Consuming and Appropriating Practical Mathematics and the Mixed Mathematical Fields, or Being “Influenced” by Them: The Case of the Young Descartes

This chapter aims to clarify how historians can address the problem of what early modern practical and mixed mathematics had to do with the contemporary transformation of natural knowledge, taking the latter primarily as a set of changes in the domain of natural philosophy. It examines this problem from the perspective of natural philosophical consumers of resources—technical, theoretical and rhetorical—provided by mathematical practitioners and devotees of the mixed mathematical disciplines. The chapter criticizes historical narratives which speak of practical or mixed mathematics ‘influencing’ and ‘shaping’ natural philosophy, proposing that the relationship is better understood as a process of appropriating and translating resources between one field and another. Also questioned are prevalent narratives in which a ‘target’ (e.g. ‘science’) is influenced by a ‘source’ (e.g. practical mathematics) to produce some grand and essential change such as the ‘birth of modern science’. Four case studies support this analysis: Three are drawn from the author’s earlier studies of the young Descartes’ aspirations in physico-mathematics and mechanistic natural philosophy; the fourth deals with the question of the appropriation and transformation of mechanics from practical and mixed mathematics into natural philosophy, in which Descartes played a part.