Paul Valéry and Geometry: Instrument, Writing Model, Practice

Abstract

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."

“Time is Production”: Process-Art, and Aesthetic Time in Paul Valéry’s Cahiers

“…] in what mathematics teaches are the possibilities of transformation-and the habit or tendency-when faced with a given relation, (from experience, or chance, or need) to operate on it without regard to its meaning outside of its form, quite freely in that respect-but exploiting only its formal properties of expression" (Valéry 2001, pp. 220-21, 23; also see Krauthausen 2010). Incompletion and the nascency of forms, their openness to further handling and prolongation, become the motors or precursors of transformative reprises and connections, offering the possibility that a capacity (habit or tendency) or "implex" can develop in response to these transformations.…”

A Writer Looking for His Writing Scene: Paul Valéry's Procedures in His Notebooks around 1894

“… 24 Mathematics also has a broad significance for Valéry, especially for his own writing (see Robinson 1963; Celeyrette-Pietri 1979; Krauthausen 2010a). …”

“…Mathematics also has a broad significance for Valéry, especially for his own writing (seeRobinson 1963;Celeyrette-Pietri 1979;Krauthausen 2010a). 25 In the original: "systèmes de notations"(Valéry 1957c(Valéry , 1266.26 In the original: "Le graphique est capable du continu dont la parole est incapable; il l'emport sur elle eń evidence et en précision.…”