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In 1920 he accepted a chair in the history of science at the Collège de France. His mathematical work mainly consists of extending and clarifying work of others, in particular Painlevé, Poincaré and Emile Picard.
In the history and philosophy of mathematics Boutroux published an extremely important work Les principes de l'analyse mathématique in 2 volumes, Volume 1 in 1914 and Volume 2 in 1919.
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