Grattan-Guinness, Ivor (ed.) Companion encyclopedia of the history and philosophy of the mathematical sciences. Vol. I. (English) Zbl 0833.01001 London: Routledge. 842 p. £150.00/hbk (set) (1994). The main concern of this reference work is to present the main branches, techniques, cultural traditions and applications of mathematics from early ages to modern times. For touching this purpose the editor has chosen to publish a subject arranged encyclopædia. It is divided into thirteen parts, each of them containing many articles. The first volume of two include 83 entries, each of them being an existing historical paper. The ancient and non-Western traditions, respectively the Western Middle Ages and Renaissance mathematics are considered in the first two parts. The other sections are devoted to the history and philosophy of the following main branches of mathematics: calculus, mathematical analysis, functions, series, methods in analysis, logics, set theory, foundations of mathematics, algebras, number theory. The articles are signed by authorities in the topics discussed. They emphasize on motivations of various mathematical theories and the historical development of specific methods.For the active fields there are also discussed aspects of current research. The entries are provided with good suggestive bibliographies. There are briefly presented the key figures in the history of mathematics. There exist relatively few works with similar purposes to that encyclopædia. The four-volume anthology by J. R. Newman is one of them [The World of Mathematics, 4 vols., Simon & Schuster, New York (1956; Zbl 0072.24301)]. These two volumes answer to a real need of a contemporary overview on mathematics and its implications. This work is a pleasant lecture for anyone interested in mathematics. It gives an authoritative overview on the development of the mathematical sciences in four thousand years and points the economic, social and cultural connotations of our science.[Part II, see Zbl 0833.01002 below]. Reviewer: Doru Ştefănescu (Bucureşti) Cited in 4 ReviewsCited in 9 Documents MSC: 01-00 General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to history and biography 01A05 General histories, source books Keywords:reference work; ancient and non-Western mathematics; Western Middle Ages and Renaissance mathematics; calculus; mathematical analysis; functions; series; methods in analysis; logics; set theory; foundations of mathematics; algebras; number theory Citations:Zbl 0833.01002; Zbl 0072.24301 PDFBibTeX XMLCite \textit{I. Grattan-Guinness} (ed.), Companion encyclopedia of the history and philosophy of the mathematical sciences. Vol. I. London: Routledge (1994; Zbl 0833.01001)