AI breaks a 30-year assumption of computer science
Computer science rarely gets a month like this. One of its foundational beliefs has been knocked down, and among those sifting through the rubble are the very researchers who built it.
On October 16, an OpenAI research model produced, in plain prose, a counterargument to the Exponential Time Hypothesis. The same day, the argument was written in Lean, a proof checker that mechanically verifies every logical step. The 67-page manuscript lists OpenAI itself as author.
Anthropic, working without any coordination, had reached the same target a few hours earlier. Its 49-page report, "A 2^o(n) Time Algorithm for 3-SAT," is credited to Claude; a Claude research model discovered the underlying algorithm the same day.
The hypothesis dates from around 1999, when Russell Impagliazzo and Ramamohan Paturi argued that no algorithm faster than exponential time exists for Boolean satisfiability. That single idea quietly supports hundreds of conditional hardness results in graph theory, databases, computational biology and geometry.
Both teams now describe a deterministic method for counting satisfying assignments in subexponential time, and both reach the same conclusion in the exponent's key term. If reviewers confirm the work, it will emerge that there is a door in one of the field's most trusted walls.
What strengthens the claim is not the models' pedigree but the verification structure around them: every conjecture passes through Lean. The review panel OpenAI assembled includes Impagliazzo and Paturi themselves, now auditing the fall of their own hypothesis, and Stefan Szeider of TU Wien has examined the shared artefacts and expects them to withstand close reading.
Caution remains essential. The result says nothing about P versus NP, the new algorithm still runs in superpolynomial time, and no practical solver will get faster tomorrow morning. What has changed is the theoretical map - and who, humans or systems, will redraw it.
Software that was summarising documents recently now produces original, machine-verified mathematics. Organisations that learn to work with such systems, rather than merely outsourcing typing, are the ones that will set the pace of the coming decade.
