### Henri Poincaré: A Scientific Biography

*Henri Poincaré: A Scientific Biography* by Jeremy Gray is an unusual book, a fundamental study of the scientific work of one of the greatest mathematicians and mathematical physicists of the three decades straddling the 19th and 20th centuries. Poincaré was an uncommonly versatile and productive scientist, being able to work simultaneously on several disparate subjects. For example, "in 1905 he published on number theory, geodesics on convex surfaces, the dynamics of the electron, a report on the French geodetic survey in Peru, and a popular philosophical paper on mathematics and logic."

The book is not a biography of Poincaré the person (except for a brief account of his childhood and education), but a story of Poincaré a public figure, a mathematician, a physicist, a profound thinker. Nonetheless, many human aspects of Poincaré's life and time, and social atmosphere in Europe of his time emerge throughout the book.

*Introduction* and the first two chapters (*The Essayist*, *Poincaré's career*) throw the most light on Poincaré's character. "He believed strongly that a knowledge claim had to come with an account of how we can know it" [p. 8]. So, for example, he "did not become heavily involved in the Dreyfus affair ... that he felt lay beyond his competence." However , he did provide expert opinion on the low quality of prosecution evidence, proving it unrealistic [p. 166-167].

Other chapters are organized topically, not chronologically. Each illuminates in depth one or other of Poincaré's works but all are set in context both historical and temathic such that each can serve as an introduction into the many subjects to which Poincaré made a contribution. Much of the book is a descriptive narrative, but the author never shies from displaying equations (even PDE and integral ones) when this is essential for the subject. I do not know whether this style has caused a price reduction, but for a book of this size, depth, and breadth, $33.10 (the amazon.com price) is an exceptional bargain.