From Expert-Guided Proof Search to Automated Open-Problem Solving
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Computer Science > Artificial Intelligence
arXiv:2610.09769 (cs)
[Submitted on 7 Oct 2026]
Title:From Expert-Guided Proof Search to Automated Open-Problem Solving
Authors:Adrián Zámečník, Matěj Kripner, Martin Koutecký, Martin Balko, Jan Grebík, Pavel Hubáček, Robert Šámal, Václav Rozhoň
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Abstract:Large language models are increasingly contributing to mathematical research, where progress often depends on efficient proof search, incremental improvements and careful verification. We describe Bolzano, a multi-agent open-source system that uses parallel prover agents with a verifier agent and maintains a human-readable research state. Initial manual use on expert-selected problems yielded 8 results whose proofs were checked by domain experts. Motivated by these case studies, we ran Bolzano without problem-specific human guidance on about 3,800 open problems extracted from four sets of papers, solving about 200 open problems. One experiment used papers accepted to STOC 2026, a top conference in theoretical computer science. There, we answered four questions raised in the papers, as confirmed by their authors.
| Comments: | Accepted at the 6th Workshop on Mathematical Reasoning and AI (MATH-AI), NeurIPS 2026 |
| Subjects: | Artificial Intelligence (cs.AI); Computation and Language (cs.CL) |
| Cite as: | arXiv:2610.09769 [cs.AI] |
| (or arXiv:2610.09769v1 [cs.AI] for this version) | |
| https://doi.org/10.48550/arXiv.2610.09769
arXiv-issued DOI via DataCite (pending registration)
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View a PDF of the paper titled From Expert-Guided Proof Search to Automated Open-Problem Solving, by Adri\'an Z\'ame\v{c}n\'ik and 7 other authors
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