\textsc{Gambit}: Generating Automated Mathematical Bounds, Inequalities, and Theorems

Conjecture and proof are the twin engines of mathematics. Despite rapid progress in automated proof, conjecture remains underexplored. Early efforts, beginning with \emph{Graffiti} in the 1980s and followed by only a handful of systems, showed that computer-generated conjectures could enter the literature, but all depended on user-specified targets and thus assumed domain expertise. To complement modern large language models and automated proof tools, we need systems that can autonomously decide what quantities are worth relating. We present \textsc{Gambit} (\emph{Generating Automated Mathematical Bounds, Inequalities, and Theorems}), which identifies promising quantities and hypotheses in structured datasets, then applies optimization-based searches and heuristic filters to propose candidate relations. Case studies in graphs and Calabi--Yau varieties show that \textsc{Gambit} both rediscovers known results and suggests novel ones, illustrating AI-driven conjecturing as a timely complement to advances in theorem proving and counterexample search.