OpenAI and Anthropic Both Claim ETH Disproof, Same Day

On October 26, 2026, OpenAI announced that its AI models produced proofs for three landmark open problems: a refutation of the Exponential Time Hypothesis (ETH), a proof of the local smoothing and Kakeya conjectures in all dimensions, and an existence proof for quantum chromodynamics including pure Yang-Mills theory. Hours later, Anthropic published its own ETH refutation, with a paper formally credited to 'Claude (Anthropic)', stating that an internal Claude research model had independently found the core algorithm on October 16, the same day OpenAI says its model reached its proof, using 14 million output tokens and no human input. Both disproofs achieve roughly exp(O(n/√log n)). ETH, proposed by Impagliazzo and Paturi in 1999, underpins over 800 published complexity-theory papers. Alignment researcher Eric Neyman described the CS result as 'the biggest breakthrough in the whole field' since 1992. Verification of the ETH result is being led by Impagliazzo and Paturi alongside Ryan Williams of MIT; OpenAI committed to making all raw data public and funding a conference on the implications. Two of the three OpenAI results come with public Lean formal proofs; the physics result remains under expert review. OpenAI confirmed no current impact on cryptosystems. The simultaneous independent discovery generated a dispute: an Anthropic mathematician publicly accused OpenAI of scooping a researcher's work, stating 'instead of contacting him to work with him, as has been suggested publicly many times, the people at OpenAI chose to do this.'