Bolzano: Case Studies in LLM-Assisted Mathematical Research

arXiv cs.CL / 4/21/2026

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Key Points

  • The paper reports new research results on six mathematics and theoretical computer science problems generated with assistance from Bolzano, an open-source multi-agent LLM system.
  • Bolzano works by coordinating rounds of interaction between parallel theorem-prover agents and a verifier agent, while carrying a persistent knowledge base across rounds.
  • Using the significance-autonomy taxonomy, the authors classify four of the six results as publishable research and find that three were produced essentially autonomously by the system.
  • The findings are presented as evidence that LLMs can make meaningful contributions to mathematical research, in line with other recent reports.

Abstract

We report new results on six 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., four of the six results reach the level of publishable research, and three of the six 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.