I was at the auction of modern art at Christie's a couple of weeks ago, and when two strong men lifted Picasso's Buste d'homme on to the easel for the audience to see, I could not help bursting into laughter.

That single eye like a telescope looking out of the forehead, the nostril high on the side of his tent-like nose and the brim of his hat like two large, flapping mouse ears were irresistibly comic. Someone paid £1,300,000 for the painting, so I hope he laughed too.

It was a feeling I have often had when going round art fairs where nowadays so many of Picasso's etchings and drawings are on sale. I find myself laughing with pleasure at them - the prancing satyrs with noses like set squares, the bathing girls ricocheting about, with their monstrous bosoms and eyes all over the place, the Jupiter with a neck like a giraffe who is holding his penis like a thunderbolt... I think you have to see Picasso as a great comic artist.

And now when I look at the Demoiselles d'Avignon of 1907, I see it for what I believe it really is - a bunch of battered old tarts, with a pretty one at the side to sharpen the contrast. Art historians say this painting marked the moment when Picasso “resolved the problem of defining volume without destroying the flat surface of the picture”.

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But why was he doing that? He was not just some technical buff, he was an artist painting people - and in this way, through square breasts, flattened faces with eyes glaring out of the wrong part of them, hands popping up where they could not logically be, he brought out the sad comedy of these women's lives. New styles are not for the sake of new styles. They serve a new human purpose, and Picasso had one here.

He started as a realistic, romantic painter. But he was to become a master of all kinds of comedy - witty comedy, wild comedy, cruel comedy, black comedy, sad comedy and the purest wit and jest.

But what, one might ask, of Guernica - that historic evocation of the bombing of a small town in the Spanish Civil War. Surely that is not a comic picture? Clearly it is not. But I have never been much struck by Guernica as a picture. I think that it gripped the world more because of the horror of the event itself than because of the merits of the painting. Compared with Goya's terrifying images of war, it makes scarcely any impact at all nowadays. I see it as an heroic attempt by Picasso to adapt his newly invented, essentially comic forms to a noble cause - but, in the long term, an unsuccessful one.

The extent of comedy in modern art to my mind goes much wider. At Sotheby's last year there were, side by side, a Giacometti sculpture of three stick-like men, a pierrot by Egon Schiele and a head of a woman by Picasso. You might have thought the three of them had a competition to try to make the funniest possible distortion of the human body without losing its essential features.

Comedy pervades the work of so many 20th-century artists that I think it will eventually be seen as the Age of Comedy in art, rather as the 18th century can now be seen as the Age of Comedy in English literature.

This spills over into contemporary art, defined roughly as art since 1960 until now. Many installation artists still look on Marcel Duchamp, the Dadaist who drew a moustache on the Mona Lisa, as their great leader - and that was 90 years ago.

At the Art Basle-Miami fair I saw an installation called Travel which consisted mainly of the young woman artist popping in and out of a great suitcase. At Charles Saatchi's opening show in his new gallery, by far the favourite work was the collection of aged statesmen colliding with each other in their wheelchairs, as if they were in bumper cars on a fairground. What was that but a newspaper cartoon in three dimensions?

If you are tempted to go to the blockbuster exhibition Picasso: Challenging the Past at the National Gallery, which shows his versions of some of the great pictures of the past beside the originals, bear in mind this way of looking at them. Many people are still baffled or outraged by his reconstructions of the human body. Others hail them with great solemnity as demolition jobs on false ways of seeing and feeling.

But I think that Picasso was always laughing inside, and always wanted to provoke laughter. It might be tender laughter, it might be satirical laughter, it might be bitter laughter. A demented, self-mocking laughter swirls round some of his own late versions of dwarves or meninas. But the comic spirit is never far away.

Picasso: Challenging the Past is at the National Gallery from Wednesday

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