Hidden harmony - geometric fantasies : the rise of complex function theory / Umberto Bottazzini, Jeremy Gray

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.

The book contains ten chapters whose titles are as follows: Elliptic functions; From real to complex analysis; Cauchy’s “modern analysis”; Complex functions and elliptic integrals; Riemann’s geometric function theory; Weierstrass’s analytic function theory; Complex function theory and differential equations; Advanced topics in the theory of functions; Several complex variables; The textbook tradition.

The authors describe contributions of great mathematicians starting from the founders of the subject – Cauchy, Riemann and Weierstrass – through d’Alembert, Poincaré, Laplace, Weyl and others. Basing on published and unpublished sources the book presents the development and role of elliptic function theory, differential equations in the complex domain, geometric function theory and the early years of complex function theory in several variables.

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. (zbMath)