This paper introduces the \emph{ Optimist}, an autonomous system developed to advance automated conjecture generation in graph theory. Leveraging mixed-integer programming (MIP) and heuristic methods, the \emph{ Optimist} generates conjectures that both rediscover established theorems and propose novel inequalities. Through a combination of memory-based computation and agent-like adaptability, the \emph{ Optimist} iteratively refines its conjectures by integrating new data, enabling a feedback process with minimal human (\emph{ or machine}) intervention. Initial experiments reveal the \emph{ 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 \emph{ Optimist}'s evolving integration with a counterpart agent, the \emph{ Pessimist} (a human \emph{ or machine} agent), to establish a dueling system that will drive fully automated graph theory research.
Categories: cs.AI math.CO