The Met’s European painting galleries, although splendidly reinstalled a few years back, get relatively light foot traffic, partly because the cultural references in much of the work have lost currency. Even a generation or two ago, the myths and religious subjects that form the basis of, say, Italian Renaissance painting would have been familiar to a general public, thanks to surviving public school variations on a “classical” education. But with changes in schooling in a country that has grown increasingly secular, viewers of art predating Impressionism typically don’t know what they’re looking at.

The 21st-century museum is going to have to find ways tell them. And this may well demand particular curatorial skills, such as ever more imaginative storytelling, and the use of quasi-ethnological approaches to presentation. Even in a media-driven age, much art is, at some basic level, personal. People made it, reacted to it, treasured it in ways we can identify with. But art is also intrinsically political, designed to shape a view of the world in empowering ways, ways that write certain people and ideas into the record and leave others out. We need to see art from both perspectives.

Museums like the Met are themselves grand history-writing-and-editing machines. Spectacle is built into them. But if they’re going to become 21st-century institutions, they’re also going to have to function in the mode of university teaching museums. Experimental — interdisciplinary, cross-cultural, self-critical, heterodox — approaches to art will have to be tried out if an audience for history, which is only as alive as our sense of investment in it, is not to be lost. (For a comparative look at some recent methods, I recommend Peggy Levitt’s “Artifacts and Allegiances: How Museums Put the Nation and the World on Display,” just out from University of California Press.)

Whether any amount of inventiveness can arrest the current retreat from art’s past is, of course, a question. Again, the metrics are paradoxical. Whereas other branches of the arts, like classical music and ballet, are attracting fewer and fewer young people, museums are attracting many, yet the interest of those visitors appears to be specific and narrow: contemporary art. And because the future lies with this audience, museums are shaping themselves to it by acquiring and exhibiting more and more contemporary work.