FEW EPISODES IN THE HISTORY OF ART attract so many origin myths as the history of abstraction. As a plotline, it’s hard to beat—an intoxicating, utopian rhetoric of a revolutionary new beginning through art—and ever more entrenched now that it can be consigned to a distant past: After all, abstraction is more than one hundred years old. Marking that centenary, the ambitious exhibition “Inventing Abstraction, 1910–1925” provided no exception to that narrative, but offered a more nuanced and considered version that speaks very much to our own time and to current cultural anxieties (as origin myths always do). Curator Leah Dickerman traced a complex social network of originating “connectors” distributed across multiple metropolitan centers in Europe and the US. The show bore the same signature style as Dickerman’s cocurated earlier and highly successful Dada (2006) and Bauhaus (2009) exhibitions at the Museum of Modern Art—a crowded hang on dark walls—refusing the aura of the sacred that inevitably attaches to such canonical works. And while “Inventing Abstraction” assembled an impressive roster of international loans, a quarter of its checklist forms the heart of the museum’s own collection.

Therein lies the rub. Almost as potent as the origin myths that stick so tenaciously to abstraction is the origin myth that clings to the role of MoMA itself in abstraction’s history, epitomized by the now very famous “Cubism and Abstract Art” show curated in 1936 by the museum’s first director, Alfred H. Barr Jr. The “inventing” in the title of this twenty-first-century show refers, then, not only to the first wave of innovative art practices of the 1910s and ’20s but also to the invention of the category by the great synthesizer Barr (an exaggeration, but true enough). Given the demands of academic scholarship today, we would expect the institution to take account of its own historical role, a topic that is reflected in two essays bringing to the fore new archival material in an often rich, expansive catalogue. But there are moments when one must ask: Is this an exhibition about the formation of abstraction, or about the formation of the Museum of Modern Art? It is about both, of course, but this duality gets in the way of thinking afresh about abstraction as a larger theoretical problem and a continuing historical project.

For a start, while the idea of the network is geographically expansive and would at first appear to pull abstraction firmly into the present day, its overlapping vectors of parallel connection and critical analysis tend to put serious limits on the kinds of questions that get asked. It was hard not to see a revisionist set of responses to Barr’s 1936 show in the early sections of “Inventing Abstraction,” especially in the introductory wall-spanning diagram making visible documented associations between the artists in the exhibition, reworking Barr’s famous flowchart. The first painting one encountered—a single Picasso—was not only a nod to Cubism as the beginning of it all but also triggered a powerful legitimating narrative running from Cubism to abstract art. Kandinsky followed next, as a key instigator of a new visual language. Although the synchronic networking of abstraction provided the exhibition with a powerful organizing matrix, then, the show struggled to contend with these competing pressures of symbolic origination and chronological firstness.

The next move was to Paris: A climactic point in this telling of abstraction’s genesis found the Delaunays—Robert and Sonia—in revelatory mode, exploring the chromatic ecstasies of the modern city, alongside Fernand Léger and Francis Picabia, who were equally fascinated by its mechanistic spectacle. Apart from Sonia Delaunay-Terk, newly cast here in a key role, all these artists figured fairly prominently in Barr’s original show. But the reassertion of Paris as a cultural node has more pointed ramifications. Robert Delaunay’s Orphism is rooted in modernity’s bedazzling optical effects and, as his later work shows, is a very different project from the more robustly systematic and relational forms of abstraction emerging elsewhere, just as Léger’s abstraction would also be a vivid if short-lived phase. This focus on Paris as the city of Orphism leads straight to a frankly local axis, with such modernizing synchronist painters as Stanton Macdonald-Wright—once spurned by Barr, whose internationalism had also been freighted with anxieties about the provincial—now at the very heart of abstraction’s formation. Besides the obvious American bent to this particular origin myth, these early sections of the show didn’t fully prepare the way toward understanding the core project of abstraction, as it became more and more ambitiously theorized as a new ordering (and disordering) system in parts of Europe, especially in the work of Piet Mondrian and De Stijl, Kazimir Malevich and the Russians, and the seriously underrepresented Polish artists Władysław Strzemiński and Katarzyna Kobro.

What I am calling abstraction’s core project is not monolithic, of course, as the works in this exhibition demonstrated well. If it is no longer possible to believe in a universal language of forms, it becomes more urgent to ask what kind of relational model could hold the existing differences together. Nowhere was this more vividly posed than in the single wall of Malevich paintings that relate so intimately to one another but also seem to exceed the very scheme they set in train. Malevich was one of the first theorists of art as a system. Rather than articulating a rational or technocratic theory, he came to describe (in wildly metaphoric language) a complex economy of actions and energies, as if the artwork were part of a nervous system. These self-differentiating formal strategies invite us to think about geometric abstraction in terms very different from the machine aesthetic that has so long been associated with it (and which gets so much attention from the familiar march onward from Cubism and Futurism). If Cubism marked a radical crisis in representation, then it was surely as part of a much more far-reaching upheaval in systems of meaning—one that, in hindsight, began to break down conventional oppositional categories such as rational and irrational, animate and inanimate, political and pure, organic and mechanical.

From our contemporary perspective, it is the first wave of abstraction bracketed in this show’s title, in all its political and psychic complexity, that should now demand our full attention—if only because the far too well entrenched story of its beginnings seems so insufficient in accounting for what it would so quickly become. A group of Prouns by polemicist, proselytizer, and protoglobe-trotter El Lissitzky—perhaps the kind of work most susceptible to established ideas of technocratic rationality—now require us to think differently about their interactive behavior as tactile surfaces. Seen here, they seemed to propose a precision haptics (rather than optics), with hand-drawn bits of graph paper and sections of shiny tinfoil picking up the imprints and reflections of their own futurity. The material worlds they produced acted as charged condensations of textures and temporalities. And Sophie Taeuber-Arp’s needlepoint compositions questioned the porosity of abstraction’s borders, in this case with handicraft and textile design (in which Taeuber-Arp was trained); the first parts of the show, though, provided little grounding for the work. Similarly, László Moholy-Nagy would outsource his so-called Telephone Pictures—and here we got the rare chance to see all three of the standard sizes he ordered—to a porcelain-enamel sign factory. The point is not that any single model of geometric abstraction had become established but that, less than ten years into abstraction, a constantly mutating set of formal maneuvers could imprint itself on such a wide range of material supports.

In many ways, these precarious borders and edges were the most intriguing elements of the show, as both formal and theoretical traces of abstraction’s volatile energy. And yet, for all the intention to present abstraction as a cross-media phenomenon, painting retains its dominance in this account. Though “Inventing Abstraction” contained many other genres, most compellingly dance, in Rudolf von Laban’s remarkable serial notations of movement and choreographic sketches by Mary Wigman, these never really dislodge the centrality of painting (even less, perhaps, than the multimedia approach Barr had also presented, showing painting alongside photography, film, design, typography, and architecture). Nevertheless, Dickerman’s exhibition (and even more forcibly the catalogue) firmly situated abstraction within the context of a protean image world as a key to its historical emergence, rather than (as it was once common to invoke) an esoteric realm of the supernatural and the spirit. This is always an imperative: to save abstraction from itself and to extricate it from the mysticism that formed part of its early rhetoric of revelation. But while it’s not such a bad thing to lose Madame Blavatsky and theosophy, we should also be careful not to lose sight of abstraction’s absurdities and excesses, however they manifest: How can we keep hold of their intensity without succumbing to metaphysics?

As part of emerging modernisms across the globe, abstraction continued to be in formation throughout the last century. Conventional historical narratives of painting, in thrall to the expressive gesture of later models of abstraction, tend to obscure but cannot repress its remarkably adaptive polymorphism, as so many of the riveting artworks in “Inventing Abstraction” reminded us at every turn. As is perhaps inevitable with such a complex and far-ranging set of problems, we are left with many questions about what was and is really at stake—aesthetically, politically, ethically—in the different modalities of abstraction. We should not forget that from its start, abstraction was contested and fought over as much from within as from outside its ranks. Networks may be very effective at tracking multiple connections and flows across widely dispersed centers and material practices. They are less effective at showing irreconcilable ideological differences, internal antagonisms, and systemic breakdowns—or, just as importantly, abstraction’s maverick, ambivalent, or simply invented protagonists. In this iteration of the origins of abstraction, I. K. Bonset, Theo van Doesburg’s Dada alter ego and muddier of the waters of art-historical categories, who figured in the 2006 Dada show, has definitely left the building. If Blavatsky can remain spirited away, perhaps Bonset might be invited back.

Briony Fer is a professor of the history of art at University College London.