The secret to creativity is knowing how to hide your sources. – Albert Einstein
An interesting actualité of the world of mathematics impinges upon the game theory of Chess. László Babai, a mathematician and computer scientist at the University of Chicago in Illinois, claims a breakthrough in complexity theory. He is presenting today (2015-11-11) his algorithm for comparing two networks for identity, a P/NP problem traditionally way to the NP end of the spectrum. If his work is validated by his peers, it could have profound impact upon the game theory assessment of intrinsic difficulty of chess.
That from the cloudy upper reaches of game theory. Down here in the trenches I was pleased to discover new two youth members, about high school senior or college freshman age, of the Denver Chess Club last night perusing a certain class of openings. They were looking at the d3 line of the Spanish, and the King’s Indian attack, and other restrained employments of the legendary White initiative.
Together we compared the strategies of 20th century White openings, which seek to demonstrate that White has an attack. Karpov is the 20th century world champion of whom it was said that he “does not believe White has an attack”. Flash forward to the 21st century where the 20th century “main lines” of 1. e4 appear to be (when properly defended by Black) a White pawn sacrifice in order to achieve enough initiative to draw the resultant pawn-down ending.
The 21st century player views the problem of the opening as that of making the opponent commit first. S/he strives to develop in such a way that the danger to the opponent does not come from a scintillating attack on the king’s bishop’s square so much as from a falling into a enter-the-midgame zugzwang, overreaching against a restrained position and finding one’s self unable to make a move that doesn’t spoil the balance.
If we could but see it, the whole game of Chess from the starting position is a corresponding squares problem, i.e., computationally it’s a network. Hence the impact of the discovery announced by Babai upon the possibilities of computer solution of chess.