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

arXiv: https://arxiv.org/abs/2610.09769 · HTML: https://mlsanity.com/paper/2610.09769/

## Key facts

- No citing papers in the map yet (data through 7 Oct 2026).
- Builds on 8 of its 14 references that are in the map.
- First posted on arXiv 7 Oct 2026.

## Builds on (most cited first, 8 of 8)

- [AlphaEvolve: A coding agent for scientific and algorithmic discovery](https://mlsanity.com/paper/2506.13131/) (2025)
- [Early science acceleration experiments with GPT-5](https://mlsanity.com/paper/2511.16072/) (2025)
- [Towards Autonomous Mathematics Research](https://mlsanity.com/paper/2602.10177/) (2026)
- [Semi-Autonomous Mathematics Discovery with Gemini: A Case Study on the ErdHos Problems](https://mlsanity.com/paper/2601.22401/) (2026)
- [Accelerating Scientific Research with Gemini: Case Studies and Common Techniques](https://mlsanity.com/paper/2602.03837/) (2026)
- [Bolzano: Case Studies in LLM-Assisted Mathematical Research](https://mlsanity.com/paper/2604.16989/) (2026)
- [Hesse's Redemption: Efficient Convex Polynomial Programming](https://mlsanity.com/paper/2511.03440/) (2025)
- [A Unified Approach to Memory-Sample Tradeoffs for Detecting Planted Structures](https://mlsanity.com/paper/2603.00770/) (2026)

## Abstract (arXiv)

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.