From Fermat to Minkowski

Lectures on the Theory of Numbers and Its Historical Development

  • Winfried Scharlau
  • Hans Opolka

Part of the Undergraduate Texts in Mathematics book series (UTM)

Table of contents

  1. Front Matter
    Pages i-xi
  2. Winfried Scharlau, Hans Opolka
    Pages 1-4
  3. Winfried Scharlau, Hans Opolka
    Pages 5-13
  4. Winfried Scharlau, Hans Opolka
    Pages 14-31
  5. Winfried Scharlau, Hans Opolka
    Pages 32-56
  6. Winfried Scharlau, Hans Opolka
    Pages 57-63
  7. Winfried Scharlau, Hans Opolka
    Pages 64-101
  8. Winfried Scharlau, Hans Opolka
    Pages 102-108
  9. Winfried Scharlau, Hans Opolka
    Pages 109-150
  10. Winfried Scharlau, Hans Opolka
    Pages 151-168
  11. Winfried Scharlau, Hans Opolka
    Pages 169-177
  12. Back Matter
    Pages 178-185

About this book


This book arose from a course of lectures given by the first author during the winter term 1977/1978 at the University of Münster (West Germany). The course was primarily addressed to future high school teachers of mathematics; it was not meant as a systematic introduction to number theory but rather as a historically motivated invitation to the subject, designed to interest the audience in number-theoretical questions and developments. This is also the objective of this book, which is certainly not meant to replace any of the existing excellent texts in number theory. Our selection of topics and examples tries to show how, in the historical development, the investigation of obvious or natural questions has led to more and more comprehensive and profound theories, how again and again, surprising connections between seemingly unrelated problems were discovered, and how the introduction of new methods and concepts led to the solution of hitherto unassailable questions. All this means that we do not present the student with polished proofs (which in turn are the fruit of a long historical development); rather, we try to show how these theorems are the necessary consequences of natural questions. Two examples might illustrate our objectives.


Excel Fermat Minkowski Natural boundary element method design development eXist mathematics number theory proof review selection theorem university

Authors and affiliations

  • Winfried Scharlau
    • 1
  • Hans Opolka
    • 1
  1. 1.Mathematisches InstitutUniversität MünsterMünsterWest Germany

Bibliographic information

  • DOI
  • Copyright Information Springer-Verlag New York 1985
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4419-2821-4
  • Online ISBN 978-1-4757-1867-6
  • Series Print ISSN 0172-6056
  • Buy this book on publisher's site