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Des géométries étatsuniennes à partir de l'étude de l'American Mathematical Society : 1888-1920

Abstract : In 1888, three students created a mathematical society in New York City. Six years later, this society became national and took the name of the American Mathematical Society (AMS). In 1920, it counted thousands of members, published many articles and reviews, and organized mathematical meetings on a regular basis all over the country. Based on the study of publications from the AMS journals until 1920, this dissertation aims at retracing a social history of Geometry, by answering two main questions: how were geometrical activities related to the AMS organized and distributed and how was geometrical knowledge transferred from or to the USA? After determining what the category of Geometry meant for the editors of various catalogues of mathematical publications, I will analyze the lessons given and received by some members of the AMS, the reviews published in its Bulletin and the mathematical meetings held by the society. The descriptions of the geometrical activities organized by the AMS, as well as the context in which they took place, will thus help us draw a cartography of Geometry. We will see that it can be defined in several ways from both an academic and a sociological perspective. I will also identify the dominant people in Geometry within the Society. More precisely, we will see who were the power holders, whether this power was scientific or institutional, according to the different forms it could take within the AMS. Among the people thus identified, I will particularly focus on three of them (V. Snyder, L. P. Eisenhart and E. J. Wilczynski). This will allow us to treat the two key questions at an individual scale rather than at the previous institutional one. V. Snyder and L. P. Eisenhart’s cases will provide us with the opportunity of studying what non-American mathematical results were taken into account and used in their works while E. J. Wilczynski’s will allow us to understand how his research was spread abroad.
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Samson Duran. Des géométries étatsuniennes à partir de l'étude de l'American Mathematical Society : 1888-1920. Histoire, Philosophie et Sociologie des sciences. Université Paris-Saclay, 2019. Français. ⟨NNT : 2019SACLS207⟩. ⟨tel-02505814⟩

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