Gauguin: Maker of Myth, Tate Modern, London

Three things have counted against Paul Gauguin in the British mind.

First, there is the misleading term "Post-Impressionist", dreamt up by Roger Fry to describe French art made after 1900 or so. Coming to Gauguin from Monet is a very bad idea indeed. Second, the house-share episode with Van Gogh in Arles has left us with the vague impression that Gauguin was somehow behind Vincent's cutting off his ear, if not his madness and suicide. The British taste for the underdog does overdogs no favours. Last, but not at all least, there is the sense that Gauguin is, well, French, which is to say prone to sleeping with under-age girls and dying of syphilis. All in all, it has been hard to separate Gauguin the artist from Gauguin the myth, which is the point of an excellent new show at Tate Modern.

Although -isms are often unhelpful, it is as well to remember that Gauguin, who was handily dead by the time Fry coined the term in 1910, did not call himself a Post-Impressionist but a Synthetist. Far from implying a descent from Impressionism, this suggested a reaction against it. Synthetists, scarily modern, believed in celebrating the flatness of their canvases with areas of strong colour separated from each other by the hard outlines of Chinese enamels. The point was not to represent the actual but to evoke the Other, whatever that Other might be. To do this, you had to make the familiar unfamiliar and vice versa – to depict Tahitian beaches and Breton hayfields as though they were interchangeable, to paint your own face as Christ's or mould it in clay as a guillotined aristocrat's.

And so one of the first works in this show, Clovis Asleep (1884), is both the domestic image of Gauguin's son and the evocation of an entirely unknowable world. The wallpaper behind the sleeping child's head – a pattern of fish and squid on a sea of blue – also reads as a projection of his dreams. Here is a scene at once mundane and strange, real and symbolic. Freud had only begun his studies with Josef Breuer the year before – it would be 1899 before he published The Interpretation of Dreams – and yet there is a premonition in Clovis Asleep of Freud's royal road to the unconscious. Gauguin's wallpaper may owe some vague debt to the Symbolists, but the psychology behind it looks forward to the 20th century rather than back to Puvis de Chavannes.

Perhaps his lack of formal art training – he was, in his youth, a trainee ship's pilot, a naval rating and a stockbroker – stood Gauguin in good stead. He may have been fiercely secular, but it is hard to imagine a less intuitive painter sensing the power of revelation as he did. The co-existence of dreams with our waking world is at the heart of his Vision of the Sermon (Jacob Wrestling with the Angel). Like all Gauguin's work, the Vision wears its structural simplicity on its sleeve – coiffed Breton peasant women, the real and visionary worlds split by a handy tree-trunk – while being philosophically complex. Gauguin may not buy into religion, but he does have a feel for the primitivism that underpins it. In his discovery of Tahiti, he is less like the French imperialist we have thought him to be than like Claude Lévi-Strauss.

This anticipation of the unconscious mind is not the only sign of his modernity. One of the many clevernesses of this show is that it scotches the idea of Gauguin as an artistic tourist, a snapper-up of the exotic. In a sense, the Tahitian setting of a work such as Te Pape Nave Nave is neither here nor there. Tahiti, like a vision or a dream, is simply a place where the rules do not apply. Freed of the need to behave like a Frenchman, Gauguin no longer has to paint like one. Instead, he can play around with things so modern, so daring, that you can still feel their strangeness now.

Cézanne, a decade older, may be seen as the grandfather of Cubism, but the heavy limbs of Gauguin's Tahitian women anticipate Picasso's bathers of the 1920s. It is hard not to see the black outlines that surround the Tahiti figures as mutating, a decade later, into the scaffolding of Analytic Cubism, Gauguin's interest in Oceanic sculpture into Picasso's African masks. And if Picasso owes a debt to Gauguin, then so much more so does his perennial adversary, Matisse. The cloisonnisme of works such as Mahana No Atua, the insistent separation and flattening-out of their areas of colour, gave Gauguin's young rival the freedom to work in a way that would once have been dismissed as merely decorative. At the end of this marvellous show, we see a Gauguin whose personal mythologising was part of a far wider and more important creation, an artist who was Post-nothing but Pre- a great deal. Fight for tickets if you have to.

'Gauguin: Maker of Myth', Tate Modern (020-7887 8888) to 16 Jan

Next Week:

Charles Darwent weighs up the latest Turner Prize. It's that time of year again