Computer science rarely gets a month like this. One of its foundational beliefs has been knocked down, and the people checking the wreckage include the very researchers who built it.
On 16 October, a research model at OpenAI produced a counterargument to the Exponential Time Hypothesis in ordinary prose. Within a day the argument had been transcribed into Lean, a proof checker that verifies every logical step mechanically. The 67-page manuscript lists OpenAI itself as the author.
Anthropic, working without any coordination, had reached the same destination hours earlier. Its 49-page paper, "A 2^o(n) Time Algorithm for 3-SAT", is credited to Claude, and the underlying algorithm was found by a Claude research model on that same day.
The hypothesis goes back to roughly 1999, when Russell Impagliazzo and Ramamohan Paturi argued that Boolean satisfiability admits no algorithm faster than exponential time. That single idea quietly props up hundreds of conditional hardness results in graph theory, databases, computational biology and geometry.
Both groups now describe a deterministic method that counts satisfying assignments in subexponential time, and both land on the same leading term in the exponent. Should reviewers confirm the work, one of the field's most trusted walls turns out to have a door in it.
What lends the claim weight is not the pedigree of the models but the scaffolding of checks around them. Every inference passes through Lean. And the review panel OpenAI assembled includes Impagliazzo and Paturi, who now find themselves auditing the collapse of their own conjecture. Stefan Szeider of TU Wien has examined the public material and expects it to survive close reading.
Caution remains in order. The result says nothing about P versus NP, and the new algorithm still runs in superpolynomial time, so no practical solver gets faster tomorrow morning. What shifted is the theoretical map, and the identity of the people, or systems, redrawing it.
For executives, the lesson sits far from complexity classes. Software that recently summarised documents is now generating original, machine-verified mathematics. The frontier of what AI can contribute to serious research is advancing faster than most planning cycles assume.
The organisations that learn to work alongside such systems, rather than merely delegating typing to them, will set the pace of the decade ahead.
Think mathematically. Engineer intelligently. Lead strategically. Build responsibly. Scale globally. Create real business value through artificial intelligence.
