Laurent Schwarz was one of the most eminent French mathematicians of the 20th century, so it’s very appropriate that the Société Mathématique de France has published his collected mathematical works in their series of “Documents Mathématiques.” The adjective “scientifiques” is important: Schwarz was a committed political activist and wrote much on political and moral topics; these volumes focus only on his mathematical work.
The material has been organized by topic. The first two volumes contain Schwartz’s papers on Analysis and Partial Differential Equations, which were of course the main focus of his career. In particular, this section includes the papers in which Schwartz created his theory of distributions, perhaps his most famous contribution to mathematics. The third volume collects papers on other subjects, with sections on Banach Spaces and Probability Theory and a final section containing a scattering of historical works, most of which are memorial pieces on the works of mathematicians: Denjoy, Hadamard, Lévy, Kolmogorov, and Dieudonné. The papers are, as usual, reproduced photographically from their original publication, even when the results don’t look all that pretty (as is the case, for example, for the notes from seminar talks).
The first volume has a section called “Quelques Photos” with five photographs taken at different times, and another called “Quelques Documents” with reproductions of some of Schwartz’s correspondence and other materials.
A very welcome feature is the inclusion of materials from Schwarz’s many “Séminaires.” Volume 1, for example, includes 24 “exposés” from the Séminaire Schwartz 1953/54, and volume 2 includes several more from 1954–1956.
Several historical introductions are included. B. Malgrange introduces the first section with an account of “La théorie des distributions,” A. Guichardet gives us “Laurent Schwatrz et les séminaires,” G. Godefroy discusses “L’influence de Laurent Schwartz en théorie des espaces de Banach,” and finally M. Émery surveys “Laurent Schwartz probabiliste.”
The overall package is well produced, attractively presented, and of great value to anyone interested in the history of mathematics in the twentieth century.
Fernando Q. Gouvêa is Carter Professor of Mathematics at Colby College in Waterville, ME.