Earlier this week OpenAI released solutions to three problems spanning math, computer science, and physics. One was an apparent refutation of the exponential time hypothesis (ETH), a long-standing claim about how hard certain computing problems must be. But within hours, rival AI company Anthropic quietly announced that one of its own models had found an almost identical proof on the very same day, 16 October, although by a different route, Science reports.
The ETH concerns a class of problems whose difficulty seems to grow exponentially. The hypothesis is that no shortcut could ever escape that exponential climb. Both companies now say their models found algorithms that are just slightly faster than exponential time, and both say their proofs have been formally checked in Lean, a programming language used to verify proofs. Still, no human has yet fully confirmed either proof.
A very different rollout
The two releases could hardly have differed more. OpenAI recruited three outside experts who spent 10 days turning an AI-generated draft into a clearer paper before anything was posted. Anthropic appointed no external reviewers at all. It simply posted its results online, and pointed people to them on X. A spokesperson said internal teams reworked the paper's introduction for clarity, and that it is important for the theoretical computer science community to lead the discussion of what the finding means, as also reported by Scientific American (open copy).
For now, the practical impact is limited. But Anthropic counted more than 800 papers whose results assume the ETH is true, and researchers say those will need to be rebuilt on safer assumptions.
This matters because two leading AI labs independently breaking a bedrock assumption of computer science on the same day suggests AI is becoming a genuine engine of theoretical discovery. At the same time, the contrasting rollouts sharpen an ongoing debate over how corporate science should be vetted, and who gets to decide, before results that reshape a field go public.