New Technologies in Mathematics Seminar

Speaker: Randy Davila, RelationalAI and Rice University

Title: Discovery in Mathematics with Automated Conjecturing

Abstract: Automated conjecturing is a form of artificial intelligence that applies heuristic-driven methods to mathematical discovery. Since the late 1980s, systems such as Fajtlowicz’s Graffiti, DeLaViña’s Graffiti.pc, and TxGraffiti have collectively contributed to over 130 publications in mathematical journals. In this talk, we outline the evolution of automated conjecturing, focusing on TxGraffiti, a program that employs linear optimization methods and several distinct heuristics to generate mathematically meaningful conjectures. We will then introduce GraphMind, a dueling framework where the Optimist proposes conjectures while the Pessimist seeks counterexamples, fostering a feedback loop that strengthens automated reasoning. Finally, we will present GraffitiAI, a Python package that extends automated conjecturing across various mathematical domains.

Bio: Randy R. Davila is a Lecturer in the Department of Computational Applied Mathematics & Operations Research at Rice University and a Library Engineer at RelationalAI, specializing in relational knowledge graph systems for intelligent data management. He earned his PhD in Mathematics from the University of Johannesburg in 2019, with research focused on graph theory and combinatorial optimization. His work explores artificial intelligence in mathematical conjecture generation, graph theory, and neural network applications to combinatorial problems. As the creator of TxGraffiti, he has developed AI-driven systems that have contributed to numerous mathematical publications. His recent projects include GraphMind, a dueling agent-based framework that pairs conjecture generation with counterexample discovery, and GraffitiAI, a Python package for automated conjecturing across mathematical disciplines.