The Mathematical Theses Defended at collège de Clermont (1637-1682): How to Guard a Fortress in Times of War

Abstract

For some thirty years, historians of science and philosophy working on the seventeenth century have endeavored to blur the edges of an opposition that had until then been generally accepted, namely, between the “new philosophy” on one hand and an “old philosophy” on the other. But philosophers of the seventeenth century themselves considered their intellectual enterprise in terms of a war between two camps, the ancient philosophers and the modern philosophers. If we historians wish to understand this war, we have to apply an elementary principle of symmetry to philosophers and take into account not only what the new philosophers said, but what the ancient philosophers said. In these circumstances, it is only natural to get interested in the school production that the theses defended in Jesuit colleges were.

In France, the most visible college was the collège de Clermont in Paris, where more than fifty theses in mathematics or in philosophy were defended between 1637 (the date of publication of the Discourse on method and of the Essays) and 1682 (the year when collège de Clermont, having received the patronage from Louis XIV, became Louis-Le-Grand). As a first examination reveals however, philosophy theses are large posters that do not really evolve during this period, while theses in mathematics are small in quarto books of about 20 pages that include rather extensive discussions in which positions are taken against those who were perceived as Aristotle’s opponents.

The paper is consequently focused on the mathematics theses only, which include not only geometry and arithmetic, but also mixed mathematics (optics, astronomy, mechanics). The first objective is to understand what these theses reveal about the early modern practices of teaching and learning, practices that varied from one teacher to another. The second objective is to understand how the Jesuit mathematicians reacted to the novatores, in particular Copernicus, Tycho, Galileo, Descartes and Pascal: here again, we want to insist on variety rather than on uniformity.