The rule book on Gustav Klimt was torn up and rewritten in the summer of 2006, when word leaked out that the cosmetics magnate Ronald S Lauder had just paid $135m for Klimt’s golden portrait of Adele Bloch-Bauer, making it the most expensive painting in history. Even by the insane standards of the art world, Lauder’s extreme purchase made no sense. With exchange rates as they were, he had spent more than £70m. Klimt was now in a bigger league than Picasso, Van Gogh or Monet.

What was particularly surprising about this crazy reevaluation was the fact that Klimt is such an indistinct figure. With Picasso, Van Gogh, Monet – and now with Francis Bacon – you know exactly how the attraction works and why the auction records are blown. These are familiar giants. Their work has been shown extensively for many years. The roles they played in the history of art are self-explanatory and huge. But Klimt was a Viennese petit maître. He didn’t create an unstoppable movement. He didn’t change art. Until Lauder splashed out on him, Klimt was a beautiful but essentially minor Viennese secret. So, why is he so valuable?

A timely show on more or less this subject has arrived at Tate Liverpool, where it forms the centrepiece of the city’s chaotic attempt at being European Capital of Culture 2008. An optimistic stream of press releases has been promising us “the first comprehensive exhibition of Gustav Klimt’s work ever staged in the UK”, so the first thing to point out is that it isn’t that. Not because there have been others – I trust there haven’t – but because this isn’t, in essence, a Klimt show. It might contain scores of works by him. And he could be described as its guiding light. What we actually have here, however, is an action replay of a fabulous creative moment in Vienna when a whole gang of brilliant art-nouveau pioneers played out a sizzling scene in the history of design. The exhibition’s subtitle – Painting, Design and Modern Life in Vienna 1900 – is a much more accurate guide to its contents than its title: Gustav Klimt.

Not that I mind. Indeed, Tate Liverpool should be thanked for bringing us this working picture of Klimt’s times rather than the parade of his masterpieces we were expecting. Because Klimt, on his own, doesn’t quite cut the mustard. I can see why besotted millionaires might adore him. I can see how prettily he reproduces and how intimately he seduces. But is he really a giant, or a pygmy under a microscope? On this showing, I would plump for the latter. His first skill was as a painter of showy bits of national symbolism that were added to the staircases and ceilings of Vienna in a grand and expensive effort to inflate the cultural presence of Austria in time for the 20th century. So good was Klimt at this porky state symbolism that, in 1883, he won the highest imperial honour available to an Austrian artist, the Golden Order of Merit (With Crown), from Franz Josef I. When we catch up with him here, he is painting a twee allegory of a naked goddess wandering through a paradise of sleeping lions and house-trained mice that dates from 1883, but could have been painted in 1530. By a minor follower of Titian.

This innate conservatism never leaves him. It is the chief reason why he never became a truly heroic modern artist. Compared with what Toulouse-Lautrec, say, or Gauguin were doing in 1899, Klimt’s Nuda Veritas – a full-length naked blonde holding up a mirror and staring madly out at us through pulsating eyes as if she has just quaffed a huge flagon of dragon’s blood – is backward as well as silly. The quotation from Schiller inscribed in gold on her frame, “If thou canst not please all men by thine actions and by thine art, then please the few; it is bad to please the many”, is excellent advice for any epoch, but doth it really requireth all this mock Teutonic medievalism to passeth it on? Methinks not.

Klimt’s wilfulness caused him to jump ship from the official state organisms and, in 1897, become the first president of the Viennese Secession, a band of ambitious young designers and painters determined to break with the past and lead their nation properly into the 20th century. At which point, the show suddenly finds an exciting modern rhythm and starts filling up with gorgeous things – the best of which were created not by Klimt but by Josef Hoffmann, the real brains behind the Secession and, to my eyes, this show’s giant.

Hoffmann could do everything. He could build spectacularly modern buildings, such as the Purkers-dorf Sanatorium; he could rethink how art galleries work and invent the white cube; he even managed to design a cutting-edge toilet-roll holder. Armed with an instinctive awareness of the key modernist truth that less is more, Hoffmann was flabbergastingly ahead of his times. There’s a cabinet here, designed for Klimt’s long-suffering “companion”, Emilie Flöge, that is as crisp and white and plain as anything you can buy today at Ikea. The show, however, insists that Klimt, too, was fully involved in these design developments, and that we need to see his painting as a crucial component of the Gesamt-kunstwerk, or total work of art. This excellent proposition that painting, architecture and the applied arts should all work together is, indeed, the principal joy of the Viennese effort. Yet based on the evidence here, my sense of these events is that Klimt never engaged fully in the revolutionary aspects of the Secession. Instead, his work kept its aesthetic distance and retreated ever deeper into a private erotic dream.

The stories that abound about Klimt and his Mercedes of a sex drive are among the chief reasons why he is so popular today. When you look at the ornate portraits collected here of the rich Jewesses to whom it was said he was particularly partial, there is no mistaking the slyness of his sensuality. Marie Henneberg drops her hand naughtily between her thighs. Eugenia Primavesi’s head and hands emerge from a wild display of painted botany, as if she had submerged herself in a bath of flowers. A steamy selection of drawings of masturbating women offers large clues to what was actually going on in his imagination. Putting his rich Jewesses in weird, thrusting poses that were apparently disguised tributes to the erect penis, Klimt blurs the divide between painting portraits and designing jewellery boxes.

Yes, the results sum up, very decorously, that decadent mix of eroticism, psychology and new money that characterised fin de siècle Vienna. But was Klimt a big understander of humanity at large, like Van Gogh and Bacon? Did he rewrite our culture through the Vesuvian force of his presence, like Picasso? No, he didn’t. And only an era that confuses celebrity with greatness and mistakes prettiness for sublimity could overestimate his achievements as spectacularly as we have.

Gustav Klimt at Tate Liverpool, until August 31

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