La méthode de Fermat: Son statut et sa diffusion. By Giovanna Cleonice Cifoletti. Cahiers d'Histoire et de Philosophie des Sciences, No. 33. Paris (Société Française d'Histoire des Sciences et des Techniques. Belin Diffusion). 1990. Pp. 243. ISSN 0221-3664. FF60.
✍ Scribed by Antoni Malet
- Publisher
- Elsevier Science
- Year
- 1997
- Tongue
- English
- Weight
- 114 KB
- Volume
- 24
- Category
- Article
- ISSN
- 0315-0860
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✦ Synopsis
Fermat's contributions have long been a matter of outstanding interest to historians of mathematics, and deservedly so. Thanks to M. S. Mahoney's work on the mathematical agenda of Vie `te and his followers-a work Giovanna Cifoletti is well acquainted with-we know now that Fermat's mathematics was part of an ''analytical'' program, the ultimate result of which would be the algebrization of mathematical thought. In Fermat's own days, however, this consequence was far from being imminent or obvious. Starting from here, Cifoletti wants to clarify the early formulations and status of Fermat's method of maxima and minima, mainly in order to understand the contemporary role of Fermat's mathematics. Two parts, unequal in almost every conceivable facet, from extension to subject matter to style, are readily discernible in this book-although they are not ostensibly marked as such. The opening, the longer and more substantial part, contains several chapters on the method of maxima and minima, its application to the determination of tangents, centers of gravity, and other problems, its first publication by He ´rigone, and its fate at the hands of Huygens and van Schooten. Cifoletti analyzes here what major figures of 17th-century mathematics, including Fermat himself, said about his method, and supplements this with a balanced review of what major historians have had to say about it. The second part (the concluding chapter) is devoted to the so-called synthetic (or formal) differential geometry, a field in 20th-century mathematics. The author is well aware that the combination is an odd one, for she feels compelled to justify it. More about this below.
One of Cifoletti's most interesting points is the suggestion that Fermat designed his techniques with a specific set of problems in mind-those implying diorismoi. Fermat and some of his followers regarded these problems, coming mostly from classical sources, as constituting a mathematical field, but this outlook was to last for a few decades only. It is thus implied that Fermat's method changed and lost its centrality as the problems inspiring it were transformed and reorganized and its domain of applicability faded away. Cifoletti's book contains interesting asides on the Renaissance filiation of adaequari, a key notion (but one soon forgotten) in Fermat's own formulation of the method, as well as on the work and obscure figure of Pierre He ´rigone (d. ca. 1643). He ´rigone was the author of the first (1642) printed version of Fermat's method (published in his six-volume Cours mathe ´matique), a publication which was to lend it, according to Cifoletti, ''sa forme canonique'' (its canonical form, p. 162). Providing an insightful study of the genre to which the Cours mathe ´matique belongs, Cifoletti emphasizes that He ´rigone's mathematical