I am currently working on a dissertation entitled, “Making the Manifold: Mathematical Libraries in Göttingen.” In the early years of the University of Göttingen’s library system, readers of mathematics would have found Göttingen’s repository of mathematical texts in primarily one place: the University Library. Starting at the beginning of the nineteenth century, Göttingen professors began to develop specialist mathematical libraries: the circulating library for the mathematical-physical seminar, the Mathematische Annalenjournal, the collection of models and instruments, and the mathematics reading room. Making the Manifold traces the development of these libraries by focusing on a product of the Göttingen library system which remains a foundational concept in mathematics today: the manifold, which is a generalization of three-dimensional physical space. The mathematical manifold (Mannigfaltigkeit) was first defined, investigated, published, and read about in Göttingen’s libraries.
The manifold concept has featured prominently in the scholarship on “modern” mathematics, which asks: how did the discipline of mathematics, once an empirical study, become both detached from the physical world, and concerned instead with constructed objects and structures? While most accounts of modernization consider it as the successive development of new ideas, I consider ideas and institutions as inseparable. I ask instead: how did mathematics, once an empirical and textual practice, become an almost exclusively textual practice? Libraries were a crucial part of this development. Not only did organized libraries make possible the proliferation of mathematical texts, mathematical practice began increasingly to reflect a practice crucial to library-formation: classification. The shared history of libraries and manifolds involves a long-standing and persistent tension between the building and breaking disciplinary boundaries, not only between mathematics and the sciences, but between mathematics and the humanities.