Hans Hofmann’s paintings were acts of self-discovery, thrashed out with all the expansiveness and forthrightness of the new American spirit. But his paintings, to a greater degree than those of his fellow Abstract Expressionists, were also compositions – conscious formal hierarchies rooted, if distantly, in European models.

Hofmann systematically passed on his painting philosophy through his celebrated school, which is currently the subject of two group exhibitions. Of the nearly 20 paintings in “Modernism and the Hofmann School,” only two are Hofmanns, but they form the linchpins in a fascinating kind of “before and after” exhibit comparing American Modernists from the first half of the 20th century to prominent Hofmann students from the second half.

As one might expect, the Modernist works here seem more derivative of French School painting. This isn’t necessarily a liability; the subtle colors of Marsden Hartley’s “Maine Seacoast, Still Life” (c. 1940-41) give an eloquent gravity to a lobster trap looming above coils of rope and a dead bird’s silvery, darting form. Equally striking is Alfred Maurer’s “Head of a Woman” (1928-32), haunting in its straitened, Cubist modeling.

Other Modernist works feel more dated. Tart greens and crimsons edge against earthier hues to convincingly model the forms of Arthur B. Carles’s undated “Nude,” but it looks rather tame next to the nudes by Hofmann students on either side: the bold, circulating hues of Robert De Niro Sr.’s “Seated Nude With Green Plants” (1970), and the vibrant stabs of color in George McNeil’s “Stiff Brocade” (1963). Both illuminate far more powerfully the struggle and contradictions of painting the figure.

On an opposite wall hang three canvases that share a surprisingly similar range of yellows, greenish-blues and rich reds. Stylistically, however, they could hardly be more different. In the early “Ten Pound Island” (1917) by Modernist Stuart Davis, yellows raggedly mete out the intervals among foreground rocks. In an untitled 1948 abstraction by Hofmann School alumnus Giorgio Cavallon, the yellows pace a limpid dance of dozens of carefully colored rectangles. Louisa Matthiasdottir, another Hofmann student, uses pale yellows to animate a jazzy sequence of rooftops and window frames in “Painter in Reykjavik” (1946), an abstracted image of a figure before a window.

Other one-time Hofmann students include Paul Georges – whose somber, weighty hues lend a kind of clunky majesty to his 1990 still life “Grey” – and Paul Resika, represented by his large, particularly luminous “Moon in the Bay” (1984-86). In it, one sees Hofmann’s “push-pull” theories transposed to a scenic view of a boat and warehouses, each plane almost bursting with plastic energy.

Hofmann himself presides nearby, with his “Interior No. 1 Pink Table, Yellow Tulips” (1937), which struggles to place vase and flowers on a table, and table within a room. It presents a classic painter’s dilemma: How to locate a warm, red desk at the far end of an ultramarine floor? (Hofmann succeeds, emphatically.)

Styles come and go, and to contemporary eyes Hofmann’s freewheeling brushwork no longer seems radical. But the exhibition neatly argues that his flamboyant style was a vehicle for an enduring discipline, one he passed on through a generation of younger painters.

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Most of these former students, along with 10 other artists inspired by Hofmann’s philosophy, appear in the Painting Center’s tribute to this remarkable painter and teacher. Hofmann’s “try anything” attitude, Geoffrey Dorfman writes in the catalog, was accompanied by “a seemingly inexhaustible positive energy and a willingness to endure, (almost invite) failure.” Indeed,his charisma is evident in this large, uneven body of work ranging from semiabstract figuration to purely geometric forms, and from seamless technique to lush painterliness.

Three paintings by Hofmann handily illustrate his attack. They vary from the dense, dark encrustations of “Image in Green” (1950); to the vast, airy washes of “Gray Monolith” (1963); to the bombastic depiction, in acrid pink and green triangles, of a Cubistic beast in “Perpetuita” (1951). All radiate the same restless compulsion to cohere discrepant elements.

Representative paintings by Messrs. Resika, McNeil, Cavallon, and De Niro grace the walls, along with Wolf Kahn’s “Blue Tangle” (2005), which conjures a deep landscape out of yellow, blue, and white flickers. The smooth geometric shapes and jangling colors of Laurie Fendrich’s “Kim” and “The Glasgow School of Art” (both 2005) ply a route halfway between Hofmann and Op Art. The delicate forms of Anne Tabachnick’s “Flower in Green Vase” (c. 1988) would seem tentative, were it not for the single plant winding muscularly up the height of this abstracted still life.

Other works seem inspired principally by Hofmann’s turgid surfaces. In “Accordion Bellows” and “Untitled” (both 2004), Jill Nathanson’s luxuriantly swirling pigments, held in diagonal stripes between monochromatic planes, show as much slyness of technique as composition. Walter Darby Bannard’s large “Shot Hurley” (2005) broadly echoes the gestures of Hofmann’s adjacent “Perpetuita,” but the artist seems interested above all in the resinous glossiness of his paint.

The exhibition’s sheer diversity of temperament, coupled with a cramped installation, gives the impression of a cacophonous classroom – appropriate to its concept, perhaps, but putting at a disadvantage smaller, more reflective works like Perle Fine’s energetic 1958 collage. Viewers will likely take home memories of potent individual works rather than an abiding philosophy. For me, certain impressions linger: Matthiasdottir’s undated “Black and Tan Sheep,” which achieves an austere monumentality in its measured hues, and Albert Kresch’s luminous “Near Cocheton” (1991), a landscape whose quietly roiling depths feel at once expansive and intimate.

“Modern and Contemporary Masters” until November 26 (20 E. 79th Street, between Fifth and Madison Avenues, 212-879-6606). “Legacy” until December 24 (52 Greene Street, between Broome and Grand Streets, 212-343-1060). Both galleries declined to disclose their prices.