Picasso is the greatest modern artist. The market says so, and the British Museum agrees.

This week a Picasso was sold at Sotheby’s for £28.5m. In the same week, an exhibition opens at the British Museum in which an ice age carving is sanctified by the simple fact that Picasso admired it – a photograph showing replicas that he owned is shown next to it, as proof this must be art. Picasso has become for us an almost religious icon of imagination, originality, genius.

Let’s give ourselves a pat on the back: we’ve got good taste. Picasso completely deserves his divine status as the god of art. Recently I looked again, in Tate Modern, at his luxuriantly erotic Nude, Green Leaves and Bust, painted in 1932. It swept me away. The baroque curves and nocturnal colours of this painting tear open the curtains of desire. When it was first shown at Tate Modern, after setting a record as the world’s most expensive painting, the price got in my eyes. Now that seems irrelevant. It’s just a marvellous work of art.

The price gets in the way right now when we look at Woman Seated at a Window, the latest Picasso to fetch a stratospheric sum. But setting the madness of the art market aside, it is another magnificent work from the same period, indeed the same year: 1932, when Picasso was in love and when, as an artist, he was exploring surrealism in his own unique way.

Near to Picasso’s Nude, Green Leaves and Bust at Tate Modern is a nude by Matisse. The Matisse is a solid bronze sculpture, while Picasso’s work is a flat picture on canvas. Yet it is the Matisse that seems two-dimensional next to the Picasso: there are simply more perceptual and imaginative layers, contradictions, tensions in the art of Picasso. Any comparison between them, for me, leaves Matisse looking like the world’s greatest wallpaper designer.

I am glad to say the world has caught up with that opinion. The exhibition Matisse Picasso in 2002 was, it turns out, the last time they would be seen by our culture as equals (with Matisse’s name first). In our fast-moving, contested and dangerous century, we look to Picasso’s fast-moving, contested and dangerous genius.

Matisse fans live in Hampstead and have read everything Hilary Mantel has ever written. Picasso fans pay bonkers sums for provocatively sensual paintings. Matisse is a delicate choice, Picasso an addiction.

As for the other touted modern genius, Duchamp … don’t get me started. Just compare that overrated loo with Picasso’s bicycle-seat bull. When he created Bull’s Head in 1942 by adding a bike’s handlebars to its seat so they became horns, Picasso put Duchamp in his place. This is the 20th century’s greatest readymade, Picasso its supreme creative figure.