"Descartes, Euler, Gauss: From surfaces to integers". Hirzebruch lecture by Werner Ballmann on Monday, November 13, University Club Bonn

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Geometric quantities of a surface, like distance, angle, or area, change when the surface is deformed. Euler discovered a quantity, the Euler characteristic, which remains unchanged. The formula of Gauss-Bonnet, a landmark result of mathematics, relates Euler characteristic with geometry. In the talk, I will present ideas of Descartes, Euler, and Gauss related to this formula.