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This paper introduces a framework for LLMs to discover and prove interesting mathematical theorems by optimizing for a metric based on proof difficulty, leading to more novel and useful mathematical knowledge with reduced overlap with existing libraries.
This paper defines intrinsic interestingness for mathematical theorems using proof-to-statement length ratio and trains a 27B model to predict proof difficulty, enabling the generation of more interesting theorems and self-expanding mathematical libraries with reduced overlap with existing knowledge like Mathlib.