‘Is there a Jewish Art?” asked the critic Harold Rosenberg in a 1966 lecture of the same title at the Jewish Museum. “They build a Jewish Museum, then ask, ‘Is there a Jewish Art?’ Jews!” Rosenberg’s pugnacious quip is just as pertinent today, considering the Jewish Museum’s provocative programming and self-questioning presentations. When it comes to Jewish culture, identity crisis isn’t so much a characteristic as a precondition.

The museum started life as a room of Judaica at the Jewish Theological Seminary in 1904 and now is a thriving, beloved, often controversial institution in the former Warburg Mansion on Fifth Avenue’s Museum Mile, and is celebrating its centenary this year. It has done so in any number of ways, including various exhibitions and events, a fund-raising campaign, and now a sumptuous tome of some of the “highlights” of its collection (“Masterworks of the Jewish Museum,” Yale University Press, 253 pages, $60).

This book presents only 120 examples from the museum’s horde of 28,000 objects, which include ceremonial Judaica, artworks, and an extensive archive of film and television footage.

In the first half-century of the museum’s life, there wasn’t much complication. The initial displays lined up Torah finials and breastplates and spice boxes in neat vitrines, in which the virtuosity and styles of different communities could be compared and marveled at. As Joan Rosenbaum, the museum’s current director, recounts in her introductory essay to the Yale volume, the collection grew exponentially in the 1920s when the vast collection of Hadji Ephraim Benguiat, which had been on loan to US National Museum, was transferred to New York. This included such exquisite works of craftsmanship as a Renaissance Torah ark, a 17th-century Torah case from Damascus, and a highly ornamental baroque Chanukah lamp that echoes the now-lost architectural decorations of wooden Polish synagogues.

Another great collector, Benjamin Mintz, brought his holdings of Polish Judaica to the 1939 World’s Fair and they remained after the outbreak of war. In the same year, the great collection of the Danzig community was sent to the seminary for safekeeping on condition of its return in 15 years if the community there was safe; if not, it should remain in New York “for the education and inspiration of the rest of the world.”

The Holocaust, inevitably, touches almost every aspect of the Jewish Museum (though not to the extent that it does the more recently formed Jewish museums in Germany, which chillingly document the loss of a civilization). A carved, wooden “grogger” from the Mintz collection, for instance, a noisemaker sounded in the Purim service at the mention of the name of Haman, dating from 1933, has the head of Adolf Hitler as one of its anvils.

There was a lot more noise coming out of Hitler images in 2002, however, with the museum’s “Mirroring Evil: Nazi Imagery/Recent Art.” This highly controversial exhibition, which looked into how contemporary artists confronted the trivialization of the Holocaust in the mass media, drew protests from survivors and others. Its curator, Norman Kleeblatt – who had debuted at the museum with a well-received and highly learned investigation of art and caricature in the wake of the Dreyfus Affair – had already raised eyebrows with an earlier show, “Too Jewish? Challenging Traditional Identities,” that looked at artists who explored stereotypes with uncomfortable humor.

Tellingly, nothing from these exhibitions makes the “masterworks” grade of the present volume, to which Mr. Kleeblatt does contribute catalog entries. But what the shows do signal is an indicative clash of values between a self-consciously sophisticated notion of art as signifier of complex cultural meanings, on the one hand, and a purer sense that anything you see in a Jewish museum ought to reflect Jewish values.

This debate reflects earlier anxieties about what art should do in a Jewish museum. In the 1960s the museum underwent a radical transformation. A new wing was donated by the patrons Albert and Vera List, and with it came a revised mandate: to showcase contemporary art. Many of the leading players in the burgeoning New York School – artists like Mark Rothko, Barnett Newman, Morris Louis, Helen Frankenthaler, Larry Rivers, Sol le Witt, Eva Hesse, Richard Serra, and Diane Arbus – were Jewish. So were critics Rosenberg, Clement Greenberg, Meyer Schapiro (a mentor to the museum, his portrait by Alice Neel features in the book), Leo Steinberg, Michael Fried, Rosalind Krauss, and the dealer Leo Castelli. There was a sense that the Jewish Museum should reflect this achievement and also make up for an absence of cutting-edge art in the city’s major museums.

The idea wasn’t at all limited to Jewish art or artists, however; the Jewish Museum assumed the mantle of presenting “advanced” art, whether by Gentile or Jew. (A lot of Judaica is made by non-Jewish craftsmen, but that’s another matter.) Looking back, it hard to work out whether the museum’s “ideological shift” as Maurice Berger describes it here, represents high-minded idealism or outrageous chutzpah: Either way, the museum staged seminal exhibitions in this period, including the first retrospective of Jasper Johns in 1964 and the sculpture survey which launched the minimal art movement, “Primary Structures,” in 1966. The appointment of Kynston McShine, an African-American, as curator signaled the progressive-mindedness of the museum in this period.

The experiment was short-lived: To the dismay of the art world, trustees axed the secular contemporary art program in 1971, retreating to its original remit as a center for Jewish history and culture. “The question of assimilation versus separatism – an issue debated by Jews for centuries – came out of the closet as a significant museological problem,” as Mr. Berger puts it. Perhaps tellingly, when the museum expanded again in the 1990s, architect Kevin Roche covered up the International Style List wing with a pastiche from the adjoining Warburg mansion.

But to regroup isn’t necessarily to regress. The assimilationist stance of the 1960s, with its emphasis on abstract and conceptual directions, smacked at once of Modernist hubris and minority apologetics.

Some would ask, who says the choice is between the avant garde and Jewishness, anyway? A beautiful 1950s Torah curtain by Adolph Gottlieb carries across the “pictograph” style of the Abstract Expressionist with a grid of symbols – some traditional, some idiosyncratic-that links the artist’s Jungian preoccupations and a sense of Jewish renewal. A wavy line forming a “W” that can be read either as udder-like forms or as a male member is interpreted as a Jungian symbol of the anima within the animus. It is also the artist’s private joke, signifying “breastplate!”

The “reactionary” trustees who wanted some Jewishness from their Jewish Museum anticipated multiculturalism and postmodernism by valuing the particular over the general, the fragment over the whole.

The anthropological tendency that now dominates the museum’s approach – whether to art and artifacts – stresses social and historical context over aesthetic experience.

This seems “museologically” more sophisticated, as well as appealing to a sober sense of what a Jewish museum should be about. Ironically, the sentiment (among protesters against “Mirroring Evil” for instance) that art should be good, if not beautiful, belongs to the more idealistic sensibility that got buried with the List wing.