# OpenAI and Anthropic Both Claim Their Models Refuted the Exponential Time Hypothesis

*2026-10-27 19:00 UTC · Science · 1 min read*

> OpenAI released AI-found solutions to three open math problems, one claiming to refute a key computer-science assumption; Anthropic published its own refutation hours later.

OpenAI released solutions to three long-standing math problems, one of which it says refutes the Exponential Time Hypothesis (ETH), a widely used assumption in computer science. The labs say their models found algorithms that solve certain hard logic puzzles in sub-exponential time. If confirmed, many papers that rely on ETH may need revisiting.

Anthropic mathematician Levent Alpöge suggested OpenAI's solutions drew on pre-existing work, and Anthropic published its own ETH refutation on GitHub hours later. Computer scientists led by MIT's Ryan Williams formed a working group and released an open letter on norms for AI contributions to research. Williams says the result questions intuitions about how tractable hard NP problems are, but that OpenAI's algorithm is probably not the best possible.

Why it matters: ETH supports the common belief that P does not equal NP. OpenAI told Williams it is reasonably confident the result does not break any cryptographic systems.

## Sources

- [techcrunch.com](https://techcrunch.com/2026/10/27/frontier-ai-labs-say-their-models-refuted-the-exponential-time-hypothesis-what-does-that-mean/)

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TechTools News · https://techtools.cz/tools/news/article/2589-openai-and-anthropic-both-claim-their-models-refuted-the-exponential-time
Česká verze: https://techtools.cz/tools/news/clanek/2663-openai-i-anthropic-tvrdi-ze-jejich-modely-vyvratily-hypotezu-exponencialniho