Learning Interestingness in Automated Mathematical Theory Formation
George Tsoukalas, Rahul Saha, Amitayush Thakur, Sabrina Reguyal, Swarat Chaudhuri
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 learning elementary number theory over hard-coded baselines.