© 2016

On the Hypotheses Which Lie at the Bases of Geometry

  • Jürgen Jost


  • Presents a revised translation of Riemann's classic text

  • Connects modern research with Riemann's text

  • Includes a biographical outline and a chronological table


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

  1. 1.c/o Springer-VerlagHeidelbergGermany

Editors and affiliations

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

Bibliographic information

  • Book Title On the Hypotheses Which Lie at the Bases of Geometry
  • Authors Bernhard Riemann
  • Editors Jürgen Jost
  • Series Title Classic Texts in the Sciences
  • Series Abbreviated Title Classic Texts in the Sciences
  • DOI
  • Copyright Information Springer International Publishing Switzerland 2016
  • Publisher Name Birkhäuser, Cham
  • eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
  • Hardcover ISBN 978-3-319-26040-2
  • Softcover ISBN 978-3-319-79880-6
  • eBook ISBN 978-3-319-26042-6
  • Series ISSN 2365-9963
  • Series E-ISSN 2365-9971
  • Edition Number 1
  • Number of Pages X, 172
  • Number of Illustrations 1 b/w illustrations, 0 illustrations in colour
  • Topics History of Mathematical Sciences
  • Buy this book on publisher's site
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“It is a modern version of the classical Riemann’s lecture about developments in the geometry and the birth of the Riemannian geometry. … it brings the basic concepts and the necessary mathematical background that will help you to read this important and classical piece of work that was Riemann’s lecture on geometry. … interesting not only to mathematicians but also to physicist and philosophers. It is an interesting and well-crafted book and I recommend it to your personal library.” (Philosophy, Religion and Science Book Reviews,, June, 2016)