Monday, August 12, 2019

"An Unresolved Mathematical Chess Problem": well, it's not quite about Lie Groups


For today, I thought I would present “An Unresolved Mathematical Chess Problem”, by Xhess Network and The Problemist. Not every post needs to be political.


The speaker poses two problems.  The first is to show Mate for White in 24 moves. The position is a complicated endgame with nights and bishops and pawns and no rooks or queens. There is an odd configuration of 4 black pawns quadrupled on the h-file. It is unclear whether this position occurred in a real game or could occur.

The solution is to realize that both sides are in practical zugzwang with White being able to move only the light bishop form a8 to h1 back and forth.

The second problem is to count the number of solutions in 24 moves possible.  The problem author wants a mathematical proof (I guess this would involve number theory and could require computer simulations, maybe a master's thesis at a university.) 
       
I suppose the collection of all possible legal chess positions is a vector space, but it is hard to describe an algebraic paradigm to map game moves to operations like what we see in group, ring or field theory. The number of possible operators seems infinite, and I don’t know what body of mathematics can really prove theorems like this.  Yet chess is such an amazing game in how it works that we don’t know where it came from.  The rules would be the same anywhere in the universe, or any universe.

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