The \emph{Optimist}: Towards Fully Automated Graph Theory Research
This work addresses the challenge of automating graph theory research, which could benefit mathematicians and AI researchers, but it appears incremental as it builds on existing methods for conjecture generation.
The paper tackles the problem of automated conjecture generation in graph theory by introducing the Optimist system, which uses mixed-integer programming and heuristic methods to generate conjectures that rediscover known theorems and propose novel inequalities, with initial experiments showing its potential to uncover foundational results.
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.