The Frick Collection in New York doesn't do many shows. But those it does are apt to be exemplary, and none more so than its present one: Goya's Last Works, a shapely group of some 50 paintings, drawings and etchings from the closing years of the great man's life. Small the show may be, but it is the first of its kind, unremittingly fascinating, and even those who think they know Goya intimately will be surprised by it.
Everyone knows the middle-aged Goya. Of him, there were several. One was the great ironist who etched the series of Caprichos, those corrosive little satires on Spanish authority, superstition and folly. Another, the fan of bullfights who left the Tauromaquia etchings as one of the benchmarks of popular Spanish identity. A third, the portraitist who painted some of the most assertive and complex images of female beauty (the Majas, clothed and naked) and vulnerability (the Condesa de Chinchon) in all European art, along with an extraordinary gallery of closely scrutinised intellectuals, politicians, priests, bluebloods and Bourbon royals. A fourth, the political artist who created that never-surpassed indictment of wartime cruelty, The Third of May, 1814, and its related etchings, the Disasters of War, provoked by Napoleon's occupation of Spain and the popular resistance it engendered.
The work of his last years, however, is much less well-known. Goya was a tough bird and he lived to a great age. The average life expectancy of a Spanish farmworker in the early 1800s was about 40. Born in 1746, Goya survived until 1828, dying at 82 - an almost incredible longevity. What was more, he kept on drawing and painting right up to the end. Almost all his life was spent in Spain, except for a youthful trip to Italy (of which very little is known) and his last four years, 1824-28, which he passed as an elderly expatriate on the French side of the Pyrenees, in Bordeaux.
What was he doing in France? Sheltering. Trying to find a modicum of political calm. His homeland had been crazy for a long time: riven and deranged by the Napoleonic occupation and the desperate resistance it provoked, wrecked again by the policies of El Deseado, "the one we long for", as Spanish proles and aristocrats called the obstinately repressive, paranoid Bourbon tyrant Ferdinand VII, who eventually regained the throne in 1823. Ferdinand abolished the new constitution, brought back the Inquisition, and launched witch hunts against Spanish liberals of all stripes. Goya feared he would be among them, though he was still officially a salaried court painter. He took refuge with a friend, and then - when Ferdinand, under pressure from the French and English, declared a brief amnesty for constitutional supporters in 1824 - he came out of seclusion and asked the king to let him go to a French spa to take the waters.
Permission granted. But Goya never went to the spa. Once safely over the Pyrenees, he headed straight for Bordeaux, to touch base with the growing colony of liberal Spanish exiles there. It included an old friend, the writer Leandro Moratin, who reported that Goya was "deaf, old, awkward and weak", without a word of French, but "so happy and anxious to see the world".
He could see it but not hear it; Goya had been deaf as a stone for 30 years. He also saw Paris briefly (though he had no contact with its artists, who included some of his admirers, such as Eugene Delacroix), but soon he was settled back in Bordeaux. There he was joined by his loyal but rather crabby companion of earlier days in Madrid, Leocadia Zorilla, and her two children. And he settled down to work.
There was nothing routine about what he produced. Its emblem was one piercing drawing in black crayon, which depicts an old man, a time-damaged patriarch with a long white beard, hobbling forward on two sticks, forging ahead. "Aun aprendo," Goya's hand inscribes above him: "I am still learning." And so he was, ceaselessly, indefatigably. There are, in all, 123 known surviving crayon sketches from his time in Bordeaux - about an eighth of his known drawings. Like the rest of his graphic work they fall into several categories, but few seem to be studies for eventual paintings.
First, there were things he saw on the streets of Bordeaux, sights that snagged his attention by their pathos or oddity - a legless beggar sitting in a clumsy wheelchair; a man on roller skates with another on a velocipede in the background; a mild, bewildered-looking giantess towering above spectators at a town fair. Then there were the drawings that recorded his horrified and sympathetic interest in something that had recurred in his work since the 1790s: the image and behaviour of the mad, society's tormented outcasts behind bars. Some of these - like Loco Furioso (Raging Lunatic), the huge eye-rolling figure pinioned in a sack, or Gimiendo y Llorando (Weeping and Wailing), a kneeling prisoner with his arms flung out in reminiscence of the man in the white shirt who was about to be executed in The Third of May - are among the most powerful pleas on behalf of victims this great, sardonic humanitarian ever made.
There are witches and monsters, too, the witches persecuting harmless young women, the monsters including an extremely weird flying dog - a mastiff with a nail-studded collar, the webbed back feet of a goose and hairy wings - diving out of the sky like some monstrous Stuka on the attack. It has what seems to be an open book tied to its back. (As the excellent catalogue, by the art historians Jonathan Brown and Susan Galassi, says: "The significance of this drawing has never been ascertained." One may bet that it never will be.) The most memorable drawing in the show, for many, will be Goya's vision of an old man grinning on a rope swing, horny feet sticking out, slicing through space like a crazy Zen patriarch - his inner self letting fly, one feels, unaffected by age.
One of the startling facts of Goya's last years was that, despite his age and debility, he was not only open to new media but enthusiastic about trying them. One of these was lithography, the reproduction of an image by drawing it directly on smooth limestone. He was a master of etching but lithography was novel: it had been invented only some 20 years before by a Munich playwright, Aloys Senefelder, then picked up by a Spaniard named José Maria Cardano, who introduced Goya to it. The result was a series of images of bullfights, collectively called The Bulls of Bordeaux. Goya had hopes of sales. He seems to have approached lithography as though it were a sort of painting, propping the heavy slabs of stone upright on an easel rather than working on them horizontally, as one would on a copper plate for etching. But although some of these tangled, clotted masses of light and dark, with their lumpish humans and wretched, dying animals, are among the best prints he ever made, they didn't sell. Folkloric Spain wasn't fashionable yet, the French were not interested in such sub-Pyrenean brutalities as the corrida, whereas the Spanish expatriates in Bordeaux tended to be afrancesados, persons of refined taste and Enlightenment principles for whom the bullfight represented exactly the gross, populist side of Spain they were glad to have left behind.
His body was failing him. "I've no more sight," he wrote to a Spanish friend in 1825. "No hand, no pen, nor inkwell, I lack everything - all I've got left is will." He was short of money, and friends proposed that he should make himself some by doing a new issue of the Caprichos, but Goya refused to compromise himself by repetition.
Instead he spoke of something entirely new in his work: miniatures on ivory. Not the licked, frozen, highly detailed miniatures one associates with the period, but expressive ones, tiny but broadly brushed relative to their surface, full of accidents, blots and runs, "of a kind I've never seen before, done entirely with the point of a brush". He said he had finished about 40 of these. Not that many survive, but the Frick show is by far the largest group of them that has ever been exhibited. And they are wonderful, charged with all the sensuality and terror of his larger works, but rarely more than three inches square, and painted in carbon black and dilute watercolour on little plaques of ivory. One is enchanted by their spontaneity - how a mere drip of paint, blotted and diluted, becomes a face, or the looming mass of a majo's cloak, or the engulfing shadow behind a figure.
These miniatures are tiny in size but large in scale, and they contain some of the most beautiful feats of controlled chance that would be seen in art until the 20th century. They show that, almost to the end of his life, to paint and to invent were, for Goya, the same.
· Goya's Last Works is at the Frick Collection, New York, until May 14.Details: 001 212-288-0700.