Yet not a tribute, because nobody can honestly admire him. You might be struck by Basquiat's work for a moment or two, but his painting is so thoughtless that these moments leave you none the wiser. Indeed, this Basquiat show is a celebration of his nullity. It's about a foolish boy who got famous without having any reason for being famous, couldn't cope, and then died. You can't discover at the Serpentine that he did anything with intelligence, care or aesthetic purpose. So we're not looking at art but at a phenomenon. Julia Peyton-Jones, the enterprising director of the gallery, writes confidently of Basquiat's "genius". She must know this isn't true but says it all the same. So the phenomenon in question is that of hype.
Basquiat was born in 1960, the son of an affluent Brooklyn attorney. A college drop-out, he began adult life as a graffiti kid. More than most boys who go around the streets with a spray gun he liked to sign his activity, using the name Samo (short for "same old shit"). The pseudonym turns up on some of his paintings. These are juvenile wall scribblings transferred to canvas, and their subjects and manner are those of graffiti: crude drawing, a few names of low-culture heroes, jeering self-promotion with an underlying strain of self-pity and desperation.
This was in the early Eighties. Basquiat wanted to make it big, whether as a rock star - he was in a band for a few weeks - or as an artist. It looks as if the latter vocation was chosen for him by others. At least three New York galleries twigged that "Samo" might be saleable. And so he was. His pictures went into rich apartments (I wish we knew more about his clientele) and Basquiat found that dealers would pay him a $5,000- a-week cash retainer. One calculation is that he spent $1m in his short lifetime (much of it on drugs). The lifestyle was also expensive: he had an affair with Madonna, a friendship with Andy Warhol. Basquiat died in 1988 from a heroin overdose. He was 27 years old.
A story for our times, says the Serpentine publicity. That may be so, but still the paintings are no good. I don't say that it is impossible to make a convincing picture out of graffiti. It is indeed possible, as one or two artists have shown. You need, though, some aesthetic sense and quite a lot of luck. Basquiat had neither. You also need to keep the picture lively. Most of the pictures at the Serpentine, however, are both cluttered and despondent. One canvas seems to aim at figurative painting of a sub- de Kooning sort. This is Boy and Dog in a Johnnypump, the most interesting thing in the show. Yet it's a failure. To imitate other artists you need to have some feeling for their work.
Basquiat, I guess, only had feeling for himself. I am reminded of a kind of painting one used to see in art schools in the Seventies. It came from people in their first year who wanted to show off and be difficult. Usually they grew out of the phase, especially if they had a decent tutor to look after them. Nobody looked after Basquiat - except that, it is said, he got other people to paint his pictures, especially when he was incapacitated by all the stuff he was taking. I doubt if Riding with Death of 1988 is from his hand, not that it matters much.
Now Durrant. I commend her show for its limpid, unforced beauty, the boldness of her four large paintings and the delicacy and variety of her smaller canvases. Durrant (born 1942) grew up as an artist at a period when it was common to make abstract paintings of a considerable size and also to work in series. The four big pictures at Francis Graham-Dixon belong to a series she calls "...Come Home By Weeping Cross". They all have the decorative motif of a repeated "V" shape with connected floral blobs, tendril-like lines in a contrasting colour and elongated, wavy triangles that come in from the perimeter of the picture. It's a good pictorial invention. Durrant can vary her shapes in a lyrical manner, and these shapes have enough area to carry some intriguing colour.
Durrant's palette is both distinguished and capable of hinting at reserves of private feelings. In fact this is an overall characteristic of her exhibition. The paintings take a dignified place in the world, but are clearly unconcerned with worldly affairs. I like the yellow, greeny-yellow, deep violet and black in the third of the series. On the other hand, the best painting is the second: its red has a slightly bouncy or ebullient quality. I don't think we'll understand this series until we see more of the paintings. But where are we going to see the best of new British painting? The Hayward Gallery is in terminal decline, the Serpentine concentrates on stunts, and sponsors aren't interested in straight art. There is a future for serious painting, but at the moment it hasn't got a home.
Jean-Michel Basquiat: Serpentine, W2 (0171 402 4103), to 21 April. Jennifer Durrant: Francis Graham-Dixon, EC1 (0171 250 1962), to 13 April.Reuse content