The Optimist: Towards Fully AutomatedGraph Theory Research

This paper introduces the Optimist, an autonomous system developed to advanceautomated conjecture generation in graph theory. Leveraging mixed-integer pro-gramming (MIP) and heuristic methods, the Optimist generates conjectures thatboth rediscover established theorems and propose novel inequalities. Througha combination of memory-based computation and agent-like adaptability, theOptimist iteratively refines its conjectures by integrating new data, enabling afeedback process with minimal human (or machine) intervention. Initial exper-iments reveal the Optimist’s potential to uncover foundational results in graphtheory, as well as to produce conjectures of interest for future exploration. Thiswork also outlines the Optimist’s evolving integration with a counterpart agent,the Pessimist (a human or machine agent), to establish a dueling system thatwill drive fully automated graph theory research.