Automatically proving unsolved math problems with AI
- What
- We developed an AI agent that searches for mathematical proofs at scale by utilizing a language where a compiler verifies the proof steps.
- Key result
- This AI agent successfully and autonomously solved several unsolved math problems and conjectures.
- Why it matters
- It demonstrated the potential for AI to drive autonomous mathematical discoveries.
Background
While large language models excel at math tasks, their lack of reliability has limited their use in actual mathematical research. To address this, combining them with languages where programs can verify every proof step has been discussed.
Method
We built an agent that automatically finds mathematical proofs by alternating between AI and verification tools.
Main results
The agent autonomously solved 9 out of 353 unsolved Erdős problems and proved 44 out of 492 conjectures from the Online Encyclopedia of Integer Sequences. It is also being deployed and utilized in research on combinatorics, optimization, graph theory, algebraic geometry, and quantum optics.
Limitations & open points
The abstract does not provide detailed information on specific computational costs or the operating time of the agent.
Glossary
- 대규모 언어 모델 — AI technology that can write and understand text like a human
- 인공지능 에이전트 — An AI program that judges and acts on its own to achieve a goal
This summary was written by AI from the paper's abstract and reviewed by the editor. Summaries on this page were translated by AI from the editor-reviewed Korean version. Check the original for exact figures and context.
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