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

Tony Feng, Trieu Trinh, Garrett Bingham, Jiwon Kang, Shengtong Zhang +19 more
1/29/2026
cs.AImath.COmath.NT

No confident code implementation found for this paper.

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.

View on arXivView PDF

Code Implementations

No confident code match yet

We couldn't find an author-owned or strongly-evidenced community implementation for this paper. Any repos shown below are weak matches — verify before relying on them.

No code implementations found yet.

Know of an implementation? Let us know in the comments below!

Similar Papers

Towards Autonomous Mathematics Research

84% match1 repo7662026

Accelerating Scientific Research with Gemini: Case Studies and Common Techniques

84% match2026

Artifical intelligence and inherent mathematical difficulty

80% match2024

Can a Lightweight Automated AI Pipeline Solve Research-Level Mathematical Problems?

79% match2026

Assessing the Creativity of LLMs in Proposing Novel Solutions to Mathematical Problems

78% match1 repo132024

Solving an Open Problem in Theoretical Physics using AI-Assisted Discovery

78% match2026

Cite this paper

@article{feng2026semiautonomous,
  title  = {Semi-Autonomous Mathematics Discovery with Gemini: A Case Study on the Erdős 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},
  year   = {2026},
  eprint = {2601.22401},
  archivePrefix = {arXiv},
  url    = {http://arxiv.org/abs/2601.22401v3}
}

Add a badge to your README

Shows whether official code is linked for this paper.

Code of Paper badge
[![Code of Paper](https://codeofpaper.com/badge/2601.22401.svg)](https://codeofpaper.com/paper/2601.22401)

Discussion