zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Jacques Hadamard, a universal mathematician. (English) Zbl 0906.01031
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.

01A70Biographies, obituaries, personalia, bibliographies
01A60Mathematics in the 20th century
01-02Research monographs (history)