Learning Interestingness in Automated Mathematical Theory Formation
George Tsoukalas, Rahul Saha, Amitayush Thakur, Sabrina Reguyal, Swarat Chaudhuri
Abstract
We take two key steps in automating the open-ended discovery of new mathematical theories, a grand challenge in artificial intelligence. First, we introduce Fermat, a reinforcement learning (RL) environment that models concept discovery and theorem-proving using a set of symbolic actions, opening up a range of RL problems relevant to theory discovery. Second, we explore a specific problem through Fermat: automatically scoring the interestingness of mathematical objects. We investigate evolutionary algorithms for synthesizing nontrivial interestingness measures. In particular, we introduce an LLM-based evolutionary algorithm that features function abstraction, leading to notable improvements in discovering elementary number theory and finite fields over hard-coded baselines. We open-source the \fermat environment at github.com/trishullab/Fermat.
BibTeX
@inproceedings{
tsoukalas2025learning,
title={Learning Interestingness in Automated Mathematical Theory Formation},
author={George Tsoukalas and Rahul Saha and Amitayush Thakur and Sabrina Reguyal and Swarat Chaudhuri},
booktitle={The Thirty-ninth Annual Conference on Neural Information Processing Systems},
year={2025},
url={https://openreview.net/forum?id=RespmwOoCH}
}