What is the greatest number of color fields that can be arranged so that each maintains a border with all others? Bernard Frize’s Heawood, 1999, a pair of painted sculptures in the permanent collection of the MAMVP, and Heawood, 2003, the thirteen digital prints that introduce this show of the artist’s mostly recent paintings, address this thorny question. The works’ namesake, British mathematician Percy John Heawood, labored over this and related problems (which originated in cartography) in the years surrounding the turn of the last century; at one point, exploring three-dimensional forms, he determined that no more than eight fields of color can abut one another on the surface of a double torus (a volume shaped, in accidental analogy, exactly like a three-dimensional figure eight). The twin Heawood sculptures are based on this formula.

Among Frize’s few forays into three dimensions (which include Peintures sur un fil [Paintings on a Thread], 1978–80, long strands of nylon coated with countless layers of paint then sandpapered to produce multicolored bars approximately six and a half feet long and an inch and a half in diameter), these double doughnuts are on examination frustrating, to say the least: Because they’re placed on the floor, one side out of sight, it’s impossible to verify if all eight color fields really are contiguous. The later, two-dimensional Heawoods, which are based on computer-generated images of the sculptures, necessarily fail to demonstrate what the 3-D originals were designed to prove. That these prints introduce an exhibition entitled “Aplat” (Flat) expresses better than anything the penchant for paradox that has guided Bernard Frize’s work from the beginning.

Perhaps this wink at topology is also an indication of the position from which we might consider the hundred or so canvases that follow in this exhibition. (The majority date from the past seven years, but there are a few works from the late ’80s and early ’90s.) Painting as Frize conceives of the practice does not have as its ultimate goal the production of objects as much as the perfection (and the testing) of processes: The canvas is thought of not as an end or an objective but as a place; it is, strictly speaking, a theater of operations. If the painting’s unfolding proves satisfactory—if it follows its course without encountering an impasse, while retaining a necessary dose of the unexpected and the possibility of leeway from its plotted course—Frize preserves the canvas. The painting, then, is a consequence, a record, rather than a goal the artist decided to achieve; it is the image of its own execution. One finds evidence of a similar kind of thinking, in which the means justify the end, among certain painters of earlier generations, no matter how dissimilar: Jean Dubuffet (particularly of the late ’50s and his final years) and Robert Ryman (especially the Rymans of the ’60s). None of this work has anything to do with the Abstract Expressionist notion of the canvas as an “arena in which to act,” as Harold Rosenberg put it in his 1952 article “The American Action Painters.” Frize situates himself at the antipodes of expressionism and existentialism: His works don’t aspire to deliver the truth of a subject but simply the trace of a game, free of metaphysics.

The viewer who would like to do more than contemplate a painting’s surface should feel free to mentally reconstruct its making. There is, in Frize, a sort of iconography of operations that enables one to retrace the istoria of the painting—and doing so is as crucial to understanding a Frize as identifying characters and scenes is to comprehending a classical painting. As in the case of Heawood, making this journey requires some knowledge and a certain amount of imagination, as the painting often confronts us with riddles that leave us to guesswork. “Suite automatique” (Automatic Series), 1996, whose six elements were on view in the second room of “Aplat,” is an example that might be relatively easy to understand. Blocks of color in varying widths are arranged horizontally and vertically in a sort of plaid or grid. These elements blur into one another, bringing to mind a certain sense of speed; the paints must have been swept down (or up) the canvas in a single gesture while still wet (this “wet on wet” technique is a consistent feature of Frize’s work). One gets the impression (the unity of the effect implying that of the execution) that a single implement was used and that it was at least the width of the canvas itself. Indeed, Frize used a tool of his own making: He attached five brushes—twelve inches, eight inches, six inches, four inches, and two inches wide, respectively—to a small board and arranged them as required. Finally, “Suite automatique’s” surprisingly frozen, even “photographic” look—which (as in many of the artist’s other works) seems to contradict the very idea of manual involvement—is explained by a layer of transparent resin that seals the painting and suspends the image inside it, as though behind a pane of glass.

Obviously, this sort of description tends to simplify things somewhat. “The execution,” as Delacroix said, “adds to the thought,” and the element of risk or impromptu modification that enters into Frize’s paintings confers on them a je ne sais quoi that escapes the narrative of their genesis. One of them, curiously dated 1986–99, is titled 35% Vrai, 60% Faux (35% True, 60% False), which suggests the existence of an inexplicable remainder, neither true nor false, where much of the painting’s interest resides. This is what the painter pursues, and where the viewer may linger. In an interview with Irmeline Lebeer reproduced in the catalogue, Frize declares, “I always try to reach a point where there’s not just one thing on the canvas, a single thing being shown, but a paradox, an antagonism, a difficulty at work.”

The large, open, curved space at the heart of the exhibition allowed one to take in a large number of the paintings at a glance and in a startling way revealed the variety of Frize’s recent production, in my opinion unrivaled in current painting. The artist, who had meticulously worked out the hanging, had placed here a sort of wild card: Jumelle (Twin), 1990, the only work in the show to include an explicit representation (a skeleton adorned with intestines, traced as if with a finger or a single small tool into the paint of the blue, black, and brownish geometric shapes that cover the canvas), recalls a contrario the fundamental figurative dimension of all we have seen elsewhere in the exhibition. A bit further on, a trio of works summed up the visual diversity of Frize’s undertaking while embodying his more or less overt flirtation with a purely pictorial form of humor or irony. Boom, 2001, is a scattering of circles within circles like decals that, on a sober surface, bring together several dozen tints (a wealth and variety that bring to mind an acute and ancient attention to resource management—in this case, of that which remains at the bottom of the paint pot); Double margarita, 1991–99, is a candy pink monochrome left to dry upside down so that a sort of allover Braille studs the surface; and NBCa, 1998, the reverse of the previous work, is covered with thousands of dimples, scooped out by a knife to reveal alternating black and white strata of paint.

Certain paintings—but this also depends on the taste of who’s looking—seem to embody a state of crisis, an awkwardness, a difficulty (our own on facing the painting, as much as what’s actually in the painting). Thus Conducteur D, 2001, a nightmare of good form and successful composition, makes me think, not without a tinge of jubilation, of some Swiss Concrete artist seized by violent delirium tremens. But the high point of the exhibition was the almost complete presentation of two large series, “Lucky” and “Portable” (both 2000). Almost—because, in an echo of the paradoxical logic according to which Jumelle was included, one canvas had been omitted from each. Comprising, respectively, twenty-two and twenty-five paintings, each series was painted in a single session as one vast canvas and then disassembled. Like many of Frize’s recent works, both “Lucky” and “Portable” required multiple executors (three, in both cases: Frize and two assistants), each using two hands to move and then pass to his accomplices the bouquet of five brushes whose regulated crisscrossing drew the uninterrupted braid that became the subject of the paintings. These traveling tangles of color tightened or loosened, became saturated or depleted through their own movement across the canvas, and offer painting’s analogue to a “train of thought” in perpetual variation.

Chance (and no doubt other factors that see to it that no one can be a prophet in his own country) would have it that Frize’s last museum show in Paris came in 1988—at the same institution (though on a different floor). More restrained, that exhibition concluded with an empty room, the ceiling of which was entirely covered with paint—a vast multicolored labyrinth thought of by its author as a sort of brain suspended above us. Distant echoes of it may reverberate in “Lucky” and “Portable.” Fifteen years later, “Aplat” has demonstrated with brio that Frize has not stopped thinking in paint and that he is still, indisputably, one of the most engaging artists of his era.

Jean-Pierre Criqui is editor in chief of Les Cahiers du Musée national d’art moderne (Centre Georges Pompidou, Paris).

Translated from French by Jeanine Herman.