Learning to Discover Interesting Mathematics
A 27B model ranks mathematical theorems by interestingness and cuts Mathlib overlap from 91.9% to 30.6%.
The paper defines a theorem's intrinsic interestingness as the ratio of its proof length to its statement length and reports a strong correlation with downstream utility. The authors train a 27B model that predicts proof difficulty more accurately than frontier general-purpose models. Optimizing for the metric yields more interesting theorems and reduces substantial or full overlap with Mathlib from 91.9% to 30.6%. The system can generate candidates, select the most interesting, and iteratively grow a machine-verified library without human-supplied targets.
- Interestingness is proof length divided by statement length
- A 27B model predicts proof difficulty better than frontier LLMs
- Substantial Mathlib overlap fell from 91.9% to 30.6%
- The system can iteratively expand a verified math library
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Recently, Large Language Models (LLMs) have been increasingly able to solve advanced mathematical problems, including many that have been open for decades. This opens the door to expansion of mathematical knowledge at unprecedented scale. Yet, while LLMs may be able to conjecture and prove more and more theorems, it remains open whether this new mathematical knowledge is interesting or useful. We define intrinsic interestingness of a theorem as the ratio between the length of its proof and the length of its statement. We show that this correlates strongly with an extrinsic measure of the downstream utility of a theorem. We identify the difficulty of a proof conditioned on a set of premises as a useful primitive for computing these metrics, and train a 27B model that predicts proof difficulty more accurately than frontier general-purpose models. Optimizing for our metric creates a model capable of producing more interesting theorems, while also reducing substantial or full overlap with Mathlib from 91.9% to 30.6%, showcasing the creation of more out-of-distribution math. We show that our system can generate candidate theorems, select the most interesting among them, and iteratively build on a self-expanding mathematical library. These metrics provide a practical and quantifiable signal for ranking conjectures and guiding proof search within formal mathematical libraries. Our framework provides a path towards self-expanding, machine-verified mathematical libraries that can choose worthwhile statements without relying on human-supplied targets.
Text extracted automatically; images, tables and formatting may be missing. Original: https://huggingface.co/papers/2609.28603