Learning Interestingness in Automated Mathematical Theory Formation

• URL: http://arxiv.org/abs/2511.14778v1
• Date: Wed, 05 Nov 2025 18:59:17 GMT
• Title: Learning Interestingness in Automated Mathematical Theory Formation
• Authors: George Tsoukalas, Rahul Saha, Amitayush Thakur, Sabrina Reguyal, Swarat Chaudhuri,
• Abstract summary: We take two key steps in automating the open-ended discovery of new mathematical theories.<n>First, we introduce $emphFERMAT$, a reinforcement learning environment that models concept discovery and synthesizing theorem-proving.<n>Second, we explore a specific problem through $emphFERMAT$: automatically scoring the $emphinterestingness$ of mathematical objects.
• Score: 14.93273836886908
• License: http://creativecommons.org/licenses/by/4.0/
• 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 $\emph{FERMAT}$, 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 $\emph{FERMAT}$: automatically scoring the $\emph{interestingness}$ 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 $\emph{FERMAT}$ environment at this URL(https://github.com/trishullab/Fermat).

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