Calculus: History and Concept
“Calculus,” wrote the mathematician John Von Nuemann, “was the first achievement of modern mathematics … it is difficult to overestimate its importance.” What does it mean to say calculus initiated modern mathematics? Beyond mathematics, what influence has calculus had on the wider world? Most importantly, what is calculus—and why does it still stand as the culmination of our mathematics curriculum?
In this course, we’ll examine the history and concepts of calculus, attempting to understand both its development and its crucial importance to nearly every mathematically rooted enterprise of modern life. We’ll proceed chronologically, tracing the development of calculus from its antecedents in ancient Greek thinking through its further development in Europe, India, and the Islamic world to its formal expression in the infinitesimal calculus of Newton and Leibniz. Carrying the story forward, we’ll look at the application of calculus to the scientific revolution, particularly the rapid advances of modern physics and astronomy, as well as the 19th-century innovations that resulted in modern definitions of limit, derivative, and integral. As we study the history of calculus, we’ll also attempt to develop an intuitive understanding of its central concepts: the derivative, which concerns “instantaneous rates of change”; the integral, which concerns the accumulation of continuous quantities (in particular the calculation of areas); and limits, which underlie the mathematical definitions of both derivative and integral. Guiding us will be selections from The Hitchhiker’s Guide to Calculus (Michael Spivak); Calculus: A Liberal Art (W.M. Priestley); The History of the Calculus and Its Conceptual Development (Carl Boyer); The Origins of Cauchy’s Rigorous Calculus (Judith Grabiner); Infinitesimal: How a Dangerous Mathematical Theory Shaped the Modern World (Amir Alexander) and The Crest of the Peacock: Non-European Roots of Mathematics (George Joseph).
Course ScheduleWednesday, 6:30-9:30pm ET
October 20 — November 10, 2021