And so the show is touching, sumptuous and barren, in that chronological order. Once he had got over his awkward formative period de Kooning achieved genuine majesty on numerous occasions; but his later work is monotonous and then tragically empty. The last room of the Tate's account of his career is a sad sight, and we know things to have become even worse. Among all the publicity for the exhibition is the claim that de Kooning has been an exceptionally influential artist. I don't understand this argument. It's true that he was much imitated by lesser artists in the Fifties, when his standing in the art world was very high. But of true and long-lasting influence - the sort that inspires artists of succeeding generations - there is none. We are looking at someone who was an exceptionally lonely figure, whatever his fame.
The loneliness began very early, after he got to America from his native Rotterdam in the late Twenties. Then he painted in spare moments or when the fancy took him. His main occupation was as a decorator. We know of works from those early American years through photographs. They are not in the present show, though there was a selection in the last de Kooning retrospective (a more thorough exhibition than the present one) organised by the Whitney Museum 10 years ago.
Anyway, those early works suggest that in a half-hearted way de Kooning was trying his hand at current American abstract art. The photos don't look very good. Such paintings must have shown de Kooning that there was no point in imitation. He turned down the opportunity to become a member of the American Abstract Artists, the dominant avant-garde group, realising I suppose that he was not to be an abstract painter. And, as things turned out, he joined Arshile Gorky, another immigrant and also a late developer in artistic terms. Their relationship lies behind the plangent figurative paintings in the first room of the exhibition.
They have a sympathy with Gorky's contemporary work, but there's also a strong sense of self-portraiture in these paintings, and a hermaphroditic note. This leads one to think there might be an element of self-portraiture in the later "Woman" series. Obviously there is self-revelation in the paintings of women, for de Kooning's technique is so frank about his failures, re- starts and worries; and this is why they feel so personal. Is de Kooning himself their real subject?
The various sets of "Woman" paintings are de Kooning's most famous works and have attracted comment of all sorts, most recently from psychobiographers and feminists. A usual criticism is that they are violent. I don't find them so. The "Woman" canvases often have a caressing quality. On occasion, I suspect, their manner was adopted from contemporary painting by de Kooning's wife Elaine. The most beautiful of them, a tiny 1949 painting on cardboard, feels like Picasso's tender pictures of his mistress painted 10 years earlier. There are other influences. But mainly the "Woman" pictures are introspective.
In these canvases de Kooning arrived at his unorthodox mastery via obsessive concentration on his technical deficiencies. The early figure paintings are moving partly because they are so helpless. De Kooning simply could not manage hands, feet, facial features, all the nuts and bolts of figural art. His claim that he had received intense training in such matters at the Rotter-dam Academy is unbelievable. And so he scrabbled and bashed away at things that would never come right and - as a lovely and unexpected gift from art to one of its devotees - he became the more expressive when his brush, his scraping and his collaging had least to do with rightness.
For a time de Kooning was a master of self-taught gaucheness. He became a major painter at the end of the Forties because there was no one to teach him and no one to restrain him. At just this period Francis Bacon in England and Jean Dubuffet in France, both self-taught, made comparable leaps into alarming modern painting. De Koon-ing's uncertainties and experiments are more interesting than theirs. He couldn't tell when a picture was finished. We know he felt anguish about adding to his pictures or leaving them in a state where some parts were obviously raw. Where was the peak of the creative process? This remains a crucial question, and I'm not sure that the Tate exhibition answers it.
The selection rather avoids unfinished or unfinishable canvases. They are absent even though they can possess an authenticity lacking in weightier paintings. At the Tate we find the more elaborate and official canvases, plastered and reworked from edge to edge. No doubt this reflects the taste of the rich collectors and museums whose purchases in the Fifties made de Kooning the most respectable of Abstract Expressionist artists. We could have been given a riskier de Kooning, especially if the exhibition had included his drawings and sculpture.
The most troubled and experimental period was from 1946 to 1953, and de Kooning's most exciting paintings remain the black-and-white abstractions begun around 1946 and shown in 1948 in his first one-man exhibition. They are also his most original works. Of course they have precedents and furthermore they relate to contemporary black-and-white paintings by Jackson Pollock and Franz Kline. None the less they seem to have come from nowhere and to have no relation to anything accepted as art. Technically, they are a mixture of oil and enamel on hardboard. There's poverty and hardness in them: beyond that, a wonderment that the world could be so cruel.
Soon after, de Kooning became celebrated. His reputation was made by Excavation of 1950, the year he represented America at the Venice Biennale. This picture hasn't come to London but is satisfactorily replaced by Attic, of 1949, and Painting, probably of 1950. Dry, fragmented and complex, such paintings prove that he was moving fast towards an inventive post- Cubist abstraction. But already the "Woman" series had begun, and with it the hankering to be an old master, or at least to have the look of classic art. The first of the big "Woman" paintings, begun in 1950 and finished two years later, is the best of them. One could fault its contradictions and untidiness - but criticisms are minor compared with the splendid and crazy nature of its ambition.
Craziness left de Kooning's art with the arrival of worldly success. Perhaps surprisingly, he found that he had a talent for majesty. Landscape- like abstractions such as Ruth's Zowie, Suburb in Havana and September Morn, all from the late Fifties, have a dignified bravura. However, one senses too much ease and repetition settling in. During the Seventies de Kooning developed a wriggling and colouristic brushwork that combines flower painting with a feeling for marine landscape. Untitled I (1977, pictured above) is a good example. One imagines such paintings done in contented solitude on Long Island. Not long afterwards, though, Alzheimer's descended, all the paintings weakened and then solitude became an awful emptiness of the mind.
! Tate Gallery, SW1 (071-887 8000), to 7 May.