Last week I mentioned Will Smith, a comedian who knew every episode of Bergerac off by heart, and who was, I assumed, the nerdiest man ever to walk the face of the Earth. Then I saw Demetri Martin. Fascinated by puzzles from an early age, Martin spent his free time at college devising 3D crosswords for his student newspaper. He once wrote a poem using only the words on a beer bottle, and, when he dropped out of law school to become a comedian, he formulated a pseudo-scientological 35-point tally sheet of his weekly progress as a human being.
Now ready to analyse his self-analysis, Martin is a mop-topped New Yorker who presents a very American kind of autobiographical show. His oddball gags are worthy of Emo Phillips ("I'm afraid of sharks," he admits, "but only in a water situation."), but it's less a stand-up act than an off-Broadway one-man play. The structure has been worked-out as intricately as those 3D crosswords, and the monologues are interspersed with slides, music and a unicycling demonstration, as Martin unravels the compulsive personality that had him studying yo-yo tricks and Rubik's cube solutions through his teens. These accomplishments may not, as he laments, make him any cooler, but they do reflect a spark of crackpot genius. Witnessing it makes for one of the Fringe's most satisfying hours.
Another fun multi-media show follows Martin's at the same venue, this one featuring the chatty, easy-going Alex Horne. With the help of a friend, a fish, and an overhead projector, Horne recreates the experiments conducted in a 1976 academic conference on laughter. Elsewhere, Howard Read interacts with a set of South Parkish animations projected onto two screens behind him. Read draws, animates and voices all of these cartoon characters, the main one being Little Howard, a cute but not too cute six-year-old boy. Thanks to Read's computing proficiency, Little Howard can hold a conversation with his creator, and in one remarkable sequence the character answers questions from the audience. However, the technology doesn't always do what it's told, and when Read has to fill the uncomfortable pauses, it's clear that his skills as an animator surpass his skills as a stand-up. His creations complain that they could do just as well without him. They're not too far wrong.
If you're in the mood for some straightforward stand-up, Dara O Briain is much better in person than he is as the host of BBC2's Live Floor Show. A comedian at the top of his game, he's irrepressibly jolly and enthusiastic, with just enough bitter, sceptical edge. You couldn't call his material hard-hitting or cutting edge, but he never resorts to the bedsit grumbles of some male stand-ups; he's bursting with stories about children's TV, swimming with sarcastic dolphins and the wrenching disappointment of a balloon safari in Africa. O Briain could talk the hind legs off Billy Connolly. Even with his phenomenal WPM rate, you feel he could have carried on for another hour - the audience would have loved if it he had.
Another TV host, the cube-headed Jimmy Carr, can be seen on Channel 4's Your Face or Mine, where his ad libs reduce co-presenter June Sarpong to the role of decorative sidekick. He's as slick as he is sick - and he's very sick indeed. A condescending, Home Counties fop, Carr specialises in one-liners, each one as honed as a haiku, and in heart-stoppingly bad taste. He also brings the same reserved manner and unreserved humour to a First World War play and a presentation of the deviant small ads he's placed in newspapers and magazines. He's so relaxed and in control that he's on stage before the audience arrives, and heckles them as they take their seats.
Other stand-ups to watch for include Alan Carr. A promising fount of bitter Northern gags, he's just a wig and a dress away from being a slightly less savage Lily Savage. Andrew Clover is infamous for performing nude, but this year he keeps his ill-fitting blue suit on. He has madcap, Rik Mayallish energy, but it's only when he blurts out his loathing of himself, his family and other people's children that he really earns his money. Emotional nakedness suits him better than physical nakedness.
As for character comedy, the best I've seen this year is by Gavin and Gavin, two blonde sisters who morph seamlessly into a dozen different people, much like the actors in the Stones in His Pockets. The setting of their show is a motivational workshop. The Gavins play all of its students, as well as a bulldozing "lifeologist" whose pathetic bumptiousness is a match for David Brent's. "It's gonna get rough today, yeah?" she sniffs. "Jungle rough." The other stand-outs are a pair of bubbly, cockney stage school wannabes who are horribly proud of their stint on 'Enders four years ago, and who can't cross the room without throwing in a pas de deux. The accents and mannerisms of each character are so shrewdly observed that the Gavins themselves disappear. Victoria Wood and The League of Gentlemen couldn't do better.
Demetri Martin, Alex Horne: Assembly Rooms (0131 226 2428). Others: Pleasance (0131 556 6550), until 25 August