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La polémique entre Poincaré et Russel au sujet du statut des axiomes de la géométrie. (The polemic between Poincaré and Russel about the status of the axioms of geometry). (French) Zbl 1030.01024
Summary: Before their well-known dispute over logistics, Poincaré and Russell polemized over the status of the axioms of geometry. At the close of the 19th century, philosophical discussions about geometry and space theory strongly influenced both the idea and the development of geometry. This paper stresses how Poincaré and Russell used mathematics to support their philosophical arguments, and shows, conversely, how their respective philosophical stances influenced their thoughts about geometry.

01A55 History of mathematics in the 19th century
01A60 History of mathematics in the 20th century
51-03 History of geometry