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Mathématiciens Français du XVIIe Siècle: Descartes, Fermat, Pascal

Michel Serfati and Dominique Descotes
Presses Universitaires Blaise-Pascal
Publication Date: 
Number of Pages: 
Collection Cerhac
[Reviewed by
Fabio Mainardi
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These proceedings, written in French, collect some essays on the three major French mathematicians of the seventeenth century: René Descartes, Pierre de Fermat and Blaise Pascal. It is worth noting that two of them were eminent philosophers and the third (Fermat) was a lawyer; they were all very well acquainted with the Latin and Greek literature and their work was often the result of an attentive analysis of Archimedes, Apollonius, Pappus and Diophantus.

The scope of these proceedings is to investigate the great mathematical masterpieces of Descartes, Fermat and Pascal, according to their literary form. It is interesting to note that the publisher is the French “Institute of studies on humanism and classical age”, not at all a scientific publisher.

The first essay, by Michel Serfati, gives the flavor of the book. It is on “constructivism and obscurities in Descartes’ Geometry: some philosophical remarks”. It is a matter of fact that the mathematical publications of that period had a structure and a style which are quite different from the contemporary ones. To the modern mathematician’s taste, they seem to lack thoroughness and precision (cf. the “obscurities” in Serfati’s essay); for instance, those publications included seldom a complete bibliography.

There is not much mathematics in the book, the focus being on the style and on the methodology of those great mathematicians, more than on their achievements themselves. It is thus hard to portray the fitting reader for this book. It is certainly not intended to be a textbook for a course, but: is it more suitable to a mathematician with an interest in philosophy, or to a philosopher interested in mathematics? Probably both.

Fabio Mainardi earned a PhD in Mathematics at the University of Paris 13. His research interests are Iwasawa theory, p-adic L-functions and the arithmetic of automorphic forms. He may be reached at

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