Tate Modern, London
From his wife to his lover, from phallic-faced women to Christ in a nappy, this giddying exhibition captures the furious pace Picasso worked – and lived – at

Picasso at 50: Savile Row suits, a chauffeur-driven Hispano-Suiza, and living in a swanky apartment near the Champs Élysées, with his wife, the Russian ballet dancer Olga Khokhlova, and son Paulo. Picasso paints in the apartment above and also works at the country home, a small dilapidated castle in the hamlet of Boisgeloup in Normandy.

It is at Boisgeloup that Picasso sculpts, having filled an outhouse with white, monumental plaster busts. Made the previous year, their rounded faces and large, prow-like, even penile noses bear a strong, if distorted, resemblance to his lover Marie-Thérèse Walter, whom he first met in the street in Paris in 1927 when she was 17. Walter is everywhere in this exhibition, in paintings and on a bronze plaque, sleeping, dreaming, swimming and seated in a chair. Her busts crowd the barn at Boisgeloup and reappear in the paintings, looming from still lifes and watching over her sleeping body.

The scene is set. Picasso 1932: Love, Fame, Tragedy, a show devoted to that single year, has travelled to Tate Modern from the Musée Picasso in Paris, where it was subtitled Année érotique. These titles are annoying. Pick a year, any year in Picasso’s long career, and day by day, week by week, month after month, an amazing trawl of letters, documents, reviews, essays and newspaper articles, friendships, loves, lunches and betrayals come piling in, while the larger events of the century thunder through like so much background noise.

Here the marginalia is largely relegated to the catalogue, although the exhibition proceeds in a largely chronological fashion. Yet somehow the work escapes, proceeding at its own pace and taking unexpected turns. And the pace is furious. While Khokhlova is in the country at the end of January, drawing up an inventory of the household linen, Picasso stays in Paris, painting a woman in a red armchair, her mouth a horizontal slit, her only other facial features a vertical pair of buttons, a face undone.

On 26 February 1932, a painting by Picasso sells at auction for a record 56,000 francs, bought by the artist’s dealer. On 8, 9 and 12 March, Picasso paints a suite of three sleeping nudes. We do not know what he did on 10 or 11 March, but he’s at it again the following Monday with Girl Before a Mirror, and then embarks on another series of reclining women, in a completely different register and tempo. On the last days of March, at Boisgeloup, Picasso paints some views of the village in the rain.

Weeks and months go by at this furious pace, interrupted by meetings, photo-sessions and lunches – as well as Paulo’s first communion (he had recently turned 13), attended by the artist’s mother, his brother-in-law up from Barcelona, and Gertrude Stein. I love these reminders of the everyday, of holidays and festivities mixed in with paintings and drawings, the to-and-fro to Boisgeloup, exhibitions being organised, letters arriving, household dramas, business getting done.

For all this, we must turn to the catalogue. In June, Picasso hangs his own retrospective, at the Galeries Georges Petit. There were no wall labels and Picasso mixes early work with his most recent. Asked how he was going to curate the show, he remarked: “Badly.” A partial recreation of the exhibition is presented on dark red walls here, including one group of paintings, hung two deep, that includes a portrait of Paulo as a harlequin, Khokhlova in an armchair, and a 1901 self-portrait painted before fame hit. Picasso mixed up past and present, period and period, style upon style. When the exhibition travelled to Zurich in September, the psychoanalyst Carl Jung decried Picasso’s work as almost schizophrenic in its variety of styles, declaring that Picasso’s “psychic problems … are in every respect analogous to that of my patients”.

Picasso is, indeed, problematic. But can we come to him now without a certain unease? Maybe it was always there. In Sleeping Woman by a Mirror (14 January), Picasso paints a woman with her head thrown back, as though asleep in the armchair, her face a sort of palette-shape with black, dragged smudges and a slash of red, barely recognisable as a physiognomy, while one of her breasts becomes the glans of a huge erect penis, climbing from between her folded legs.

Only in the mirror behind her chair do we see an identifiable profile. Ten days later, he paints another sleeping woman – again resembling Walter. One half of her sleeping face is both a cheek and a closed eye – and, inescapably, an engorged penis. This double-take image just sits there, part of her dream, as she rests, her body heavy and rounded in sleep, hands softly clasped on her lap, her mouth a slight smile.

Further spatial and pictorial anomalies complicate the paintings of reclining women Picasso worked on throughout February and March. A face in profile looms through a curtain, leaves become cock and balls, heavy black shadows come from nowhere to cross a woman’s body, binding her into the picture plane.

Later, bodies become pneumatic, like inflatable beach toys, cartoonish, boneless, and like various sorts of undersea life, curved about themselves like bivalves and cephalopods. Hands become flippers or tentacles. These sleeping forms have a strange sort of interioriority, like the subjective sensation one sometimes has, before falling asleep, of one’s body image dissolving or regressing to an unformed foetal state. They also evoke the sensation, during sex, that one’s body’s boundaries are confused with those of a partner. At a certain point, one is barely human.

Dream images and mirror images, reflections and divisions, things splitting apart and folding in on themselves like dough being worked, one part of a body being taken for another – they are all part of Picasso’s process and imagery during the first half of 1932. These plastic deformations and inventions take place among plants and busts and bowls of fruit, in armchairs and on beaches, against the sky and in rooms where the dark patterned wallpaper closes in.

“I paint,” Picasso said, “the way some people write an autobiography.” He said he regarded his paintings as the pages from his diary. Yet things are more complicated than that. If his art is a coded record of his life, Picasso’s work is more than picaresque or confessional, revealing the turns of his mind and his curiosity, his unconscious at play. As much as his art is observational, or a riff on motifs and themes, it is also a kind of fiction. He made stuff up. Paintings are paintings and people are people. Appearances are deceptive, however autobiographical we may take Picasso’s art to be. There are rapes and rescues from drowning, imagined fears and frightening desires, things that have happened and things that never should.

Later in the year, Picasso turned to that most vivid and horrible crucifixion, Matthias Grünewald’s 1512-16 Isenheim Alterpiece, to begin a long series of black and white ink drawings. Christ’s loincloth is given a nappy-pin. He interrupted these grisly images to paint and draw pipe-playing fauns and sleeping women. Idyll and horror come side by side.

There is such emotional – as well as formal and pictorial – variety here, whatever the constant preoccupations of Picasso’s art. One room towards the end is devoted to canvases less painted than drawn, the charcoal line grazing the nub of the surface, emptiness dirtied by washy rubbings out and overdrawing, presenting us with process and invention at its most naked: immediacy and revision, thinking and rethinking a way through to an image. A portrait of Walter, in a pensive attitude, has been ploughed through a thick layer of white paint, right to the canvas beneath. The image is extremely tender, but it has been made as if with a knife.

• Picasso 1932: Love, Fame, Tragedy is at Tate Modern, London, from 8 March to 9 September.