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Lagrange, Servois and the Foundations of Calculus

Philadelphia Area Seminar History of Mathematics PASHoM

Thursday, April 10, 2025 - 6:00pm to 8:30pm

Professor Rob Bradley

Adelphi University

Location

Villanova University

Mendel 103

We begin with informal conversation and a light supper (from 6:00 PM, if desired; donation $10). The talk will begin at 6:30 PM. Free Parking is available at Lot L3 at the pedestrian bridge over Lancaster Pike between Spring Mill Road (PA 320) and Ithan Ave. Zoom link: https://villanova.zoom.us/j/91964019309?pwd=QmhlS3hncSs1Tm5LemZ1T082OG1JQT09 Meeting ID: 919 6401 9309 Passcode: 105071

Abstract: The differential and integral calculus was crafted in the late 17th century. It was clearly a powerful tool and, when applied carefully, it always seemed to give correct results. But nobody could explain why it worked. The mathematical community spent much of the 18th century seeking foundations for the new calculus. Amidst the competing notions of fluxions, limits, and infinitely small increments, Joseph-Louis Lagrange (1736-1813) proposed a new foundational scheme in 1772. He further elaborated this scheme, based on expansion of functions into power series, in his 1797 book Théorie des fonctions analytiques. In this talk, we will examine Lagrange’s proposed foundations, and the further elaborations of his program due to by François-Joseph Servois (1768-1847).