At an unfortunate moment during the Georg Baselitz show at the Royal Academy, in the final room, where the ageing maestro’s latest work is collected – and where he tries to sum up his career as he strives to arrive at a grand late style – I was prompted to remember that hilarious Fawlty Towers sketch in which a group of Germans come to stay, and Basil instructs the staff not to mention the war. Being Basil, he cannot resist mentioning it relentlessly.

“Will you stop talking about the war?” complains one German.

“You started it!” Basil retorts. “We did not start it,” insists the indignant guest.

“Yes you did. You invaded Poland!”

It’s the other way around at the Baselitz show. Here, it’s the visiting German who cannot stop mentioning the war. Every Baselitz offering in this magnificent display of Teutonic painterly heft has a war angle to it. Sometimes it’s merely a question of mood: a doomed black atmosphere, a fractured presence. Elsewhere, as in the final room, where every face in every picture seems to have had a Hitler moustache added to it, it’s unmissable and specific. And hilarious. Baselitz is as compelling a painter as he is because the ultimate absurdity of war seems never to escape his attention. Even his most notorious painterly act – the ridiculous policy of painting everything upside down – strikes you as perfectly reasonable when compared with Germany entrusting the nation’s destiny to the Führer.

Baselitz was born in 1938, in Saxony. The nearest big town was Dresden. And for irrefutable proof of the traumatic impact the 1945 bombing of Dresden had on his psyche, you need only peep into the difficult room at the halfway point of this event, in which 20 paintings from the so-called ’45 Series are gathered. All the pictures show the upside-down head of a woman: a mother, a lover. All are as blurred and spluttering as a candle going out. All have been painted in fragile tempera, on wooden panels that appear to have been attacked first by a maniac with an axe. Slash, slash, slash – the violence enacted on these surfaces is truly extraordinary. Yet the fragile head of the woman traced on the 20 splintered panels survives. Something lives on. Something can’t be destroyed. And that something is what Baselitz always paints.

How to be a proud German painter in a world that loathes German pride? That is the question. It was not his dilemma alone: a generation faced it. But Baselitz tackles it with a fabulous combination of urgency and insolence. Most of the show is arranged chronologically, but the opening display, in the rotunda, has big, agenda-setting ambitions. We are surrounded by a gang of large, lolloping German soldiers, frozen in awkward poses, painted in 1965, when Baselitz was already a few years into his career.

These are usually referred to as Baselitz’s Heroes, and are said to evoke Germany’s battered spirit in the postwar years. Their shirts are ripped. Their flies are open. Their bits are dangling. It has also been suggested that these are self-portraits, particularly the image of a one-legged soldier holding a palette and brush that is actually called Blocked Painter. But what I like most about these clumsy losers is their air of comic melodrama. To me, they look as if they might have escaped from the pages of a Sgt Rock comic. If Baselitz is looking back on his pitiful national inheritance, then he is doing so with an explosive mixture of sadness and scorn.

I love this untameability. And I recommend that it be borne in mind when – also in the first room – we encounter what seems to be a sculpture of Adolf Hitler raising his arm in a Nazi salute. I first saw this shocking thing at the Venice Biennale in 1980, where it caused a predictable storm. The explanation trotted out then was that it was not meant to be Hitler, and that the gesture was not meant to be a Nazi salute; that we were all wrong to see it that way. But on the evidence here, in the company of this many pint-sized Hitlers with stuck-on moustaches, I think we can safely assume that Baselitz knew exactly what he was doing. Just as Basil Fawlty could not stop mentioning the war, so Baselitz cannot stop mocking his nation’s choice of Führer.

The second room rewinds to the start of his career. Baselitz grew up in the former East Germany and only decamped to the West when he was 20. As soon as he came out of art school, however, he set about provoking the hell out of anyone who was watching with a series of creepy portrayals of masturbating men. The most memorable of these in-yer-face onanists, a blobby chap in a spooky painting called The Big Night Down the Drain, is apparently a portrait of the Irish poet Brendan Behan, who had turned up on stage in Berlin so drunk that he didn’t realise his flies were open. According to Baselitz, Behan’s dangling howitzer seemed to bring a sense of occasion to the event. And poetry that might otherwise have been forgotten became unforgettable.

The upside-down paintings that follow should therefore be seen as products of another event-making strategy. Their imagery is simple – faces, figures, a landscape, a nude. But the act of turning them upside down endows them with instant drama. As the show unfolds in a series of impeccably presented steps, you begin to grasp various larger truths about Baselitz. Although he continually uses scorn and cheek, there is an immense underlying sadness to all his output. Stylisti-cally too, we never stray far from the frenzied brushwork that characterised the experiments of his great predecessors, the German expressionists. A heritage has been lost, and we are watching a lament on that loss.

Another reason this show is so good is that its story line is completed so neatly. In the final gallery, Baselitz revisits the imagery of all his best-known paintings and redoes them in a series of what he calls “remixes” – at speed, with fewer colours, and with less angst. This is the stretch of the show in which the comic Hitlers suddenly appear. It’s as if the painter is finally admitting that everyone in his art was the Führer in disguise. Is this a weird final confession? Or is it, as I prefer to see it, another excellent bit of provocation?

Over at the Serpentine Gallery, the interesting spectacle awaits you of an American artist trying to work in the manner of a German one. Matthew Barney has never hidden his admiration for the late Joseph Beuys. Much of what Barney does, Beuys did before him. Even the wilful obscurity of Barney’s output, the difficulty most observers will have in making any sense of it whatsoever, is Beuysian in tone. As is the presentation of the artist’s persona in a shamanistic light, as if his actions had cosmic implications. We also witness the use and reuse of a narrow range of evocative substances. Beuys kept using lard. Barney keeps using petroleum jelly.

But where Barney, a fêted figure in American contemporary art, differs from Beuys is in his gravitas. Beuys had lots of it. Barney doesn’t have any. I stopped believing in him halfway through the new film he has made with his partner, the Icelandic singer Björk. Set on a Japanese whaling ship, the film is a poetic record of Barney and Björk’s identification with the fate of a whale. Indeed, at the end of the film, they both turn into whales. Björk manages somehow to carry it off. Barney does not. Balding, nervous, slight, he looks like a Yale University graduate playing at being a shaman. Which is what he is.

Georg Baselitz, Royal Academy, SW1, until Dec 9; Matthew Barney, Serpentine Gallery, W2, until Nov 11

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