Dazzling demons

It was all over. The Reich was finished, Hitler dead, his charred jaw bone all Russian pathologists could find of him in the smouldering ruins of Berlin. Hundreds of miles to the south, in Austria, an SS unit prepared to stage its own private apocalypse.

On May 7 1945, they arrived at Immendorf Castle in southern Austria. The German soldiers already billeted there were ordered to leave. That morning, German forces in Austria had signed their surrender, to take effect the next day; for these SS men, it was the last night of the war.

Schloss Immendorf was a beautiful setting for their final night of power and freedom. The castle's massive fortifications were softened with sloping tiled roofs, so that it resembled a Loire chateau, set in spacious parkland, with ivy growing up the walls. A curving staircase led to a grand interior full of art treasures, stored here by the Reich to save them from air raids on Vienna.

Among this store were 13 paintings by Gustav Klimt. It seems that these were on view in the castle apartments: the Nazis, the castle's owner later reported, looked at the paintings with appreciation, and one was heard to say that it would be a "sin" for the Russians to get their hands on them. Klimt's sensual art turned out to be a fitting backdrop for the events of that night: according to a 1946 police report, the SS officers "held orgies all night in the castle apartments". Who knows what this means, but it is a strange and macabre image - the SS holding their orgies as Klimt's maenads and muses looked on.

The next day, the SS unit laid explosives in the castle's four towers and walked out. One man went back and lit a fuse, and a tower burst into flames. As the fire spread, explosives in the other towers detonated. Schloss Immendorf burned for days. Nothing survived of its interior, and the gutted shell was later demolished. According to the eyewitness reports that reached Vienna months later, amid the chaos of defeat, not a single work of art survived.

Klimt's fame has survived this loss, and yet he divides people. For every person who finds his work gorgeous, seductive, sexy, there is a sophisticate who will point out that his art is surely a bit vulgar, with all that gold; a bit slavish in its ostentatious celebration of rich women; and a bit, well, soft-centred. It's a negative view that is an accident of history, of what has survived of his work and what hasn't. Behind the Klimt everyone knows, the opulent artist of desire, stands another Klimt - a painter who was years ahead of Picasso and Matisse, a great destroyer of traditions and a creator of terrifying beauty.

Klimt was born in Vienna in 1862. He was a craftsman's son and trained as a painter, becoming a high-class decorator who painted the walls and ceilings of some of the most opulent public buildings in Vienna. He rapidly became the definitive visual artist of the last years of the Habsburg empire, a star in a culture of great daring: the composer Gustav Mahler, the writers Arthur Schnitzler and Robert Musil, and the architect Adolf Loos were Klimt's contemporaries. But the contemporary he most resembled was Sigmund Freud, the inventor of psychoanalysis. With their unabashed eroticism, Klimt's paintings share a basic belief about human nature with Freud, who shocked the world with his insistence that sexuality is at the centre of everyone's emotional life. You could even compare Freud's sessions, listening to his women patients as they lay on his couch, with Klimt's portrait practice. Klimt was a very private man who never married, but it was said that he slept with most of the women he portrayed: certainly his bold drawings point to an intimacy that goes beyond the polished eroticism of his paintings.

More than 60 years after the end of the second world war, many questions remain about the paintings burned at Schloss Immendorf. How did so much of Klimt's work come to be lost that day? Why was it there? And has this loss deprived us of a proper understanding of Klimt's genius?

What is left is eye-catching - and expensive. Two years ago, Ronald S Lauder, a former US ambassador to Austria and owner of the Neue Galerie in New York (his own museum of German and Austrian art), bought Klimt's Portrait of Adèle Bloch-Bauer I for $135m (£68.4m), a record (since broken) for art sold at auction. This story was all glitter and gold. The fabulous opulence of Klimt's 1907 portrait, which encloses its subject in a shining carapace of yellow metal and glassy mosaics, as if the painting were a reliquary for her pale flesh, was mirrored by the mania of the art market.

I visited the Schloss Belvedere gallery in Vienna, where there is a tangible sense of this painting's loss. Portrait of Adèle Bloch-Bauer I did not come out of a vacuum, or somebody's private vault: it came from this public collection, and the museum shop still sells a postcard of it. The Belvedere still has the richest collection of Klimts anywhere - including his famous The Kiss - but for anyone who was lucky enough to have seen Adèle Bloch-Bauer here, the loss is surprisingly enormous. I visited the gallery in 2001, when this magnificent painting was still on view, and returning to find it absent is far weirder than I would have thought. Why is this? Does it belong in Vienna after all?

Portrait of Adèle Bloch-Bauer I was sold as pure beauty, pure art - pure value. People were unaware of its history. No newspaper article in 2006 - not even the one I wrote in this paper, in a hurry, to explain how a Klimt could be worth so much money - dwelt on the reason it was removed from Austria and sold. In 1998, the Austrian parliament brought in a law paving the way for restitution of works of art seized by the Third Reich to heirs of their rightful, Jewish owners. Heirs of Ferdinand Bloch-Bauer, whose portrait of his wife by Klimt had stayed in Austria's public collections since its confiscation as Jewish property in 1938, brought a case and in 2006 won it. They sold the portrait immediately to Lauder.

Klimt's art is deeply entwined with the story of Jewish Vienna, and the fate of a community that - until Hitler forcibly unified Germany and Austria in 1938 - was central to the city's modernising culture. This community was doomed: by 1945, the Nazis had murdered 50,000 Austrians solely because they were Jewish. Klimt's art is full of traces of these lost people, and at the Belvedere, I found a crucial clue to their shared past.

Klimt's Judith and Holofernes hangs beside a window looking out over Vienna so that its darkness and light is set off against the bright sky. Painted in 1901, it is for me one of his truly great paintings. Unlike The Kiss or Portrait of Adèle Bloch-Bauer I, it cannot for one second be dismissed as merely beautiful. This menacing Judith brings us closer to those works destroyed in 1945.

At the British Library in London, I later consulted a portfolio of Klimt's paintings, published in Vienna in 1914. A lavish volume with gold lettering and big, clear reproductions, it is an invaluable record of the lost works - but I also noticed something odd, a strange slip. The painting of Judith and Holofernes is reproduced here, but it has been given the wrong title: in Vienna in 1914, it was known as "Salome". This was, in fact, quite a hard fantasy to maintain, as the painting, encased in metal, has the words "Judith und Holofernes" moulded into it.

In the Book of Judith, Judith saves the Israelites by visiting the enemy Holofernes in his tent and beheading him. She has been represented in many ways in European art, but rarely as sexually as in Klimt's painting. His Judith doesn't just expose her breasts through her blue gauze and gold gown as she holds Holofernes' severed head, she swoons in ecstasy, as if the killing were not a virtuous act but a sensual pleasure. You can see why Klimt's patrons wanted to explain away its disturbing quality by misidentifying her as Salome, the evil princess who demanded the head of John the Baptist. But the renaming went deeper than this. The patrons who made Klimt's art possible, who loved and understood it, were overwhelmingly Jewish - and Judith happens to be a Jewish heroine.

Klimt was a kind of neoclassicist; as well as painting this biblical story, he had a passion for Greek art and mythology. But instead of celebrating the rationalism of the Greeks, he evoked their dark side. A profound influence on his work was Friedrich Nietzsche's 1872 book The Birth of Tragedy, which argues that Greek tragedy grew out of music, the purest of the arts because it taps into the deepest, most primitive parts of the psyche (the book is addressed to his friend Wagner, whose music famously does just that). Klimt dramatised this radical theory of art in two paintings, Schubert at the Piano and Music II, painted as a pair in the late 1890s: in the former, Schubert gives a drawing-room performance; in the latter, the more primal image of a Greek lyre-player is flanked by mythological monsters. Both paintings were burned in 1945.

Klimt got his chance to develop his revolutionary ideas about art and the irrational when he was commissioned to create ceiling paintings for the ceremonial hall of Vienna University. This, his most ambitious commission, resulted from 1900 to 1907 in three huge paintings - Philosophy, Jurisprudence and Medicine - designed to be fixed to the ceiling and seen from below, painted one by one in increasingly embattled circumstances.

Philosophy, the first to be finished, was an explicit Nietzschean manifesto. In The Birth of Tragedy, Nietzsche argues that western culture is driven by a superficial confidence in facts and a coarse drive to manipulate the world: this "optimistic" rationalism, he writes, must now give way to a tragic sensibility that accepts the uncertainties of our perceptions. In other words, while science as it was understood seemed to offer certainties, Nietzsche championed a more subjective understanding of the world. Klimt's Philosophy makes this idea movingly visible with its great, agonised column of human bodies - loving, longing, being born and dying. The universe through which they cascade is a vertiginous empty space dotted with stars.

Of course, I know this painting only from looking at a black and white photograph of it. Philosophy is gone forever - burned in 1945 along with Medicine and Jurisprudence, paintings that express the same pessimistic view of the world. But even looking at these paintings in monochrome reproduction, you can see their power. Look at them long enough, and you start to grasp how devastating their deep, unresolved spaces, their fierce erotic energy, must have been for the professors of Vienna University. They didn't like Philosophy - in fact, they hated it; they understood that Klimt was attacking everything they stood for.

In 1904, Klimt decided to terminate his contract with the university and pay back his fee. The man who came to his rescue, buying Philosophy and eventually owning all three of the huge canvases, was his greatest patron: a Jewish factory owner named August Lederer. This businessman and his wife, Serena, became Klimt's most dedicated collectors, owning the university paintings, Music II and Schubert at the Piano, several landscapes, a portrait of Serena and, later, his Frieze. Their Vienna home had a room for Renaissance masterpieces, and another devoted to Klimt. But in 1938, the Nazis moved quickly to seize Jewish property in Austria, and the Lederer collection was confiscated.

Strangely enough, in 1943 the Third Reich sponsored an exhibition of Klimt's work in Vienna. Famously, the Nazis hated all modern or "degenerate" art, but the exhibition revealed there was nuance to their position, at least in Austria - they evidently decided to celebrate Klimt as a national icon. So it wasn't out of contempt but in order to preserve them that, after being shown in Vienna, most of the Klimts in the Lederer collection were transported to Schloss Immendorf - where they were eventually incinerated.

Lederer died before the war, and Serena Lederer in 1943; their son Erich survived and later reclaimed the one great work from the Lederer collection that had escaped the fire by being stored elsewhere - Klimt's Beethoven Frieze, an ambitious cycle of wall paintings the artist created for a Beethoven-themed exhibition at Vienna's temple of modern art, the Sezession. Here, Klimt had tried to turn art into music: the empty spaces between his golden figures resemble the immense stillnesses and voids in the music of Wagner or Mahler. The most spectacular scene, in which the demons threatening human happiness include a giant ape and a group of emaciated Furies, plummets you into the dark, irrational depths of myth.

A replica of the Beethoven Frieze (the original is on permanent view at the Vienna Sezession) will be shown in Tate Liverpool later this month, and people will argue over an artist who can look, according to your mood, either subversive or a bit flashy. But it is only the vicissitudes of history that have created this doubt. Seen whole, with all his works redeemed from destruction, Klimt could never be dismissed as an artist of mere dazzle or surface beauty: the lost paintings he created for Vienna's university were the first great revolutionary works of the 20th century

· Klimt is at Tate Liverpool from May 30. Details: 0151-702 7400. www.tate.org.uk/liverpool

The life of Klimt

1862 Born Vienna, the son of an engraver. Trains at Vienna School of Applied Art

1886-8 Decorates Burgtheater, Vienna

1894 Commissioned to decorate University of Vienna's ceremonial hall, resulting in a 10-year struggle with university authorities and eventual withdrawal of his work

1897 Founding chairman of Vienna's avant-garde art group, the Sezession

1902 Sezession stages Beethoven exhibition. Klimt contributes a frieze illustrating Beethoven's 9th Symphony

1907/8 Paints The Kiss

1905-11 Decorates dining room of Stoclet Palace, Brussels

1905-1917 Portraits and landscapes come to dominate Klimt's work. His younger contemporaries, Oskar Kokoschka and Egon Schiele, make his later art look tame

1918 Dies in Vienna of pneumonia, aged 55