Infinitesimal: How a Dangerous Mathematical Theory Shaped the Modern World

UCLA historian and mathematician Alexander (Geometrical Landscapes) gives readers insight into a real-world Da Vinci Code–like intrigue with this look at the history of a simple, yet pivotal, mathematical concept. According to classic geometry, a line is made of a string of points, or “indivisibles,” which cannot be broken down into anything smaller. But if that’s so, how many indivisibles are in a line, and how big are they? And what happens when you divide the line into smaller segments? It seemed that indivisibles weren’t really indivisible at all, a “deeply troubling” idea to the medieval Church and its adherents, who demanded a rigidly unchanging cosmos with no surprises. Churchmen and respected thinkers like Descartes railed against infinitesimals, while Galileo, Newton, and others insisted the concept defined the real world. The argument became an intellectual and philosophical battleground, in a Church already threatened by doctrinal schisms and social upheaval. Focusing on the Jesuits, beginning with the German Jesuit mathematician Christopher Clavius, Alexander explores this war of ideas in the context of a world seething with political and social unrest. This in-depth history offers a unique view into the mathematical idea that became the foundation of our open, modern world. Agent: the Garamond Agency. (Apr.)