Learning to Discover Interesting Mathematics (arxiv.org)

Researchers have made significant strides in enhancing the capabilities of Large Language Models (LLMs) to tackle complex mathematical problems, potentially accelerating advancements in mathematics. By defining a metric for the intrinsic interestingness of mathematical theorems—measured as the ratio of proof length to statement length—this work investigates the viability of LLMs generating theorems that are not just valid but also useful. The team trained a 27B model that outperformed existing models in predicting proof difficulty and created a system that can generate new theorems while selectively pruning overlaps with existing mathematical knowledge. The implications of this research extend to the development of self-expanding, machine-verified mathematical libraries, offering a quantifiable method for assessing and ranking theoretical contributions. This advancement not only enhances the efficiency of theorem discovery but also lays the groundwork for LLMs to autonomously curate and advance mathematical research, potentially leading to breakthroughs in theories that have remained unexplored for decades. By optimizing the generation of interesting theorems, this approach signals a shift towards machine-driven exploration of mathematics, which could reshape the field in fundamental ways.