The Mathematical Imagination is an archaeology of the undeveloped potential of mathematics for critical theory. As Max Horkheimer and Theodor W. Adorno first conceived of the critical project in the 1930s, critical theory steadfastly opposed the mathematization of thought. Mathematics flattened thought into a dangerous positivism that led reason to the barbarism of the Second World War. The Mathematical Imagination challenges this narrative and argues that it has obscured how mathematics provided three lesser-known German-Jewish thinkers—Gershom Scholem, Franz Rosenzweig, and Siegfried Kracauer—with metaphors to negotiate the crises of modernity during the Weimar Republic. Their theories of poetry, messianism, and cultural critique borrowed ideas from the philosophy of mathematics, infinitesimal calculus, and geometry in order to refashion cultural and aesthetic discourse. Drawn to the austerity and muteness of mathematics, these friends and forerunners of the Frankfurt School found in mathematical approaches to negativity strategies to capture the marginalized experiences and perspectives of Jews in Germany. This vocabulary, in which theory could be both mathematical and critical, is missing in the intellectual history of critical theory—from the work of second-generation critical theorists such as Jürgen Habermas to contemporary critiques of technology. Building on the work of Martin Jay and Susan Buck-Morss, The Mathematical Imagination shows how Scholem, Rosenzweig, and Kracauer’s engagement with mathematics uncovers a more capacious vision of the critical project, one with tools that can help us confront and intervene in our digital, and increasingly mathematical, present.