Since the early part of the 20th century, topology has gradually spread
to many other branches of mathematics, and this book demonstrates how
the subject continues to play a central role in the field. Written by a
world-renowned mathematician, this classic text traces the history of
algebraic topology beginning with its creation in the early 1900s and
describes in detail the important theories that were discovered before
1960. Through the work of Poincaré, de Rham, Cartan, Hureqicz, and many
others, this historical book also focuses on the emergence of new ideas
and methods that have led 21st-century mathematicians towards new
research directions.
*"This book is a well-informed and detailed analysis of the problems and
development of algebraic topology, from Poincaré and Brouwer to Serre,
Adams, and Thom. The author has examined each significant paper along
this route and describes the steps and strategy of its proofs and its
relation to other work. Previously, the history of the many technical
developments of 20th-century mathematics had seemed to present
insuperable obstacles to scholarship. This book demonstrates in the case
of topology how these obstacles can be overcome, with enlightening
results.... Within its chosen boundaries the coverage of this book is
superb. Read it!" (*MathSciNet)
"[The author] traces the development of algebraic and differential
topology from the innovative work by Poincaré at the turn of the century
to the period around 1960. [He] has given a superb account of the
growth of these fields.... The details are interwoven with the narrative
in a very pleasant fashion.... [The author] has previous written
histories of functional analysis and of algebraic geometry, but neither
book was on such a grand scale as this one. He has made it possible to
trace the important steps in the growth of algebraic and differential
topology, and to admire the hard work and major advances made by the
founders." (Zentralblatt MATH)
