Semi-Autonomous Mathematics Discovery with Gemini: A Case Study on the Erd\H{o}s Problems
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.