A machine just solved math problems that stumped humans for decades. Google DeepMind’s AlphaProof Nexus, a system that fuses large language models with the Lean formal proof assistant, has autonomously cracked 9 out of 353 open Erdős problems and proved 44 out of 492 open conjectures from the Online Encyclopedia of Integer Sequences (OEIS).
The cost per problem: a few hundred dollars. The problems themselves had, in some cases, gone unsolved for longer than most people reading this have been alive.
What AlphaProof Nexus actually does
AlphaProof Nexus addresses AI hallucination by pairing an AI model’s generative capacity with formal proof-checking through the Lean proof assistant. The AI proposes a proof, and then a separate verification system checks every logical step. If the proof doesn’t hold up, it gets rejected.
The results were documented in an arXiv preprint (2605.22763v1) published on May 21, 2026. All formal proofs and selected natural language versions have been made available in a GitHub repository that was updated between May 20 and 22, 2026. Example problems tackled include variants #125, #138, #741, and #12 from the Erdős problem catalog, with proofs shared via discussions on erdosproblems.com.
The system uses what DeepMind calls “agentic loops” associated with proof-checking, iterating and refining proofs against the formal checker until they either pass or the system concludes it can’t solve the problem.
A basic agent variant of the system also solved 9 Erdős problems, but at a higher computational cost, suggesting that the full Nexus architecture is more efficient rather than more capable in raw terms.
Why Erdős problems matter
Paul Erdős was one of the most prolific mathematicians in history, responsible for posing hundreds of problems across combinatorics, number theory, and graph theory. Many of these problems come with cash bounties he personally attached to them.
Solving 9 out of 353 open Erdős problems is roughly 2.5%. Each one represents a frontier of mathematical knowledge where professional mathematicians have made little or no progress, sometimes for decades.
Proving 44 out of 492 open OEIS conjectures, roughly 9%, demonstrates that the system can operate across a range of mathematical domains rather than being narrowly specialized.
AlphaProof Nexus builds on DeepMind’s previous work with AlphaProof, which achieved silver-medal level performance at the 2024 International Mathematical Olympiad. The jump from Olympiad solver to research-level prover is significant: Olympiad problems are designed to be solvable within hours by talented humans, while open research problems have no such guarantee.
What this means for AI verification and crypto
AlphaProof Nexus has no direct connection to cryptocurrencies, digital assets, or tokens. DeepMind built this for mathematical research, with anticipated applications in combinatorics, algebraic geometry, and optimization.
The core technology, AI-driven formal verification, sits at the intersection of several problems the crypto industry cares about. Smart contract auditing, zero-knowledge proof generation, and cryptographic protocol verification all rely on the same fundamental capability: ensuring that logical statements are provably correct.
Formal verification is the process of mathematically proving that software behaves as intended. It has historically been expensive and slow, requiring specialized human expertise. A system that can autonomously generate and validate formal proofs for a few hundred dollars per problem changes the economics of that equation.
Zero-knowledge proofs, the cryptographic technique underpinning privacy-focused blockchains and layer-2 scaling solutions, require rigorous mathematical construction. Errors in ZK circuit design can compromise both privacy and security.