It is one of the most shuddered-at chapters in the story of art. In July 1937, Nazi officials turned up in full uniform alongside evening-suited cultural eminences of the Third Reich at an art gallery in Munich for the opening of the Exhibition of Degenerate Art. They came not to praise modern art, but to laugh at it.

Pablo Picasso, Henri Matisse, Marc Chagall, Otto Dix, Georg Grosz, Ernst Ludwig Kirchner – the masters of modernism, including giants of Germany's own avant garde, were shown in this exhibition as deviant, decadent practitioners of so-called Degenerate Art – "Entartete Kunst". Sections of the show had titles such as "Total Madness", "The Prostitute Raised to a Moral Ideal", "The Negroisation of Art". Modern art was interpreted in the catalogue as a conspiracy by Russian Bolsheviks and Jewish dealers to destroy European culture. The admiration for African carvings that had so fired Picasso and other artists was taken as proof of modern art's racial degeneracy.

Vile stuff – but the Nazi attitude to modern art may have been radically misunderstood. An amazing discovery in 21st-century Munich turns the story of art and the Nazis on its head.

Cornelius Gurlitt's flat looks meagre in photographs. It is located in an apartment block in Munich that, from the outside, appears to have seen better days. Yet in that flat lay secrets of the Third Reich only now accidentally uncovered. Intrigued by Gurlitt's lack of German identity documents and odd behaviour while crossing the border on a trip to Switzerland, police raided his home and found a hoard of more than 1,500 works of art including pieces by Picasso, Matisse, Renoir, Paul Klee, Emil Nolde, Franz Marc, Otto Dix and Oskar Kokoschka. The understandably reclusive Gurlitt turned out to be the son of Hildebrand Gurlitt, an art dealer who played a key role in the Nazi roundup of "degenerate art". Although half-Jewish, and the cousin of the "degenerate" composer Manfred Gurlitt, the Nazis considered him a useful expert. This is not just any haul of stolen goods: it may turn out to be one the most important recoveries of lost art ever. For it takes us to the heart of the cultural policies and crimes of the Third Reich.

It raises massive questions about the fate of art in and after the second world war. As the allies entered Germany in the last phase of the war they took with them experts, nicknamed the "monuments men", whose job was to find out where the Nazis had stashed looted works of art. For it was not just modern art the Nazis abused. All over Europe, they seized the best masterpieces from the finest museums. Many of these, including such treasures as Titian's Danae and Van Eyck's Ghent altarpiece, were found stashed in mountain tunnels and mines. Others, including many of the works of art shown in the Degenerate Art exhibit, are believed lost for ever. Paintings such as Van Gogh's The Painter on his Way to Work and 14 masterpieces by Gustav Klimt are written off as destroyed. But is it possible a Nazi network preserved a secret world of stolen art after 1945? Is it even possible such art was used to fund neo-Nazi activities or maintain war criminals in quiet comfort?

To put it another way: were Hildebrand Gurlitt and his son unique, or is the find in Munich a clue to some larger network of Nazi art hoarders sitting on secret treasures all this time in postwar Europe, living off occasional covert sales of the Picassos that they keep among the canned foods in their anonymous flats?

One thing is certain: this story comes from the dark heart of Nazi Europe. Munich was Hitler's art capital. As a young man, famously, he wanted to be an artist. He wasted an inheritance trying to get an art education in Vienna. While Klimt was creating modern art there, Hitler was going to the opera to hear Wagner (conducted by the modernist Gustav Mahler), and soon eking a living painting drab topographic scenes. Eventually he left for Munich, where he survived as a hack painter of typical German scenery until the first world war gave him a new life as a soldier. Hitler loved Munich, and when he came to power lavished money on its art scene. The city's expressionist painters were in trouble. But while Degenerate Art pilloried them, in 1938 Hitler opened a huge exhibition of "proper" German art at the newly built House of German Art, a grand neo-classical temple to the art of a new, fascist Europe. Where the year before thousands had flocked to see the art they were told to hate, far fewer went to see Nazi-favoured art.

This is where the cliches start. It is conventional to contrast the avant-garde art the Nazis maligned with the traditionalism and conservatism of the art they admired. But the National Socialist nightmare was not "conservative". It was, in its own way, horribly modern – it imagined a different, perverted vision of modernity. The House of German Art still survives in Munich. Today it is used as an alternative arts centre. Video and installation look subversively great in its grand icy halls. You wouldn't call these rooms old-fashioned. Rather they have a chilly neo-classical hauteur that speaks of sublime ambition. This is the neo-classical modern art of Nazism that can still be seen in Leni Riefenstahl's terrifying films – some of the most disturbingly beautiful ever made – and the designs of Hitler's architects Paul Troost and Albert Speer.

Hitler did not hate art – he loved it. Other leading Nazis just saw it as money. Goering, greedy and corrupt, amassed art because it symbolised wealth and power. Munich was at the centre of the regime's cultural pretensions. The Gurlitt hoard is a survival of the Nazis' strange and ambivalent attitude to art, from Hitler's aesthetic New Order to the simple philistine greed that probably motivated most of their art theft.

Gurlitt's cache reveals that many assumptions about the Nazis and art are simply untrue. The Degenerate Art exhibition was real enough – but did it really mean the Nazis hated modern art? It is because we take this for granted that no one has been searching for lost "degenerate" works such as those in the flat in Munich. Some works from the Entartete Kunst exhibition, many seized from once-progressive German museums, were sold abroad afterwards. Others have vanished. As the war began and Nazi racial policies became ever more explicit, more modern and pre-modern works were seized or bought for a pittance from Jewish owners. Much was destroyed. Or was it?

An American soldier examines part of Herman Goering's personal collection of looted art, recovered as the allies invaded Germany in 1945. Photograph: Bettmann/Corbis

One of the most suspicious cases is that of Klimt's lost works. Fourteen paintings by this Austrian visionary of dreams and desire were stored in an Austrian castle during the war. In 1945, an SS battalion reportedly held an orgy there before setting the castle alight. The Klimts are presumed lost, but there were rumours that some might have been spirited away. Now, surely, such stories need to be re-examined. The 1,500 works hidden by the Gurlitts, father and son, were also presumed lost.

The allies tend to blame themselves for art lost in Germany in the 1940s. Almost every major German city was bombed by Britain and the US during the second world war. Firestorms ravaged museums and art stores as well as killing thousands of civilians. "Bomber" Harris, Britain's Bomber Command mastermind who insisted this was the way to win the war, was apparently responsible for burning paintings such as Van Gogh's Painter on the Way to Work and Caravaggio's first version of St Matthew, as well as his portrait of a courtesan.

Perhaps the single most significant fact that has so far come out about Hildebrand Gurlitt is that he claimed his collection of looted art was destroyed in the bombing of Dresden. So it was the allies who burned it. If he lied so easily about that, what about other Nazi-owned art that supposedly vanished in wartime air raids?

The massive destruction the Nazis brought down on Germany created chaos in 1945. As the "monuments men" were seeking out stolen art treasures in Alpine mines, it seems Gurlitt was carefully and quietly preserving his personal hoard.

The reason he got away with it is that he had grabbed so many modernist works. Ever since 1937, it has been assumed that "degenerate art" was either sold abroad or destroyed. The "monuments men" went searching for Titians, not Picassos. But the Munich hoard proves the naivety of this assumption. Even in the mind of Hitler, modern art was bizarrely fascinating. You do not put on an exhibition of something you do not want to look at. In some strange way the Nazis needed modern art, as a demonic image of their nightmares. The Degenerate Art exhibition is, after all, the biggest backhanded compliment ever paid to the avant garde. Many people think art has no influence on the world. Hitler knew it did. The old saw that he hated modernism is just too simple. He loved to hate it. What you love to hate, you want to keep, somewhere, if only as a freakshow curiosity.

Other Nazis simply went along with Hitler's taste in public but did not really know what the would-be artist in him was talking about. In Mussolini's Italy, the Futurist movement was cosy with fascism. There was no reason – Italy proved – that fascists needed to spurn modernism. Some German modern artists, notably Nolde, were themselves sympathetic to the far right.

Then there was greed. In the end, the National Socialists were thugs, criminals and murderers. The idea that most of them believed deeply in ideological discriminations about art is not that plausible. For men like Gurlitt, modern art made a good stash. He and his son sat on the hoard while his claim that it was lost in a firestorm was taken at face value.

Now the books on Nazi loot need to be reopened. It seems only too possible that other Gurlitts hid away other art treasures in the chaos of defeat.

In one of the last photographs ever taken of Adolf Hitler he is in the bunker in Berlin contemplating Albert Speer's design for a new art capital to be built at Linz. Much as he loved Munich, this city was closer to his childhood home. Its massive new museum was to have contained all the art treasures of conquered Europe.

While Hitler doted on his cultural fantasies, paintings were vanishing into fruit cellars and attics. It was so easy to write them off in the Führer's Götterdämmerung.



Read Jonathan Jones on the masterpieces that are missing in action