Mathematics & Machine Learning Seminar

Automated conjecturing is a branch of artificial intelligence aimed at modeling one of the most creative aspects of mathematics: forming interesting conjectures. Early efforts in symbolic reasoning date back to the late 1950s, but it was Siemion Fajtlowicz's Graffiti program in the 1980s that first produced conjectures compelling enough for mathematicians to study and prove. Since then, the field has developed new frameworks that integrate computation, logic, and heuristic search to explore how machines can participate in mathematical discovery.

In this talk, I'll describe the evolution of these ideas and introduce the newest version of TxGraffiti, our automated conjecturing system. The current design organizes conjectures into logical types—inequalities, equalities, dominance relations, and conditional statements—and employs optimization, convex geometry, and symbolic lifting to refine and generalize results. These updates have broadened TxGraffiti's scope from graph theory to polyhedral geometry, number theory, and even string theory, illustrating how automated systems can now generate structured, interpretable conjectures that meaningfully complement human mathematical reasoning.