
05815124
b
2011b.00046
Grabiner, Judith V.
A historian looks back. The calculus as algebra and selected writings.
MAA Spectrum. Washington, DC: The Mathematical Association of America (MAA) (ISBN 9780883855720/hbk). xv, 287~p. (2010).
2010
Washington, DC: The Mathematical Association of America (MAA)
EN
A30
I10
E10
C30
calculus
A.L. Cauchy
I. Newton
G. W. Leibniz
history of calculus
Maclaurin
Lagrange
Cauchy
rigor and psychology in mathematics
teaching of mathematics
Zbl 0517.01002
Zbl 0719.01009
Zbl 0714.01032
Editorial remark: Accidentally, this book has been issued twice for reviewing. Therefore, we display both reviews, by adding the second one to the originally published review: The author (born 1938) is a wellknown historian of mathematics with particular interests in the use of history in teaching and in the historical development of rigor and method, exemplified by the development of the calculus. She has published two books: The origins of Cauchy's rigorous calculus. Cambridge, Massachusetts  London: MIT Press (1981; Zbl 0517.01002)/2005, and The calculus as algebra. J.L. Lagrange, 17361813. New York etc.: Garland Publishing, Inc. (1990; Zbl 0719.01009). The present book, appearing in the prominent Spectrum series of the Mathematical Association of America (MAA), republishes the latter of the two books and adds 10 articles, several of which have won prizes from the MAA. Referring often to works on the psychology of mathematics (Hadamard, Polya) the author addresses the results of her investigations not principally to other historians, but to mathematicians and teachers of mathematics. Reviewer: Reinhard SiegmundSchultze (Kristiansand) The author has been recognized as an authority on the history of the calculus even before the publication of her ``Origins of Cauchy's rigorous calculus" [Cambridge, Massachusetts  London: MIT Press. X, 252 p. (1981; (1981; Zbl 0517.01002)] and this anthology of writings contains the key publications that elaborate further on this theme. Over onethird of the book consists of the author's 1966 dissertation, first published in 1990, ``The calculus as algebra. J.L. Lagrange, 17361813" [New York etc.: Garland Publishing, Inc. (1990; Zbl 0719.01009)], here with an updated bibliography. The other ten papers, described as ``reprints,'' are new typesettings, with no indication of original paginations, and most are from journals published by the Mathematical Association of America. They contain significant explorations not only of the main names such as Newton and Leibniz, but also of Euler, d'Alembert anda topic in which the author has also specializedColin Maclaurin, In addition to aspects of the history of calculus, these papers are successful examples of making mathematics and its history accessible to a wide audience; for example, a teacher of any subject may find useful insights in ``The centrality of mathematics in the history of Western thought." [Proc. Int. Congr. Math., Berkeley/Calif. 1986, Vol. 2, 16681681 (1987; Zbl 0714.01032)].
Reinhard SiegmundSchultze (Kristiansand) / Albert C. Lewis (Austin)