This project is a cross-disciplinary investigation into the emergence of a particular form of mathematization, a specific blending, into one compound, of theoretical sciences and experimental methods. We call this mixture “mathematical physics,” to distinguish it from other seventeenth century competing attempts to mix physics and mathematics.

Mathematical physics so understood is both an actor’s category and a term we propose for historiographic use. Disentangling its main characteristics requires a fair amount of historical expertize, as well as philosophical and historiographic investigations. This is what our project aims to undertake by putting at work the skills of an interdisciplinary team of philosophers and historians of early modern science for 30 months (until December 2019).

We believe that the introduction of this new historiographic category is likely to bring important clarifications in many current debates in history and philosophy of science. First, it will help disentangle between two types of early modern approaches to the investigation of nature which were, so far, conflated together: a top-down, experimental and instrumental approach – the mathematical physics – and a bottom-up approach which blends axioms of mathematics with principles and axioms of natural philosophy, i.e., the physico-mathematical approach. A clearer understanding of their particularities and differences will give us a more fine-grained picture of the wide spectrum of early modern forms of mathematization in the period between Bacon and Newton, and will deepen our understanding of the intricate relations between “theories” and “experimental practices” in the early modern world. Furthermore, our proposal will open up new fields of cross-disciplinary investigation, building bridges between historians of early modern mathematics, historians of philosophy and historians of science.

In the first 12 months of the project, our main goal will be to disentangle and clarify the camps subsumed under these two historiographic labels, tracing their characteristic and distinctive features and relating them to the historical context of the late sixteenth and early seventeenth century methodologic and meta-mathematical debates over the nature of *scientia* and the possibility of blending physics and mathematics. Our investigation will cover a wide selection of texts coming from different traditions, disciplines and genres, but focusing on a common set of problems, all derived from two texts: Aristotle’s *Posterior Analytics* and Proclus’ *Commentary on the first book of Euclid*. Both texts have a rich interpretative tradition; our investigation will follow one particular trend, i.e., Proclus’ attempt to redefine the Aristotelian division of the sciences in such a way to make `mixtures’ and ‘blendings’ not only possible but also desirable, as markings of the “true” *scientia*. This is the trademark of what has been called “the Proclean tradition”. Historians of mathematics have documented its importance (de Risi, forthcoming; Rabouin 2009, 2017); but, apart from this, the “Proclean tradition” has, so far, been virtually invisible to the historians of early modern science and to historians of early modern philosophy (with some notable exceptions, Domski 2013, Hattab 2016). Therefore, the first step in our project will be to uncover and make explicit seventeenth century philosophers’ engagement with the Proclean tradition. Our first objective is to disentangle the elements of this Proclean tradition and to show how it inspired various forms of “mixing” and “blending” which replaced, eventually, the Aristotelian model of subalternation. In order to do this, we will investigate a number of meta-mathematical and methodological debates, questions regarding the nature of the *scientia* and the relationship between theoretical and practical (operative) sciences. We will show that the Proclean tradition opened the way to a richer and more sophisticated understanding of mixing physics and mathematics (and more generally, a richer understanding of the “mixed-mathematics”). The second objective of our project is to show how various types of “mixing” and “blending” physics and mathematics made possible by the Proclean tradition were transmitted further in the seventeenth century, in the works of mathematicians, philosophers or practitioners of mechanical arts, in the particular context of experimental philosophy. Our work hypothesis is that the experimental context gave a particular twist to these diverse methodological and meta-mathematical discussions, facilitating the emergence of mathematical physics.

The second and the third year of the project will be devoted to the investigation of a number of relevant case studies and to begin a more thorough mapping of early modern forms of mathematization, in the context of experimental philosophy. Key figures in our investigation will be Francis Bacon, Rene Descartes, John Wilkins, Isaac Barrow and Isaac Newton. However, this list is tentative, since it will depend on the predictability of funding. Nevertheless, the advantage of working on case-studies is that we can define individual research papers quite well and pursue them regardless of the variations of the team. These individual investigations will be in-depth case studies of particular solutions to problems of “mixing” and “blending” experimental investigations and theoretical contents in the top-down approach characteristic of mathematical physics. They will constitute the material for the original articles which will be published by members of our team at the end of the second year of the project.