On the Hypotheses Which Lie at the Bases of Geometry

  • Bernhard Riemann
  • Jürgen Jost

Part of the Classic Texts in the Sciences book series (CTS)

Table of contents

  1. Front Matter
    Pages i-x
  2. Jürgen Jost
    Pages 1-8
  3. Jürgen Jost
    Pages 9-28
  4. Jürgen Jost
    Pages 29-41
  5. Jürgen Jost
    Pages 43-118
  6. Jürgen Jost
    Pages 119-146
  7. Jürgen Jost
    Pages 147-153
  8. Jürgen Jost
    Pages 155-162
  9. Back Matter
    Pages 163-172

About this book


This book presents William Clifford’s English translation of Bernhard Riemann’s classic text together with detailed mathematical, historical and philosophical commentary. The basic concepts and ideas, as well as their mathematical background, are provided, putting Riemann’s reasoning into the more general and systematic perspective achieved by later mathematicians and physicists (including Helmholtz, Ricci, Weyl, and Einstein) on the basis of his seminal ideas. Following a historical introduction that positions Riemann’s work in the context of his times, the history of the concept of space in philosophy, physics and mathematics is systematically presented. A subsequent chapter on the reception and influence of the text accompanies the reader from Riemann’s times to contemporary research. 

Not only mathematicians and historians of the mathematical sciences, but also readers from other disciplines or those with an interest in physics or philosophy will find this work both appealing and insightful.


Hermann Weyl commentary Riemannian geometry general relativity theory geometry and space notion of space

Authors and affiliations

  • Bernhard Riemann
    • 1
  1. 1.c/o Springer-VerlagHeidelbergGermany

Editors and affiliations

  • Jürgen Jost
    • 1
  1. 1.Geometrische MethodenMax Planck Inst. for Mathematics in theLeipzigGermany

Bibliographic information

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