A talk titled “Learning Mathematics Through Combinatorial Game Theory” was delivered by Prof. Urban Larsson, Department of Industrial Engineering and Operations Research (IEOR), IIT Bombay, on 24 September 2026. The talk was held from 3:30–4:30 PM at Ramanujan Hall, Department of Mathematical Sciences.
Abstract: Combinatorial Game Theory (CGT) is a rich mathematical theory that connects games with areas of mathematics, including algebra, number theory, and computer science. Its development was profoundly influenced by John Conway's monumental volume On Numbers and Games, which introduced, among other things, the theory of surreal numbers.
How can students learn advanced mathematics by creating the mathematical objects they are going to study? In several courses on CGT, I have asked students to invent their own simple rulesets rather than working only with established games. The students then play their games, analyze them, and prove theorems about them. Their own rulesets become examples through which they discover and develop the theory.
This approach reverses the usual direction of teaching. Instead of first presenting a theory and then giving students examples to analyze, students first create examples and are then led to the concepts and results needed to understand them. The students have produced many original rulesets, and in several cases their analysis has led to mathematical questions and theorems of their own.
I will describe this approach and give examples of student-created games and the mathematics that emerged from studying them. The goal is to illustrate how CGT, through both playing and mathematical analysis, can provide a setting in which students actively discover advanced mathematics.
