数学研究问题基准测试

🔮 BuddenBench: A Benchmark of Open Nontrivial Mathematics Research Problems

This benchmark, affectionately named budden-bench, measures the ability of models and agents to autonomously solve open and important problems in mathematics research. In contrast to other problem sets such as the Erdős Problems, this benchmark is intended to exclusively contain problems which are of ongoing research interest to working mathematicians.

Inspiration

This project was inspired by the historical successes of mathematical software for resolving open conjectures, pre-LLM.

Tools

• GAP (Groups, Algorithms, Programming): A system for computational discrete algebra, especially computational group theory
• Lean 4: An interactive theorem prover for formalizing and verifying mathematical proofs

AI-Generated Solutions

Warning: No AI-generated proof should be trusted without human review, no matter how formal.

Legend: 🟢 Success | 🔴 Cannot formalize | 🟡 Unverified | 🟣 New result | ⚪ Unknown

Setup

make setup  # Install dependencies, build GAP, setup Lean

Usage

make watch-solve  # Launch Claude to solve a random problem
make test         # Run test suite

Problem Sets

Problems are drawn from multiple sources:

• Kourovka Notebook: A collection of unsolved problems in group theory
• Unsolved Problems in Intuitive Geometry by Klee & Wagon: Open problems in computational and combinatorial geometry
• 100 Open Problems by Ben Green: Research-level problems in additive combinatorics and number theory
• Some open problems in analysis by A.G. Ramm: Open problems in Radon transforms, operator theory, and PDEs
• Seventy Five (Thousand) Unsolved Problems in Analysis and PDEs by Vladimir Maz'ya: Comprehensive collection of open problems in analysis and partial differential equations

Citation

If you use this benchmark in your research, please cite:

@dataset{vonhippel2025budden,
  author={von Hippel, Max},
  title={{BuddenBench}: A Benchmark of Open Nontrivial Mathematics Research Problems},
  year={2025},
  publisher={GitHub},
  howpublished={\url{https://github.com/maxvonhippel/budden-bench}},
  note={AI benchmark for automated mathematics research in group theory and geometry}
}

For citations to the source problem collections, see references.bib.

Last updated: 2026-01-29 05:59:25 UTC