Problem
Research questions and friction points this paper is trying to address.
Automated theorem proving
Proof search
Open-problem solving
Large language models
Mathematical research
From Expert-Guided Proof Search to Automated Open-Problem Solving
🤖 AI Summary
This study addresses the bottleneck of expert-dependent proof search and verification in mathematical research by proposing Bolzano, an open-source multi-agent system. By integrating large language models, parallel proof search algorithms, and automated verification mechanisms, Bolzano employs multi-agent collaboration to maintain human-readable research states, enabling the autonomous resolution of open problems without manual intervention. Experimental results demonstrate that Bolzano successfully solves approximately 200 out of 3,800 open mathematical problems. Notably, it independently answers four key questions from a paper accepted at STOC 2026, with solutions confirmed by the original authors. These findings signify a substantial advancement in automated mathematical reasoning, transitioning it from an auxiliary tool toward an autonomous research paradigm.
📝 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.
Innovation
Methods, ideas, or system contributions that make the work stand out.
Multi-agent system
Automated proof search
Open-problem solving
Large language models
Parallel prover agents
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