Explore the fascinating world of Ramsey Theory in this 23-minute video lecture. Discover how complete chaos is impossible, even in complex systems, as you delve into high-dimensional tic-tac-toe, the Hales-Jewett Theorem, and Van der Waerden's theorem. Learn why lower-level structures always emerge when dimensions are large enough, and follow along with a proof sketch of Van der Waerden's theorem. Gain insights into the mathematical principles that demonstrate the inherent order in seemingly chaotic systems.
Why Complete Chaos Is Impossible - Ramsey Theory
Overview
Syllabus
Friends and Strangers Theorem
What is Ramsey Theory?
High dimensional Tic-Tac-Toe
Hales-Jewett Theorem
Van der Waerden's theorem
Proof sketch of Van der Waerden's theorem
Summary
Brilliant.org/TreforBazett
Taught by
Dr. Trefor Bazett
