Descartes and Mathematics

Descartes is one of the few geniuses in history who was able to bequeath epoch-making contributions to philosophy and to mathematics at the same time. In addition, his contributions to these areas are not independent but rather feed on each other. The mutual relation of philosophy and mathematics is reflected in the interpretation of analysis and synthesis in both mathematics and philosophy; the conception of proof; the claim that physics is nothing but geometry; the theory of eternal truths; the conception of infinity; his ontological and epistemological views on extension and number; the role of sense, imagination, and reason in mathematics and its relation to his account of human nature; the transition from a mathematical paradigm of certainty to the claim that mathematics needs to be founded on metaphysics and the role of skepticism in this transition; the development of the method and the notion of mathesis universalis ; and the structure of the Geometry . Rather than try to touch upon all these topics, I will focus in greater depth on the last two: the development of method and the structure of the Geometry , because this will give an insight into what, using Brunschwicg's happy expression, could be called the philosophie mathématique of Descartes, and it will help us to understand the grounds for his foundational choices