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On the Hypotheses Which Lie at the Bases of Geometry

  • Book
  • © 2016


  • 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 book series: Classic Texts in the Sciences (CTS)

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Table of contents (7 chapters)


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.


“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)

Authors, Editors and Affiliations

  • Geometrische Methoden, Max Planck Inst. for Mathematics in the, Leipzig, Germany

    Jürgen Jost

  • c/o Springer-Verlag, Heidelberg, Germany

    Bernhard Riemann

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

  • DOI:

  • Publisher: Birkhäuser Cham

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer International Publishing Switzerland 2016

  • Hardcover ISBN: 978-3-319-26040-2Published: 26 April 2016

  • Softcover ISBN: 978-3-319-79880-6Published: 22 April 2018

  • eBook ISBN: 978-3-319-26042-6Published: 19 April 2016

  • Series ISSN: 2365-9963

  • Series E-ISSN: 2365-9971

  • Edition Number: 1

  • Number of Pages: X, 172

  • Number of Illustrations: 1 b/w illustrations

  • Topics: History of Mathematical Sciences

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