Semi-Autonomous Mathematics Discovery with Gemini: A Case Study on the Erdős Problems
This work addresses the problem of automating mathematics discovery for researchers, but it is incremental as it focuses on verifying existing conjectures rather than generating new ones.
The researchers tackled the challenge of verifying open conjectures in mathematics by using Gemini to evaluate 700 problems from the Erdős Problems database, resulting in the resolution of 13 problems (5 with novel solutions and 8 by identifying existing literature).
We present a case study in semi-autonomous mathematics discovery, using Gemini to systematically evaluate 700 conjectures labeled 'Open' in Bloom's Erdős Problems database. We employ a hybrid methodology: AI-driven natural language verification to narrow the search space, followed by human expert evaluation to gauge correctness and novelty. We address 13 problems that were marked 'Open' in the database: 5 through seemingly novel autonomous solutions, and 8 through identification of previous solutions in the existing literature. Our findings suggest that the 'Open' status of the problems was through obscurity rather than difficulty. We also identify and discuss issues arising in applying AI to math conjectures at scale, highlighting the difficulty of literature identification and the risk of ''subconscious plagiarism'' by AI. We reflect on the takeaways from AI-assisted efforts on the Erdős Problems.