DeepMind AlphaProof Nexus solves 9 Erdős problems
Key insights
- DeepMind's AlphaProof Nexus solved 9 open Erdős problems and 44 OEIS conjectures, with two problems unsolved for 56 years.
- Each proof cost a few hundred dollars at inference, dramatically undercutting the human effort previously required.
- All formal Lean proofs are public on GitHub, making the results machine-verifiable and independently checkable.
Why this matters
The cost threshold of a few hundred dollars per research-level proof means any well-funded lab or startup can now run autonomous math discovery as a background process. Formal verification via Lean ties AI output to machine-checkable proofs, which removes the trust gap that has blocked AI math claims from entering peer-reviewed mathematics. DeepMind's lead over OpenAI (9 Erdős problems vs. 1) in a single week signals that agentic proof systems are entering a competitive scaling phase where proof throughput becomes a measurable benchmark metric.
Summary
Google DeepMind's AlphaProof Nexus cracked 9 of 353 open Erdős problems and proved 44 OEIS conjectures, some unsolved for over 56 years, at just a few hundred dollars per proof.
The system pairs Gemini with Lean, a formal proof verifier, running as an autonomous agentic loop. All proofs are publicly posted on GitHub. A 15-year-old algebraic geometry question was resolved in the same run.
Essentially: (Google DeepMind, Lean) turns decades of unsolved math into a compute budget line item.
- Nine Erdős solutions vs. OpenAI's one last week, from a pool of 353 open problems.
- Cost per proof: a few hundred dollars at inference prices.
- DeepMind explicitly frames this as research-level math, not AGI.
Formal verification makes AI-generated proofs machine-checkable, which redefines what peer review means for mathematics.
Potential risks and opportunities
Risks
- Academic journals and prize committees lack established protocols for crediting AI-solved theorems, creating attribution disputes that could surface within 12-18 months as more proofs are published.
- Labs racing to match DeepMind's throughput may publish insufficiently verified AI proofs before Lean formalization is complete, contaminating mathematical literature in ways that are slow to correct.
- The low per-proof cost could enable state-level actors to fund adversarial cryptographic or number-theoretic research at scale, with minimal human oversight of which problems are being targeted.
Opportunities
- Lean ecosystem contributors and tooling projects (Leanprover community, Formal Abstracts) gain commercial leverage as the infrastructure layer for AI-verified mathematics scales up.
- Universities and research institutes running open problem catalogs (OEIS Foundation, Erdős Prize fund administrators) could partner with DeepMind or replicate the pipeline for discipline-specific unsolved problems.
- Inference providers serving long-context agentic math workloads (Together AI, Fireworks AI) are positioned to capture a new research compute category as labs attempt to replicate and extend AlphaProof Nexus results.
What we don't know yet
- Whether DeepMind plans to continue running AlphaProof Nexus against the remaining 344 open Erdős problems and on what timeline.
- The degree of human scaffolding required to formalize each problem in Lean before autonomous solving begins, which affects the true cost and scalability claim.
- Whether the 44 OEIS conjectures solved carry comparable mathematical significance to the Erdős problems, or represent lower-hanging computational targets.
Originally reported by the-decoder.com
Read the original article →Original headline: Google DeepMind AlphaProof Nexus Solves 9 Open Erdős Problems and 44 OEIS Conjectures at Cost of a Few Hundred Dollars Each