Who painted the first abstraction? Some believe it was Kandinsky, and others Arthur Dove, or the Chicago artist Manierre Dawson. In any event, Americans have had a hand in abstract painting since its very beginnings around 1910. Toward mid-century, a second generation of abstractionists thrived, even with the ascendancy of Social Realism and Regionalism. The American Abstract Artists group was founded in 1936, and works by John Ferren, Ilya Bolotowsky, and other Americans were exhibited at the Museum of Non-Objective Art, the precursor to the Guggenheim.

Why are most of these painters relatively unknown today? In two words: Abstract Expressionism. Not only is the New York School considered modern America’s first truly native art movement; for influential critic Clement Greenberg, it also uniquely satisfied history’s requirement for an art examining its own means and materials. By the 1960s, in the turbulent wake of the New York School, the finesse and self-possession of works by Bolotowsky, Ferren, and their kin seemed like tokens of vanquished Old World aesthetics.

Since then, however, scholars and collectors have steadily warmed to their work. Hollis Taggart’s “Order and Intuition” provides a quick but rewarding overview of their achievement in an exceedingly elegant exhibition of more than 30 paintings from the Patty & Jay Baker Naples Museum of Art. (The Florida museum acquired all works from the Atlantic Records co-founder, Ahmet Ertegun, who amassed a large collection of American modernists in the late 1970s.) While varying in style — a few boast an organic painterliness, but most are crisply geometric — the paintings all reflect a European self-containment. Their compositions tend to hold the walls rather than claiming the surrounding space, Ab-Ex-style. As one might expect, a few feel rather derivative. Others, though, show considerable energy and discrimination — which is to say that, like their European models, which varied from the brilliance of Hans Arp to the predictability of Amédée Ozenfant, they reflect a wide range of temperaments.

The best have an urgency of rhythm — lively formal sequences that would have appealed to the musically attuned Ertegun. In his small, striking canvas “Perhaps” (1940), Werner Drewes (a student of Klee and Kandinsky) briskly opposes light and dark triangles within a pool of limpid cobalt blue. Bright orange and yellow bars punctuate a dense surrounding perimeter of greens and browns. This chattering but coherent whole is itself framed by a plane of vacant gray-blues. The same delight in color sequences appears in several other dynamic canvases by the artist, including the tiny, vivacious “Light and Sea” (1943), which seems to be a sketch for a larger painting on view in the gallery’s rear office. (Though not officially part of the exhibition, this room contains several related works.)

The selection includes a single, diminutive painting by Morgan Russell, a pupil of Matisse and co-founder of the Synchromism movement, which emphasized the symphonic potential of abstract forms. A blossoming of hues — from full-speed, spectral hues to nuanced grays — radiates from the center of his “Synchromy No. 6” (1914-15), imparting a vital fullness in its 8-inch-tall dimensions.

One of three paintings by Bolotowsky captures not only the geometric style, but also some of the dynamism of the French painter Jean Hélion. This 1937 composition unfolds in echoing curves located by sudden pressures: an anchoring dark green, a rich purple beckoning from a distant triangle. A very vertical canvas (1949-54) by Burgoyne Diller might be a stretched Mondrian, measuring out a white rise with slivers of red, blue, and yellow. Less engaging is Wilfrid Zogbaum’s 1936-38 composition, in which evenly weighted colors don’t quite fulfill the promise of jazzy, offbeat angles.

Albert Eugene Gallatin’s greatest impact on New York painting may have been his collection of works by Picasso, Gris, Léger, and Mondrian, on view in his Washington Square gallery in the late ’20s and ’30s. Aesthetic intelligence vies with plastic compulsions in his several paintings at Hollis Taggart. A composition of tilting planes from 1939-40 is handsomely inert ­— pert in style, but pictorially stolid. But in a more energetic abstraction from 1938, a jaunty progression of off-verticals — an earthy, retiring red, various weights of blue, and cool and warm off-whites — is nimbly contained by denser notes above and below.

Some works fall outside the usual geometric idiom. The sculpturesque modeling of machine forms in Paul Kelpe’s 1937 painting represents a peculiar hybrid of avant-garde subject matter and conventional rendering. With their tight rectangles and radiating hairlines, Dwinell Grant’s two canvases (both 1947) suggest two-dimensional versions of Naum Gabo’s sculptures. A medium-sized 1942 canvas by Dove comes closer to representation, with moody, luminous greens and orange-browns suggesting trees reflected in a lake. Oscar Bluemner’s colors in his stylized landscape “Pagoda” (1922-27) strike me as merely electric rather than sympathetically charged; by contrast, the hues in his modest gouache acquire some momentum in fleshing out a Boston scene. Meanwhile, George L.K. Morris, a student of Léger, proves himself an adept colorist with the keen divisions and redivisions of his “Balinese Dancer” (1934). Here, a small core of interlocking forms, brilliant white and inky black, is bracketed by planes of gray-purple, orange-red, and brown; articulated by suggestions of fingers, elbows, and knees, the discordant rhythms somehow build as a figure’s mobile presence.

The sparkling diversity of the paintings in “Order and Intuition” is readily apparent, once the expedience of a single, streamlined narrative for art history is put aside. And it should be; while Abstract-Expressionism’s explorations were embracing, they weren’t comprehensive. As brave as Pollock’s mature compositions are, his overall rhythms mostly preclude the sense of internal scale and focus that galvanize Picasso’s greatest images; Rothko’s vibrant colors are only more accessible than Giotto’s or Veronese’s because of his extreme simplification of drawing. Abstract-Expressionism’s excesses provoked the cerebral coolness of Pop and Minimalism. Perhaps its omissions will renew an appreciation of the kind of abstraction that inspired these paintings at Hollis Taggart.

Until October 25 (958 Madison Ave., between 75th and 76th streets, 212-628-4000).