“GIVEN THE FINE ARTS, architecture, painting, and sculpture, I feel caught in the middle,” Frank Stella said recently. For anyone with a passing knowledge of the work he has made over the course of the past fifty years, the statement is hardly surprising; for anyone who has kept up in the past fifteen, neither is the comment that followed: “Now I can’t stop thinking about architecture.” The oddity comes with what Stella said next: “I can only blame the pursuit of abstraction.”

It may seem a little unfair, in order to decipher this last remark, to begin years ago and worlds away, with the “Black Paintings.” Has any other artist’s early work ever so thoroughly conditioned his subsequent reception? But Stella’s “pursuit” did commence circa 1958 with those allover bands of black derived from support and frame, each subsequent canvas delivering a fresh blow to the flat picture plane’s promise of spatial illusionism and, in turn, exemplifying the high modernism whose critical articulation coincided with their making. “What you see is what you see” telegraphed how tautologically his odyssey began: For him, abstract painting was its own justification, intrinsically worthy. To hear Stella now describe his architectural forays as another stop on a quixotically ongoing crusade toward abstraction sounds peculiar, and maybe a little self-indulgent. Architecture is perhaps the least autonomous of all media, demanding collaboration, viability, use, habitation—is it even possible to conceive of its practice in the absence of these things, as an activity valid in and of itself?

For Stella, well, yes. As director Philippe de Montebello states in his foreword to the catalogue for “Frank Stella: Painting into Architecture” at the Metropolitan Museum of Art, “None of his buildings has yet been built.” The twenty-five paintings, reliefs, sculptures, and models included in the recent exhibition, curated by Anne L. Strauss and Gary Tinterow, index a history of false starts and near misses: a kunsthalle and garden park for Dresden, Germany, whose city council’s go-ahead was overruled by the state of Saxony in 1991; a pavilion for the rooftop of Alessandro Mendini’s Groninger Museum, in the northern Netherlands, which was scrapped in 1992 due to changes Stella made before construction; a 1994 gatehouse for Peter B. Lewis’s Frank Gehry–designed residence outside Cleveland, which never materialized. However close Stella has come, and however bona fide his architectural affiliations (a decades-long friendship with former studio mate Richard Meier; a teaching stint at Yale’s School of Architecture in 1995; a collaboration with engineer Peter Rice from Ove Arup and Partners in the late 1980s and early ’90s), his experience with that most practical of media remains primarily conceptual. It is certainly personal: Some of his most compelling projects were not designed as the result of a commission or invitation. The model for Chapel of the Holy Ghost, 1992, one of five works installed on the Met’s roof in a companion show still on view, was inspired by a spiral-shaped rubber sun hat the artist bought on a Brazilian beach. Imagine standing under a few of Gehry’s signature swoops, ribboned, spliced, and splayed into interlocking spherical forms; that Stella has conceived a structure that would so effectively command heavenward contemplation makes one sorry he lacks a client.

The indoor exhibition was jammed into a single first-floor gallery, and in tracing an evolution from Marrakech, a 1964 canvas of alternating fluorescent bands of pink and yellow, to The Ship (Section) (In Progress), 2007, a hulking lattice of fiberglass and carbon fiber elevated twenty feet off the ground, it tried to do too much with too little. Still, a narrative emerged, however picaresque: Jarmolince III, 1973, one of a series of shaped collage reliefs inspired by Polish synagogues bombed in World War II, showed Stella’s move away from the wall and into the third dimension, while the arabesque aluminum projections of The Dart (D-15) 1X, 1990, enameled in an assortment of black-and-white patterns, represented his departure from rectilinearity. Severinda, 1995, however, should have been left in the studio. An arcing fiberglass wall covered with an abstract riot of color and atrocious computer-generated engraving, it made an already cramped room more so and, in taking up so much space, impeded the apprehension of continuity in Stella’s architectural projects.

Indeed, despite the scattershot selection, a few consistent motifs emerged. In addition to the beach-hat corkscrew, a design also used in the model for the Lewis gatehouse, Stella favors an undulating figure shaped like a leaf, horizontal and perforated, as if by veins, into crystalline facets. These forms never feel wholly organic—the phantom of the rectangle seems to linger in even the most open-ended of his schemes—but at their best they do conjure, as Paul Goldberger notes in his catalogue essay, the fluidity of early twentieth-century German Expressionism in the hands of architects such as Bruno Taut, Erich Mendelsohn, Hermann Finsterlin, and Otto Bartning. The apertures created by the venation of two converging leaves in Guest House (Model), 2007, for example, call up some of Taut’s gemlike plans as much as they do an Erector set. But while this maquette, anchored by three conical plinths, features models of plumbing, stairways, and furniture, it’s unclear exactly how it would be transformed into a habitable unit—how its gaping openings and uneven expanses would be covered by floors or windows. Stella himself acknowledges, “It’s hardly designed to be a permanent residence.”

Coinciding with the Met shows, an exhibition at Paul Kasmin Gallery tracked Stella’s current sculptural production with seventeen works, most made in the past two years. The concurrence was at once a bonus and a liability. The gallery show’s focus offset the diffusion of the museum exhibition, revealing a Stella who still works in reliable series, with a given set of formal variables that he manipulates, over and over, before moving on to the next cycle. Here it was wall-mounted assemblages that combine coils of stainless steel tubing with more angular configurations of nylon RPT that are either left white or spray-painted. The problem was that seeing certain forms in the gallery as “sculpture” and then seeing similar ones in the museum as “architecture” (if only architectural models) imperiled the plausibility of the second category. One’s experience of standing beneath the spliced helix of K.34 (Large Version), 2007, at Kasmin was not much different from that of standing in The Broken Jug (Left-Handed Version), 2007, at the Met; the former just happened to be suspended from the ceiling. To cite another example, the conjunction of spiral, cube, and star in the massive sculpture K.3 (Large Version), 2007, on view in the gallery, is repeated in Remembering Henry, 2007, a model for a mausoleum for curator Henry Geldzahler, on view in the museum where he worked, but rooting the latter in a half-moon base does not make it any less suitable for the kind of contemplation one associates with sculpture or any more tenable as a built structure.

Yet it is perversely the niggling literalism of such comparisons that suggests how to gauge the relationship of Stella’s recent work to contemporary architectural theory and practice. To venture such an estimation would require, first—paradoxical as it might seem—abandoning the question of whether what he is making now can properly qualify as architecture. While Stella is likely the only person in the world kept up at night by this question, the answer (probably not) is immediately clear to anyone who looks closely at his models. Even if we were to disregard the obvious (and profound) hitches that his edifices offer no protection from the elements and little place to stand or walk, let alone live or work, various congeries of red tape seem to keep them from being constructed. In the absence of this real-world standard, it’s even easier to be cynical about Stella-as-architect and see him as another instance of an artist who fancies himself a designer; another example of architecture’s ever-mounting vogue in cultural discourse; another illustration of Minimalism turned domestic and pictorial, its critical imperatives nullified.

But these dismissals are too facile, and it was curiously a comparison with an exhibition devoted to another artist, the Museum of Modern Art’s summer retrospective of Richard Serra’s sculpture, that afforded the most suggestive means of evaluating Stella’s architectural aptitude. Serra’s and Stella’s outdoor works both filtered Manhattan, but in opposite ways: In MoMA’s Sculpture Garden, walking inside one of Serra’s torques, one could only look up, not out, at the surrounding monoliths; on the roof of the Met, in front of the webbed openings of Stella’s leaflike, carbon-fiber Chinese Pavilion, 2007, one looked across and through, surveying the city’s monumentality with a horizontal, antimonumental lens. It is this emphasis on the lateral, and its attendant exchange between interior and exterior, that Stella advocates for building today. Goldberger’s essay quotes from a 1994 lecture Stella gave at the Architectural League of New York: “We might be able to find a way to lift our bridges, slim our towers and build across them, span them horizontally so that light and air can get to the ground below them. Otherwise, what’s the point of cleaning up the environment? Are we doing it so we can breathe more easily as we jog through a forest of steel and concrete?” These are romantic, lofty aspirations, challenges that his work, to its credit, raises. Stella, the consummate problem solver, may have met a set of problems he can’t crack, but someone else—an architect—might.

“Frank Stella on the Roof” is on view at the Metropolitan Museum of Art, New York, through October 28.

Lisa Turvey is a New York–based art historian.