How to Develop a Proper Theory of Infinitesimals I - Famous Math Problems

Explore the contentious history and modern approaches to infinitesimals in mathematics through this 40-minute lecture. Delve into Archimedes' method of infinitesimal balancing, Cavalieri and Leibniz's contributions to calculus foundations, and the 1960s non-standard analysis. Discover a new perspective on infinitesimals using dual complex numbers, originally introduced by Clifford in the 1870s. Gain insights into this fundamental concept that has puzzled mathematicians for millennia and learn about its applications in quadrature and calculus.