DeepMind announced that its new AI, AlphaProof Nexus, has produced formal proofs for a range of previously open mathematical questions. The results appear in a peer‑reviewed paper in the journal Science. The system uses Gemini 3.1 Pro to write proofs in the Lean formal language and checks each step automatically.
What AlphaProof Nexus achieved
The paper reports that AlphaProof Nexus solved nine of the 353 Erdős problems that are still listed as open, including two that had been unsolved for 56 years. It also proved 44 conjectures from the OEIS integer‑sequence database, settled an open question in algebraic geometry, and tightened a known bound in min‑max optimization – a method used in training some AI models.
How the system works
AlphaProof Nexus builds on Gemini 3.1 Pro, which drafts proofs in Lean and receives immediate feedback from the Lean verifier. When a draft fails, Lean returns an error message that guides the next attempt. For especially tough sub‑problems, the system can call a specialized tool called AlphaProof. The team shared the nine Erdős solutions online before the paper was published.
Why it matters
For mathematicians, the AI provides a new way to explore hard problems and verify proofs automatically, potentially speeding up research. For anyone using AI tools, the improvement in min‑max optimization could lead to more efficient training of future models. The peer‑reviewed publication shows that AI‑generated proofs are being taken seriously by the scientific community, though broader validation is still needed.
