An unusual public race between the two leading AI labs is unfolding in theoretical computer science. Hours after OpenAI announced that its models had produced a proof that the Exponential Time Hypothesis (ETH) is false, Anthropic released its own refutation of the same 1999 conjecture — and made clear it believes the credit is shared at best. Anthropic mathematician Levent Alpöge suggested that OpenAI's result built on existing work, framing the Anthropic proof as independent rather than derivative. The exchange turns a milestone in AI-assisted mathematics into a public priority dispute between rivals.
Independent panel will judge both claims
The verification burden now falls on a small group of complexity theorists: Russell Impagliazzo and Ramamohan Paturi of the University of California San Diego together with Ryan Williams of MIT will examine OpenAI's proof. Williams said parts of the argument look routine, but flagged two or three "alien-looking" components that will need close scrutiny before anyone declares a foundational result overturned. OpenAI has published both the natural-language proof and a machine-checked Lean formalization on GitHub, and agreed to the panel's request that all raw data be made public along with funding for a dedicated conference.
Why a refutation would matter
ETH, proposed in 1999, asserts that certain logic problems — centered on Boolean satisfiability — require exponential time, and it anchors hundreds of papers across graph algorithms, computational biology, databases and computational geometry. A verified refutation would not make those problems instantly tractable, but it would reopen the question of how much faster they can actually be made and force a re-examination of results that assume exponential lower bounds. The episode also marks a new phase in frontier-lab competition: scientific priority in mathematics and theoretical computer science is now being contested in public, within hours, by AI systems and the labs behind them — with independent academics, not marketing departments, holding the final word.
Key Facts
Anthropic released its own ETH refutation hours after OpenAI's announcement
Anthropic mathematician Levent Alpöge suggested OpenAI built its proof on existing work
An independent panel — Impagliazzo, Paturi and Ryan Williams of MIT — will scrutinize the OpenAI proof
Williams flagged two or three alien-looking parts of the argument that need close review
ETH was proposed in 1999 and underpins hundreds of papers in graph theory, computational biology, databases and geometry
OpenAI published its proof and a machine-checked Lean formalization on GitHub
Sources: OpenAI, Anthropic, TechCrunch, Kill The AI, MIT, threerouter
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