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Un " rapprochement curieux de l'algèbre et de la théorie des nombres" : études sur l'utilisation des congruences en France de 1801 à 1850

Abstract : Gauss introduced the notion of congruence in 1801 in the Disquisitiones Arithmeticae. The standard historiography connects its history to the development of algebraic number theory, a history built around a group of German mathematicians. However other authors in the first half of the nineteenth century published works related to congruences from different perspectives. We study here some of them while focusing on the French scene between 1801 and 1850. From a global reading of the texts of our corpus, we first show that congruences did not develop in France as an autonomous field, but as one tightly linked to the theory of equations. However, the different practices thus encountered were far from uniform, whether in terms of methods, tools or disciplinary configurations. We then study arithmetical works of Euler, Lagrange, Legendre and Gauss in order to understand some of the origins of the multifarious activity analyzed in our first part. Finally, we focus on the work of two authors, Louis Poinsot and Augustin Louis Cauchy, who played a key role in elaborating and circulating results and practices related to congruences, but who have virtually disappeared from twentieth-century histories of number theory.
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https://tel.archives-ouvertes.fr/tel-00653748
Contributor : Jenny Boucard <>
Submitted on : Tuesday, December 20, 2011 - 10:40:45 AM
Last modification on : Wednesday, December 9, 2020 - 3:11:51 PM
Long-term archiving on: : Wednesday, March 21, 2012 - 2:24:26 AM

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  • HAL Id : tel-00653748, version 1

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Jenny Boucard. Un " rapprochement curieux de l'algèbre et de la théorie des nombres" : études sur l'utilisation des congruences en France de 1801 à 1850. Histoire et perspectives sur les mathématiques [math.HO]. Université Pierre et Marie Curie - Paris VI, 2011. Français. ⟨tel-00653748⟩

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