Science · 2026-10-27 · Afternoon briefing

OpenAI, Anthropic claim breakthroughs in dueling proofs

OpenAI has released three major proofs that it claims solve long-standing problems in mathematics, physics, and computer science. The announcement was immediately followed by rival firm Anthropic, which published its own independent result just hours later. Both companies now claim to have disproved the Exponential Time Hypothesis, a foundational tenet of computer science first suggested in 1999.

The releases are controversial. OpenAI has kept the large language model that generated the proofs proprietary, withholding the prompts and computational methods used. The move also contradicts recommendations from the Advisory Group on Mathematics and Artificial Intelligence, an expert panel OpenAI itself organized. One of the proofs relates to the Yang-Mills problem, one of seven unsolved 'Millennium Problems' established by the Clay Mathematics Institute in 2000.

Summary written by Cup of News with AI from the sources below. Check the originals for the full story.

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• Dueling proofs from OpenAI and Anthropic astound scientists
• OpenAI Claims Navier–Stokes Breakthrough, Sparking Research Dispute
• OpenAI touts math breakthrough. Mathematicians dispute credit
• Some OpenAI math discoveries are ‘jewels,’ if verified. But mathematicians are wary of ‘slop.’
• OpenAI Is Pissing Off a Bunch of Mathematicians—Again

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