Geometrization or mathematization: Christiaan Huygens’s critiques of infinitesimal analysis in his correspondence with Leibniz. (English) Zbl 1244.01006

Chareix, Fabien

Dascal, Marcelo, The practice of reason. Leibniz and his controversies. Philadelphia: John Benjamins Publishing (ISBN 978-90-272-1887-2/hbk). Controversies 7, 33-49 (2010).

On the basis of their correspondence, the author compares the different attitudes of C.Huygens and G.W.Leibniz towards the use of infinitesimal methods in physics. Huygens criticized Leibniz’s application of the infinitesmal calculus whereas his own infinitesimals are closely bound to geometry. The author shows that according to his letters and papers from 1684 to 1690 “Huygens strictly follows a Cartesian epistemology of mathematics where geometry is the only legitimate ground for the use of infinitely small entities” (p.43). The author writes “that Huygens, having tested Leibniz’s new calculus, refuses to admit its value, and he criticizes its complexity in the making of physics” (p. 44). With this he raises reasonable doubts about the standard opinion according to which Leibniz developed his calculus under the personal influence of Huygens.
For the entire collection see [Zbl 1194.01003].

Reviewer: Volker Peckhaus (Paderborn)

MSC:

01A45	History of mathematics in the 17th century
00A30	Philosophy of mathematics
01A70	Biographies, obituaries, personalia, bibliographies

Keywords:

infinitesimal calculus; mathematization of physics; geometrization of physics; infinitely small entities