REVIEWS

摘要

Alexander, Amir, Infinitesimal:How a Dangerous Mathematical Theory Shaped the Modern World, Scientific American / Farrar, Straus and Giroux, 2014. 352 pp, $27. ISBN 978-0- 374-1768-5. Extract:The secret spiritual history of calculus, Scientific American 310 (4) (April 2014) 82-85, http://www.scientificamerican.com/article/the-secret- spiritual-history-of-calculus/, with subsequent letters at 311 (2) (August 2014) 6-7. I have urged elsewhere that calculus be "intellectualized" and re-embedded in the historical context of culture and science, thereby returning it to the fold of the liberal arts. Central to that rebirth could be the question of infinitesimal numbers:Do they exist? If so, how should we calculate with them? Even if not, are they useful pedagogical constructs? Author Alexander situates "indivisibles" at the heart of a battle of the Jesuits against the "disorder" of established truth that infinitesimals represented. However, the emphasis in the book is definitely on religious conflicts, and one must wonder if infinitesimals were really so important or were just a pawn and sideshow in those struggles. Mathematics occupies only about 30 pages of the book, which ends its tale around 1650-before the era of Newton, Leibniz, and George Berkeley's objections, and long before the legitimation in the 20th century of number systems involving infinitesimals.