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Oeuvres Mathématiques, Volume I: René Thom

René Thom
Société Mathématique de France
Publication Date: 
Number of Pages: 
Documents Mathématiques
[Reviewed by
Michael Berg
, on

The book under review is the first volume of the collected works, or more precisely the Œuvres Mathématiques, of the French mathematician René Thom, the great topologist known for his pioneering work on cobordism theory and, much later, catastrophe theory. To be precise, the present work is not part of Thom’s œuvres complètes, except of course by definition: the official goal is to have the present collection be a well-defined subset, cut out by the requirement (translated by me from the French) to the effect that “We concentrate mainly on mathematical articles that were reviewed in Mathematical Reviews…” The Œuvres Complètes proper are available on a CD-Rom launched in 2003 by the IHES.

The book under review advertises faithful reproductions of Thom’s papers in their original version, free of typographical modernization (no TeX here); however, there’s an exception to the preceding in that the present volume includes two works from 1957 which were not covered in MathRevs for the simple reason that they were not published: one concerns a proof of a theorem due to Solomon Lefschetz that uses Morse theory, while the other has to do with Stein varieties. The book comes equipped with a large number of expert Notes et commentaires, which naturally supplement the material very well, and there are a number of photographs, including one on p. 210 which leaves the reader wondering what the discussion must have been about, given the clear animation of the two men being photographed, namely, Thom and Dennis Sullivan (in 1974).

Books like these are a major contribution to the mathematical culture and the history of modern mathematics, in that they convey the contributions of the figures featured in their original format, collected in such a way that common traits, developing themes, and subsequent impact can be examined and gauged with something like 20/20 hindsight. Another work that immediately comes to mind along these lines is the Grothendieck-Serre Correspondence, and it is apposite to note that this work, too, concerns the famously fecund French school of the middle and later 20th century (note, however, that while Grothendieck and Serre were Bourbaki members, Thom was not). In any case, the Société Mathématique de France is doing the mathematical community a great service in producing these wonderful works.

Michael Berg is Professor of Mathematics at Loyola Marymount University in Los Angeles, CA.

The table of contents is not available.