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Mathematics and the Historian's Craft: The Kenneth O. May Lectures

Glen Van Brummelen and Michael Kinyon, editors
Springer Verlag
Publication Date: 
Number of Pages: 
CMS Books in Mathematics
[Reviewed by
Michael Berg
, on

This collection of twelve essays, constituting nigh on the full set of Kenneth O. May Lectures given at the Annual Meetings of the Canadian Society for History and Philosophy of Mathematics since 1988, are presented in this volume as a tribute to Kenneth May himself, one of the founding fathers of the CSHPM.

The essays, varying greatly in nature as well as scope, concern themes of interest to the Society and, by extension, to Kenneth May. My own tastes run to the following samples: Ivor Grattan-Guiness’ preliminary (and cautionary?) discussion of the interplay between mathematical history and mathematical heritage; Judith Grabiner’s discussion of whether Newton’s calculus was a dead end (read the essay to find out Grabiner’s answer to this provocative question); Karen Hunger Parshall on the emergence of the American mathematical research community; and Joseph Dauben’s remarkably insightful and informative essay on Cantor’s set theory, filled with a wealth of information about Georg Cantor himself, and also some of his contemporaries.

I wish to call special attention however to two long articles by Rudiger Thiele, titled, “The Mathematics and Science of Leonhard Euler (1707-1783),” and “Hilbert and his Twenty-Four [!] Problems.” These articles burst at the seams with marvelous scholarship and insights and contain wonderful anecdotal material (as well as a large number of photographs and illustrations). The former article is in itself a beautiful compact biography of the most prolific mathematician of all (pace Erdös), while the latter discusses something altogether surprising and evocative: what was Hilbert’s twenty-fourth Paris problem, which he struck from his final list? It was to be “

riteria of simplicity, or proof of the greatest simplicity of certain proofs. [To] develop a theory of the method of proof in general&#8230;&#8221; (p. 280). So why did Hilbert opt to avoid this omit this question? Obviously this investigation is intrinsically fascinating and the according (dense) article is well worth reading carefully.</p>
<p>And, as already indicated, this book contains a lot of interesting material besides: there is something for just about every one, not just specialists in the History of Mathematics. Recommended!</p>
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<p>Michael Berg is Professor of Mathematics at Loyola Marymount University in California.</p>
Preface.- Introduction: The Birth and Growth of a Community by Amy Shell-Gellasch.- History or Heritage? An Important Distinction in Mathematics and for Mathematics Education, by Ivor Grattan-Guinness.- Ptolemy's Mathematical Models and their Meaning, by Alexander Jones.- Mathematics, Instruments and Navigation, 1600-1800, by Jim Bennett.- Was Newton's Calculus a Dead End? The Continental Influence of Maclaurin's Treatise of Fluxions, byJudith V. Grabiner.- The Mathematics and Science of Leonhard Euler (1707-1783), by Ruediger Thiele.- Mathematics in Canada before 1945: A Preliminary Survey by Thomas Archibald and Louis Charbonneau.- The Emergence of the American Mathematical Research Community, by Karen Hunger Parshall.- 19th Century Logic Between Philosophy and Mathematics, by Volker Peckhaus.- The Battle for Cantorian Set Theory, by Joseph W. Dauben.- Hilbert and his Twenty-Four Problems, by Ruediger Thiele.- Turing and the Origins of AI, by Stuart Shanker.- Mathematics and Gender: Some Cross-Cultural Observations, by Ann Hibner Koblitz.