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AI Labs Claim ETH Refutation as Computer Scientists Organize Response

OpenAI and Anthropic claim their models refuted a longstanding computational-complexity assumption; MIT's Ryan Williams is organizing the field's response.

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Context photograph · Bermix Studio / Unsplash
THE KEY FINDING

The story in focus

OpenAI and Anthropic each released claims that their AI models refuted the Exponential Time Hypothesis, a durable computer science assumption. MIT professor Ryan Williams is organizing the computer science community's response, starting with an open letter seeking feedback and discussion of norms around AI contributions.

  • OpenAI released solutions to three math problems, including a claimed rejection of the Exponential Time Hypothesis.
  • Anthropic released its own refutation of ETH hours after its mathematician suggested OpenAI's work built on pre-existing results.
  • MIT professor Ryan Williams is organizing the computer science community's response, alongside ETH's original authors Russell Impagliazzo and Ramamohan Paturi.
  • Williams said OpenAI checked and was reasonably confident the work does not imply breaks to cryptographic systems.
  • Williams said many papers relying on ETH's durability will need revisiting if the claims hold up.

What the labs claim

TechCrunch reports that OpenAI released solutions to three blockbuster math problems, one being a surprise rejection of the Exponential Time Hypothesis (ETH), a durable assumption in computer science that plays a large role in how researchers understand what is difficult to compute.

Anthropic mathematician Levent Alpöge suggested OpenAI was basing its solutions on pre-existing work, and hours later Anthropic released its own refutation of ETH. The claims are that the models produced algorithms solving a specific class of tricky logic puzzles in sub-exponential time, faster than previously thought possible. If true, the labs may have refuted ETH.

The community response

MIT professor Ryan Williams is organizing the computer science field's response. Williams, who has criticized OpenAI's approach in the past, agreed to collaborate with the frontier labs. OpenAI asked him to help interpret the solution along with UC San Diego computer scientists Russell Impagliazzo and Ramamohan Paturi, who first published ETH in 1999.

Their first step was an open letter calling for feedback from interested scientists and discussion of norms around AI contributions. Williams said some parts of OpenAI's proof may be routine, but two or three alien-looking parts convinced him the whole community needs to work on it together. He said the work could affect many researchers' papers and that cryptocurrency questions were raised, but OpenAI checked and was reasonably confident the result does not imply breaks to cryptographic systems.

What did OpenAI and Anthropic claim about the Exponential Time Hypothesis?

Each lab released claims that its AI models produced algorithms solving a specific class of logic puzzles in sub-exponential time, which would refute the Exponential Time Hypothesis if the proofs hold up.

Sources & further reading

Source report: 27 Oct 2026. Event and publication dates may differ.

  1. Frontier AI labs say their models refuted the Exponential Time Hypothesis. What does that mean? ↗TechCrunch

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