DeepMind and OpenAI Both Solve Erdős Problems in the Same Week
In the same week, two independent AI systems cracked problems from Paul Erdős's famous open-problems list — some unsolved for over half a century. Google DeepMind's AlphaProof Nexus and an OpenAI general-purpose LLM each produced formal, verifiable proofs without being purpose-built for the specific problems. Four separate intelligence reports flagged this convergence, making it the most corroborated story in this analysis cycle.
What the Source Actually Says
Google DeepMind VP of Research Pushmeet Kohli announced AlphaProof Nexus on 2026-05-25 alongside arxiv paper 2605.22763v1. The system is an agentic framework for formal proof search powered by Gemini that, when run against open formal math problems, solved nine open Erdős problems — including two open for 56 years — plus 44 OEIS problems, a 15-year-old open problem in algebraic geometry, and a 7-year-old open question in min-max optimization. AlphaSignal reported the per-solve cost at a few hundred dollars each. Kohli frames the result explicitly: "These results show the massive potential of even simple agentic loops powered by Gemini."
Within days, OpenAI researcher Noam Brown announced that an OpenAI LLM had solved the Erdős planar unit distance problem — open since 1946. Brown was precise about the mechanism: "This is a general-purpose LLM. It wasn't targeted at this problem or even at mathematics. Also, it's not a scaffold. We have not pushed this model to the limit on open problems." The significance comes from the generality — no specialisation, no custom scaffold, no targeted training for the domain. Ethan Mollick added useful scale context: each solve cost roughly 0.6–6.3 kWh, the electricity equivalent of 20 miles of EV driving.
Strategic Take
Two uncoordinated labs, the same week, the same class of unsolved problems, both using general-purpose models: that convergence is the signal. Formal proof search is no longer a specialist AI domain requiring elaborate scaffolds. Teams building on AI for science, legal reasoning, or formal verification should treat this week as a capability inflection point.