Alice Tully Hall at Lincoln Center, which closed in May for a major makeover by the architects Diller Scofidio + Renfro, is scheduled to reopen toward the end of next year. The renovation marks the first in a series of “interventions,” as architects like to say, which will update and upgrade the cultural center without destroying its principal buildings or overall distinctiveness. The next phase will address what’s always been the center’s greatest shortcoming: the plaza entry from Columbus Avenue. A grade separation of automotive and pedestrian traffic, among other enhancements, should eliminate the complicated and dispiriting process of getting into Lincoln Center. Both on 65th Street and at the plaza entry, Lincoln Center and its architects seek to weave the center into the fabric of surrounding streets. Expect a lot of commotion for the next few years.

They’re taking the right approach. Lincoln Center has embedded itself in New Yorkers’ minds as an icon of their city. Yet its functional shortcomings, and its physical aloofness, have been manifest since the place opened in the 1960s. In the 1990s, when talk of the center’s physical deterioration got much press, and ideas of what to do about it poured in from all quarters, we faced the very real possibility that the whole thing might be torn down and replaced. That won’t happen — and that’s good.

In 1961, Jane Jacobs castigated the idea of Lincoln Center. She said that each of its occupants — the Metropolitan Opera, the New York Philharmonic, the New York City Ballet, and others — could bring new life to a different part of the city. She also hated the “superblock” planning mentality that reigned over the Lincoln Square urban renewal project, the idea of supplanting mapped streets with campuses of buildings. Of such superblocks, she said, good city neighborhoods cannot be made.

The crossing of Broadway with Columbus Avenue (also known as Ninth Avenue) resulted, according to Manhattan’s gridiron street plan, in “Lincoln Square.” Its name, as with Times Square, came to cover the surrounding neighborhood. Lincoln Square bore much in common with Hell’s Kitchen to its immediate south. These were tough, working-class neighborhoods where people lived in block after block of tenements. The city called Lincoln Square a “slum,” and in came the master builder, Robert Moses, to work his renewal charms. Planning people used to use the phrase “scorched earth” to describe such wholesale neighborhood transformations, where virtually everything old yielded to the new. Today, few vestiges of old Lincoln Square remain — even the name is seldom spoken anymore.

From 59th to 70th streets, between Broadway and the Hudson River, Moses and others built the New York Coliseum and Coliseum Park Apartments, the Amsterdam Houses, Lincoln Center, and Lincoln Towers. The last — the gigantic middle-income housing project stretching between 68th and 70th streets west of Amsterdam Avenue — rose on the site of tenements that, between their condemnation and their demolition, served as sets for the film version of “West Side Story” (1961), which gives a pretty vivid picture of the old Lincoln Square.

Moses conceived of Lincoln Center in the 1950s. The planets surely aligned. The Metropolitan Opera Company had been striving to get out of its garment district home since the 1920s. The Philharmonic feared that its home, Carnegie Hall, was going to be torn down. And the New York City Ballet, which had become one of the most glittering cultural attractions of the city, felt it deserved a facility tailored to its needs, which the company lacked at City Center. Also, Fordham University, which signed on to the project before anyone else, desperately needed to reconfigure its scattered Manhattan operations.

Moses conceived but did not shepherd Lincoln Center, yielding in that capacity to John D. Rockefeller III, whose interests lay less in the arts than in foreign affairs. And therein lay the motive force for Manhattan’s cultural center. At the end of World War II, New York became the de facto capital of everything, including, to the consternation and bewilderment of European capitals, of culture. How could the arts flourish so in a society where government cared so little for the arts? How could it be that the greatest Russian choreographer in the world, George Balanchine, won his plaudits in New York when the Russians, after all, pumped disproportionate sums into state support of ballet? As a Cold War instrument, the bunching together of these institutions, in a complex with a readily graspable and kind of midcultglitzy visual profile, filled the bill so far as Moses and Rockefeller saw it — and so far as most New Yorkers saw it.

It’s not an architectural masterpiece. But it’s a powerful image, one that says much about New York and America in the “American Century.” And like the city itself, it just needs to be made a bit more user-friendly.