NYU defines an interestingness metric for theorems and trains a 27B model to discover new math
nyuniversity · hf · 2026-09-26
NYU researchers propose quantifying a theorem's intrinsic interestingness as the ratio of proof length to statement length, showing it strongly correlates with downstream utility.
- They identify proof difficulty conditioned on premises as a key primitive and train a 27B model that predicts it more accurately than frontier general-purpose models
- Optimizing for this metric cut substantial/full overlap with Mathlib from 91.9% to 30.6%, yielding more out-of-distribution math
- The system generates candidate theorems, selects the most interesting, and iteratively grows a self-expanding, machine-verified library
- These metrics offer a practical signal for ranking conjectures and guiding proof search without human-supplied targets
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