Calculation and Chess

Chess has long appealed to mathematicians and computer scientists. "The problem is sharply defined, both in the allowed operations (the moves) and in the ultimate goal (checkmate)," information theorist Claude Shannon wrote in a 1950 paper titled "Programming a Computer for Playing Chess." "It is neither so simple as to be trivial nor too difficult for satisfactory solution."

Investigating the chess-playing problem represents an attractive avenue for developing problem-solving techniques that can be used for practical applications, Shannon noted.

Shannon estimated that there are about 10¹²⁰ possible 40-move games. This number is so large that it dwarfs even the most generous estimates of the number of atoms in the universe. If each atom were replaced by a supercomputer, it would still be impossible to complete all the calculations for a perfect game's first move.

Taking a broader perspective, mathematician James Byrnie Shaw wrote in his 1912 book review titled "What is Mathematics?", published in the Bulletin of the American Mathematical Society: "The game of chess has always fascinated mathematicians, and there is reason to suppose that the possession of great powers of playing that game is in many features very much like the possession of great mathematical ability…. One has only to increase the number of pieces, to enlarge the field of the board, and to produce new rules which are to govern the pieces or the player, to have a pretty good idea of what mathematics consists."

Like a chess game, though infinitely more varied, mathematical research offers myriad choices and innumerable paths. Despite whatever help computers can provide in enumerating possibilities and calculating prodigiously, it is human intuition, inspiration, experience, creativity, and knowledge that bring meaning to those endeavors.