Mathematicians Euler, de Moivre and Vandermonde studied the knight's tour. The game structure and nature of chess is related to several branches of mathematics. Many combinatorical and topological problems connected to chess were known of for hundreds of years. In 1913, Ernst Zermelo used it as a basis for his theory of game strategies, which is considered as one of the predecessors of game theory. The number of legal positions in chess is estimated to be between 10 and 10, with a game-tree complexity of approximately 10. The game-tree complexity of chess was first calculated by Claude Shannon as 10, a number known as the Shannon number. Typically an average position has thirty to forty possible moves, but there may be as few as zero (in the case of checkmate or stalemate) or as many as 218. The most important mathematical challenge of chess is the development of algorithms which can play chess.

The idea of creating a chess playing machine dates to the 18th century; around 1769, the chess playing automaton called The Turk became famous before being exposed as a hoax. Serious trials based on automatons, such as El Ajedrecista, were too complex and limited to be useful. Since the advent of the digital computer in the 1950s, chess enthusiasts and computer engineers have built, with increasing degrees of seriousness and success, chess-playing machines and computer programs. The groundbreaking paper on computer chess, "Programming a Computer for Playing Chess", was published in 1950 by Shannon. He wrote: The chess machine is an ideal one to start with, since: (1) the problem is sharply defined both in allowed operations (the moves) and in the ultimate goal (checkmate); (2) it is neither so simple as to be trivial nor too difficult for satisfactory solution; (3) chess is generally considered to require "thinking" for skillful play; a solution of this problem will force us either to admit the possibility of a mechanized thinking or to further restrict our concept of "thinking"; (4) the discrete structure of chess fits well into the digital nature of modern computers.

1990s chess-playing computer The Association for Computing Machinery (ACM) held the first major chess tournament for computers, the North American Computer Chess Championship, in September 1970. CHESS 3.0, a chess program from Northwestern University, won the championship. Nowadays chess programs compete in the World Computer Chess Championship, held annually since 1974. At first considered only a curiosity, the best chess playing programs, for example Rybka or Hydra, have become extremely strong.

In 1997 a computer won a match against a reigning World Champion for the first time: IBM's Deep Blue beat Garry Kasparov 3½–2½ (it scored two wins, one loss and three draws). Nevertheless, from the point of view of artificial intelligence, chess-playing programs are relatively simple: they essentially explore huge numbers of potential future moves by both players and apply an evaluation function to the resulting positions, an approach described as "brute force" because it relies on the sheer speed of the computer. With huge databases of past games and high analytical ability, computers also help players to learn chess and prepare for matches.

Additionally, Internet Chess Servers allow people to find and play opponents all over the world. The presence of computers and modern communication tools have also raised concerns regarding cheating during games, most notably the "bathroom controversy" during the 2006 World Championship.