Irreverent jokes can be made about it that would have no point if people did not recognise this nightmare-like image of anguish. On my mantelpiece I have an undulating, blow-up rubber Scream, which the Artists' Rights Society has been trying to get suppressed on behalf of Munch's heirs. It should not be so pompous. It is quite funny and no worse than the back- handed tribute paid by Duchamp to the Mona Lisa when he painted a moustache on her in the Twenties.
Of course, millions more people see the Mona Lisa every year than see The Scream (4.7 million at the Louvre last year, as against 300,000 at the National Gallery in Oslo).
The Mona Lisa has been given today's accolade of fame: bullet-proof protection against the kind of lunatic who will try to destroy any celebrity, whether it be John Lennon or Michelangelo's Pieta. The Louvre has discovered that nearly everyone who goes there wants to see this picture, and package tours charge like bison down the Grande Galerie to stand six-deep in front of the thick glass obscuring this small picture with its treacly varnish.
The Japanese, who are brand snobs, as well as being admirers of all things French, are paying for her to be redisplayed with better lighting in a room of her own.
But the Louvre dares not clean off the yellowed varnish. The world has got used to this tobacco-tinted face and landscape, they say, but they also fear the brickbats of the do-not-touch-a-masterpiece lobby. These zealots tend to think, wrongly, that the more famous a work of art, the more difficult its conservation.
So the Mona Lisa has a big problem. She is almost invisible and is likely to remain so. There is an exquisite, magical, blue landscape of mountains and rivers behind her, but who has seen it now for decades, apart from a handful of privileged scholars?
Why do we go to look at this old-fashioned looking woman with her famous smile? Has she not become a little like Liz Hurley - famous for being famous - rather than for the deeply meaningful experience we get from looking at her?
Her super-star status is really a invention of the 19th century, when the Renaissance, of which she is a product, was a period which everyone knew well and identified with. She was seen to be at the top of a chain of excellence which went something like this: Italy is the most artistic nation in the world; the Renaissance is the most glorious period of Italian art; Leonardo is one of, if not the, most glorious Renaissance artist and the Mona Lisa is his most ineffably mysterious and romantic work-therefore, the Mona Lisa is the greatest painting in the world.
She became the centre-piece of one of the world's greatest museums, and as the English mademoiselle gazed upon her, she knew what to think because Walter Pater had devoted many poetic passages to describing the effect that Leonardo's paintings had on him.
Finally, the Mona Lisa was crowned by the thrill of infamy when it was briefly stolen at the beginning of this century.
So that is what lies behind the postcards, chocolate boxes, scarves, ads, tea-trays and other flimflam that bears the Mona Lisa's image and brings the tourists from the Osaka to venerate at its shrine.
But quite apart from the cultural gap which separates us from her, we have great difficulty in "seeing" her with our intelligence and emotions. Over-exposure makes us artistically deaf and blind. She is like Vivaldi's Four Seasons, overheard down the telephone and in lifts; can we ever listen to that music properly again
It is not surprising that the Mona Lisa is being overtaken in the fame stakes. The Scream is stronger meat: anguished and tormented for a century that sees itself as anguished (although it is actually a work of 1893).
Painterly, but not finicky, for an age that does not look for craftsmanship. Strident, not to say melodramatic, for eyes used to instant effect. Nightmare-like for a quick, enjoyable shiver, and cartoon-like for the screen-age.
It has become famous quite independent of its origins (how many people can call to mind another picture by Munch or know anything about fin-de- siecle Norway?) through the sheer strength of the image reproduced again and again in art books. (Van Gogh's Sunflowers became the most famous Impressionist painting in Japan because one standard school textbook illustrated it as a typical work, and so everyone knew it.)
And then The Scream also had the good fortune to be stolen, on the night the1994 winter Olympics started in Norway. The painting was found six months later, but in the meantime it had enjoyed plenty of free publicity.
The museum in Oslo, like most good museums today, has a professional approach to marketing and is obviously flying a kite with its claim for the The Scream. But it is probably right that more people identify with it than with the Mona Lisa.
A footnote: why did we get her name so wrong"? In Italy, she is called La Gioconda ("The Smiling One"), never Mona Lisa. Our version of the name should be "Monna", the contraction of "Madonna" (my lady). "Mona", as every Italian knows, is dialect for the female private parts.
Anna Somers Cocks, a former keeper of the Victoria & Albert Museum, is editor of `The Art Newspaper'