Semi-Autonomous Mathematics Discovery with Gemini: A Case Study on the Erd\H{o}s Problems
Abstract
We present a case study in semi-autonomous mathematics discovery, using Gemini to systematically evaluate 700 conjectures labeled 'Open' in Bloom's Erd\H{o}s 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 Erd\H{o}s Problems.
Cite
@article{arxiv.2601.22401,
title = {Semi-Autonomous Mathematics Discovery with Gemini: A Case Study on the Erd\H{o}s Problems},
author = {Tony Feng and Trieu Trinh and Garrett Bingham and Jiwon Kang and Shengtong Zhang and Sang-hyun Kim and Kevin Barreto and Carl Schildkraut and Junehyuk Jung and Jaehyeon Seo and Carlo Pagano and Yuri Chervonyi and Dawsen Hwang and Kaiying Hou and Sergei Gukov and Cheng-Chiang Tsai and Hyunwoo Choi and Youngbeom Jin and Wei-Yuan Li and Hao-An Wu and Ruey-An Shiu and Yu-Sheng Shih and Quoc V. Le and Thang Luong},
journal= {arXiv preprint arXiv:2601.22401},
year = {2026}
}
Comments
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