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(2017) From Riemann to differential geometry and relativity, Dordrecht, Springer.
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.
Publication details
DOI: 10.1007/978-3-319-60039-0_1
Full citation:
Papadopoulos, A. (2017)., Looking backward: from Euler to Riemann, in L. Ji, A. Papadopoulos & S. Yamada (eds.), From Riemann to differential geometry and relativity, Dordrecht, Springer, pp. 1-94.