Paper defines theorem interestingness metric, 27B model beats frontier models at proof difficulty
Pascallisch · x · 2026-09-26
A new arXiv paper (2609.28603) by Niket Patel, Remi Munos, Julia Kempe et al. tackles whether AI-generated theorems are actually interesting. Key points:
- Defines a theorem's intrinsic interestingness as the ratio of proof length to statement length, and shows it correlates strongly with downstream utility.
- Uses proof difficulty conditioned on premises as a primitive, training a 27B model that predicts proof difficulty more accurately than frontier general-purpose models.
- Optimizing for the metric yields more interesting theorems and cuts substantial/full overlap with Mathlib from 91.9% to 30.6%, i.e. more out-of-distribution math.
- The system generates candidate theorems, selects the most interesting, and iteratively expands a self-growing, machine-verified library — a practical signal for ranking conjectures and guiding proof search.
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