Making the Manifold: Bernhard Riemann's Habilitation Lecture, Mathematics, and German Universities

Abstract

This dissertation examines mathematician Bernhard Riemann’s (1826-1866) creation of his 1854 habilitation lecture at the University of Göttingen in order to characterize scholarly labor and, by extension, mathematical labor. Riemann’s habilitation lecture lies at the intersection of two prominent transformation narratives: of German universities into “modern research universities” and of mathematics into “modern mathematics.” Riemann’s lecture, “On the Hypotheses Which Underlie Geometry,” is widely regarded as a foundational work in mathematics that later inspired modernist mathematicians. It is also an excellent exemplar of the broader genre of the habilitation lecture, which was a product of decisive university reforms.I provide a new account of scholarly labor in this pivotal moment by locating Riemann in the three academic spaces in which he developed his lecture: the library, the private residence, and the professor’s home. Each chapter focuses on one space; the dissertation as a whole provides an expansive picture of how young scholars conducted research at the University of Göttingen. I show that using each space required a certain kind of labor, which in turn shaped Riemann’s eventual habilitation lecture: organizing knowledge (the library), exercising moderation (Riemann’s residence), and conforming to academic social norms (professors’ homes). In forming his habilitation lecture, Riemann enacted each of these forms of labor with a corresponding epistemic tool: the notion (Begriff), the case (Fall), and generalization. By following Riemann’s creation of his habilitation lecture in these spaces, I provide an account of the function of these tools in academic research. Historians have considered the topics of this dissertation—Riemann’s habilitation lecture, the University of Göttingen, mathematics, Riemann himself—as exemplary in different ways, or even as exceptional. I scrutinize similar claims to exemplarity in Riemann’s habilitation lecture itself, and thereby historicize “particularist” and “generalist” narratives as a product of the nineteenth-century German university. A central difficulty of the habilitation lecture was to properly define the relationship between the general and the particular, not only in one’s research, but also in presenting oneself to the scholarly community.