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arXiv · 2610.09769

From Expert-Guided Proof Search to Automated Open-Problem Solving

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.

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Adrián Zámečník, Matěj Kripner, Martin Koutecký, Martin Balko, Jan Grebík, Pavel Hubáček, Robert Šámal, Václav Rozhoň. 2026-10-07. From Expert-Guided Proof Search to Automated Open-Problem Solving. https://arxiv.org/abs/2610.09769

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