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Gustav Klimt: the Tate's much-hyped new show reveals a painter who's all style and no substance

I should say, straight out, that I'm not an admirer, and later on I'll be being rude. But many people must be looking forward to this show. Since the great Art Nouveau revival of the 1960s, Gustav Klimt has become one of our favourite painters. Once his feasts of flesh and opulent decoration were a purely Viennese delicacy. Now The Kiss hangs on bedroom walls across the world.

Klimt is about as familiar as an artist can be – or at least, one whose work is known mainly through reproduction in posters, calendars and books. Most of the famous pictures remain in Austria, and have hardly been seen in Britain. Gustav Klimt: Painting, Design & Modern Life in Vienna 1900 is the biggest Klimt exhibition ever staged here, and a centrepiece of Liverpool's year as European Capital of Culture.

But beware, you Klimt-lovers; Tate Liverpool has only 23 of his paintings. That includes Nuda Veritas, The Three Ages of Woman and Judith/Salome. It doesn't include all the other famous ones; The Kiss, the Adele Bloch-Bauer portrait, Hope, Judith and Holofernes, Danäe, Pallas Athene, Death and Life, The Virgin.

The exhibition covers these absences by broadening its agenda, taking in the whole "Vienna Secession" aesthetic of which Klimt's work was part: clean-lined geometry, sinuous curves, plane surfaces and sudden, isolated outbreaks of pattern. It bulks itself out with domestic objects designed by Klimt's contemporaries – seats, desks, beds, cutlery, tea-sets. At times, you feel you're in a furniture show.

But there is one spectacular piece. The ground-floor gallery holds an exact, full-size replica of Klimt's 34 metre-long mural, the "Beethoven Frieze". It's meant to illustrate Beethoven's Ninth Symphony, converting it into a series of allegorical tableaux, in which human figures strive, yearn, encounter evil, but win through to embrace and rise in ecstatic bliss.

It shows Klimt on top form. Figures blend into seas of pattern. The surface is so adorned and embossed in gold foil and gems and precious bits that it becomes a kind of low relief. Yet these episodes are punctuated by stretches of utterly empty off-white plaster. And then there's a whole section solidly filled with massive writhing snakes.

Klimt's inspirations are manifold. The influence of Greek pots, with their linear figures, is strong. There are Japanese prints in there, and Egyptian tomb painting, and gold-backed icons and medieval manuscripts. All the imagery comes from Wagner. Klimt is a virtuoso mixer; his most striking dissonance is between classical graphic purity and sensational decoration.

So give him his due. He's a brilliant and original stylist. Yet there comes a point where you have to say: OK – but seriously? Very elegant, very startling – but seriously? The "Beethoven Frieze" is a perfect example of the Klimt problem: design, superb; content, null. How can you believe in this parade of clichés? The forces of evil, for example, are a cast of ridiculous stage villains. Seductive snake-haired naked women, with "wicked" expressions; an enormous snaggle-toothed gorilla, looking like one of those oversized stuffed toys you win at a fairground.

Depicting evil, Klimt comes up with cartoon minxes and a joke monster. Depicting good, he offers a knight in shining armour with a set jaw and a defiant pose. Klimt began his precocious career as an accomplished academic painter (Tate Liverpool has the early work, Fable). He revolutionised his style, but never lost his talent for lifeless allegory.

Reality does not intrude. Design conquers all. Pattern, ornament, outlandish and incredible shape-making, override every resistance. You see it in his treatment of the human figure. Look at the roll-mopped bodies of the nymphs in the last scene of the frieze, or the almost illegibly flattened and attenuated forms of the lesbian mermaids in Water Snakes – they might be sheets of pastry, to be stretched wide or folded over or cut out anyhow.

You see this in his portraits, like the one of Eugenia Primavesi, where her body is smothered in a camouflage of multi-candy-coloured fabric. You see it in his landscapes, which play a game of "can you tell what it is yet?", as the green world is corralled into such artificial patterns that it's hard to recognise.

But seriously: what's it about, all this flagrant artifice? Yes, it's a dramatic turn against realism, and Klimt is not alone in that among late 19th-century artists. But I can't see that his anti-realism about anything much – apart from making things look neater, less complicated, more stylish.

His art excludes all rough energies. It reduces the world to a beautiful consistency. Beyond that seems to be an utterly blank, unmotivated artist. The famous Kiss is quite passionless. Nothing drives him, not even sex.

Obviously, he's interested in sex. There's a wall here of his watery pencil-drawings, in which women open their legs and masturbate. And his paintings are occasionally sexy, but their sexiness is a matter of expertise. Klimt belongs to the Mr Spock school of pornography. He knows what turns on the human male, and he presses the right buttons – cascading tresses, pneumatic bottoms – without apparently sharing in the desires he inflames.

So don't talk wisely about "the Vienna of Freud" and the birth of psychoanalysis. A far more relevant reference would be to an older Viennese institution – the Spanish Riding School. As in formal equestrianism, what you see in Klimt is the gratuitous triumph of design over life.

Compare Klimt to that other star of Art Nouveau, the English illustrator Aubrey Beardsley. His art is just as artificial – but he knows how outrageous his shape-making is, as well as exquisitely beautiful. There's a sophisticated irony at play in Beardsley – life is only made fine through the most absurd pretences.

Nothing like that crosses Klimt's mind. He just likes the way it all looks so smart. He's basically thick. But when you start to compare Klimt and Beardsley line for line, the contrast really bites. You realise how much Klimt gains from reproduction – and reduction. Make his images small, and their lines look taut and definite. At actual size, you see how approximate and uncertain they are. On any scale, Beardsley's draughtsmanship is as tense as a tight-rope walker.

So my advice is to stick to your posters and calendars. But if you do go to Liverpool, don't miss another show in the city – Art in the Age of Steam at the Walker Art Gallery. It has some great pictures in it, by Manet, Monet, Van Gogh – serious artists.

Gustav Klimt: Painting, Design & Modern Life in Vienna 1900, Tate Liverpool (0151-702 7400; www.tate.org.uk/liverpool), to 31 August