Acep Hale


The Secret Spiritual History of Calculus

Editors' note: Countless students learn integral calculus—the branch of mathematics concerned with finding the length, area or volume of an object by slicing it into small pieces and adding them up. What few realize is that their calculus homework originated, in part, in a debate between two 17th-century scholars. In 1635 Italian mathematician Bonaventura Cavalieri declared that any plane is composed of an infinite number of parallel lines and that any solid is made of an infinite number of planes. His “method of indivisibles” became a forerunner of integral calculus—but not before surviving attacks from Swiss mathematician Paul Guldin, ostensibly for empirical reasons. Amir Alexander of the University of California, Los Angeles, has found far more personal motives for the dispute. In this adaptation of a chapter from his forthcoming book, he explains that Guldin and Cavalieri belonged to different Catholic orders and, consequently, disagreed about how to use mathematics to understand the nature of reality.

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