The article describes the application of combinatorial game theory to the solution of some problems in the game of Go. Combinatorial game theory treats win-lose games between two players in which the last player to move wins. These games are completely characterized by a certain set of trees, the trees have canonical forms, and there is a natural equivalence relation and operation on the trees such that the equivalence classes form an Abelian group. The theory was developed in the book `Winning ways for your mathematical plays' by \textit{E. R. Berlekamp, J. H. Conway} and \textit{R. K. Guy} [Vol. 1, 2 (1982; Zbl 0485.00025)], and applied to Go by them. What was shown there is that certain Go positions decompose in such a way that the theory can be applied to determine the winner. These Go positions, when shown to professional Go players, defeated them: they could not solve them. However, a computer program based on the theory did solve them, and, remarkably enough, does so without look-ahead. The interest in this article is a concise and amusing introduction to combinatorial game theory and one of its remarkable applications. It is accompanied by some speculation on its meaning for mathematics. First, the author reports that Berlekamp believes that some of the ``rules of thumb'' known to professional Go players can be formulated in combinatorial game-theoretic terms. This would be a remarkable fact, when the computer chess world has basically succumbed to brute-force searching. Second, the author speculates that combinatorial game theory is an example of the beautiful diversity of mathematics, a diversity that will defeat all attempts to unify all of mathematics.
scientific article; zbMATH DE number 727215