To put it plainly: Moma, to give it the acronym by which it is always known, made modern art mandatory in America. It did this not only by collecting it, showing it, moving big money into place behind it and evangelising for it, but by setting the prime example whereby, in the US, the function of the museum shifted from accumulation to teaching. This came to apply to almost all museums, not just those dedicated to a hitherto enigmatic or marginal "modernism".

In the process it spawned lots of younger museums given over to "modern art" - roughly, art since about 1890. But although many of these are powerful in their own cities and countries, and some are actually better-endowed than the original, for sheer cachet nothing beats having your name as a Moma benefactor somewhere near (though necessarily below) those of Blanchette, David or Nelson Rockefeller. Moma - a deliciously Oedipal acronym! - will never escape the scent of big-mother power, not so long as there is an art world in Manhattan.

Still less will the museum ever be forgiven its prominence, especially by artists who are not represented in its collections. It is and has been for decades a vastly influential place, and its assembly has been the work of many hands over three-quarters of a century: directors such as Rene D'Harnoncourt, senior curators such as William Rubin and (until his tragically early recent death from cancer) Kirk Varnedoe, and so on. A lot of singularly gifted and original minds (together with quite a few that were less so) have worked for Moma across the years. But originally, and in its essence, it was the brainchild of one man, an American, Alfred Hamilton Barr (1902-81).

In fact, Barr's role in creating Moma, and working as its first director from 1929, the year its doors opened, to 1967, when he retired, was so fundamental to the direction that art-appreciation in America would take that thinking about him is a little like looking back on the career of a Henry Ford or a Thomas Edison. His work, in terms of museum practice and art education, was that basic. There was American visual culture before Barr's career, but it was nothing like what came during and after it. And the instrument of change, the megaphone of newness in the cultural sphere, and the means by which the new art was shown to be not just a weird, disjointed and rebellious episode in culture but a new and very serious canon, was Moma.

Is there anyone alive with adult, first-hand memories of how modern art was viewed by Americans in 1929? Few, if any; it was too long ago. It's easy to be misled by the buildings. America was filled with a myth of newness that came fairly blasting out of the great structures that were beginning to fill Manhattan - the whole ethos of the skyscraper, of vibrant monumental Deco, of Raymond Hood (Rockefeller Center) and William van Alen (Chrysler Building) and Donald Deskey (Radio City). The general public found these things unconditionally thrilling: their height and size and dominating oomph were symbols of American prometheanism, an antidote to the miseries of the depression.

But who was going to feel that about equally modernist paintings or sculptures? Practically no one, that's who. Their newness was merely puzzling or alienating; the great museums that were developing didn't want to make space for them, and the small ones had little or no clout. Basically, the only new Amercian art that Americans liked was "regionalism" - the narratives of an idealised or somewhat cornily heroic America, mostly set in the big acreage west of New York, done by Thomas Hart Benton and Grant Wood. So one had to begin the campaign of evangelising from scratch, more or less, and that was where Barr - the son of a clergyman, fittingly enough - came in.

Moma began collecting in an almost incredibly favourable environment. Barr in the 30s was like a big-game hunter alone on the African veldt, surrounded by walking trophies in vast supply. The idea that anyone could, so to speak, just walk into a shop or an artist's studio and buy (relatively) cheap works of art that turned into historical masterpieces, things of the order of Picasso's Demoiselles d'Avignon, major Matisses, Leger's Three Women, great Russian Constructivist canvases and other sublime etceteras, is a lost dream today. Barr, however, could and did. It was as though someone from an older encyclopedic museum - the Metropolitan, say - had been given a time machine on which he could zip back to the Roman cinquecento or the siglo d'oro in Madrid, and start hoovering. Nobody except private collectors in Europe and the States, and not too many of them, wanted this stuff. Modern art wasn't museum art until Barr, that beaky, wren-like man in his faintly absurd yurt of an overcoat, made of a felt-like cloth so thick that you could almost prop it in the corner instead of hanging it up, came along.

And it wasn't just art he wanted. Barr was at heart a pedagogue. Earlier museums had begun as repositories of royal or ducal treasures, or as holding-places for imperial loot. America had no such tradition. To Barr, a work of art was crystallised knowledge - of itself, of the style in which it was embedded, of the ideas around it. This is another of the aspects of museum philosophy that we accept as though it had always been in place - but its strongest point of origin was early Moma. Even the longish informative label (now largely abandoned) was a teaching-aid of Barr's, not used until much later by older museums.

Probably the crucial inspiration in his development of museum-craft was a visit he made to the Bauhaus in Dessau. Ultimately this set the pattern whereby Moma viewed all visual culture, all artifacts made or imagined, as a totality. Not just paintings and sculpture, prints and drawings (and architecture, necessarily), but also typography, theater, still photography, film, industrial design (Moma was the first museum with floor lamps, phones, Bauhaus chairs and a real car in it) and every kind of mass-produced object whose industrial essence went counter to the fine-handiwork rubric under which utilitarian objects had previously been admitted to museums - a desk being OK if it was by Reisener in the 18th century, but non-OK if it had been made by the thousand in a European factory, like the designs of Thonet. Without saying so, Moma set out to turn into the antithesis of William Morris's messianic and delightful belief in the supremacy of the shaping hand. It would celebrate the shaping machine, the template, the big production run. And also, of course, the singular Hand as well. Moma came out wanting everything and its opposite. All were parts in the great symphony of a new culture, the total Gesamtkunstwerk (phew) whose very existence proved the uniqueness of Modernity.

This meant promoting tolerance, not only between the public and the art, but between the various factions, movements and splinters of the wide Modernist enterprise. Though a missionary endeavour, Moma could not preach too narrow a set of doctrines. Picabia may have hated Cezanne, but Moma needed both. And yet there were self-evident biases. Barr's great loves were the School of Paris, from Cezanne on to Giacometti; German Weimar culture, especially the Bauhaus; Russian Constructivism; and Surrealism. (His 1936 show of Fantastic Art, Dada and Surrealism was one of the most influential exhibitions ever mounted by a museum; likewise, the epochal Modern Architecture: International Exhibition, 1932, curated by Henry-Russell Hitchcock and the young prodigy Philip Johnson, changed the course of American building.) Barr was always a bit sceptical of the claims that the New York School had surpassed the School of Paris, but there can be no question that Moma was one of the prime factors in the transfer of market and curatorial power from the Seine's banks to the Hudson's. Well before Barr yielded his director's chair to others, Moma had become the Kremlin of late modernism.

Moma didn't like Pop Art, at least not at first, so that with the exception of Andy Warhol's Gold Marilyn - which even those who despise most Warhols, myself included, concede to be a masterpiece - it is short in that area. It has been badly neglectful of serious depictive art, and this left it woefully short on the great figures in modern British painting from Walter Sickert on, such as Frank Auerbach or Lucian Freud: Rubin couldn't bring himself to think of Freud as a "modern artist" at all, even though he, unlike so many of the figures on Moma's walls, was alive.