Nine of 353 open Erdos problems fell to a Google DeepMind system called AlphaProof Nexus, and two of those had stood unproven for 56 years. Science published the study.
Gemini 3.1 Pro is the engine underneath, writing and refining proofs in Lean, the formal language built for machine-checked mathematics. After every edit Lean checks the draft, and the errors it returns shape the following attempt. When a sub-problem proves stubborn, the model may invoke AlphaProof, a dedicated proof tool.
Other results stack up alongside the Erdos work. An open algebraic geometry question was resolved, a known bound was sharpened in min-max optimization, the technique behind training some AI models, and 44 conjectures from the OEIS integer sequence database were established. Even with AlphaProof removed from the loop, DeepMind reported, the nine Erdos results still came through.
How AI mathematics ought to be published is already a live dispute, and the paper lands squarely in it. Rather than send hundreds of AI-generated proofs through review, OpenAI recently posted them on GitHub, prompting a boycott call from the Association for Human Mathematics, which Terence Tao leads.
DeepMind took the long way around. Ahead of publication the team posted its solutions online, then submitted the work to a journal, which makes AlphaProof Nexus one of the earliest AI proof systems to clear standard review instead of sidestepping it.
