It isn't that they can't see the solution. It is that they can't see the problem.
The Point of a Pin in The Scandal of Father Brown.
Sherlock Holmes in Babylon
Sherlock Holmes in Babylon and Other Tales of Mathematical History, Marlow Anderson, Victor Katz and Robin Wilson (eds.), 2004, X+ 387 pp., $49.35, ISBN: 0-88385-546-1, The Mathematical Association of America, P.O. Box 91112, Washington, D.C. 20090-1112. Tel: 1-800-33-1622 or www.maa.org
This survey of the history of mathematics from “ancient times” through the eighteenth century is comprised or 44 articles selected from contributions made to the series of journals published by the Mathematical Association of America. Compiling a collection of readings for a dedicated task is often a difficult and questionable undertaking: however, this book’s editors have done an admirable job. They supply us with a highly readable, useful reference on selected developments in the history of mathematics. Each article is an in-depth examination of the historical foundations of a specific concept or movement. Authors are, or were, involved members of the mathematical community and many, such as: David Eugene Smith, Florian Cajori and Julian Cooledge, are readily recognized for their contributions as mathematical historians.
Of course, one problem with any collection of readings is balance and scope. Editors are limited by what material is available. Sherlock Holmes in Babylon is divided into four sections: Ancient Mathematics; Medieval and Renaissance Mathematics; The Seventeenth Century and The Eighteenth Century. Perhaps reflecting the membership/writership of the MAA, the concern with “Ancient Mathematics” appears weak; while two of the eleven articles discuss the work and life of Hypatia of Alexandria, no article, per se, is devoted to the greatest mathematician of ancient times, Archimedes! In contrast, the considerations of seventeenth century accomplishments (14) provide a thought-provoking glimpse of the profound mathematical accomplishments and some of the personalities of the period. I found this section to be the most informative. “The Eighteenth Century” is dominated by the work of Leonard Euler, as might be expected – five out of the ten articles are devoted to him. Each section is prefaced by a forward and followed by an afterward which provides a brief, but excellent, bibliography for further reading. Diagrams and illustrations accompany many of the articles.
This book is a useful, enjoyable reference, especially for secondary school teachers and university instructors whose principle concern is the teaching of calculus. I highly recommend it for personal and institution library acquisition.
Frank J. Swetz, Professor Emeritus, The Pennsylvania State University at Harrisburg