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Reception of Cantor's set theory in France

Par Wei Guo FOO et Nathan GROSSHANS (étudiants en master 1 à l'Ecole polytechnique en 2013)
03 Feb. 2022

While set theory has immense applications to modern mathematics and computer science, it was regarded by a few mathematicians in the 1880s as an abstract subject which was divorced from the reality. Set theory arose in the 19th century, mainly due to the works of Georg Cantor. In this article, we seek to lay out some of the events which we find important in the study of the reception of set theory in France. The first event would be the recognition of the usefulness of Cantor's set theory by Mittag-Leffler, who then proposed to Hermite and some other French mathematicians (Poincaré, Appell, and Picard) to publish Cantor's works in Acta Mathematica. Next, we give a few examples of how set theory was used in France. In these examples, we have Poincaré with his complex analysis, Camille Jordan with his Cours d'analyse de l'École Polytechnique, and Paul Tannery with his attempted proof of the continuum hypothesis. We find that set theory did not meet full opposition from the French mathematical community. It only received partial acceptance, which we will elaborate in the later sections.