The original version of this story appeared in Quanta Magazine.
Calculus is a powerful mathematical tool. But for hundreds of years after its invention in the 17th century, it stood on a shaky foundation. Its core concepts were rooted in intuition and informal arguments, rather than precise, formal definitions.
Two schools of thought emerged in response, according to Michael Barany, a historian of math and science at the University of Edinburgh. French mathematicians were by and large content to keep going. They were more concerned with applying calculus to problems in physics—using it to compute the trajectories of planets, for instance, or to study the