Richard Hamilton: The shock of the nude

In the last year of his life, the artist Richard Hamilton was preparing a final major work.

The painting, based on a short story by Balzac, "The Unknown Masterpiece", about the search for artistic perfection, would encompass all his feelings about the perfection of beauty in the female nude, the possibilities of technology and the impossibility of total realism. As it was, conscious in his final weeks that he would not be able to complete it, he allowed the National Gallery to incorporate three of his Photoshop studies in a show of his works he was already planning with them.

The result, Richard Hamilton: the Late Works, now on display in the light-filled Sunley Room of the NG, is a wonderful tribute to this great artist who died in September of last year, aged 89. It is not the show that the artist precisely intended. It is certainly not the grand retrospective now being planned by Tate Modern in association with other galleries around the world, scheduled for next year. But in its way it is the most appropriate tribute to an artist who never stopped experimenting or engaging with the public world about him right until the end.

The story on which the "Balzac" triptych (the three studies are shown side by side) is based is the classic one of the artist's reach for the unattainable. In it, Balzac tells the tale of a great artist who declares that he is painting a portrait of a nude so perfect that it will be as real as reality itself. His artist friends gather, only to look on a picture of daubs and inchoate splashes in which only a bit of a foot in the corner seems real. Overwhelmed by his failure, the artist dies, having destroyed all his works.

It is the ultimate romantic story of art taken up by the most literate and most technically proficient of modern artists. His intention had been to compose a picture, using computer graphics and a photograph of a 19th-century nude, which he would then paint showing the incomparability of paint in delineating the human form, but adding in a separate photograph of a model's foot as the one unpainted part. One can only speculate, and sense the loss, of the final picture as it might have been painted.

As it is, we have three digital images of the composition printed on canvas. The nude is there, perfect in shape and skin tones, calculated precisely according to ideals of beauty. She languishes, sure of herself, but divorced from the gathering around her of three artists representing youth (Poussin), middle age (Courbet) and old age (Titian), each a commanding figure reproduced from their self- portraits. The nude is perfect in her symmetry but unreal in her glassy, digital skin, photographically exact but artistically artificial.

It is a theme that draws together the Balzac works and the others on display in this exhibition. As concepts, Hamilton saw them quite separately. But no artist compartmentalises his creative ambition that clearly, particularly in his later years when the need to draw together the strands of a life and lessons learned becomes more pressing.

Hamilton's original thought had been to make the National Gallery show a counterpoint to his more fiercely direct show of political art at the Serpentine, the Modern Moral Matters of two years ago. It was a wonderful and surprising exhibition, proving that the old boy had lost none of his political anger as he portrayed Tony Blair as a cinematic cowboy and Israel's settlement grab of Palestinian land through the eye of a map.

The NG exhibition, in contrast, is cool and almost academic, dealing with the issues of space and perspective, beauty and the imagery of art history, in which he was well versed. Hamilton had worked as a draughtsman for machine tools during the war and took to computer graphics and 3D simulation like a duck to water. The results, some Photoshop prints on canvas, others touched up or half-painted in oils, are works that are at once hyper-realistic in their surfaces but otherworldly in their depiction of space.

You can ascribe the presence of nudes in so many of his pictures to the voyeuristic obsessions of old men and some may find his depiction of the Annunciation with a naked girl on the mobile somewhat shocking. But their intention is far from salacious. They are much more a concern with beauty as portrayed through the classical nude that runs throughout Western art, reinvented in this case with photographic exactitude.

His major point of reference in his later years, as in his earlier career, was the French Dadaist, Marcel Duchamp. His nudes directly acknowledge his idol's works. Descending Nude (2006) is modelled on Duchamp's famous Nude Descending a Staircase, No. 2 just as a fascinatingly complex study of reflections in The Passage of the Bride from 1998-9 refers back to Duchamp's The Bride Stripped Bare by Her Bachelors, Even (The Large Glass) of 1915-23, which Hamilton himself had reconstructed.

But then Hamilton applies this imagery to something both very old and very modern, which is the examination of space using the Renaissance elaboration of perspective. In his digital print, Chiara & Chair (2004), the perspective is spelt out in lines so that the viewer is made aware not just of a view of a naked lady vacuuming the floor of a living room but the view from the other end, with the added layer of the presence of Hamilton's own picture Lobby from 1985-7 hanging on the wall.

Lobby is indeed an eerie masterpiece of complex perspective in which the eye is caught both by the emptiness of the room, the soullessness of its reflecting glass and the puzzle of its staircases. It is easy in describing these works to make them sound intellectual and referential. They are that. But Hamilton was a master of effect. In imitating Fra Angelico's porticoed loggia in The Passage of the Angel to the Virgin (2007) and the Dutch 17th-century painter, Pieter Saenredam in his cathedral-like depiction of the Sainsbury Wing (The Saensbury Wing) from 1999-2000, complete with minuscule nude in the foreground and his own painting of the Northern Irish troubles as an altarpiece in the far end, he created magisterial works of both immediacy and ambiguity.

One wishes he had finished his last major work. But in its stead we have this fresh and vibrant show of one of the most influential artists of the post war as he reached his end, still pushing the possibilities of art. Not to be missed. And it's free.

Richard Hamilton: the Late Works, National Gallery, London WC2 (020 7747 2885) to 13 January