AI Solves Open Math Problems via Formal Proof Search
A new AI system has autonomously resolved 9 of 353 open Erdős problems and proved 44 of 492 OEIS conjectures, demonstrating the power of large language models combined with formal verification in Lean. The research, conducted by an unnamed team, deployed agents in combinatorics, optimization, graph theory, algebraic geometry, and quantum optics. The most capable agent solved each Erdős problem at a cost of a few hundred dollars. A simpler agent alternating LLM generation with Lean verification replicated the successes but proved costlier on the hardest problems. This is the first large-scale evaluation of using LLMs to generate formal proofs for open mathematics problems. The findings highlight the potential of AI-aided formal proof search to advance mathematical research, despite LLMs' general unreliability in reasoning.
Key facts
- AI agent autonomously resolved 9 of 353 open Erdős problems.
- Agent proved 44 of 492 OEIS conjectures.
- Cost per Erdős problem: a few hundred dollars.
- First large-scale evaluation of LLMs for formal proof search on open problems.
- Agent deployed in combinatorics, optimization, graph theory, algebraic geometry, and quantum optics.
- Basic agent alternating LLM generation and Lean verification replicated successes but was costlier.
- Research uses Lean as formal proof language.
- Study published on arXiv (2605.22763).
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Institutions
- arXiv
- arXivLabs
- Semantic Scholar