism, Automatism, Fluxus and by the end of the hour they should be able to relate Eighties Neo-Expressionism back to Van Gogh and Post-Impressionism. Maybe.

The idea came out of an invitation to deliver a series of art lectures on some P&O cruises in the Caribbean and Europe last year. “To make them slightly more interesting I signed up for a comedy course on the top floor of a London pub to find out how comedians bring different subjects alive and engage their audience.”

“A friend of mine in TV asked if I wanted to do stand-up in Edinburgh and I said, ‘Not a chance’. But then I thought about it and decided that an amusing lecture might work.”

He is at the Fringe as himself rather than as an ambassador for Tate, but his family may yet have to get used to holidays in Scotland. “I’m not expecting glowing reviews but if it goes reasonably well I might come back.”

So far the show has had one preview, this week in front of family and friends in the packed front room of a rented holiday cottage on the Hebridean island of Colonsay. “I got heckled a lot,” he said. “It was a bit too long and I didn’t get through it but it was fun and everybody got 100 per cent on their exams. And they really didn’t all know about Constructivism and Duchamp’s urinal beforehand.”

Tickets for Double Art History with Mr Gompertz are available at www.underbelly.co.uk