The Development of Mathematics in Medieval Europe

The Development of Mathematics in Medieval Europe: The Arabs, Euclid, Regiomontanus, Menso Folkerts, 2006, Variorum Collected Studies Series CS811, xii + 340 pp. hardcover, $119.95, ISBN 0-86078-957-8. Burlington, VT: Ashgate Publishing Co. http://www.ashgate.com.

In this book, Menso Folkerts, an eminent historian of medieval mathematics, has compiled a collection of twelve of his articles that help illuminate European mathematical activity during the period from the twelfth through the fifteenth centuries.  This work is a continuation of his previous Essays on Early Medieval Mathematics: The Latin Tradition (2003), which concentrated on European developments from the eighth to the eleventh centuries.  Two of his articles in this collection appear, for the first time, in English language translation.  Another two articles (chapters IV, V) remain in the original German. Featured in the scholarly discussions are: the transmission of the Hindu-Arabic numeral system and calculation methods; the translation and commentaries on Arabic versions of Euclid’s Elements in Latin and the work of Johannes Regiomontanus (1436–1476), the most important Western mathematician of his time.

This book provides a valuable resource for the period, a time of mathematical transition that is often misunderstood.  Informative and easily readable, Folkerts has done an excellent job in sharing his knowledge and scholarship with his readers.  The discussion of European reception of the Elements is detailed, up-to-date and particularly valuable in helping to obtain an appreciation of the mathematical climate of the times. Further, the examination of the scope and depth of Regiomontanus's mathematical activities does much to enhance an appreciation of his contributions. Extensive notes and bibliographies encourage further research on the subjects considered; however, the cost of the volume might discourage individual purchase.  This is an excellent research resource and highly recommended for university library acquisition.

Frank Swetz, Professor Emeritus, The Pennsylvania State University

See also the MAA Review by Fernando Q. Gouvêa.