Physics in Riemann's mathematical papers

Athanase Papadopoulos (1, 2)

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

Riemann's mathematical papers contain many ideas that arise from physics, and some of them are motivated by problems from physics. In fact, it is not easy to separate Riemann's ideas in mathematics from those in physics. Furthermore, Riemann's philosophical ideas are often in the background of his work on science. The aim of this chapter is to give an overview of Riemann's mathematical results based on physical reasoning or motivated by physics. We also elaborate on the relation with philosophy. While we discuss some of Riemann's philosophical points of view, we review some ideas on the same subjects emitted by Riemann's predecessors, and in particular Greek philosophers, mainly the pre-socratics and Aristotle. The final version of this paper will appear in the book: From Riemann to differential geometry and relativity (L. Ji, A. Papadopoulos and S. Yamada, ed.) Berlin: Springer, 2017.

Mots clés: AMS Mathematics Subject Classification: 01-02; 01A55; 01A67; Keywords: Bernhard Riemann; space; Riemannian geometry; Riemann sur-; face; trigonometric series; electricity; physics

Domaines: Histoire et perspectives sur les mathématiques [math.HO]; Topologie géométrique [math.GT]

Athanase Papadopoulos. Physics in Riemann's mathematical papers. 2017. ⟨hal-01628080⟩