Matthew Handelman's book proposes the following narrative: Critical theory has been at odds with mathematics, to a large extent due to the Frankfurt School's critique of the Enlightenment and instrumental reason. But in the Weimar Republic, a few intellectuals were inspired by mathematics to develop critical and/or Jewish-mystical theories of knowledge. Today, as digital humanities mathematize humanistic research, we might be inclined to follow the Frankfurt School thinkers and decry this as an anti-critical development. However, we may also follow the aforementioned Weimar-era thinkers and use mathematics to open up new forms of critical knowledge.

The book opens with a chapter about the Frankfurt School (focusing on Theodor Adorno and Max Horkheimer, and to a lesser extent Walter Benjamin), who criticized mathematics as a form of thought detached from real materiality. As such, mathematics was seen as a tool for depoliticizing thought by making it formal and immaterial (in both senses of the word). The next three chapters counter this stance by studying the work of Gershom Scholem, Franz Rosenzweig, and Sigfried Kracauer, who used mathematics to develop new mystical-critical approaches.

Scholem drew an analogy between mathematics and knowledge of the divine: both indicate an inexpressible world removed from our own (that of platonic pure forms and that of the divine, respectively). Yet just as the meaningless, formal symbols of mathematics can, precisely by their meaninglessness, produce knowledge of the platonic world of abstract mathematics, likewise, some forms of privative poetic language, which break meanings down, can produce knowledge of the divine. As modern mathematics produces this knowledge with its unhistoricized formalism, so knowledge of the divine can arise even as historical mystical traditions deteriorate. Those symbolic traditions, Scholem argued, have power beyond the continuity of their transmission.

Rosenzweig took his inspiration from the generative power of the infinitesimal in mathematics: a materially non-existent, subjective element, at the origin of mathematical descriptions of real motion (at least according to the philosophical tradition championed by Hermann Cohen). Rosenzweig understood the infinitesimal as a means of knowing, even reconstituting the world from below, as it were, by means of local and particular actions. According to Rosenzweig, this view of infinitesimals also allows us to take seriously other “non-existents” (not existing in the sense of not being given materially and objectively to human perception), such as God, World, and Self, and use them to ground knowledge.

Kracauer thought of mathematics as a synthetic a priori between thought and materiality. Social theory cannot be reduced to such a synthetic a priori because of the contingencies of empirical social reality. However, metaphors of projection and transformation can help us reconstruct from observed social products their supervening metaphysical social structures. The latter are historical syntheses that shape our perception and production of reality in a manner similar to that of the Kantian synthetic a priori. The problem with the capitalist-rationalized-mathematized world, then, is not the use of mathematics as such, but the reductive, simplistic understanding of mathematics, which impoverished our insight into the historical a priori, and which Kracauer sought to expand so as to allow for the advance of critical reason.

That concludes (my reconstruction of) Handelman's reconstruction of the three thinkers’ relation to mathematics—or more precisely what he calls “negative mathematics”—those aspects of mathematics that exceed positivist scientific views. But Handelman's introduction and conclusion envelop this reconstruction into an argument about the tensions between critical theory and digital humanities. Instead of viewing digital humanities as an instrumental foreclosure of humanistic critique, Handelman suggests that we may follow the three Weimar-era thinkers and explore the potential for critical interaction between the humanities and mathematical (or digital) tools.

While I found the reconstruction of the three protagonists’ thinking interesting and informative (at least for someone who, like me, knows little to nothing about these thinkers, but is interested in both mathematics and critical theory), the enveloping argument seems less compelling. I agree that digital humanities are not merely a threat to critical thinking—they can also be an opportunity. However, I find that Scholem, Rosenzweig, and Kracauer may not guide us well in this respect.

Indeed, the 1920s were a time when mathematics engaged in self-questioning. This self-questioning resulted in several metaphysical frameworks, such as the Platonism and formalism represented by Scholem and the neo-Kantian trajectories followed by Rosenzweig and Kracauer. Today, however, mathematics seems so smug that it hardly ever bothers to question itself, so one would have to make a genuine effort to draw any critical inspiration from it. Moreover, it was not so much mathematical tools that inspired the three thinkers Handelman studies, but rather philosophies of mathematics. Today, however, philosophy is not the site of interaction between the digital and the humanities. Rather, they meet each other along the lines of data management and processing.

Mathematics today suffers from two kinds of misunderstanding: overvaluation (mathematics as the highest absolute truth, therefore mathematization necessarily makes anything truer, more certain, better) and undervaluation (mathematics as meaningless, formal drudgery that dissociates from any material reality). Our evaluation of digital humanities should not fall prey to either of these traps, but I remain unconvinced that Scholem, Rosenzweig, and Kracauer can lead us away from these misunderstandings. Indeed, all three thinkers depend on ontologies that separate mathematics from material reality (in line with the problematic evaluations of mathematics), rather than on the pragmatic if often-presumptuous tools of the digital humanities.

Handelman's book may help us understand Jewish mystical and critical thought in 1920s Germany, perhaps even inspire us to rethink the critical potentials of language, interpretation, and action as mediated by some philosophies of mathematics. In that respect, Handelman's book is to be recommended. However, in order to rethink critical theory in the age of digital humanities, I believe we need other inspirations.