Gerhard Richter, Tate Modern, London

Resist though he might, this modern German master cannot help but work wonders on canvas

In 1972, Gerhard Richter represented Germany at the Venice Biennale. You can see a recreation of 48 Portraits, the work he showed there, in the foyer outside his new exhibition at Tate Modern. Before you do, though, you might want to look at another of Richter's Venice-related works, Verkündigung nach Tizian ("Annunciation, after Titian"), in Room 5.

While in Venice, Richter, then rising 40, wandered into the Scuola Grande di San Rocco. There, his eye seems to have been caught not by Tintoretto's famous programme of wall and ceiling paintings but by Titian's rather less obvious Annunciation. Perhaps he was taken by the loose brushwork. Or it may have been that he found the postcard of the Annunciation more satisfying than any of the available Tintorettos. At any rate, Richter went home to Düsseldorf with the card in his pocket and, the following year, painted Annunciation after Titian.

Of these three words, "after" ("nach") seems the most dispensable. Obviously based on Titian, clearly an Annunciation, Richter's work shows the angel Gabriel saying "Hail, thou that art highly favoured" to an appalled Mary. But it is also itself a kind of announcement: here, it says, is a new dispensation in painting. It is the nach of Richter's title that really matters, because his image is, and sets out to be, a long, long way after Titian.

In 1936, the German critic, Walter Benjamin, published his essay, "The Work of Art in the Age of Mechanical Reproduction". Benjamin argued that the "ritualistic value" of originality was lost in a day when images could be endlessly reproduced. Implicit in this was the idea that modern man no longer saw in a painterly way, but in a reprographic one. Richter's Annunciation isn't based on an original but on a reproduction of it, a postcard. With each step away from Titian, the image becomes harder to read, more hazy and meaningless.

What Richter is really saying is that painting is dead: he makes a Titian in 1973 to show that you can't make Titians in 1973. And yet that is what he has done. It isn't Richter's first meditation on the death of painting. In the 1960s, with Sigmar Polke, he had helped invent Capitalist Realism, a kind of German take on Pop. A work such as Klorolle (1965) hinted that you could still paint properly, but not the proper subjects of High Art. It was possible to use old-fashioned words such as "perspective" and "grisaille", but only if they were applied to, say, lavatory rolls. Now, in 1973, Richter found that he was allowed to paint Annunciations after all, but that he couldn't paint them in an Old Masterly way.

At the heart of Richter's painting are rather old-fashioned ideas of propriety that date back to Goethe. Art, especially painting, is a serious moral issue. What makes Richter great is that paint isn't merely a conceptual flag of convenience. His answers to the problems of painting are painterly ones.

No matter how much he tries, he simply can't not paint. In the impossible blurriness of Annunciation after Titian, Richter's artist's eye sees another possibility: abstraction. The picture doesn't look like an Old Master, but it does look good. By 1977, he is making canvases with titles such as Abstraktes Bild. They may not be of anything recognisable, but they are none the less of something – modelled, three-dimensional forms which look like (and may very well be) blobs of paint. They are, if you like, representational abstracts, which makes them difficult to place, unsatisfactory.

Only in the mid-1980s does Richter finally find what he seems to have been looking for – a way of painting sincerely. For the past 20-odd years, he has made vast, scratchy-looking abstracts, their paint laid on with planks of wood. Here, at last, is a real painting for our time; except not quite. Alongside these, the German master, 80 next year, has also been making works such as Ella that toy with photo-realism, and others that lie somewhere between. I doubt there is a painter alive who has had as great an influence on younger artists, from Luc Tuymans to Glenn Brown. Paint, Richter says, is one big problem.

To 8 Jan (020-7887 8000)

Next Week:

Charles Darwent wanders the Turbine Hall, Tate Modern, with Tacita Dean

Art Choice

The immersive video artist Pipilotti Rist offers an Eyeball Massage at her exuberant new show at London's Hayward Gallery (till 8 Jan). Meanwhile, Bath's Holburne Museum takes a look at Gainsborough's Landscapes, arranging his works thematically (till 22 Jan).