Editorial illustration for Google DeepMind's AlphaProof Nexus Solved 44 Conjectures, an Open Geometry Question

Google DeepMind's AlphaProof Nexus Solved 44...

By AI Daily Post Edited by Brian Petersen, Editor-in-Chief

October 12, 2026 • 3 min read

Nine of 353 open Erdős problems, two of them unsolved since 1969. That's the headline result from a new Science paper out of Google DeepMind, describing a system called AlphaProof Nexus that spent months working through unsolved math problems and, unlike most AI math claims this year, actually submitted its work for peer review before publishing.

The system pairs Gemini 3.1 Pro with the formal proof language Lean, which checks every line of a draft proof and kicks back error messages the model can use to revise its next attempt. For the toughest sub-problems, Nexus calls in AlphaProof, a specialized proof engine, though DeepMind says the Erdős results held up even without that extra help.

The timing matters. OpenAI recently posted hundreds of AI-generated proofs to GitHub without journal review, prompting Terence Tao and the Association for Human Mathematics to call for a boycott of that approach. DeepMind's decision to run Nexus through formal peer review puts it on the other side of that fight, and the Erdős problems are just one piece of a longer list of results the team is reporting.

Google Deepmind's AI solved dozens of open math problems on its own, per a new study in Science. AlphaProof Nexus cracked nine of 353 open Erdős problems, two unsolved for 56 years.

Google Deepmind's AlphaProof Nexus solved dozens of open math problems and actually got peer reviewed - THE DECODER

Why this matters

Nine Erdős problems and 44 OEIS conjectures aren't vanity metrics. They're peer-reviewed in Science, with solutions posted online before publication so other mathematicians could check the work. That's a different bar than a benchmark score or a cherry-picked demo. Two of those Erdős problems sat unsolved for 56 years, which tells you AlphaProof Nexus isn't just pattern-matching known proof templates, it's finding paths humans missed.

For researchers, the algebraic geometry result and the min-max optimization bound matter more than the raw conjecture count. Min-max optimization underpins training for some AI models, so an improved bound is a tool other teams can actually use, not just a trophy. Gemini 3.1 Pro drafting and revising proofs suggests the workflow is replicable, not a one-off stunt tuned for this paper.

Watch whether DeepMind opens up the proof-search method itself, or keeps it locked inside Gemini. The gap between "solved it once, got published" and "mathematicians can use this as a daily collaborator" is where the real story sits next.