Bolzano: Case Studies in LLM-Assisted Mathematical Research
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arXiv
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| Main Authors: | , , , , , , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866911620984209408 |
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| author | Balko, Martin Grebík, Jan Hubáček, Pavel Koutecký, Martin Kripner, Matěj Rozhoň, Václav Šámal, Robert Zámečník, Adrián |
| author_facet | Balko, Martin Grebík, Jan Hubáček, Pavel Koutecký, Martin Kripner, Matěj Rozhoň, Václav Šámal, Robert Zámečník, Adrián |
| contents | We report new results on eight problems in mathematics and theoretical computer science, produced with the assistance of Bolzano, an open-source multi-agent LLM system. Bolzano orchestrates rounds of interaction between parallel prover agents and a verifier agent while maintaining a persistent knowledge base that is carried across rounds. Classified using the significance-autonomy taxonomy of Feng et al., six of the eight results reach the level of publishable research, and five of the eight were produced essentially autonomously by Bolzano. Our results provide evidence that LLMs can contribute meaningfully to mathematical research, complementing recent reports by Bubeck et al., Woodruff et al., and others. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_16989 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Bolzano: Case Studies in LLM-Assisted Mathematical Research Balko, Martin Grebík, Jan Hubáček, Pavel Koutecký, Martin Kripner, Matěj Rozhoň, Václav Šámal, Robert Zámečník, Adrián Computation and Language Artificial Intelligence Machine Learning Logic in Computer Science We report new results on eight problems in mathematics and theoretical computer science, produced with the assistance of Bolzano, an open-source multi-agent LLM system. Bolzano orchestrates rounds of interaction between parallel prover agents and a verifier agent while maintaining a persistent knowledge base that is carried across rounds. Classified using the significance-autonomy taxonomy of Feng et al., six of the eight results reach the level of publishable research, and five of the eight were produced essentially autonomously by Bolzano. Our results provide evidence that LLMs can contribute meaningfully to mathematical research, complementing recent reports by Bubeck et al., Woodruff et al., and others. |
| title | Bolzano: Case Studies in LLM-Assisted Mathematical Research |
| topic | Computation and Language Artificial Intelligence Machine Learning Logic in Computer Science |
| url | https://arxiv.org/abs/2604.16989 |