Mathematics, physics and philosophy in Riemann's work and beyond

TL;DR

This paper introduces a multi-authored book that explores Riemann's work across mathematics, physics, and philosophy, highlighting its historical impact and interdisciplinary significance.

Contribution

It provides a comprehensive overview of Riemann's diverse contributions and their influence on various fields, connecting mathematical developments with philosophical and physical insights.

Findings

Riemann's work significantly impacted topology and geometry.

The book covers interdisciplinary links between mathematics, physics, and philosophy.

Riemann's ideas continue to influence modern scientific thought.

Abstract

This is the introduction I wrote for the multi-authored book "From Riemann to differential geometry and relativity", edited by L. Ji, A. Papadopoulos and S. Yamada (Berlin, Springer verlag, 2017). The book consists of twenty chapters, written by various authors. This introduction, besides giving the information on the content of the book, is a quick review of the topics on which Riemann worked and of the impact of this work on mathematics (topology, complex geometry, algebraic geometry, integration, trigonometric series, Riemannian geometry, etc.), philosophy and physics.