Semi-Autonomous Mathematics Discovery with Gemini: A Case Study on the Erdős Problems

Abstract

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.

Reclassify Erdos-935 as Independent Rediscovery, bringing the number of autonomous solutions down to 5. (Explanation in Addendum 4.1) Elaborate on Footnote 3. Slightly reword various phrases in the Introduction in response to feedback