DeepMind's AlphaProof Nexus solves nine Erdős problems, including two open 50+ years

DeepMind's AlphaProof Nexus has autonomously solved nine open problems from Paul Erdős's catalog of 353 formalized mathematical challenges. Two of those problems had remained unsolved for more than five decades. The agent also proved 44 previously open conjectures from the Online Encyclopedia of Integer Sequences (OEIS). DeepMind published the results on May 25, 2026, in a preprint on arXiv, alongside full proofs on GitHub.

The system ran all 353 formalized Erdős problems through its pipeline, halting attempts that exceeded 3,000 iterations. Of the nine successful solves, each cost only a few hundred dollars in compute—though the total spend across the full sweep was considerably higher. The agent generates candidate proofs, submits them to the Lean proof assistant for formal verification, parses errors, and iterates. An evolutionary search layer manages branching proof trees, retaining promising intermediate steps and pruning dead ends.

How the agent works

AlphaProof Nexus builds on the core loop of generate-verify-refine but adds evolutionary search over proof branches. The agent maintains a pool of partial proofs, scores them by progress toward a valid Lean certificate, and spawns variations from the most promising candidates. This structure lets it explore large proof spaces without exhaustive enumeration. The arXiv paper details the scoring heuristics, branching strategy, and Lean integration.

DeepMind appears to be the first major lab to publish an agent evaluation at this scale on genuinely open mathematical problems. The choice to treat unsolved conjectures as a benchmark—rather than closed competition sets—suggests a shift in how labs will measure reasoning capability. With nine Erdős problems and 44 OEIS conjectures now closed, the bar for "solved by AI" is rising fast.