The Decoder reported on 12 October that Google DeepMind's AI system AlphaProof Nexus solved open maths problems, citing a new Science study. It cracked nine of 353 open Erdős problems, two of them unsolved for 56 years. DeepMind put those solutions online before the paper appeared. The Decoder adds 44 proven conjectures from the OEIS, a database of integer sequences, and an answer to an open question in algebraic geometry. It also lists a better known bound in min-max optimization, a technique behind the training of some AI models.
The Decoder says Gemini 3.1 Pro sits at the core, drafting proofs and revising them in Lean, a formal proof language. After each edit, Lean tests the draft and returns errors that shape the next try. For harder sub-problems, the system can call AlphaProof, a specialised proof tool. DeepMind says the nine Erdős problems fell even without it. The Decoder does not name the two 56-year-old problems, give the computing cost, or say who reviewed the paper.
Because Lean tests each draft, the proof steps are machine-checked, not only read by a person, and the paper also went through peer review. The Decoder contrasts this with OpenAI, which put hundreds of AI proofs on GitHub rather than in journals. Terence Tao's group, the Association for Human Mathematics, has called for a boycott. For buyers of AI tools, the question is what checks an output before anyone relies on it.