Randy Davila | Recent Developments in Automated Conjecturing

Video Description

Math and Machine Learning Reunion Workshop Speaker: Randy Davila, RelationalAI, Rice University Title: Recent Developments in Automated Conjecturing Abstract: The dream of a machine capable of generating deep mathematical insight has inspired decades of research—from Fajtlowicz’s Graffiti program in graph theory and chemistry to DeepMind’s neural breakthroughs in knot theory. In this talk, we briefly trace the evolution of automated conjecturing systems and present recent advances that deepen our understanding of what it means for machines to conjecture—a pursuit long embodied by our system, TxGraffiti. Building on this legacy, we introduce a new framework that integrates optimization, enumeration, and convex geometric methods with creative heuristics and symbolic translation. This extended system produces not only conjectured inequalities, but also necessary and sufficient condition statements, which can then be automatically ranked by IRIS (Inequality Ranking and Inference System) model and translated into Lean 4 for formal verification. The result is a flexible architecture capable of generating precise, human-readable, and logically rigorous conjectures with minimal manual intervention. We showcase results across a range of mathematical areas, including graph theory, polyhedral theory, number theory, and—for the first time—conjectures in string theory, derived from the dataset of complete intersection Calabi–Yau (CICY) threefolds. Together, these developments suggest that with the right blend of structure, strategy, and aesthetic, machines can generate conjectures that not only withstand scrutiny but invite it—offering a glimpse into a future where AI contributes meaningfully to the creative process of mathematics.