Anselm Kiefer: Il Mistero delle Cattedrali, White Cube Bermondsey, London

Like a stroke patient dealing with years of after-effects, German culture has not yet rid itself of the Nazi past. A pair of major exhibitions, currently overlapping in London, show that at least two of the country’s most renowned artists remain engaged with the totalitarian trauma. Tate Modern’s comprehensive show by Gerhard Richter, which runs until Sunday, presents his meditations on the Nazis in his own family, and on atrocities carried out during the 1970s by the Red Army Faction in response to Germany’s refusal to face up to the past. White Cube Bermondsey meanwhile is offering a display of recent work by Anselm Kiefer. It is a unique opportunity to see two great compatriots struggle with their country’s collective memory-loss, and defective backwards vision.

Kiefer was born in 1945, 12 years after Richter. His artistic fame began with student photography and, in particular, a 1969 diploma piece entitled “Occupations”, in which he showed photographs of himself at various European locations in uniform and giving the Nazi salute. This piece of agit-prop sprang from the same grievance that would soon turn the Baader-Meinhof gang to terrorism – that Germany was still not owning up to its past – and it outraged a society for which the Nazi era was still largely tabboo. But cocking a snook, however controversially, soon palled and Kiefer turned to painting and to three-dimensional art that probed the roots of German history more deeply.

Myth, landscape and architecture appear as both the creations and the determinants of 20th-century German realities. Kiefer’s art is self-consciously in the Romantic tradition – the symbolism of Caspar David Friedrich is not too far away – but it is anti-Romantic in that it obdurately refuses to hope. A recent film about Kiefer by Sophie Fiennes is entitled Over Your Cities Grass Will Grow, a minatory quotation from the Book of Isaiah referring to what was once a central preoccupation of western art, though largely absent since the Romantic age: the vanity of human wishes, the inevitability of destruction.

As the work on show at the White Cube testifies, Kiefer has developed this theme of material and ideological entropy on an increasingly gigantic scale. Two of the largest paintings here, each the size of cinema screens, are of the Berlin airport at Tempelhof, which closed to traffic in 2008. It had been planned under the Third Reich as the portal to Hitler’s fantasy city of Germania and its sweeping, colonnaded, semi-circular terminal was one of the largest free-standing buildings in the world. Later it was an important receptacle for US aspirations in West Berlin – the Americans even built a bowling alley inside one of Tempelhof’s vast halls. The airport now stands bereft of function and derelict of meaning, a mockery of its grandiose conception, bringing to mind 18th-century capricci by painters such as Giovanni Panini, melancholically obsessed as they were with ruins. Kiefer, however, is less motivated by the pleasure of contemplating decay than by a profound pessimism that, while it knows where best to look for meaning, knows also that it will not find any.

Kiefer’s achievement is powerful in all its aspects. The texture of his painting, for example, is painstakingly prepared to complement its subjects. The catalogue summaries of his painting media underline the point: “oil” doesn’t just mean oil paint, but sump oil; salt, resin, charcoal, plaster, brickdust and ashes are found in the mixture. The result is a painted surface that appears to be afflicted, not with the patina of age, but the leprosy of advanced disintegration. It works as a representation of both the idea of entropy and of the process itself.

A feature of these paintings is the attachment of large objects in front of them: metal bird wings, measuring instruments. While these play their roles in the paintings behind, they are also patent Kiefer sculptural objects in their own right, comparable to his giant-sized books made from sheets of lead. They resemble items of architectural salvage that, having made schematic sense in their original contexts, are now deracinated remnants that both demand and resist interpretation. Of Kiefer’s standalone sculptures there is just one relatively light and readable piece here. “Merkaba” is a rust-eaten, three-seated tandem bicycle made out of scrap, whose riders are symbolically represented by dishes suspended from the crossbar, each holding a different unidentified element. I like this piece, but it seems oddly misplaced in a show otherwise so weighty.

The comparison with Richter shows that he and Kiefer have overlapping interests, but are in fact opposites. Richter’s strength is his conceptual variability – from figuration to abstraction, from political comment to family portraits. Kiefer, on the other hand, bears down with moral force on a closely packed set of ideas, centred on landscape and myth, and his is, in more than one sense, the weightier achievement.

Until February 26, whitecube.com