Sources and Studies in the History of Mathematics and Physical Sciences

Hidden Harmony—Geometric Fantasies

The Rise of Complex Function Theory

Authors: Bottazzini, Umberto, Gray, Jeremy

  • ​Presents the first complete account of the development of the work and ideas of Cauchy, Riemann, and Weierstrass in complex function theory
  • Analyzes the history of elliptic function theory and its implications for the development of complex function theory as the first full-length treatment of the interactions between these two fields
  • Examines the interaction of complex function theory with other fields, including number theory, mechanics, and differential equations​
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Hardcover $189.00
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  • ISBN 978-1-4614-5724-4
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Softcover $189.00
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About this book

​This book is a 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is the first history of mathematics devoted to complex function theory, and it draws on a wide range of published and unpublished sources.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 authors from d’Alembert to Hilbert, and Laplace to Weyl.

Particular 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 devoted to the creation of a textbook tradition in complex analysis by considering some seventy textbooks in nine different languages. The 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 actors lived and worked by paying attention to the rise of mathematical schools and of contrasting national traditions.

The book is unrivaled for its breadth and depth, both in the core theory and its implications for other fields of mathematics. It documents the motivations for the early ideas and their gradual refinement into a rigorous theory.​

Reviews

“There is much in this book that will educate, be appreciated by, and no doubt provoke mathematicians as well as historians of mathematics and of science. … It stands its ground as a scholarly treatise that fills many lacunae in the extant historical literature. It will surely provoke further debate and research. As a bonus, it comes filled with treasures for both the specialist and the novice.” (Tushar Das, MAA Reviews, July, 2015)

“The book is devoted to the history of complex (analytic) function theory from its origins to 1914. … The book is highly recommended for historians of mathematics, mathematicians with historical interests, and everyone who is interested in complex function theory and its history. It offers a wealth of information that is well documented.” (Karl-Heinz Schlote, Mathematical Reviews, October, 2014)

“This comprehensive, massively researched volume … is a detailed historical account of the development of analytic function theory in the 19th century, tracing its rise and ramification through that period up until about 1910. … It is a very dense and scholarly work, suitable for specialists. Summing Up: Recommended. Graduate students, researchers/faculty, and professionals/practitioners.” (D. Robbins, Choice, Vol. 51 (9), May, 2014)

“This book is the first one devoted to the history of complex function theory. The authors present the rise of analytic function theory from its origins to 1914. … This book is of great interest and help, not only for mathematicians interested in complex function theory, but also for everyone who likes the history of mathematics.” (Agnieszka Wisniowska-Wajnryb, zbMATH, Vol. 1276, 2014)

Table of contents (11 chapters)

  • Introduction

    Bottazzini, Umberto (et al.)

    Pages 1-13

  • Chapter 1 Elliptic Functions

    Bottazzini, Umberto (et al.)

    Pages 15-79

  • Chapter 2 From Real to Complex Analysis

    Bottazzini, Umberto (et al.)

    Pages 81-130

  • Chapter 3 Cauchy’s “Modern Analysis”

    Bottazzini, Umberto (et al.)

    Pages 131-216

  • Chapter 4 Complex Functions and Elliptic Integrals

    Bottazzini, Umberto (et al.)

    Pages 217-258

Buy this book

eBook $149.00
price for USA (gross)
  • ISBN 978-1-4614-5725-1
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $189.00
price for USA
  • ISBN 978-1-4614-5724-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $189.00
price for USA
  • ISBN 978-1-4939-4611-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Hidden Harmony—Geometric Fantasies
Book Subtitle
The Rise of Complex Function Theory
Authors
Series Title
Sources and Studies in the History of Mathematics and Physical Sciences
Copyright
2013
Publisher
Springer-Verlag New York
Copyright Holder
Springer Science+Business Media New York
eBook ISBN
978-1-4614-5725-1
DOI
10.1007/978-1-4614-5725-1
Hardcover ISBN
978-1-4614-5724-4
Softcover ISBN
978-1-4939-4611-2
Series ISSN
2196-8810
Edition Number
1
Number of Pages
XVII, 848
Number of Illustrations and Tables
36 b/w illustrations, 2 illustrations in colour
Topics