Looking backward: From Euler to Riemann

Athanase Papadopoulos (1, 2)

1 IRMA - Institut de Recherche Mathématique Avancée
2 Department of Mathematics, Brown University

We survey the main ideas in the early history of the subjects on which Riemann worked and that led to some of his most important discoveries. The subjects discussed include the theory of functions of a complex variable, elliptic and Abelian integrals, the hypergeometric series, the zeta function, topology, differential geometry, integration, and the notion of space. We shall see that among Riemann's predecessors in all these fields, one name occupies a prominent place, this is Leonhard Euler. The final version of this paper will appear in the book \emph{From Riemann to differential geometry and relativity} (L. Ji, A. Papadopoulos and S. Yamada, ed.) Berlin: Springer, 2017.

Domaines: Topologie géométrique [math.GT]; Variables complexes [math.CV]; Géométrie différentielle [math.DG]; Histoire et perspectives sur les mathématiques [math.HO]

Athanase Papadopoulos. Looking backward: From Euler to Riemann. 2017. ⟨hal-01614429⟩