OpenAI says its internal models helped prove a result many researchers assumed was true but could not demonstrate: the Exponential Time Hypothesis, a long-standing pillar of computational complexity, has been disproven — and the work appears to have touched open problems far beyond it.
The claim, shared this week, is unusually precise for frontier-lab research. OpenAI says its models produced a disproof of the ETH, a conjecture tied to the running time of certain satisfiability algorithms, and that the result was checked in Lean, the formal proof checker used in verified mathematics. Separate model outputs also addressed work related to the Kakeya conjecture and physics problems. Outside experts are now reviewing the claims.
The Exponential Time Hypothesis sits at the heart of algorithmic pessimism: the idea that some problems have a lower bound on how fast they can be solved that grows exponentially with input size. Proving it false does not crack a commercial code, but it would rearrange what researchers believe about the limits of computation itself, with implications for cryptography, program verification and the design of AI systems that reason about code and logic.
The deeper story is procedural. The result was produced by internal models, not by a human mathematician working alone, and it will stand or fall on the external review of the Lean-checked proof. For an industry under pressure to show that frontier AI produces verifiable science rather than plausible-sounding text, a machine-assisted theorem carrying a machine-checked certificate is the strongest possible display of capability — and the cleanest test of it yet.
If the review survives, the second-order effect extends beyond mathematics. Researchers who currently treat AI-generated theorems as curiosities will have to build review protocols for them. The gap between generation and verification is now a research discipline in its own right, and the labs that close it first will define what counts as done.
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