Numbers

  • Heinz-Dieter Ebbinghaus
  • Hans Hermes
  • Friedrich Hirzebruch
  • Max Koecher
  • Klaus Mainzer
  • Jürgen Neukirch
  • Alexander Prestel
  • Reinhold Remmert

Part of the Graduate Texts in Mathematics book series (GTM, volume 123)

Table of contents

  1. Front Matter
    Pages i-xviii
  2. Introduction

    1. K. Lamotke
      Pages 1-6
  3. From the Natural Numbers, to the Complex Numbers, to the p-adics

    1. Front Matter
      Pages 7-7
    2. K. Mainzer
      Pages 27-53
    3. R. Remmert
      Pages 55-96
    4. R. Remmert
      Pages 97-122
    5. R. Remmert
      Pages 123-153
    6. J. Neukirch
      Pages 155-178
  4. Real Division Algebras

    1. Front Matter
      Pages 179-179
    2. M. Koecher, R. Remmert
      Pages 181-182
    3. M. Koecher, R. Remmert
      Pages 183-187
    4. M. Koecher, R. Remmert
      Pages 189-220
    5. M. Koecher, R. Remmert
      Pages 249-264
    6. F. Hirzebruch
      Pages 281-302
  5. Infinitesimals, Games, and Sets

    1. Front Matter
      Pages 303-303
    2. A. Prestel
      Pages 305-327
    3. H. Hermes
      Pages 329-353

About this book

Introduction

A book about numbers sounds rather dull. This one is not. Instead it is a lively story about one thread of mathematics-the concept of "number"­ told by eight authors and organized into a historical narrative that leads the reader from ancient Egypt to the late twentieth century. It is a story that begins with some of the simplest ideas of mathematics and ends with some of the most complex. It is a story that mathematicians, both amateur and professional, ought to know. Why write about numbers? Mathematicians have always found it diffi­ cult to develop broad perspective about their subject. While we each view our specialty as having roots in the past, and sometimes having connec­ tions to other specialties in the present, we seldom see the panorama of mathematical development over thousands of years. Numbers attempts to give that broad perspective, from hieroglyphs to K-theory, from Dedekind cuts to nonstandard analysis.

Keywords

Finite calculus development mathematics story

Authors and affiliations

  • Heinz-Dieter Ebbinghaus
    • 1
  • Hans Hermes
    • 1
  • Friedrich Hirzebruch
    • 2
  • Max Koecher
    • 3
  • Klaus Mainzer
    • 4
  • Jürgen Neukirch
    • 5
  • Alexander Prestel
    • 6
  • Reinhold Remmert
    • 3
  1. 1.Mathematisches InstitutUniversität FreiburgFreiburgGermany
  2. 2.Man-Planck-Institut für MathematikBonnGermany
  3. 3.Mathematisches InstitutUniversität MünsterMünsterGermany
  4. 4.Lehrstuhl für Philosophie und WissenschaftstheorieUniversität AugsburgAugsburgGermany
  5. 5.Fachbereich MathematikRegensburgGermany
  6. 6.Fakultät für MathematikUniversität KonstanzKonstanzGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4612-1005-4
  • Copyright Information Springer-Verlag New York Inc. 1991
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-0-387-97497-2
  • Online ISBN 978-1-4612-1005-4
  • Series Print ISSN 0072-5285
  • About this book