How a Dangerous Mathematical Theory Shaped the Modern World
Scientific American Books / Farrar, Straus & Giroux
Shortlisted for the Phi Beta Kappa Award in Science
It’s intuitively appealing to imagine a line as composed of infinitely small individual points – or “indivisibles,” as they’re called in mathematics. After all, we know that wood is a composite of individual fibers, and a rope is composed of individual strings, so we would expect the same to be true of the lines and solids of mathematics. But while the concept of indivisibles might seem natural to us today, it was once savagely criticized. Indeed, in the 17th century indivisibles were deemed so dangerous by the Jesuits that they were decreed heretical.
What made this idea – one that fuels the calculus, and innumerable discoveries and inventions from kitchen appliances to iPhones – so threatening, and how it went on to redefine the nature of science is the story that Amir Alexander tells in Infinitesimal: How a Dangerous Mathematical Theory Shaped the Modern World. To the Jesuits, the infinitely small upended the belief in a world that operated according to strict and predictable laws – and the hierarchy that enforced them. To Galileo, Newton, and scores of other mathematicians and scientists who challenged that hierarchy, it made scientific progress possible.
The statement that “the mathematical continuum is composed of distinct indivisibles” sounds innocent enough to us, but it had world-changing repercussions. Had the concept of the infinitely small been stifled, scientific advancement would have been stymied; with its victory, a new and dynamic science could emerge and, along with it, social and political freedoms on a scale never before known.