Creativity and Computation: a History of the Mathematical Sublime

In contemporary discourse, the categories of creativity and computation are typically treated as opposites, or at most as mutually exclusive complements in the battle for consumer attention. A visual artist might be called in, for instance, to improve the interface that mediates between computational technology and user (a division of labor that informs the plotlines of several recent fictional works). A large language model can be “trained” on the creative output of human authors (a division of labor that has recently led to class action lawsuits). Students can generate formulaic B+ papers by feeding an appropriate prompt into ChatGPT, but not the “spark” of originality that characterizes the best essays. AI can write scripts and produce graphics on command, but not real art—whereby “real art,” like “original essay,” has suddenly become a category that requires legally implementable definition.

The project took its point of departure from the hypothesis that this discursive opposition is particular to our contemporary moment, and that the logic of its particularity requires analysis, against the backdrop of a historical perspective that can help to isolate what has changed. Within the contemporary framework, “computation” names a domain of finitely expressible rules and algorithm-governed behavior, of countable parameters and binary code. “Creativity,” on the other hand, belongs to the implicitly infinite domain of whatever transcends computation’s reach. The question of the creativity-computation relationship is therefore as mathematical as it is philosophical, and historical reflection must proceed accordingly.

Certain aspects of the infinite-finite distinction have remained relatively stable for centuries; many others, however, have not. Mathematical techniques for calculating with, counting, and conceptualizing the infinite changed radically over the second half of the 19th century, in ways that laid the groundwork for the 20th century invention of computational technologies. During this period, philosophical and mathematical approaches to the question of finite cognitive limits—and to the “sublime” structure of what necessarily transcends them—fed into each other constantly and transformatively. The mathematicians who revolutionized the discipline, from Bernhard Riemann to Kurt Goedel, were educated primarily at German universities, in an intellectual context saturated with German Idealist philosophy, and they viewed their new analytic methods accordingly, as the “fruit” of prior creative syntheses. Increased computational power was for them a byproduct of new insights into the underlying unity of previously disparate mathematical domains, and so also, into the question of what mathematics was actually about.

This way of thinking about the relationship between creativity and computation remains operative across wide swaths of contemporary mathematics, including inside of computation theory itself. Yet even as computational power has grown—and become terminologically indistinguishable from the machines that now perform the lion’s share of such “mechanical” operations—the category of creativity has all but disappeared from the public discourse about cognition, except as a cipher of loss or compensatory supplement. The implicit assumption of tropes like the “network sublime,” the “tsunami of text,” and the “digital ocean” seems to be that our ability to compute, or at least to invent new technologies for doing so, has definitively outstripped our ability to generate new frameworks of sense-making within which to embed our results. Existing pre-histories of the digital paradigm tend to focus, usefully but one-sidedly, on the ways in which computational paradigms of the past prepare and prefigure this now-familiar contemporary perspective. The project pushed back against such an implicitly teleological approach by analyzing a series of creative-computational intersection points, from the mid-19th century to the present, which undermine the digital-analog binary as currently conceived and push us to repose the question of what computation means.