Paul Valéry and Geometry: Instrument, Writing Model, Practice

In the course of the nineteenth century, the development of non-Euclidean geometries and topology led to wide-ranging discussions on the foundations of mathematics. The new mathematical objects and the accompanying disputes also became a source of fascination for literature. A paradigmatic instance of this is the French writer and theorist Paul Valéry (1871-1945), whose Cahiers (1894-1945) show a constant preoccupation with mathematical problems. What is remarkable here is the fundamental significance Valéry ascribes to mathematics for his own work. Initially, he searched in topology for a tool to advance his reflection on psychology. Although this project ultimately failed, mathematics became for Valéry an ideal—since "operative"—mode of writing, one against which to measure his own literary writing and note-taking. However, the result of this formalization, which he pursued over decades, was neither mathematic literature nor, indeed, literary mathematics, but a form of writing that had a significant effect upon the twentieth-century understanding of literature: the aim of producing a finished work was shifted into the background to make room for writing as a "life-form."