Riemann on geometry, physics, and philosophy—some remarks

Jeremy Gray

pp. 97-110

in: Lizhen Ji, Athanase Papadopoulos, Sumio Yamada (eds), From Riemann to differential geometry and relativity, Berlin, Springer, 2017

Abstract

Riemann's paper "On the hypotheses that lie at the foundations of geometry' is one of the fundamental papers in the creation of modern geometry. We analyse its content, look at the influence the work of Gauss and Herbart exercised on Riemann, and discuss other of Riemann's papers that shed light on his ideas, in particular on his appreciation of the concept of curvature.