At the Tate Picasso’s late paintings seem almost to be different paintings from those they seemed to be at Beaubourg. There they looked, by common consent, more aggressive and explosive and electric, here more luminous, more beautiful, more grand. The differences in the selection, the hang and the ground-plan have not been crucial enough to account for so extreme a difference of effect. Clearly the Tate’s having daylight, a light that is soft and diffuse, must be relevant, but the difference has also been there, though not as extreme, at times when the lighting has been mixed or purely electric. It must, therefore, mainly be due to the architecture. In Paris the spaces were not enclosed by the walls: above the tops of the manifestly temporary partitions you could see those hyperactive Beaubourg ceilings. Here, the moveable walls reach the ceilings and these are vaulted, so that the paintings are surmounted by an amplitude of space in which to breathe. Those vaulted spaces do not suit every sort of art, and there are some paintings in the show which look less telling than they did in Paris. But others look greater than I have seen them look before and the list of outstanding late paintings which I propose in the catalogue demands the addition of the Reclining Man and Woman with a Fruit Bowl of 29 December 1969 and The Embrace of 1 June 1972. And by and large the paintings do look very much at home in these vaulted spaces.

It could well be, as Michel Strauss suggested while we were standing in the biggest space, that Picasso’s art always tends to look at home in spaces akin to those of Medieval churches. Indeed, it seems to me that at the Tate many of the late paintings look as if they are Medieval wall-paintings. Since everything they are contradicts the aesthetics of the easel-painting tradition, to say that they look like frescos here is to say that here they come into their own. That consummation, by the way, has nothing to impede it when they are framed by nothing more than a baguette or by nothing at all.

I have been focusing on the main body of an exhibition which has a misleading title because an accurate one would have been too cumbersome. An oversimplified title, ‘Late Picasso’, is complemented by a subtitle, ‘Paintings, Sculpture, Drawings, Prints 1953-1972’, which in fact contradicts it, because late Picasso surely begins in 1964 (the starting-point of Christian Geelhaar’s pioneering show at Basle in 1981 of ‘Pablo Picasso. Das Spaetwerk’). And the exhibition is essentially one of paintings, drawings and prints of 1964-1972, prefaced by a selection of paintings and sculptures with a starting-point at the turn of 1953-54. It is a point which marks both the arrival in Picasso’s life of Jacqueline, his last love, and the death of Matisse, his lifelong cherished rival.

The opening rooms are haunted by Matisse. What Picasso meant by his famous statement that Matisse had bequeathed him his odalisque is illustrated by a painting as great as any he did in the course of the Fifties, the Nude in front of a Garden of 29 and 31 August 1956. This joyful, grateful hymn to Jacqueline, this celebration of ‘the lineaments of gratified desire’, is composed in a language that is joyfully, gratefully taken over from that of Matisses done in Nice between 1919 and 1924: we are reminded of the Odalisque with Magnolias, for instance, even by the way in which the garden in the background is turned into a decorative screen, while the flanking shutters, not at all a Picassian device, are an evocation of any number of Matisses of that period, as is the ideogram for a palm tree in the top left corner of Nude in a Rocking-Chair of 26 March 1956. And the first two works in the exhibition, the Shadow of 29 December 1953 and the Nude in the Studio of 30 December, painted while Matisse was still alive, are no less redolent of his reclining nudes in interiors. Nor is the imitation confined to what might be called Matisse’s decorative side. For one thing, it also embraces his stark, sculptural aspect. The exhibition’s biggest painting, the Nude under a Pine Tree of 20 January 1959, obviously alludes to Cézanne, but its palette, its stylisations, its atmosphere, make it closely akin to the monumental Bathers by a River which Matisse completed in 1917. The reclining nude in the foreground, and the table-top just behind her in the grisaille version, dated 11 February 1955, of the Women of Algiers, after Delacroix, are another evocation of Matisse the cutter-out of forms. And then there are the imitations of Matisse as draughtsman in line. The most intriguing of these is not in the exhibition. It is the set of 21 portrait heads of Artur Rubinstein made on 19 July 1958 – a forgery, almost, not only in the character of the line but in the particular way each image evolves from the last, and above all in the choice of concluding image. That degree of competitive identification with Matisse is found again in one of the most consummate pieces of virtuosity in the exhibition, the pencil drawing of a Reclining Nude dated 11 August 1969.

Evocation of previous art, including his own, is of course a constantly conspicuous feature of Picasso’s last twenty years. (With his love of allusion added to his conscientious dating of works, he might have been aiming to ensure full employment for posterity’s art historians.) From December 1954 till February 1963 his painting was all but taken over by the making of variations – mostly sets of them – on complex compositions by the masters, often compositions with a sizeable cast of characters; during those years he did remarkably few other paintings of much interest (a notable exception is a series of small paintings of reclining nudes – one of them is in the show – done in April 1960). After that, while the work remains full of references to old masters, those references, in the paintings as against the prints, are always to pictures of one or two figures or to one or two figures from a picture – for the simple reason that the later paintings generally confine themselves to an archaic simplicity of composition. In the preceding years Picasso was testing himself against post-Renaissance European painting at its most ambitious – the realisation of complex human dramas more often than not in a style that exploited the expressive potential of the free handling of oil paint. The apogee of both the complexity and the painterliness came in 1961-63 in the Déjeuner sur l’Herbe and Rape of the Sabines series. Interestingly, the painterliness was at its maximum in the latter series – above all, in the large grisaille which can be seen as a sort of compressed version of Guernica – whose dual models in Poussin and David are not painterly in style. Having gone further here than ever before into the post-Renaissance tradition, Picasso soon turned his back on it to work, more characteristically, in a pre-Giottesque tradition.

If his painting of the period preceding his late style is its antithesis, his sculpture of that period can be seen as something of a preparation for it, in so far as it was dealing – both in the mainly wood constructions of 1954-58 and in, what evolved from them, the sheet-metal pieces of 1961-62, his final sculptures – in forms that are at once large and dynamic, at once grand and comic: in other words, they anticipate paintings such as the Woman Pissing. Which is to speak as if they were not in themselves a body of work which is one of Picasso’s greatest post-war achievements. Indeed, the absence from the exhibition of the over-life-size group of Bathers made from bits of wood in 1957 is surely its most serious deficiency. And yet, they might have been redundant, given the commanding, enigmatic presence and the sculptural virtuosity of the light-hearted little Head of Woman, a project for a monument realised in polychromed wood in 1957. It is an object lesson in what it is to be an unassuming masterpiece and in what it is to be a totally three-dimensional sculpture. It is a head in the round composed of a succession of profiles. It consists of two squarish boards intersecting at right angles and stuck into a cylinder representing the neck; behind the point of intersection, one board is deflected by 30 degrees; the colours are black, white, touches of grey, and the natural colour of the wood. It must be one of the few sculptures in the world every aspect of which – there are essentially eight aspects, each at a point of the compass – presents a view which works and a view which is totally unexpected, with a power to surprise that does not diminish after a hundred encounters. It is the sort of piece which establishes that, while it may be open to question whether Picasso is this century’s greatest painter, he is undoubtedly its greatest sculptor.

The late style surely emerges in October 1964 with works such as the two large paintings of The Artist and his Model dated 25 October and 26 October/3 November, two of the numerous pictures in a series on that theme which had started early in 1963 and two of many in which painting the model means just that rather than doing a painting of her. The new style did not come as a clean break with the past: the large and highly complex Artist and his Model dated 16 November and 9 December 1964 is retrospective in style. But the decisiveness of the break is very clear when The Sleepers of 13 April 1965 – naked woman and black-suited bearded gent napping together on the grass – is compared with the Déjeuner sur l’Herbe series of which iconographically it is an obvious extension. If the unique and astonishing style of the late paintings, with their cursory facture, their uncompromising immediacy, the boldness of their slangy language and the boldness of their Byzantine frontality, is to be characterised by a phrase, I would single out a remark made by John Cage as he went round the exhibition, that he was struck by ‘the absence of tranquillity in a centred composition’.

The late paintings seem to me to be divisible into three phases of unequal length – a head, a body and a short tail. The first phase lasted until the illness which in November 1965 compelled Picasso to undergo major surgery. The paintings are mostly of nude women, nude couples, artist and model. They are painted like enormous water-colours, with their areas of transparent colour and areas of emptiness. They have an astonishing radiance and elation and sense of release. But that sense of release seems to have to do with painting itself, with being able to let go, with no longer caring. It is not like the gaiety about life of the 1956 Nude in front of a Garden; it is not relaxed, not even in the hymn to that goddess of irrigation, the Woman Pissing. Every important picture of the period is comical and is rather frantic in its comedy and sometimes rather bitter.

Picasso’s resumption of painting in 1967 initiated the second phase. Suddenly, the iconography is dominated by the fancy dress of musketeers, dwarfs, smokers of pipes and so forth, though that is not evident in the present exhibition because the curators have exercised a marked bias away from these pieces and in favour of female nudes and of couples supping, kissing or fucking. The eroticism is forthright and violent. The sense of doing it is there, vividly, electrically, but not much sense of touch. The sensuousness of flesh which is so intensely present, for all the summariness of the style, in the nudes of April 1960 and survives in the Woman Pissing, has evaporated, except on rare occasions – above all, in the Woman with a Pillow of 1969.

Around the middle of 1970 the range of mood seems to narrow, becomes more consistently uneasy, menacing, feverish, melancholic, brooding upon the imminence of death. Sometimes this is symbolised by the intrusion of skull-like forms, as in The Embrace of 26 September 1970, or nightmarish forms, as in the Reclining Nude of 14 and 15 November 1971; sometimes it is directly illustrated, as in the Nude Man and Woman of 18 August 1971. The composition, with the old man filling the centre foreground and staring out of the picture, strongly recalls – and it is difficult to believe that Picasso was not recalling it – the First Steps of 21 May 1943, with the toddler where the man is and the woman again placed to one side of the background. But in the old man’s face fear in the face of the unknown has been replaced by the blankness of acceptance, while here the woman is no longer using her hands to help but only to try and comfort as she reaches out to touch the man on the shoulder and he seems oblivious to this contact. A friend recently widowed told me that the woman’s gesture reminded her of how, when she herself made a similar gesture some days before her husband’s death, he responded in a way that made it clear he was beyond wanting any human contact. It was as if he was with the dead.

Death’s nearness nonetheless brought no radical change of language in Picasso’s painting until it had only a few months to go. I suggest in the catalogue that he had a very brief final phase whose most distinguishing feature is an uncanny, swimmy sort of atmosphere which seems to have to do with loss and departure and floating away. I cite four examples – three very late works, Landscape, 31 March 1972, Reclining Nude and Head, 25 May 1972, The Embrace, 1 June 1972, and one painted six months earlier, Reclining Nude, 7 September 1971 – and at the Tate these were brought together in the final room in the hope that they would make sense visually as a group. They clearly did, and the next step was to see whether there were any other paintings that seemed to belong with them. It turned out that there was one, probably because of its fluidity of form and its close affinity to the Landscape: the Musician of 26 May 1972. The room’s five paintings certainly do exemplify a final style of which there are surely some further examples.

The room is dominated by the amazing Reclining Nude and Head, which besides being a very great painting is also a very enigmatic one, most atypically of Picasso, for whom it was a point of honour to make his subject-matter clear. John Richardson, the first writer to insist on the primacy of this painting among late Picassos, affirms that the central structure, ‘two huge eyes balanced on a wedge of a nose, balanced on a tiny mouth, balanced in turn on a rudimentary vagina ... unquestionably stands for Jacqueline’, and sees the horizontal structure with its ‘vestigial arms and legs and nipples’ as a recumbent figure but also, following Jacqueline’s interpretation, as a coffin emblazoned with a cross. I would like to advance a suggestion, since the recumbent figure’s torso is surely male, that the work is a Pieta. Oddly enough, the thought did not occur to me when, shortly after the exhibition was set up, I was in Venice looking at the late Titian Pieta and thinking how the luminous heavy globules of paint in the background resembled Picasso’s use in this picture of thick white paint to make a blinding light. It was the following day, the moment I saw the Picasso again, that the penny dropped. The coin could easily be a dud. But perhaps not.

Jacqueline’s central and totemic position in this icon as tragic queen, figurehead, sustainer, self-exposer, survivor, is an allegory of her having played, on the evidence of her appearances in the works, a more comprehensive role in Picasso’s life than any of his other women, not least because she was part of that life for nearly twenty years, was there when it came to an end – more crucially, even, was there throughout the terrible passage from his being an old man who had retained his youth to being a non-man. Picasso probably didn’t become a truly great erotic artist, one who transcends stereotypes and arrives at objectifying his own particular experience, until he started composing his celebrations of the joys of making love to Marie-Thérèse Walter. He was then 45, so that all his great erotic art came out of relationships between an ageing man and a young woman. Until Jacqueline’s advent the emotional range of those relationships, as shown in the art, tends to be fairly narrow: the swooning raptures of Marie Thérèse, Dora Maar as Tragic Muse, Françoise Gilot, pastoral deity.

The relationship with Jacqueline is wider and richer and more human, especially in its exchanges of vulnerability. For instance, in the time of his impotence he has to humiliate her in his art as he had no one else, and there are drawings in which it looks as if the humiliation was more than a fantasy – drawings, which do look as if done from life, of her using her fingers to open up her genitals for display as in a hard-porn close-up. The sense of complicity between them recalls, in its total transcendence of shame, the erotic correspondence in 1909 between James and Nora Joyce. Joyce, as Richard Ellmann puts it, ‘wishes to possess his wife’s soul, and have her possess him, in utter nakedness. To know someone else beyond love and hate, beyond vanity and remorse, beyond human possibility almost, is his extravagant desire.’ Picasso, in contrast, insists – so many stories confirm it – on a certain distance. Ever the actor-dramatist, he needs to be in control, needs an asymmetrical relationship – father and offspring, god and mortal, artist and model (that perennial theme which for him was the most flexible of metaphors and also only a metaphor, since in reality he hardly ever painted from the model). Above all, Pygmalion and Galatea, the myth implicit in those images of the artist painting the model’s body, painting her into existence. And in creating her image, his interest is not in telling what it may feel like to be her, only in telling what it feels like to have her. The complicity there is between him and her is surely less than the complicity, often at her expense, between him and himself, between himself as artist and as audience.