Discovering mathematical concepts through a multi-agent system
This work is significant for researchers in automated mathematical discovery, offering a new paradigm for autonomously identifying complex mathematical concepts.
This paper introduces a multi-agent system for computational mathematical discovery that generates conjectures, attempts to prove them, and refines its approach based on feedback and data. The system successfully recovered the concept of homology from polyhedral data and linear algebra knowledge, inspired by Euler's conjecture.
Mathematical concepts emerge through an interplay of processes, including experimentation, efforts at proof, and counterexamples. In this paper, we present a new multi-agent model for computational mathematical discovery based on this observation. Our system, conceived with research in mind, poses its own conjectures and then attempts to prove them, making decisions informed by this feedback and an evolving data distribution. Inspired by the history of Euler's conjecture for polyhedra and an open challenge in the literature, we benchmark with the task of autonomously recovering the concept of homology from polyhedral data and knowledge of linear algebra. Our system completes this learning problem. Most importantly, the experiments are ablations, statistically testing the value of the complete dynamic and controlling for experimental setup. They support our main claim: that the optimisation of the right combination of local processes can lead to surprisingly well-aligned notions of mathematical interestingness.