Henri Poincaré: Impatient Genius - Hardcover

From the reviews:

“Henri Poincaré (1854-1912) is arguably one of the two greatest mathematicians of the late-19th and early-20th centuries. ... The volume is roughly divided into two parts: the first part is an account of Poincaré’s life, with particular focus on his professional exploits; the second is a discussion of many aspects of his mathematics. The latter strongly emphasizes differential equations, dynamical systems, and mathematical physics ... . Summing Up: Recommended. Mathematics and history of science collections serving upper-division undergraduates through faculty.” (S. J. Colley, Choice, Vol. 50 (7), March, 2013)

“The very readable book conveys a good impression to the reader about Poincaré’s life and work supported by many illustrations. ... the book is of special interest for historians of mathematics, mathematicians and mathematical physicists with historical inclinations, but also a reader with a lower mathematical training will gain a colourful insight into the life and personality of a genius.” (Karl-Heinz Schlote, zbMATH, Vol. 1272, 2013)

“With this book, Verhulst did a marvelous job in sketching not only the person of Henri Poincaré, but also by restricting to ... the differential equations and dynamical systems, among the diverse subjects that Poincaré worked on, he succeeds very well in communicating the essence of what the theory is about. ... This is a book obviously interesting for historians of mathematics, but also for any mathematician ... who want to catch a glimpse of the person and the mind of a genius.” (A. Bultheel, The European Mathematical Society, October, 2012)

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