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Chapitre d'ouvrage Année : 2023

Mathematics, history of mathematics and Poncelet: the context of the Ecole Polytechnique

Résumé

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 historical and philosophical reflections about mathematics. Indeed, many practitioners of mathematics at the time, with most of whom Poncelet was in contact, also conducted historical work on mathematics and wrote on the philosophy of mathematics. However, we argue that, in this context, Poncelet had a unique practice, 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 part 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 insist notably on the importance granted to collective work and to reading in students’ learning (Part 2). In this respect, instrumental were 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 related production of historical works that relied on it and were thought to be useful to each 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 professors, 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 kept practicing mathematics in this way.
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halshs-03931263, version 1 (09-01-2023)

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  • HAL Id : halshs-03931263 , version 1

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Bruno Belhoste, Karine C.C. Chemla. Mathematics, history of mathematics and Poncelet: the context of the Ecole Polytechnique. K. Chemla, Jose Ferreiros, Lizhen Ji, Erhard Scholz, Chang Wang. The Richness of the History and Philosophy of Mathematics, Springer, In press, Archimedes. ⟨halshs-03931263⟩
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