DeepMind's AlphaProof Nexus lands in Science, proving 9 Erdős problems and 44 sequence conjectures
新智元 · wechat · 2026-10-17
DeepMind's AlphaProof Nexus appears in Science, having proven 9 Erdős problems and 44 OEIS integer-sequence conjectures — including two subproblems open for 56 years.
Key points
- Erdős Problem 12 solved both ways: constructive grouping via the Chinese remainder theorem yields an infinite set avoiding divisibility relations, plus a counterexample refuting the proposed sub-1 exponent cap. Terence Tao then showed a restriction in the AI proof could be dropped.
- Architecture: multiple proof agents share drafts, a reviewer agent picks the best, Gemini decomposes goals and calls AlphaProof, solved subgoals are cached.
- Ablation: Gemini 3.1 Pro + Lean alone solved all 9 problems across attempts; AlphaProof alone solved none.
- Nexus also found new parameter settings for AnchoredGDA and proved an O(1/t) convergence guarantee.
Science's companion commentary: "AI for research mathematics has arrived."
More from Research
- Work in progress: geometric structure of GPG projections as Markov chain coarsening — michaelchchoi · 2026-10-18
- Backprop-free pretraining gets 2.3x speedup as Noise method crushes Dust record on 8 GPUs — inductionheads · 2026-10-18
- q3dviewer: open-source Qt+OpenGL tool for painter-like point cloud editing — 4310sy · 2026-10-18
- Smarter Every Day's Destin to defend PhD dissertation on impact fusion — CatAstro_Piyush · 2026-10-18
- Brain implants are restoring speech to people with ALS, Science reports — EricMTrautmann · 2026-10-18
- Formal Verification of LLM-Generated Code: Slides from FATTW 2026 Talk — CatAstro_Piyush · 2026-10-18