Mathematics, History of Mathematics and Poncelet: The Context of the Ecole Polytechnique

Résumé En

Jean-Victor Poncelet (1788-1867) is known as a geometer whose mathematical contributions were crucial for the development of what would later become projective geometry. In this chapter, we focus on his practice of mathematics, and notably on the fact that Poncelet systematically intertwined mathematical activity with both historical and philosophical reflections about mathematics. Indeed, many practitioners of mathematics at the time, most of whom Poncelet was in contact with, also conducted historical work on mathematics and wrote on the philosophy of mathematics. However, we argue that, in this context, Poncelet’s practice of mathematics was unique, being characterized by an intimate interrelation between these three fields of inquiry. Our aim here is more specifically to shed light on the shaping of Poncelet’s practice. We suggest that his training at the École Polytechnique, between 1807 and 1810, played an important role in this respect. Our argument unfolds in three main steps. We point out characteristic features of the training of students at the École Polytechnique that, in our view, left a hallmark on Poncelet’s mathematical practice. We particularly bring to the fore the importance given to collective work and to reading in students’ learning (Part 2). In this respect, two aspects were instrumental: the constitution of a collection of books at the library of the École—which aimed to be a collection of reference for “the arts and the sciences”—and the production of historical works that relied on this collection and were thought to be useful for the learning and the advancement of mathematics (Part 3). Lastly, we focus on the journal established at the École in 1804, Correspondance pour l’École Polytechnique à l’usage des élèves de cette école, which reflects several aspects of the life at the École. We argue that the journal gives clues about how, like teachers, students were encouraged to practice mathematics, in particular geometry, in relation to elements of their history (Part 4). This publication shows how this interest in history meshes with an emphasis on the comparison between methods. It also indicates that former students continued to practice mathematics in this way.