Hidden Harmony—Geometric Fantasies

The Rise of Complex Function Theory

  • Umberto Bottazzini
  • Jeremy Gray
Part of the Sources and Studies in the History of Mathematics and Physical Sciences book series (SHMP)

Table of contents

  1. Front Matter
    Pages i-xvii
  2. Umberto Bottazzini, Jeremy Gray
    Pages 1-13
  3. Umberto Bottazzini, Jeremy Gray
    Pages 15-79
  4. Umberto Bottazzini, Jeremy Gray
    Pages 81-130
  5. Umberto Bottazzini, Jeremy Gray
    Pages 131-216
  6. Umberto Bottazzini, Jeremy Gray
    Pages 217-258
  7. Umberto Bottazzini, Jeremy Gray
    Pages 259-341
  8. Umberto Bottazzini, Jeremy Gray
    Pages 343-486
  9. Umberto Bottazzini, Jeremy Gray
    Pages 487-566
  10. Umberto Bottazzini, Jeremy Gray
    Pages 567-664
  11. Umberto Bottazzini, Jeremy Gray
    Pages 665-689
  12. Umberto Bottazzini, Jeremy Gray
    Pages 691-759
  13. Back Matter
    Pages 761-848

About this book

Introduction

Hidden Harmony—Geometric Fantasies describes the history of complex function theory from its origins to 1914, when the essential features of the modern theory were in place. It is the first history of mathematics devoted to complex function theory, and it draws on a wide range of published and unpublished sources. In addition to an extensive and detailed coverage of the three founders of the subject—Cauchy, Riemann, and Weierstrass—it looks at the contributions of great mathematicians from d’Alembert to Poincaré, and Laplace to Weyl.

Select chapters examine the rise and importance of elliptic function theory, differential equations in the complex domain, geometric function theory, and the early years of complex function theory in several variables. Unique emphasis has been placed on the creation of a textbook tradition in complex analysis by considering some seventy textbooks in nine different languages. This book is not a mere sequence of disembodied results and theories, but offers a comprehensive picture of the broad cultural and social context in which the main players lived and worked by paying attention to the rise of mathematical schools and of contrasting national traditions.

This work is unrivaled for its breadth and depth, both in the core theory and its implications for other fields of mathematics. It is a major resource for professional mathematicians as well as advanced undergraduate and graduate students and anyone studying complex function

theory.

Keywords

complex function theory differential equations in the complex domain elliptic function theory geometric function theory

Authors and affiliations

  • Umberto Bottazzini
    • 1
  • Jeremy Gray
    • 2
  1. 1., Dipartimento di Matematica 'F. Enriques'Università degli Studi di MilanoMilanoItaly
  2. 2., Department of Mathematics and StatisticsThe Open UniversityMilton KeynesUnited Kingdom

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4614-5725-1
  • Copyright Information Springer Science+Business Media New York 2013
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-1-4614-5724-4
  • Online ISBN 978-1-4614-5725-1
  • About this book