Semi-Autonomous Mathematics Discovery with Gemini: A Case Study on the Erd\H{o}s Problems
🤖 AI Summary
This work proposes a semi-autonomous discovery framework that integrates artificial intelligence with human expertise to investigate 700 mathematical conjectures labeled as “open” in Bloom’s Erdős Problem Database. Leveraging the Gemini large language model for natural language reasoning and automated literature comparison as an initial screening step, candidate solutions are subsequently evaluated by domain experts for correctness and novelty. The study reveals that many problems deemed “open” stem not from intrinsic difficulty but from challenges in literature retrieval—termed “information occlusion.” Among the 13 problems successfully resolved, five yielded novel AI-generated solutions, while eight were traced to previously published results. This research represents the first large-scale demonstration of human–AI collaborative verification in mathematical conjectures and highlights the risk of “unconscious plagiarism” inherent in AI-assisted scholarly discovery.
Application Category
📝 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.
Problem
Research questions and friction points this paper is trying to address.
Erdős problems
open conjectures
mathematics discovery
literature identification
subconscious plagiarism
Innovation
Methods, ideas, or system contributions that make the work stand out.
semi-autonomous discovery
AI-assisted mathematics
conjecture verification
literature identification
subconscious plagiarism
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