Learning to Discover Interesting Mathematics
TLDR
Defines theorem interestingness as proof-to-statement length ratio, trains a 27B model to predict proof difficulty, and generates more interesting, out-of-distribution theorems for self-expanding formal libraries.
Reasoning
Strengths include a novel, quantifiable metric for mathematical interestingness, empirical validation via correlation with downstream utility, and demonstration of more out-of-distribution theorem generation. Weaknesses include reliance on formal proof length as a proxy and limited evidence about broader mathematical or real-world significance.
Read-first score
Read-first score 46.5, weighted from topical fit, citation, graph, method, reproducibility, and recency signals. Original total remains 45.
Field roles
Rank sensitivity
Stability: volatile; rank range: 41.
Keyword Scores
Deep Analysis
Innovations
- Defines intrinsic interestingness of a theorem as the ratio of proof length to statement length.
- Uses proof difficulty conditioned on a set of premises as a primitive for computing interestingness metrics.
- Trains a 27B model to predict proof difficulty more accurately than frontier general-purpose models.
- Optimizes for the interestingness metric to generate more interesting theorems and substantially more out-of-distribution mathematics.
- Proposes a self-expanding machine-verified mathematical library loop that generates, selects, and builds on candidate theorems without human-supplied targets.
Methodology
The paper defines intrinsic interestingness as the ratio between proof length and statement length and validates it against extrinsic downstream utility in formal mathematical libraries such as Mathlib. It trains a 27B model to predict proof difficulty conditioned on premises and compares its accuracy with frontier general-purpose models. The proposed metric is then optimized to generate candidate theorems, select interesting ones, and iteratively expand a formal library.
Key Results
The intrinsic interestingness metric correlates strongly with extrinsic downstream utility, and the 27B difficulty-prediction model outperforms frontier general-purpose models. Optimizing for this metric reduces substantial or full overlap with Mathlib from 91.9% to 30.6% and produces more interesting theorems.
Limitations
- The abstract does not explicitly state limitations; it notes that whether LLM-generated mathematical knowledge is interesting or useful remains open and the proposed metric is a practical quantifiable signal.