Part history and part mathematics, this book chronicles the account of how the concept of the infinitesimally small (the precursor to calculus) crept its way into mathematical thinking. The substance of the story lies in the fact that this idea was not immediately accepted by certain religious circles. To wit, a world made by a logical creator would be exact and unchanging, where everything was perfectly measurable, a premise that could not coexist with the approximations calculated via infinitesimals. If the infinitesimal is the core thread of the story, the tapestry woven is a rich amalgam of Christian history, mathematics, philosophy, geopolitics, and psychology. The author takes us on an interesting journey which includes, among other things, insightful summaries of the Jesuits and the English civil war. He also considers Euclidean geometry, including some of its proofs, as well as how “indivisibles” were used to approximate the same results. Along the way we meet interesting personalities, the luminaries behind and against this revolutionary idea. My only gripe is that the ultimate significance of this story, that is, how mathematics of the infinitesimal shaped the modern world, is relegated to the short epilogue. Nevertheless, there is much to learn here, and the narrative is tight and clear, keeping the reader’s attention throughout.
Rafael Romero, PhD