The Philosophy of Mathematics: Privation and Representation in Gershom Scholem’s Negative Aesthetics

Chapter 2 investigates the moment in 1917 when the philosophy of mathematics revealed to Gershom Scholem the symbolic potential of privation. Mathematics—in particular, the translation of logic into the symbols and operations of mathematics known as mathematical logic—produced novel results by discarding the conventional representational and meaning-making functions of language. Drawing on these mathematical insights, Scholem’s theorization of the poetic genre of lament and his translations of the biblical book of Lamentations employed erasure on the level of literary form to symbolize experiences, such as the Jewish diaspora, that exceed the limits of linguistic and historical representation. For Scholem, both poetry and history can mobilize deprivation as a means of retaining in language a symbol of experiences and ideas that remain unsayable in language and inexpressible in history—accounting for the erasure of exile and finding historical continuity in moments of silence, rupture, and catastrophe.

The Problem of Mathematics in Critical Theory

This introduction lays out the eclipse of mathematics in Max Horkheimer and Theodor W. Adorno’s self-fashioning of critical theory and proposes an alternative paradigm for mathematics in critical thought, which this study calls negative mathematics. Radicalizing Edmund Husserl’s linkage of the mathematization of nature and the worsening political situation in Europe in the 1930s, the foundational phase of Horkheimer and Adorno’s critical project defined itself against mathematics as the reification and instrumentalization of reason. In the work of Gershom Scholem, Franz Rosenzweig, and Siegfried Kracauer, however, negative mathematics—mathematical approaches to lack, absence, and discontinuity—revealed ways of expressing Jewish experiences and perspectives otherwise erased by secularization and modernization. This development of negative mathematics is situated in a history of German-Jewish intellectual appeals to mathematics since Moses Mendelssohn. In the hands of Scholem, Rosenzweig, and Kracauer, it crystalized into theory that drew on mathematics to reconfigure the limits of representing minoritarian groups and ideas.

Who’s Afraid of Mathematics? Critical Theory in the Digital Age

This book’s conclusion explores the persistence of intellectual anxieties related to mathematics in current debates over computational and quantitative approaches to humanistic inquiry known as the digital humanities. The digital humanities offer broader access to cultural and aesthetic products and new insights into their composition, circulation, and interrelations. And yet those skeptical of the digital humanities—akin to Horkheimer and Adorno’s criticism of the Logical Positivists—accuse digital humanists of uncritically yielding to business and science, objecting that reorienting the humanities around technology and code forfeits politics and language, history and critique. Negative mathematics offers a third way for the humanities to move between naïve positivism and critical rejectionism. Drawing on Scholem, Rosenzweig, and Kracauer, this third way finds in mathematical-computational approaches to negativity new ways to retain the silences of marginalized ideas and erasures of minoritarian experiences in historical and aesthetic thought.

Geometry: Projection and Space in Siegfried Kracauer’s Aesthetics of Theory

Chapter 4 investigates how geometry revealed to Siegfried Kracauer a style of cultural critique that worked toward a more reasonable society through critique. For Kracauer, geometric metaphors of space and projection fulfilled a seemingly impossible task: in a world vanquished of divine authority, geometry bridged the divide between the raw contingency of materiality and the necessity of mathematical reasoning. Kracauer’s Weimar-era essays, such as “The Mass Ornament” (1927), transformed these metaphors into an aesthetic strategy that, through the space of the text, sought to confront readers with the capitalist misuse of reason and provoke critical self-reflection. For Kracauer, the marginalized figure of the societal observer, the cultural critic, even the Jew took on the role of correcting the historical trajectory of Enlightenment. This vision of critique suggests that critical theorists look to the performativity and positionality of criticism for modes of cultural intervention in our hyper-rationalized and digitized present.

The Trouble with Logical Positivism: Max Horkheimer, Theodor W. Adorno, and the Origins of Critical Theory

How did critical theory, at least as it was first envisioned by Max Horkheimer and Theodor W. Adorno, come to be so opposed to mathematics? Chapter 1 examines the transformation of Horkheimer, Adorno, and Walter Benjamin’s prewar confrontation with Logical Positivism into a history of thinking that equated mathematics with the downfall of Enlightenment. According to the first generation of critical theorists, the reduction of philosophy to the operations and symbols of mathematics, as proposed by Logical Positivists such as Otto Neurath and Rudolph Carnap, rendered modern philosophy politically impotent and acquiesced to the powers of industry and authoritarian government. This initial phase of critical theory defined itself against the Logical Positivists’ equation of thought and mathematics, subsuming mathematics in their interpretation of reason’s return to myth and barbarism. Horkheimer and Adorno’s postwar texts and the work of second-generation critical theorists perpetuated this image of mathematics, canonizing it as an archetype of instrumental reason, reification, and social domination.

Infinitesimal Calculus: Subjectivity, Motion, and Franz Rosenzweig’s Messianism

By way of Leibniz’s and Newton’s calculi and Hermann Cohen’s neo-Kantianism, Chapter 3 explores how infinitesimal calculus allowed Franz Rosenzweig to embed messianism into the daily work of thought. Through metaphors of space and subjectivity, the idea of the differential—the infinitely small quantity—synthesized the finitude of lived experience with the infinitude of the Absolute. In Rosenzweig’s The Star of Redemption (1921), the differential revealed a world in which the thinking individual works toward the redemption of the world, thus arguing for the modern relevance of Judaism despite the apparent world-historical hegemony of Christianity. For Rosenzweig, the differential pointed to a “messianic theory of knowledge,” which made room for the truths verified by belief alongside those proved by mathematics. It also underscored the epistemological significance of marginalized beliefs and experiences—even of those people who stand on the sidelines of so-called world history—in the project of redemption.