SHELFCRITTER AI Digest

MODEL

AlphaProof Nexus

modeltopic-notedeepmindmathlean

Overview

AlphaProof Nexus is DeepMind‘s combined Gemini 3.1 Pro + Lean proof-drafter stack, with AlphaProof as a fallback sub-tool for harder cases. The underlying work traces to a May 2026 arXiv preprint (arXiv:2605.22763); The Decoder’s Oct 12 coverage frames it as “peer-reviewed Science” (doi.org/10.1126/science.aej2213), though independent search this cycle did not surface a clear journal-acceptance surface — treat the “peer-reviewed” framing as reported by The Decoder, not independently confirmed.

Timeline

  • 2026-10-13-AI-Digest — DeepMind‘s AlphaProof Nexus is reported by The Decoder (Oct 12) to have solved 9 of 353 open Erdős problems (two unsolved for 56 years), proved 44 OEIS conjectures, resolved an open algebraic-geometry question, and improved a min-max bound. Load-bearing softener: per Google‘s own note (via The Decoder), AlphaProof didn’t actually carry the 9 Erdős wins — Gemini 3.1 Pro drafted the successful proofs directly in Lean, with AlphaProof reserved for harder sub-tool calls. Reframe worth carrying: [[Gemini]] 3.1 Pro drafting Lean proofs on open problems, with AlphaProof as a fallback, not AlphaProof solving open math. Watch: the first independent Lean-side verification of the published proofs and the actual journal entry if one lands.

Key Developments

  1. 9/353 Open Erdős Problems Solved via Gemini 3.1 Pro + Lean, With AlphaProof as Fallback (October 13, 2026): The headline figure is 9 of 353 open Erdős problems solved, two unsolved for 56 years, plus 44 OEIS conjectures proved, an open algebraic-geometry question resolved, and a min-max bound improved. The structural detail worth carrying is that Gemini 3.1 Pro — not AlphaProof — drafted the successful Lean proofs directly, with AlphaProof reserved as a sub-tool for harder cases. The “peer-reviewed Science” framing is The Decoder’s; independent confirmation of a journal acceptance did not surface this cycle. The May 2026 arXiv preprint (arXiv:2605.22763) is the primary technical source.

See also: DeepMind, Gemini, MOC - Major Companies.