An impossible game at the heart of math

Strategy stealing, the axiom of determinacy, and why it's incompatible with the axiom of choice. #SoME3

Resources to learn more and other interesting notes:
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Chomp:
Play online: https://www.math.ucla.edu/~tom/Games/...
Wikipedia article: https://en.wikipedia.org/wiki/Chomp
List of known best first moves: https://sites.math.rutgers.edu/~zeilb...
Also check out chapter 18 in the book "Winning Ways for Your Mathematical Plays"
Zermelo's Theorem: https://en.wikipedia.org/wiki/Zermelo...)

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The Axiom of Determinacy:
Wikipedia article: https://en.wikipedia.org/wiki/Axiom_o...
Borel Determinacy Theorem: https://en.wikipedia.org/wiki/Borel_d...

The argument in the video is essentially given as Proposition 28.1 in the book The Higher Infinite by Akihiro Kanamori, but it is stated in more complicated terms. You can also find some discussion of it at this link: https://mathoverflow.net/questions/49...

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The Axiom of Choice:
Wikipedia article: https://en.wikipedia.org/wiki/Axiom_o...
Banach-Tarski Paradox: https://en.wikipedia.org/wiki/Banach%...
Vsauce Video on Banach-Tarski Paradox:    • The Banach–Tarski Paradox  


Corrections: