The Optimist: Towards Fully Automated Graph Theory Research

This paper introduces the Optimist, an autonomous system developed to advance automated conjecture generation in graph theory. Leveraging mixed-integer programming (MIP) and heuristic methods, the Optimist generates conjectures that both rediscover established theorems and propose novel inequalities. Through a combination of memory-based computation and agent-like adaptability, the Optimist iteratively refines its conjectures by integrating new data, enabling a feedback process with minimal human (or machine) intervention. Initial experiments reveal the Optimist's potential to uncover foundational results in graph theory, as well as to produce conjectures of interest for future exploration. This work also outlines the Optimist's evolving integration with a counterpart agent, the Pessimist (a human or machine agent), to establish a dueling system that will drive fully automated graph theory research.