History of Mathematics (Providence) 14. Providence, RI: American Mathematical Society; London: London Mathematical Society (ISBN 0-8218-0841-9/hbk). xxv, 574 p. $ 79.00 (1998).

This book is the first comprehensive biography of Jacques Hadamard (1865-1963), one of the greatest mathematicians of the 20th century.
He was born in Versailles into a Jewish family. The authors offer a detailed account of the years of his youth. Hadamard learned the violin at an early age and developed a passion for reading. In school he did excellently and won several prizes. He studied mathematics at the École Normale Supérieure and at the Sorbonne and attended classes by Tannery, Darboux, Hermite, Picard and Poincaré.
Hadamard’s first mathematical triumph was the proof of the prime number theorem where he used his newly created theory of entire functions of finite genus.
Hadamard worked with great success and striking discoveries in many fields of mathematics. He was already in his time a living legend, as Hardy put it.
On the other hand tragic incidents darkened his life: his two sons Etienne and Pierre were killed in the first world war and his last son Mathieu died in the second world war, where he had joined de Gaulle’s Free French Force.
The second part of the book is devoted to the mathematical work of Hadamard, beginning with chapters on analytic function theory and number theory, then turning to analytical mechanics, geometry, calculus of variations, functional analysis and ending with chapters on elasticity, hydrodynamics and partial differential equations. The authors describe and analyse the mathematics very well and put it in the historical context, so that one can get really new insights.
Let us mention only one example. When the authors discuss Hadamard’s counterexample to one aspect of the Dirichlet problem they do not forget to mention that Prym already gave a counterexample 35 years before and present clearly the essence of Prym’s technical complicated example.
There are many biographies on important mathematicians, but there are only a few which treat the mathematical work adequately. The book under review belongs to the latter type, so that also the professional mathematician is completely satisfied.
The book is based on extensive use of archival sources and on interviews with persons who knew Hadamard. The volume also includes a detailed bibliography, an excellent index and hundreds of drawings and photographs.
This book is a superb piece of work and can be thoroughly recommended.