The work of the philosopher-mathematician, Albert Lautman (1908-1944), situated within the French historical epistemological landscape of the 20th-century, is characterized by a fascinating an unique interplay between metaphysics, mathematics and history. According to Lautman, philosophy of mathematics is a synthetic study of mathematical problems seen from a Platonic meta-mathematical perspective. So it is up to the philosopher of mathematics to describe the ideal reality that guides the development of mathematics.
This project aims to determine the full extent of Lautman’s mathematical philosophy. Firstly, it will defend the thesis that Lautman’s historical perspective does not only challenge the foundationalist conception of philosophy of mathematics, but also that his unique Platonism puts the unity of mathematics, the nexus between mathematics and physics, and the relation of mathematics to reality back at the center of reflection. Secondly, through two case studies, this project has the ambition to critically assess Lautman’s impact on contemporary philosophical and scientific developments. In particular, a philosophical case study will reflect on the influence of Lautman’s mathematical philosophy on Gilles Deleuze and the recent turn to materialism. A physico-mathematical case study will evaluate the relation between Lautman, catastrophe theory (René Thom) and the practice of dynamic modelling.