Bolzano: Case Studies in LLM-Assisted Mathematical Research
Authors: Martin Balko, Jan Grebík, Pavel Hubáček, Martin Koutecký, Matěj Kripner, Václav Rozhoň, Robert Šámal, Adrián Zámečník
Organizations: Department of Applied Mathematics, Charles University · Computer Science Institute, Charles University · Institute of Mathematics, Czech Academy of Sciences · Institute of Formal and Applied Linguistics, Charles University
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.