Two frontier AI systems, working independently, have produced something no human mathematician managed in three decades: a disproof of the Exponential Time Hypothesis.
OpenAI announced that its research model found a natural-language disproof of ETH on 16 October and formalised it in Lean, the machine proof checker, the following day. The 67-page manuscript credits "OpenAI" as the author.
Hours earlier, Anthropic had posted its own 49-page paper, "A 2^o(n) Time Algorithm for 3-SAT", credited to "Claude, Anthropic". An internal Claude research model found the core algorithm on the same day, 16 October.
ETH, proposed by Russell Impagliazzo and Ramamohan Paturi around 1999, says no algorithm can solve the Boolean satisfiability problem faster than exponential time. It is the foundation for hundreds of conditional hardness results across graph theory, databases, computational biology and computational geometry.
Both teams now claim a deterministic algorithm that counts satisfying assignments in subexponential time, with the same leading term in the exponent. If the claim holds, a load-bearing wall of complexity theory comes down.
The verification machinery is unusually strong. The proof is formalised in Lean, which checks every step mechanically. Stefan Szeider at TU Wien, who reviewed the released material, expects it to withstand scrutiny. Most striking: OpenAI commissioned an independent review group that includes Impagliazzo and Paturi themselves - the authors of the conjecture are auditing its refutation. Their open letter says it could change an important part of computer science.
The limits matter as much as the result. P versus NP is untouched. The new algorithm is still superpolynomial, so no faster SAT solver ships from this. What changed is the map of what is theoretically possible, and who - or what - redraws it.
For business leaders, the signal is not the mathematics. It is that AI has crossed from drafting text and code into producing original, machine-verified research. The assumption that machines cannot do novel science just took a body blow, and the capability frontier is now moving faster than most planning cycles.
The companies that treat AI as a research partner, not a typing assistant, will set the pace of the next decade.
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