On the Mathematics Hidden Behind Games

This paper by Yannick Rochat and Sophie Bémelmans, presented at DiGRA 2026, argues that mathematics is pervasive in game design yet rarely examined within game studies scholarship, which the authors frame as a "disciplinary divide" between mathematical research on games and humanities-oriented game studies. Its purpose is twofold: to trace historical interactions between mathematics and games, and to encourage video game researchers to engage more seriously with mathematical concepts as tools for creation, not only for optimisation or analysis.

The historical overview traces mathematical play from ancient games of chance and territory-capture games through early modern recreational mathematics, such as Euler's Seven Bridges of Königsberg problem and Kirkman's Schoolgirls problem, which contributed to graph theory and combinatorial design. It also charts the formal solving of games from the nineteenth century onward, including Connect Four and Checkers, and notes how games such as Nim and Tic-Tac-Toe were used in the 1950s to demonstrate computer capabilities and suggest machine "intelligence."

Two contemporary case studies anchor the argument. The first examines mathematician and board game designer Frank Crittin, whose games such as Tower Up, based on the four-colour theorem, evolve away from their mathematical origins as balance and player pleasure are prioritised through playtesting. The second analyses Hyperbolica, a video game set in non-Euclidean hyperbolic and spherical geometries, showing how mathematics shapes mechanics, aesthetics, and player experience. The authors conclude that mathematics operates across structure, mechanics, and aesthetics, and call for research integrating mathematical models, design practice, and player experience. The paper is a short, conceptual contribution, relying on historical literature and illustrative examples rather than empirical data.