The book describes the life of Henri Poincaré, his work style and in
detail most of his unique achievements in mathematics and physics. Apart
from biographical details, attention is given to Poincaré's
contributions to automorphic functions, differential equations and
dynamical systems, celestial mechanics, mathematical physics in
particular the theory of the electron and relativity, topology (analysis
situs). A chapter on philosophy explains Poincaré's conventionalism in
mathematics and his view of conventionalism in physics; the latter has a
very different character. In the foundations of mathematics his position
is between intuitionism and axiomatics.
One of the purposes of the book is to show how Poincaré reached his
fundamentally new results in many different fields, how he thought and
how one should read him. One of the new aspects is the description of
two large fields of his attention: dynamical systems as presented in his
book on `new methods for celestial mechanics' and his theoretical
physics papers. At the same time it will be made clear how analysis and
geometry are intertwined in Poincaré's thinking and work.In dynamical
systems this becomes clear in his description of invariant manifolds,
his association of differential equation flow with mappings and his
fixed points theory.
There is no comparable book on Poincaré, presenting such a relatively
complete vision of his life and achievements. There exist some older
biographies in the French language, but they pay only restricted
attention to his actual work. The reader can obtain from this book many
insights in the working of a very original mind while at the same time
learning about fundamental results for modern science
