Cauchy and the Creation of Complex Function Theory
Cauchy and the Creation of Complex Function Theory by Frank Smithies, published by Cambridge University Press on July 10, 2008, is a detailed examination of the development of complex analysis through the work of Augustin-Louis Cauchy. This reissue spans 228 pages and is presented in English. The book explores the historical context of the eighteenth century, leading into Cauchy’s contributions, including his proof of the residue theorem and advancements in power series expansions.
Readers will find an in-depth analysis of Cauchy’s methodologies and the challenges he faced, including initial missteps and contradictions stemming from overly ambitious assumptions. The text delves into the controversies surrounding the emergence of complex function theory, offering insights into Cauchy’s thought processes during this pivotal time. By utilizing a comprehensive range of original sources, Smithies provides a thorough account that is positioned as a significant contribution to the history and philosophy of mathematics.
Official synopsis Publisher
In this book, Dr. Smithies analyzes the process through which Cauchy created the basic structure of complex analysis, describing first the eighteenth century background before proceeding to examine the stages of Cauchy’s own work, culminating in the proof of the residue theorem and his work on expansions in power series. Smithies describes how Cauchy overcame difficulties including false starts and contradictions brought about by over-ambitious assumptions, as well as the improvements that came about as the subject developed in Cauchy’s hands. Controversies associated with the birth of complex function theory are described in detail. Throughout, new light is thrown on Cauchy’s thinking during this watershed period. This book is the first to make use of the whole spectrum of available original sources and will be recognized as the authoritative work on the creation of complex function theory.
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