Seeking to plump up the art historical heft of a largely forgotten American master, “Burgoyne Diller and Hard-Edge Abstraction: Underpinnings and Continuity” at the Spanierman Gallery would have us believe that Diller was essential to the genesis of the hard-edge abstraction that emerged at the end of the 1950s. That the premise of the charming new show at the Spanierman Gallery is almost certainly wrong seems scarcely to matter.

Hard-edge abstraction, associated pre-eminently with Barnett Newman, was a reaction to the so-called gestural abstraction that had dominated the New York School since the end of World War II. In response to the exuberant painterliness of the drips of Pollock, the swerves of de Kooning, the operatic strokes of Franz Kline, and the all too human wobbles of Rothko’s rectangles, here was a new kind of sullenness so sharp and so glacial in its geometric rectitude as to abolish almost all trace of human touch.

In the work of Burgoyne Diller (1906–65), as well as in that of several other artists in the Spanierman show, it is surely possible to find a comparable degree of geometric severity. But in their effects and in their relation to the previous history of art, these paintings are very different from the hard-edge abstractions of Newman and his many followers. One of the curious things about Diller, a native New Yorker, is that even though he was a little younger than Newman, de Kooning, and Arshile Gorky, he seems to belong to a far earlier era of American painting. This may be because he hit his stride by his mid-20s, while they were still struggling to find themselves well into their 40s. In the history books, Diller is thus the pre-eminent American exemplar of Mondrian’s neo-plasticism, with its diminutive, sparely geometric exercises in primary colors. His most representative works were done in the 1930s. A good example at Spanierman is “Early Geometric,” from 1934. A mere 20 inches by 24, this simple harmony of blue, yellow, and black against a grayish field is relieved by a small red ball representing the one concession to curvature. The comparison between this and what the New York School would produce in the next decade is dramatic. Quite aside from questions of size and form, Diller’s work, for all its competence, embodies a moment when American art was still subservient to that of Europe. What is so startling about the New York School, by contrast, is that it represents the first moment when American art began to lead and European art began to follow.

Even though hard-edge abstraction is programmatically opposed to the gestural abstraction of the earlier New York School, it is closer to Pollock and de Kooning than to Burgoyne Diller and his followers. The sheer scale of the work produced by both factions of the New York School — these things take up an entire wall! — stands in stark contrast to the genteel, cabinet-sized works that European painters such as Mondrian (and his American followers) produced almost exclusively in the 50 years before World War II.

No less important, both factions of the New York School — the gestural and the hard-edge — parade a self-confidence, an almost ornery self-assertiveness, that is practically ill-bred compared with the shy, Dutch introspection of Mondrian (and his American followers). That is to say, there are a lot of right angles both in Diller and in Newman, but if they are largely academic in Diller, in Newman they acquire a new and almost polemical force.

Thus the predominant quality in the works at Spanierman is their impeccable politeness. Small and exquisitely finished in the main, these 26 paintings in all seem eager to please, and they do. Surely there is a great deal of variety to them, within the context of their shared geometric abstraction. Helen Lundeberg’s “Silent Interior,” from 1952, is a slight meditation in shifty shades of gray. Both in scale and in formal vocabulary, Karl Benjamin’s “Red White Blue,” from 1958, is almost charmingly backward in the crisp geometry of its lozenge-like forms. By 1960, Diller is learning from Newman, in his noble “Second Theme.” At 6 feet by 6 feet, it is far larger than his earlier works, with a far starker contrast between the dominant black zones and the yellow, orange, and white interventions.

But the best work on view at Spanierman is by Alexander Lieberman. Though famous as an editor at Vogue, he has never quite gotten his due as an abstract painter. Here he is seen in “Omega,” from 1962. This work consists of the simple, flawlessly constructed juxtaposition of a dark stripe and a reddish ball against a dazzling saffron-colored field.

Notwithstanding the fact that Diller and his acolytes learned something from Newman and his acolytes, the grids and right angles of the former — even into the ’60s — stand as the last, faltering gasp of that geometric abstraction that ultimately had its origins in Cubism.

By contrast, the hard-edge abstraction of Newman and his kind ushers in the next phase in the teleology — as he might put it — of art, a sullen snub to his contemporaries and a foretaste of the even more severe reductiveness that would soon be seen in conceptualism.

Until January 5 (45 E. 58 St., between Madison and Park avenues, 212-832-0208).