Physics in Riemann's mathematical papers

TL;DR

This paper explores Riemann's mathematical ideas that are influenced by physics and philosophy, highlighting the interconnectedness of his scientific and philosophical perspectives in his work.

Contribution

It provides an overview of Riemann's mathematical results motivated by physics and discusses the philosophical background influencing his scientific ideas.

Findings

Riemann's mathematical ideas are deeply intertwined with physical concepts.

His work is motivated by and related to problems in physics.

Philosophical influences from Greek thinkers are evident in his scientific approach.

Abstract

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.