Chess is a game of concentration, strategy, and guile. But it is also a game of numbers. A brief history of interesting chess facts reveals that the relationship between mathematics and chess is deep and storied.
The 8 by 8 grid of the chessboard itself has long been used to express mathematical calculations, concepts, and problems. In medieval England, the chessboard was the model for the accounting tables used by financiers to keep records and settle accounts, and a checkered cloth patterned after the chessboard was the symbol of royal collections. In fact, "Chancellor of the Exchequer, " the royal collections official established by the Normans, got its name from the Old French word "eschequier" which derived from "eschec" meaning "chess."
A number of important problems of math theory have emerged from the mathematical study of chess. The Knight's Tour, which has found application in systems theory and computer science, first appeared as early as 900 B. C. In a classical Sanskrit poem. Other math concepts developed through the study of chess include the Eight Queens Problem, the Mutilated Chessboard Problem, Rook Polynomials, and the Rook Reciprocity Theorem, which have variously contributed to areas of number theory, matrix theory, computer science, and algorithm studies.
On the other hand, applying mathematics to chess, you can arrive at some staggering numbers. Mathematicians and scientists have calculated that the estimated number of possible chess games is greater than the estimated number of electrons in the entire universe. There are 318,979,564,000 possible ways just to play the first four moves on each side of a chessboard. The longest single game theoretically possible would be 8,949 moves. When you consider that the longest officially recorded game took more than twenty hours with 269 moves, it is hard to imagine how long a game could theoretically last. On the other end of the spectrum, the shortest officially recorded game involved only one move.
Chess and math have a long association. Not only has chess inspired mathematicians to develop concepts and problems, but some chess facts themselves are mathematically surprising. Math and chess offer ways of looking at each other that are both enriching and entertaining.
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