OpenAI and Anthropic each published proofs that a long-standing conjecture in complexity theory — the Exponential Time Hypothesis — is false, and OpenAI handed the verification to outside researchers.
OpenAI said on 26 October that an internal model had proved the Exponential Time Hypothesis false, with a Lean proof, and Anthropic released its own refutation hours later. Both papers date the core result to 16 October. OpenAI also announced results from its internal models in three fields: maths, computer science and physics.
Why it matters
This is not a product launch — it is a milestone for AI as a research tool. The Exponential Time Hypothesis has stood for decades, and the fact that two different labs’ models independently refuted it suggests AI systems are becoming genuinely useful for open problems in mathematics, not just for writing code and text. There are caveats: Lean checks the theorem as written, and the working group led by the conjecture’s authors says its involvement is not a certification of the result. But the direction is clear — the day belonged to proofs written by AI, and to outside researchers checking them.
Sources: AI News Briefing, 28 October 2026; The Diary of AI, 27 October 2026.