At 87, he ought to be slowing down a bit. His voice, he says, is weaker, and his mobility isn't what it was (he went round the Cezanne exhibition in a wheelchair). But intellectually he hasn't slackened off. Last year he curated an exhibition, on the theme of shadows, for the National Gallery. Next month, he will lecture in Italy. For some years he's been involved in a large collaborative venture with the American animal painter Stanley Meltzoff ("I fear we've taken on too much, nothing less than the why and how of rendering visual reality in paint"), and he is also trying to finish a long-gestating book on primitivism. He works most days: "If I didn't, I'd get bored."
In his Hampstead home, dressed in a tweed jacket and Reebok trainers, Gombrich seems caught between two worlds: the old Vienna of his parents (Mahler, Bruckner and Hugo von Hofmannsthal were acquaintances of theirs) and the London of his grandchildren. He came here 60 years ago, before the Anschluss, to work for the Warburg Institute, which had also moved to London to escape Nazism (it was founded in Hamburg). It was a job which brought him into stimulating contact with other Jewish intellectual refugees. But he also had a new wife and young son to support, and the job was not especially well-paid. He solved this problem after the war, which he spent monitoring German radio broadcasts, by writing The Story of Art.
How The Story came into being is itself a famous story. In his twenties, in Vienna, Gombrich had written a world history for children. It took him only a few weeks, and proved an unexpected success. The same publisher suggested a follow-up, on the history of art. Gombrich didn't see how he could write such a book for children. But later he thought it might be possible for an older audience, teenagers and up: "In German-speaking countries, there were many single-volume histories of art. But in England I was aware of only one. I didn't have a particular reader in mind when I wrote the book - though my own son was 13 when it came out. It proved popular with students, partly because it was so inexpensive, but I never conceived it as a textbook - I'd taken trouble to avoid jargon, and I didn't like the idea of students using the book for swotting or having art rammed down their throats."
Commercially, The Story of Art has been an astonishing success (translated into 23 languages, it's now in its 16th edition). Academically, it has become unfashionable. The complaints are predictable: that Gombrich fails to get the measure of present-day art, ignores women painters, is Eurocentric and elitist. On the last charge, he is unapologetic. "I don't believe in elitism in politics, but in sport surely everyone believes in it and I don't see why it can't be accepted in art, too. Alfred Brendel is simply a better pianist than most others. Not everyone can do what a genius can, and not everyone can produce a masterpiece even after long training."
Though Gombrich believes in values (that art can embody human attributes such as tact, dignity and grace) and in value judgments (that Rembrandt is superior to tribal art), he is far from snooty or austere. He has always had a taste for the playful: for tricks of perspective, jokes, puns. And as The Essential Gombrich demonstrates, he is also fascinated by various forms of popular or "low" art, not least cartoons: "They too can be done well or badly, can be trivial or inspired. They demand a different approach from the art historian than does Tintoretto. But they give great pleasure. I do think that certain kinds of commercial art - posters, say, or the work of Saul Steinberg - are more creative in our own time than studio art. The same is true of photography. And even advertising."
Gombrich's lack of interest in modern art has also been exaggerated. When I ask him which 20th-century artists have meant most to him, aside from Picasso, he mentions Paul Klee ("so inventive and unpretentious"), Magritte and Morandi; among contemporaries, Bridget Riley, Anthony Gormley and Lucian Freud ("a marvellous craftsman: I admire him enormously - but who wouldn't?"). Undeniably, though, Gombrich's ideas, and taste, were formed in turn-of-the-century Vienna: "I have a certain kind of prejudice, not against contemporary art, but against the kind of theory taught in art schools. Young artists are being inducted in an ideology both of self-expression and of what Karl Popper [a friend] called historicism. Everything's based on the idea of doing something new, and attracting attention, and of the media making you famous for a day or sometimes a little longer.
"I wouldn't say I have no feeling or interest in the modern situation, but I do think it's a tragic one. Since the conquest of reality by photography, art has become very difficult. Art schools still promote the idea that you have to fight against the bourgeoisie, or the Academy. But it seems a phantom fight now, just shadow boxing."
Gombrich says this sadly rather than cantankerously, and adds: "You have to remember I am also old, and it isn't so easy for me to get to galleries. I may have missed the point of contemporary art. Possibly I do. Probably I do. But the rejoinder 'You don't understand' isn't good enough. Sometimes you do understand, and still don't like it." What about Damien Hirst and co? "Pyrotechnics, that was an early example of installation art, wasn't it? - but not quite on the same level as Michelangelo."
Does he feel that the kind of audience for whom he wrote The Story of Art in 1950 no longer exists? "To my great surprise, that's not the case. Think of the incredible success of exhibitions like Vermeer, Monet, Frans Hals and Cezanne, or of how Florence is having to consider closing its doors. There is still a great desire to know about the art of the past. It may be a reaction. It may be that stories of high prices paid for art have had an influence. It may be a kind of short cut - it's easier to take in a painting quickly than to read a Shakespeare play. But cultural tourism or not, it is a fact."
Gombrich has certainly helped influence how people look at paintings. He is a sceptic and a demystifier. He draws on the discoveries of both science and psychology. He can be sharply opinionated, as when he dissects the modern "regressive" Western taste for child art and the primitive. He likes to treat art, not as self-expression, but as coming out of recognisable traditions and using discussable techniques. Yet he also acknowledges "the limit to what we can explain. With the Velzquez portrait of Pope Innocent X currently on show at the National Gallery, part of me just wants to say it's a masterpiece and fall silent."
Though he has spent his life among paintings, he isn't a collector: "I've never had enough money, and I don't have the possessive instinct. My model in this is music: you can't own Beethoven's Ninth, only the CD of it." Forced to choose between the different art forms for a desert island, it's music he would take: "I could survive without paintings and books, perhaps, but not without Haydn's string quartets." As a young man, he wrote poetry - "Who doesn't?" - but he has never painted. "At university, we tried to learn what was involved in holding a brush and palette. It was instructive. But I never wanted to be an artist."
Though uneasy that the title The Essential Gombrich will seem immodest, Gombrich is pleased that the collection exists, if only to correct the impression that he's a one- or two-book man: "Someone once said to me at a party, 'I own your book'. I wanted to say, 'Which one?' " In fact, he has published some 14 books, including a major study of the decorative arts (The Sense of Order), a biography of Aby Warburg, and four volumes of essays on his special subject, the Renaissance. Still busily reading others' books, too, he shows me, as I leave, a study of the Chauvet cave paintings - here a bison, there a horse - and murmurs approvingly about the subtle lines and colours. "Think of it: 15,000 years before Lascaux, 30,000 years before our own era. It's astonishing. It really shouldn't exist. One can only marvel."
Gombrich has been marvelling at art for as long as anyone can remember. May he go on a good few years more.
'The Essential Gombrich', ed Richard Woodfield, is published by Phaidon, at pounds 29.99 (pounds 19.99 paperback), on Thurs.Reuse content