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Henri Poincare - Impatient Genius (Hardcover, 2012 ed.)
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Henri Poincare - Impatient Genius (Hardcover, 2012 ed.)
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The book describes the life of Henri Poincare, his work style and
in detail most of his unique achievements in mathematics and
physics. Apart from biographical details, attention is given to
Poincare'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
Poincare'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 Poincare 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 Poincare'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 Poincare, 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
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