Google DeepMind has unveiled an AI agent that independently solved 9 open Erdős problems. The agent, AlphaProof Nexus, pairs large language models with the Lean proof language to automatically verify mathematical reasoning. According to the paper, it also resolved 44 of 492 open OEIS conjectures and contributed to work in optimization, graph theory, algebraic geometry, and quantum optics.
AlphaProof Nexus makes AI more useful for real mathematical research by enforcing formal verification for every proof. Large language models can sound convincing while being wrong. Lean eliminates that risk by checking every logical step before a proof is accepted.
The researchers highlight the mix of language model, compiler feedback, and formal proof search as key. The agent doesn’t just generate text—it proposes hypotheses, receives errors, and adapts its strategy.
Google DeepMind evaluated AlphaProof Nexus on 353 formally encoded Erdős problems. The most capable agent solved 9 of them, at a computational cost of a few hundred dollars per problem. A simpler variant without all the bells and whistles later proved the same 9, but was pricier on the hardest cases.
The system also proved 44 open conjectures from the Online Encyclopedia of Integer Sequences. The team reports that the agent cracked a 15-year-old open question on Hilbert functions and found a stronger convergence guarantee for an optimization algorithm.
AlphaProof Nexus ingests a math problem as a Lean file with a missing proof. Within scoped sections, the agent can introduce new lemmas, definitions, and proof steps. Lean then automatically checks whether the proof holds.
The full agent runs multiple roles. A prover sub-agent searches for proofs, a validator checks results, and a rater sub-agent scores which partial attempts look promising. Those attempts are stored in a population database with Elo-style rankings.
The results signal a shift from AI assisting with text to aiding formal discovery. That matters for research: mathematicians can spend less time verifying complete arguments and focus more on the hardest intermediate steps.
The team remains cautious. Most Erdős problems are still open, and the system works best in areas where Lean already has strong libraries. Even so, the paper shows AI agents can do more than restate known proofs—they can chart new, formally checkable paths.
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