Pablo Picasso, seventy-three years young, has taken up with a new woman. He chooses to announce the fact, in characteristically idiosyncratic style, by painting a series of pictures inspired by Eugene Delacroix’s The Women of Algiers of 1834. Delacroix’s Romantic masterpiece is a sombre and melancholic work, implacably opposed to the spirit of orientalist sexual fantasy that cheapens most nineteenth-century paintings of the Exotic East. In a dark and richly decorated sultan’s harem, three women wait in a condition of saddened boredom. What does Picasso make of this dispiriting sexual purgatory, more than a hundred years later? He turns its claustrophobic space into a buzzing confusion of Cubist planes and patterns. The women waiting have been stripped naked. One of them kicks her legs up in the air, while another bares her ingeniously rearranged breasts in a provocative manner. In Delacroix’s picture the sultan is nowhere to be seen, but in Picasso’s version he is present by implication, albeit invisible, as Picasso himself. This is his harem. To the left stands the towering figure of Jacqueline, the only woman to have been given a recognisable face. The picture was a kind of love letter, Picasso’s way of telling her that from now on she would be the one. It was also his final goodbye to Olga, to Marie-Therese, to Francoise and all the others.

“My work is like a diary,” Picasso once said. “It’s even dated like a diary”. He inscribed his final version of The Women of Algiers with the impressively precise date 14 February 1955. The picture hangs in the culminating room of the National Gallery’s new exhibition, “Picasso: Challenging the Past”, among a number of other themes and variations on the works of the Old Masters. Manet’s enigmatic Dejeuner sur l’Herbe, itself a provocative variation on Titian’s celebrated pastoral, La Fete Champetre, is successively reinvented by Picasso, as orgy and existential confrontation. Velazquez’s Las Meninas, likewise appropriated, becomes a meditation on the peculiar plight of the modern artist. Picasso turns the most famous picture of the Spanish Golden Age into a black-and-white ghost of its former self. The King and Queen of Spain, reflected in Picasso’s distorting mirror, become childish doodles with wonky, smiling faces. Their children and their dwarves turn similarly Picassoid, while even their brooding mastiff has been turned into the silhouette of Picasso’s own dachsund, a mutt economically named Lump. The figure of Velazquez himself has metamorphosed into a totem pole with twinned heads of a playing card jack. The single artist has become two. Is he Velazquez-Picasso, or Picasso-Velazquez? Is the modern master kissing the Old Master, or seeking cannibalistically to ingest him? Probably a bit of both.

The National Gallery’s show might itself be described as a variation on a theme. The ur-idea for such an exhibition was Picasso’s own. In 1947, shortly after he had donated ten of his most celebrated paintings to the Musee de l’Art Moderne de la Ville de Paris, the French authorities asked him if there was anything he would like in return for his generosity. He asked for the opportunity to hang his own pictures in the Louvre. For one day only, his request was granted. The museum was shut and only a handful of people were invited. That nearly secret event, more than fifty years in the past, was the pretext for “Picasso et les Maitres”, a celebratory examination of the painter’s relationship with the masters of the past – which recently closed in Paris, having broken all attendance records. It was arguably the most ambitious exhibition about Picasso ever staged, filling the galleries of the Grand Palais and spilling over into both the Musee d’Orsay and the Louvre itself. The National Gallery’s exhibition rings changes on the same idea and includes several of the same loans. Inevitably, given the nature of the Sainsbury wing basement galleries, it is a much smaller and more intimate affair – a modest study in influence and inspiration, rather than an out-and-out blockbuster.

In London, the decision has been made to hang Picasso’s paintings alone, rather than in the company of pictures by the Old Masters that may or may not have inspired them. There are some advantages to this approach. Many of the juxtapositions in Paris seemed wilful – shotgun weddings arbitrarily arranged between Picasso’s paintings and works from the past to which, worst case, they bore little if any relation. There are no such forced comparisons at the National Gallery, where viewers are implicitly encouraged to make their own connections between the art of Picasso and the venerable traditions of Western European painting enshrined elsewhere in the museum. In other ways, the show is compromised by its limitations. Particularly in his later years, it was Picasso’s habit to work and rework a particular picture through numerous variations. The National Gallery exhibition fails to convey the urgency and vitality of that nearly cinematic, frame-by-frame process of transmutation. So for example, all of Picasso’s myriad variations on Las Meninas, or Le Dejeuner sur l’Herbe, or Les Femmes d’Algers,are compressed to a mere handful of canvases – and in one or two cases they are not even the pick of the bunch.

There is the sense, throughout, that Picasso is too big, too raucous, too unconstrained to be confined in this modest suite of rooms. But that lends the exhibition its own kind of enchantment. With only himself for company, Picasso’s endlessly inventive artistic personality seems all the more bruisingly powerful. In any case, Picasso used the art of the past in so many ways that no exhibition could do more than scratch the surface of the subject. His variations on the work of another artist could be a soliloquy, or a conversation with a friend. On other occasions he went to his predecessors for help and moral support, as he did in the 1930s and 1940s, the years of Guernica and The Charnel House, suddenly looking to Goya for inspiration. There are no hard and fast rules.

The National Gallery’s show treats the artist as if he were a one-man museum, or a one-man history of art, which is probably just as Picasso would have wanted. Room by room, he works through the different genres, yet because each gallery spans more or less his entire career, with all its changes of gear and direction, the sequence of images is never predictable. Self-portraiture is the subject of the first gallery, which sets the tone. One moment Picasso is in the peasant village of Gosol, in 1906, painting himself with black eyes and a mask-like expression – thinking, in equal measure, about Cezanne’s flatness and the hieratic impassivity of ancient Iberian and African art. Suddenly it is 1938 and he has metamorphosed into a comic-book version of Van Gogh, wearing a vivid straw hat and sticking out a bright green tongue to lick at the ice-cream cone clutched in his bright-blue hand. Within an instant he has changed again, becoing a disgraceful old man kissing his voracious lover. 

The exhibition is a switchback-ride of impromptu leaps and lurches through Picasso’s impossibly fertile career. The journey moves from self-portraits to nudes, from nudes to muses, from muses to still lifes and beyond. Picasso paints Olga, his wife in the immediate aftermath of the First World War, as if he were Ingres and she were a Second Empire matron. Then he paints his new girl, Marie-Therese, as a Surrealist fantasy of sensuality and sexual abundance – her face is two faces, both sun and moon, as if to say that at this moment she has become everything to him. But nothing stays still in this show and in the blink of an eye the rollercoaster has gone all the way back down to Cubism, that subtle enchanter’s art of shivered fragments, slices of violin and pitcher and snatches of newsprint, laid out on the cafe table of the mind.

The overall effect is enlightening, or at least provoking, creating unpredictable patterns from all these kaleidoscopic shards. The artist who could not bear to paint in one style was the same restless man who could not bear to have only one woman in his life. The inventor of Cubism was the same artist who loved to play at being this or that Old Master. To be a Cubist is to embrace multiple points of view, while to paint endless variations on the work of other artists is to dream of having multiple personalities. In the end all these different Picassos do, miraculously, feel like one. There is something pathological about the artist’s restlessly protean personality, which is the one thread through it all. Perhaps it comes down, ultimately, to his terror of death. Everything he does is a raging against the dying of the light. Picasso the painter of nudes creates funerary monuments to the spirit of his own eros. Picasso the still-life painter muses on the skull and the guttering candle. Picasso the minotaur, tracked down to the centre of his labyrinth, shows the wide-open eyes of fear.