NYU Team Teaches LLMs to Judge Theorem Interestingness, Boosting Autonomous Math Discovery 4.3x
NYU's Julia Kempe group (Niket Patel, @KempeLab) released "Learning to Discover Interesting Mathematics," targeting the next bottleneck in AI math discovery: LLMs can already prove long-standing results, but finding interesting theorems without human guidance remains hard. The team proposes a quantifiable interestingness framework and trains a 27B model to predict proof difficulty, outperforming frontier general models; incorporating the metric yields a 4.3x improvement in LLM autonomous discovery of interesting theorems.
Confirmed
- The core primitive is proof difficulty under given premises; intrinsic interestingness is defined as proof length (difficulty) divided by statement length—easy to state, hard to prove
- The metric correlates strongly with downstream usefulness; @RexDouglass reports a correlation of 0.756
- Rankings on Lean/mathlib match intuition: trivial identities score low, Fermat-style variants near the top
- With the metric, LLM discovery of interesting theorems improves 4.3x
- The trained 27B model beats frontier general models at predicting proof difficulty
Why it matters
- @Pascallisch notes the goal is not endless piles of true theorems but genuinely valuable mathematics—moving from proving to problem selection
- @RexDouglass notes the metric is computable over Lean/mathlib, offering an actionable tool for automated theorem proving and ranking math libraries
2026-09-26 ~ 2026-09-27 · 5 related posts
Primary sources
- NYU defines an interestingness metric for theorems and trains a 27B model to discover new math — nyuniversity ·
- Paper defines theorem interestingness metric, 27B model beats frontier models at proof difficulty — Pascallisch ·
- Quantifying math interestingness with Lean: difficulty over description length predicts utility at ρ=0.756 — RexDouglass ·
- Researchers teach LLMs to find interesting theorems, boosting interestingness 4.3x — CatAstro_Piyush · 2026-09-26
- [source] Paper defines theorem interestingness metric, 27B model beats frontier models at proof difficulty — Pascallisch · 2026-09-26
- Researchers teach LLMs to find interesting theorems, boosting discovery 4.3x — burny_tech · 2026-09-27
- [source] Quantifying math interestingness with Lean: difficulty over description length predicts utility at ρ=0.756 — RexDouglass · 2026-09-27
1 near-duplicate retellings: nyuniversity