AI System Gemini Tackles Open Erdős Problems in New Study

Global: Semi-Autonomous Mathematics Discovery Using Gemini

A team of researchers from several institutions announced on Jan. 29, 2026 that their AI system, Gemini, was used to evaluate 700 conjectures listed as “Open” in Bloom’s Erdős Problems database. The study reports that the hybrid approach yielded progress on 13 problems, delivering five apparently novel solutions and uncovering existing proofs for eight others.

Methodology Overview

The authors employed a two‑stage workflow: first, Gemini performed natural‑language verification to filter the large set of conjectures, narrowing the search space to a manageable subset. Second, human experts reviewed the AI‑generated candidates to assess correctness, originality, and relevance to the original problem statements.

Key Findings

Out of the 13 addressed problems, five were solved through what the authors describe as “seemingly novel autonomous solutions,” while the remaining eight were matched to previously published results that had not been widely recognized in the Erdős database. The researchers argue that the “Open” designation for many of these problems stemmed more from obscurity in the literature than from inherent difficulty.

Interpretation of Results

The paper suggests that AI‑assisted exploration can surface overlooked solutions, potentially accelerating the resolution of long‑standing mathematical questions. However, the authors caution that the apparent novelty of AI‑generated proofs must be rigorously validated against existing work.

Challenges and Risks

Two principal challenges emerged: the difficulty of exhaustive literature identification and the risk of “subconscious plagiarism,” where the model may reproduce existing arguments without explicit citation. The study highlights the need for robust verification mechanisms to mitigate these concerns.

Broader Implications

These findings contribute to ongoing discussions about the role of artificial intelligence in mathematical research, underscoring both its promise for accelerating discovery and the ethical considerations it raises.

Future Directions

The authors propose expanding the methodology to larger conjecture sets, improving the AI’s ability to cite sources accurately, and developing guidelines to address ethical issues associated with AI‑generated mathematical content.

This report is based on information from arXiv, licensed under Academic Preprint / Open Access. Based on the abstract of the research paper. Full text available via ArXiv.