Henri Poincaré: Impatient Genius

ISBN-13: 9781489999146 / Angielski / Miękka / 2014 / 260 str.

Ferdinand Verhulst

Opis

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

Recenzje

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)

Spis treści

The early years.- Academic education, 1873-1879.- Impressive results in Vesoul and Caen.- Career in Paris.- The prize competition of Oscar II.- Philosophy and essays.-  At the end, what kind of a man?- Automorphic functions.- Differential equations and dynamical systems.-  Analysis Situs.- Mathematical Physics.- Poincaré.- Historical data and biographical details.- References.- Index.-

O autorze

Ferdinand Verhulst is a Professor at the University of Utrecht.

Blurb

This book describes the life and work of Henri Poincaré, detailing most of his unique achievements in mathematics and physics. It is divided into two parts—the first on Poincaré’s life, and the second on his contributions to the mathematical sciences. Apart from biographical details, attention is given to Poincaré’s results on automorphic functions; differential equations and dynamical systems; celestial mechanics; mathematical physics, in particular the theory of the electron and relativity; and topology (analysis situs). A chapter on philosophy explains Poincaré’s conventionalism in mathematics and his view of conventionalism in physics. The book shows how Poincaré reached his fundamentally new results in many different fields, how he thought about problems, and how one should read his work. Simultaneously, it is 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-point theory. There is no comparable book on Poincaré presenting such a relatively complete vision of his life and the working of his very original mind. Scientists and engineers as well as general readers interested in the history of science will find this book of interest.

Reviews of this book:"The title of this biography is particularly well chosen : Henri Poincaré was a true genius, and he was impatient. It gives a fair picture of both the man and the scientist, completed by particularly well chosen illustrations.

Jean Mawhin, Université Catholique de Louvain, Belgium

"Ferdinand Verhulst has written a true scientific biography, introducing Poincaré the man, his cultural milieu, and his mathematics. This book shows why, a century after his death, Poincaré's ideas still shape a substantial part of the mathematical sciences."

Philip J Holmes, Princeton University, USA