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The Scientific Legacy of Poincaré
Edited by: Éric Charpentier, Université Bordeaux 1, Talence, France, Étienne Ghys, École Normale Supérieure de Lyon, France, and Annick Lesne, Université Pierre et Marie Curie, Paris, France
Translated by Joshua Bowman
A co-publication of the AMS and the London Mathematical Society.
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History of Mathematics
2010; 391 pp; hardcover
Volume: 36
ISBN-10: 0-8218-4718-X
ISBN-13: 978-0-8218-4718-3
List Price: US$89
Member Price: US$71.20
Order Code: HMATH/36
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Henri Poincaré (1854-1912) was one of the greatest scientists of his time, perhaps the last one to have mastered and expanded almost all areas in mathematics and theoretical physics. He created new mathematical branches, such as algebraic topology, dynamical systems, and automorphic functions, and he opened the way to complex analysis with several variables and to the modern approach to asymptotic expansions. He revolutionized celestial mechanics, discovering deterministic chaos. In physics, he is one of the fathers of special relativity, and his work in the philosophy of sciences is illuminating.

For this book, about twenty world experts were asked to present one part of Poincaré's extraordinary work. Each chapter treats one theme, presenting Poincaré's approach, and achievements, along with examples of recent applications and some current prospects. Their contributions emphasize the power and modernity of the work of Poincaré, an inexhaustible source of inspiration for researchers, as illustrated by the Fields Medal awarded in 2006 to Grigori Perelman for his proof of the Poincaré conjecture stated a century before.

This book can be read by anyone with a master's (even a bachelor's) degree in mathematics, or physics, or more generally by anyone who likes mathematical and physical ideas. Rather than presenting detailed proofs, the main ideas are explained, and a bibliography is provided for those who wish to understand the technical details.

Readership

Undergraduate students, graduate students, and research mathematicians interested in Poincaré's life and work.

Reviews

"The articles are very well written, indeed, and are of course autonomous. But even non-specialists will want to sample these wares. The mathematics is presented clearly and very accessible, and the numerous historical accounts and asides make add an additional welcome cultural element to whole experience.

"[This book] is bound to be a hit across the mathematical spectrum: it has something for every one interested in any aspect of Poincaré's work, which is to say, something for every one."

-- MAA Reviews

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