Keep exploring at ► https://brilliant.org/TreforBazett. Get started for free for 30 days — and the first 200 people get 20% off an annual premium subscription!

Normal tictactoe can always be drawn. But what if it lives in high dimensions? It turns out that no matter how large a tictactoe board you have or how many players want to play, there always is a dimension long enough that guarantees the 1st player will always win. The theorem behind this, HalesJewett, is part of a family of theorems in Ramsey theory that show how lower level structures (like straight lines of the same colour) are always going to occur if the dimension is large enough. That is, you can't have a system that is totally without order. In this video we explore these tictactoe generalizations, the Van Der Waerden theorem and sketch it's proof.

Reference: This undergrad level book introducing Ramsey Theory has lots more detail on all the theorems and more: https://www.sfu.ca/~vjungic/RamseyNot...

0:00 Friends and Strangers Theorem
2:56 What is Ramsey Theory?
3:36 High dimensional TicTacToe
7:58 HalesJewett Theorem
10:37 Van der Waerden's theorem
14:42 Proof sketch of Van der Waerden's theorem
21:23 Summary
21:57 Brilliant.org/TreforBazett

Check out my MATH MERCH line in collaboration with Beautiful Equations
►https://beautifulequations.net/pages/...

COURSE PLAYLISTS:
►DISCRETE MATH:    • Discrete Math (Full Course: Sets, Log...  
►LINEAR ALGEBRA:    • Linear Algebra (Full Course)  
►CALCULUS I:    • Calculus I (Limits, Derivative, Integ...  
► CALCULUS II:    • Calculus II (Integration Methods, Ser...  
►MULTIVARIABLE CALCULUS (Calc III):    • Calculus III: Multivariable Calculus ...  
►VECTOR CALCULUS (Calc IV)    • Calculus IV: Vector Calculus (Line In...  
►DIFFERENTIAL EQUATIONS:    • Ordinary Differential Equations (ODEs)  
►LAPLACE TRANSFORM:    • Laplace Transforms and Solving ODEs  
►GAME THEORY:    • Game Theory  

OTHER PLAYLISTS:
► Learning Math Series
   • 5 Tips To Make Math Practice Problems...  
►Cool Math Series:
   • Cool Math Series  

BECOME A MEMBER:
►Join:    / @drtrefor  

MATH BOOKS I LOVE (affilliate link):
► https://www.amazon.com/shop/treforbazett

SOCIALS:
►Twitter (math based):   / treforbazett  
►Instagram (photography based):   / treforphotography