Philadelphia Area Seminar History of Mathematics PASHoM

Thursday, March 20, 2025 - 6:30pm to 8:00pm

Professor Tomas Guardia

Gonzaga University

Rithmomachia is a Greek Number Theory-based abstract-strategy math board game. It was created as a learning device to support the teaching-learning process of the quadrivium --arithmetic, geometry, astronomy, and music. Rithmomachia was an intellectual game that developed in the elite of the Cathedral Schools and Universities of the Middle Ages. The pieces of Rithmomachia have numbers printed on them. These numbers follow a pattern. To play, one makes a mathematical operation to capture a piece with either the values on the pieces or the values and spaces that separate them. There are many ways to capture a piece: encounter, ambush, assault, power and root, progression, and surrounding. In this talk, we will introduce the Fiboquadratic numbers, their generalization to Fibo (p)-ic numbers, and their natural extension to Metal (p)-ic numbers. We will see how this fascinating medieval board game led to recent problems in Number Theory, Combinatorics, and Cryptography. We will present the ongoing projects of the Gonzaga Rithmomachia Research Center, the open problems we are looking to solve, and potential collaborations in the field.