Automated Theory Formation and Interestingness in Mathematics

Advances in modern learning systems are beginning to demonstrate utility for select problems in research mathematics. A broader challenge is that of developing new theories automatically. This area has a rich history, and is tied to some of the earliest work in AI. In particular, a central question in this study was measuring the “interestingness” of mathematical concepts.

In this talk, I will review this historical context and present our recent work on using large language models to synthesize interestingness measures that guide theory exploration in elementary number theory from scratch. I will conclude by outlining potential future research directions in this domain.

Joint work with Rahul Saha, Amitayush Thakur, Sabrina Reguyal, and Swarat Chaudhuri.