When CAN'T Math Be Generalized? | The Limits of Analytic Continuation скачать в хорошем качестве

When CAN'T Math Be Generalized? | The Limits of Analytic Continuation

There's often a lot of emphasis in math on generalizing concepts beyond the domains where they were originally defined, but what are the limits of this process? Let's take a look at a small example from complex analysis where we actually have the tools to predict when this is impossible. This video is a participant in the third Summer of Math Exposition (#SoME3) hosted by 3Blue1Brown to encourage more math content online. To learn more, see this: https://3blue1brown.substack.com/p/so... =Chapters= 0:00 - Intro 1:15 - Extending a Geometric Series 3:39 - Complex Power Series 6:23 - Analytic Continuation 8:30 - Analyzing the Gap Series 11:51 - Visualizing the Gap Series 19:21 - Gap Theorems =============================== This video was generously supported in part by these patrons on Patreon: Marshall Harrison, Michael OConnor, Mfriend. To support future videos, become a patron at   / morphocular   Thank you for your support! =============================== CREDITS The music tracks used in this video are (in order of first appearance): Icelandic Arpeggios, Checkmate, Ascending, Orient, Faultlines =============================== The animations in this video were mostly made with a homemade Python library called "Morpho". It's mostly a personal project, but if you want to play with it, you can find it here: https://github.com/morpho-matters/mor...