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and unpublished sources.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. "
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