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Landmark writings in Western mathematics 1640–1940. (English) Zbl 1090.01002

Amsterdam: Elsevier (ISBN 0-444-50871-6/hbk). xvii, 1022 p. (2005).
This remarkable book is itself a landmark publication in history of mathematics. It is devoted to eighty-nine principal writings which “have made a major inpact on the branches and aspects of mathematics to which they refer” (p. IX). They were published during the period 1640–1940 and are grouped in 77 articles written by 77 authors.
The editor Grattan-Guinness convincingly explained the organization of the articles, some principal limitations, the choice of the writings, the mathematical level. Table 1 groups the writings by principal branches of mathematics: geometries; calculus; functions, series, differential equations; algebras; number theory; real and complex analysis; set theory, foundations; general mechanics; astronomy; probability and statistics; history, general; dynamics; mathematical physics; topology; social and life sciences.
A typical article begins bibliographically with the publication history of the writing(s). The career of the author is briefly reviewed, principal features of the writing(s) are described. The impact of the writing(s) is followed by a bibliography of relevant items. Thus the book begins with Descartes’ “Geometry”, Wallis’ “Arithmetic of the infinite”, Huygens’ book on the pendulum clock and ends with Kolmogorov’s “Foundations of the theory of probability”, Seifert’s, Threlfall’s, Alexandroff’s and Hopf’s books on topology, and Hilbert’s and Bernays’ “Foundations of mathematics”. The book is a must item for every mathematical library.

MSC:

01A05 General histories, source books
00B60 Collections of reprinted articles
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