OpenAI and Anthropic each say their models refuted the Exponential Time Hypothesis
See how this story connectsOpenAI released AI-produced solutions to three long-standing problems in mathematics, computer science and physics. One is a refutation of the Exponential Time Hypothesis (ETH), published in 1999 by Russell Impagliazzo and Ramamohan Paturi, which holds that a class of logic puzzles needs exponentially more time to solve as variables grow. Hours later Anthropic released its own refutation of ETH, after its mathematician Levent Alpöge suggested OpenAI’s solution built on earlier work. Mathematicians received OpenAI’s work on GitHub. Computer scientists led by MIT’s Ryan Williams, with Impagliazzo and Paturi, formed a working group, published an open letter asking for feedback, and asked OpenAI to share the proofs publicly and fund a conference. Physicists formed a group that will decide how their result is released. Williams said OpenAI told him it had checked that the result breaks no cryptographic system.
Why it matters
If the refutation holds, the many papers of the past decade that assume ETH will need to be revisited.
- When
- 26 Oct 2026
- ID
WTA-N-2026-0466- Where
- United States
- Who
- OpenAI, Anthropic, MIT; Ryan Williams
- Topics
- Mathematics, Research, Frontier models
Summary written with AI by wheresthe.ai, from TechCrunch and the reporting credited above. We could not open the primary document, so it is marked Reported. Checked against the source on 28 Oct 2026.
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Cite this story
WTA-N-2026-0466: “OpenAI and Anthropic each say their models refuted the Exponential Time Hypothesis.” wheresthe.ai, 26 Oct 2026. https://wheresthe.ai/d/openai-anthropic-eth-refutation-claims-2026-10/ (source: TechCrunch).
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