In Amsterdam I once had a “steak Picasso” in a restaurant. It was a steak surrounded by diced fruit and vegetables of many colours. That caught neatly what is still a widespread view of Picasso – the painter who chopped up the world and presented it as an amazing new dish for the eye.

The new Picasso exhibition at the National Gallery, Picasso: Challenging The Past, to some degree supports that view. It is supposed to show one aspect of Picasso’s work: the way in which he took the art of the past and reshaped it in his own fantastic, bull-in-a-china shop fashion. (There exist many portraits by him – one of them in the exhibition – showing himself as a crazy-looking bull.)

However, this show is not quite the same as a similar one held last autumn in Paris. It does not set Picasso’s pictures directly alongside the great works, such as Velázquez’s The Maids of Honour, of which Picasso painted his own versions. Instead, it illustrates such works in the free brochure you get when you go in, and indicates where you can go and see them.

Also, this exhibition displays many pictures that are not direct variations on earlier works, but which simply show what Picasso did in various established genres, such as still lifes, or the nude portrait.

So it offers a good selection from many phases in Picasso’s long and incredibly energetic career.

It was only in about 1907, when he was 26, that he gave up naturalistic painting and began producing what we think of as typical Picassos. This show includes one or two lovely paintings from the earlier period – tender, delicate portraits of women he met among the circus people with whom he was friendly at the beginning of the century. They give no idea of what was to follow.

But then like a thunderclap come the “distortions”, which continue in one form or another for the rest of his life. Picasso from this time on was experimenting with new ways of portraying people.

He showed the front view and the side view of a head jammed together so that you could look at them simultaneously. He moved eyes and noses and ears all over the face. He simplified the naked bodies of his lovers into soft amd voluptuous coloured circles.

There are two oil paintings here of a man in a straw hat, one from 1938, one from 1971. In the earlier one, the big hat looks as if it is made of strings of yellow light, one eye is higher than the other and both gleam with strange excitement as they gaze in different directions, the face is blue, the hair and unshaven bristles are like rubies, and the man holds an ice-cream cone like a spanner in his pudgy fingers.

He has a chaotic kind of grandeur. In the other picture the yellow straw hat is like a wildly tossing sea, the eyes look crazed, and all the more so because they are of different sizes, and the yellow nose is out of place in a way that suggests the man’s mind is equally out of place.

The two pictures show Picasso’s extraordinary virtuosity in dealing with basically the same subject. But what is lacking in them is any human feeling – apart from one. And that is a grim sense of humour about the astonishingly different objects that a human being can turn into.

In fact, I think that much of Picasso’s later work can best be seen as comic. It is the spirit of comedy that his “distortions” – or perhaps what we should rather call his inventions – serve best.

There are many pictures here of nudes, mainly pictures of his wives and lovers. These were the subjects with which he was most obsessed. But even here, though the humour is gentle, I feel it is always present. The women may have magnificently rounded bodies, and splendidly independent eyes that see all round them – but in a remarkable number of the pictures their feet are disturbingly large.

The main hall of the gallery is devoted to three specific masterpieces, and one classical theme, the Rape of the Sabines, on which Picasso played many variations in the late 1950s and early 1960s. Picasso showed his unfailing virtuosity here, in the heart of this exhibition – but he turned all the pictures into horrors.

In his versions of Manet’s mysterious and charming picture, Lunch on the Grass, he turns the nude women into greasy white, slug-like forms with drooping caterpillar heads. In his variations on Delacroix’s famously High Romantic painting, Women of Algiers, one woman looks like a rat on webbed feet, another like a sharp-edged piece of mechanism with breasts and bottom. In Picasso’s Maids of Honour, the royal mastiff becomes a featureless outline of a dachsund.

In these pictures, Picasso seems to be exploding with jealousy and hatred. Yet even here he remains himself – and you can detect a trace of humour somewhere in his soul. Only now, with the artist in his seventies, it has become very black humour indeed.

www.nationalgallery.org.uk