Science· 2026Q1
Advancing mathematics research with AI-driven formal proof search
- 3citations
- Q1SCImago
- 2026year
Short summary
An AI agent autonomously resolved 9 open Erdős problems and proved 44 conjectures from the On-Line Encyclopedia of Integer Sequences by combining large language model (LLM) proof generation with formal verification in Lean.
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Key points
- AI agent successfully resolved 9 of 353 open Erdős problems.
- AI agent proved 44 of 492 On-Line Encyclopedia of Integer Sequences (OEIS) conjectures.
- Method combines LLM-based proof generation with formal verification in Lean.
- Agent is being deployed in research areas like combinatorics, optimization, and quantum optics.
AI-generated from the title and abstract; the full text is not read.
Abstract
Large language models (LLMs) increasingly excel at mathematics tasks, but their unreliability limits their utility in mathematics research. A mitigation is to use LLMs to generate formal proofs in languages such as Lean, in which the compiler verifies every proof step. We present the first demonstration of this method’s value in solving open problems at scale. We built an artificial intelligence agent for formal proof search that autonomously resolved nine of 353 open Erdős problems, proved 44/492 On-Line Encyclopedia of Integer Sequences conjectures, and is being deployed in combinatorics, optimization, graph theory, algebraic geometry, and quantum optics research. Even a basic agent alternating LLM-based generation with Lean-based verification replicated the Erdős successes. These findings demonstrate the power of formal proof search as an enabler of autonomous mathematical discovery.
The authors' abstract, as published at the source. Science, 2026 · DOI ↗
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Field: Computational Theory and Mathematics
Computational Theory and MathematicsComputer Science