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Currently Playing: Poincare Conjecture and Ricci Flow | A Million Dollar Problem in Topology

How do we use Riemannian Geometry and Surgery Theory to crack a million-dollar problem in topology? Ricci flow, that's how. In this video, we tackle the only Millennium Prize Problem that's been solved so far, and find the deep mathematics uncovered in the process. --- Official Problem Statement: https://www.claymath.org/millennium-problems/poincar%C3%A9-conjecture --- Follow me! Twitter: https://twitter.com/00aleph00 Instagram: https://www.instagram.com/00aleph00 __ Music Info: Documentary - AShamaluevMusic. Music Link: https://www.ashamaluevmusic.com Intro: (0:00) Poincare Conjecture: (0:45) Riemannian Geometry: (2:31) Ricci Flow: (4:17) Surgery Theory: (7:10) Proof of Poincare Conjecture: (7:26)