Looking backward

from Euler to Riemann

Athanase Papadopoulos

pp. 1-94

in: Lizhen Ji, Athanase Papadopoulos, Sumio Yamada (eds), From Riemann to differential geometry and relativity, Berlin, Springer, 2017

Abstract

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.