  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.
