Modern Birkhäuser Classics

Bernhard Riemann 1826–1866

Turning Points in the Conception of Mathematics

Authors: Laugwitz, Detlef

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  • Presents the work of Bernhard Riemann from a historical perspective
  • Discusses the impact of Riemann's work on math, physics, and philosophy
  • Examines the philosophy of Riemannian thought
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eBook 42,79 €
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  • ISBN 978-0-8176-4777-3
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Softcover 51,99 €
price for Spain (gross)
  • ISBN 978-0-8176-4776-6
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About this book

The name of Bernard Riemann is well known to mathematicians and physicists around the world. College students encounter the Riemann integral early in their studies. Real and complex function theories are founded on Riemann’s work. Einstein’s theory of gravitation would be unthinkable without Riemannian geometry. In number theory, Riemann’s famous conjecture stands as one of the classic challenges to the best mathematical minds and continues to stimulate deep mathematical research. The name is indelibly stamped on the literature of mathematics and physics.

This book, originally written in German and presented here in an English-language translation, examines Riemann’s scientific work from a single unifying perspective. Laugwitz describes Riemann’s development of a conceptual approach to mathematics at a time when conventional algorithmic thinking dictated that formulas and figures, rigid constructs, and transformations of terms were the only legitimate means of studying mathematical objects. David Hilbert gave prominence to the Riemannian principle of utilizing thought, not calculation, to achieve proofs. Hermann Weyl interpreted the Riemann principle — for mathematics and physics alike — to be a matter of "understanding the world through its behavior in the infinitely small."

This remarkable work, rich in insight and scholarship, is addressed to mathematicians, physicists, and philosophers interested in mathematics. It seeks to draw those readers closer to the underlying ideas of Riemann’s work and to the development of them in their historical context. This illuminating English-language version of the original German edition will be an important contribution to the literature of the history of mathematics.

"There is excellent referencing throughout… Quotes are given almost always both in English and in the original German. Many readers will feel the original German brings them a bit closer to Riemann and his contemporaries… Laugwitz’s expertise on historical matters is most impressive… Thanks are due to both author and translator for making it much easier to enter into the literature on Riemann." —MAA Online

"...the author has succeeded admirably...stating the technical details clearly and correctly while writing an engaging and readable account of Riemann’s life and work... Any reader of this book with even a passing interest in the history or philosophy of mathematics is certain to become engaged in a mental conversation with the author... The format of the book is excellent, especially the plentiful supply of photographs of people and places... The book will serve as an interesting read and also a useful reference... It is highly recommended." —Bulletin of the AMS

Reviews

"Laugwitz’s 1996 book in German is an excellent place to begin a study of [Riemann’s] life, work, and influence. The 1999 translation…into English is especially welcome… There is excellent referencing throughout… Quotes are given almost always both in English and in the original German. Many readers will feel the original German brings them a bit closer to Riemann and his contemporaries… Laugwitz’s expertise on historical matters is most impressive… Thanks are due to both author and translator for making it much easier to enter into the literature on Riemann."   —MAA Online

"...the author has succeeded admirably...stating the technical details clearly and correctly while writing an engaging and readable account of Riemann’s life and work... Any reader of this book with even a passing interest in the history or philosophy of mathematics is certain to become engaged in a mental conversation with the author... The format of the book is excellent, especially the plentiful supply of photographs of people and places... The book will serve as an interesting read and also a useful reference... It is highly recommended."   —Bulletin of the AMS


Table of contents (5 chapters)

Table of contents (5 chapters)

Buy this book

eBook 42,79 €
price for Spain (gross)
  • ISBN 978-0-8176-4777-3
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover 51,99 €
price for Spain (gross)
  • ISBN 978-0-8176-4776-6
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
  • The final prices may differ from the prices shown due to specifics of VAT rules
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Bibliographic Information

Bibliographic Information
Book Title
Bernhard Riemann 1826–1866
Book Subtitle
Turning Points in the Conception of Mathematics
Authors
Translated by
Shenitzer, A.
Series Title
Modern Birkhäuser Classics
Copyright
1999
Publisher
Birkhäuser Basel
Copyright Holder
Springer Science+Business Media New York
eBook ISBN
978-0-8176-4777-3
DOI
10.1007/978-0-8176-4777-3
Softcover ISBN
978-0-8176-4776-6
Series ISSN
2197-1803
Edition Number
1
Number of Pages
XVII, 357
Number of Illustrations
40 b/w illustrations
Additional Information
Originally published as a monograph
Topics