In short
- OpenAI and Anthropic claim their models found an algorithm that refutes the Exponential Time Hypothesis (ETH).
- Anthropic published its result with a formal Lean proof, but without independent peer review.
- The result is theoretical and does not speed up real-world computing.
In short: on 27 October 2026 OpenAI and Anthropic announced that their models found an algorithm that refutes the Exponential Time Hypothesis (ETH), an important assumption in computer science. According to TechCrunch, the scientific community is reacting with a mix of excitement and caution.
What the labs claim
- Anthropic published a paper in a repository describing an algorithm that solves 3-SAT in sub-exponential time, faster than ETH assumed.
- According to the repository, an internal Claude research model found the result and AI models wrote the Lean formalisation of the proof.
- The repository stresses the result is purely theoretical and says nothing about solving formulas in practice.
- According to TechCrunch, OpenAI announced a similar result earlier, and an Anthropic mathematician suggested it built on existing work.
What is still uncertain
- Anthropic cites no independent review. The repository admits the match between the Lean statements and the paper must be checked by hand, and the build shows two warnings about unproven gaps in a comparison file.
- MIT’s Ryan Williams is organising the field’s response. According to TechCrunch, he finds parts of the proof routine, but “two or three alien-looking parts” need the community to work on them together.
- OpenAI says it checked whether the result breaks cryptography and is reasonably confident it does not.
How to read this
These are claims from model makers who have an interest in showing breakthroughs. Until experts confirm the proof, I treat it as promising, not settled. I cover research in the research and papers hub.