Bernhard Riemann 1826–1866

Turning Points in the Conception of Mathematics

  • Detlef Laugwitz

Part of the Modern Birkhäuser Classics book series (MBC)

Table of contents

  1. Front Matter
    Pages i-xvii
  2. Detlef Laugwitz
    Pages 1-63
  3. Detlef Laugwitz
    Pages 64-180
  4. Detlef Laugwitz
    Pages 181-218
  5. Detlef Laugwitz
    Pages 219-292
  6. Detlef Laugwitz
    Pages 293-340
  7. Back Matter
    Pages 341-357

About this book

Introduction

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

Keywords

Calculation Finite History of Mathematics calculus complex analysis function geometry interpret mathematical philosophy mathematics philosophy proof real analysis

Authors and affiliations

  • Detlef Laugwitz
    • 1
  1. 1.Department of MathematicsTechnische HochschuleDarmstadtGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-0-8176-4777-3
  • Copyright Information Springer Science+Business Media New York 1999
  • Publisher Name Birkhäuser, Boston, MA
  • eBook Packages Springer Book Archive
  • Print ISBN 978-0-8176-4776-6
  • Online ISBN 978-0-8176-4777-3
  • Series Print ISSN 2197-1803
  • Series Online ISSN 2197-1811
  • About this book