Géométrie, Topologie, Riemann, et les nuances vivantes de la pensée mathématique chez Bachelard (avec un contrepoint autour de Simone Weil)

Abstract

In this paper we examine many Bachelard references to geometry and topology, and, in particular, to Riemann’s work. Building on those readings, we propose a “living geometry” perspective on Bachelard’s understanding of mathematics, according to some contemporary geometry trends. In counterpoint with Bachelard, we provide a footnote apparatus (basso continuo), around Simone Weil’s reflections on mathematical thought.