The Integral That Changed Math Forever

Video Description

To try everything Brilliant has to offer—free—for a full 30 days, visit https://brilliant.org/AbideByReason/ . You’ll also get 20% off an annual premium subscription. The Riemann Integral was developed as a way to calculate the area under a curve. Then came a function that was impossible to integrate. This dilemma would lead one mathematician, Henri Lebesgue, to invent an entirely new approach. The Lebesgue Theory of Integration was a much better theory of integration and it would ultimately change the way we think about the integral forever. _____ Join my Patreon community: https://www.patreon.com/abidebyreason Support the channel with a one-time donation: https://ko-fi.com/abidebyreason _____ Video on the Vitali Set: https://youtu.be/hs3eDa3_DzU What is a Hilbert Space? https://youtu.be/FFPXm-tuOt8 What is a Banach Space? https://youtu.be/Zjo1ACFm5WI _____ Article on the Lebesgue Integral: https://arxiv.org/pdf/2309.08908 Music: Epidemic Sound Animations created using Manim: https://www.manim.community/ Illustrations and Thumbnails: Christine Kosakowski This video was sponsored by Brilliant