Surreal Numbers And Mathematical Games

A talk from EMF 2014 by Tom Hall

On Sunday August 31, 2014 at in Stage C

John Conway created/discovered the Surreal Numbers (along with the game of life cellular automaton) while pondering the game of Go. They include all the reals and rationals you probably know but also infinite and infinitesimal values, lots of them. Combinatorial Game Theory is an additive theory of games with perfect information and no chance element. Fortunately, though it touches on things at the core of Mathematics, it requires almost no other concepts to understand it It turns out some Games are Numbers, however any Game that is interesting enough to be worth playing is not a Number. We need a new language to describe them (whence Uppitiness, Atomic Weight and Chilling). We will find out how to play the Nim perfectly, realise Dots and Boxes has more to it than you thought, play Col, Snort and Cutcake, understand the Tweedledee and Tweedledum argument, learn Hackenbush and maybe begin to analyse Go and chess end games.


View this video on YouTube.