Why Chess and Mathematics Are So Closely Connected: Combinatorics, Graph Theory, and AI

I’ve been thinking lately — why do we so naturally associate chess with mathematics? What is it about chess that makes it so special?

Chess and Mathematics Share the Same Way of Thinking

Chess and mathematics demand the same core skills: logic, analysis, and strategic thinking. In both fields, every decision carries consequences, and success depends on the ability to think several steps ahead and evaluate alternatives. Chess is, in a sense, a “mathematical problem” played out on a board — one where players draw on combinatorics, probabilistic reasoning, and strategic planning.

Mathematical Methods Behind Chess Analysis

The mathematics of chess goes far deeper than it might first appear. Several branches of mathematics are directly at work every time a game is played.

Combinatorics helps estimate the number of possible positions and move sequences, making it possible to calculate lines several moves deep. Graph theory treats the board and its legal moves as a network structure, where squares are connected by the possible movements of pieces — this simplifies the search for optimal paths and the identification of controlled zones. Probabilistic calculations allow players and engines alike to assess the winning chances of any given position, especially during computer-assisted analysis where AI evaluates all conceivable outcomes. Algorithms and artificial intelligence — systems like AlphaZero — discover optimal strategies by training on millions of games.

Chess as a Laboratory for Mathematical Research

Chess is not merely a game. It is a proving ground for mathematical research and discovery, where logic and calculation become the keys to victory.

P.S. In November there will be a video about one such study — a piece of research that turned the world of mathematics upside down, or at least the world of dozens and hundreds of mathematicians. The script is ready.