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Source: https://www.canal-u.tv/chaines/utls/p... Université de tous les savoirs, Perspectives sur les mathématiques actuelles Production and online publication: June 29, 2000 Speaker: Alain Connes is professor emeritus at the Collège de France and IHES. His awards include the Fields Medal (1982), the Crafoord Prize (2001) and the CNRS Gold Medal (2004). More information: https://alainconnes.org/ Description: My intention is to first explain how the notion of geometric space has evolved through non-Euclidean geometry, Riemannian geometry which is the cornerstone of Einstein's general relativity. I will then discuss the intervention of the quantum world and the profound change it causes in geometric notions. I will also say a few words about renormalization. Regarding my presentation, my intention is to first explain how the notion of geometric space evolved through non-Euclidean geometry, and Riemannian geometry which is the cornerstone of Einstein's general relativity.