OpenAI and Anthropic both say their AI models have disproved one of computer science's best-known assumptions, the Exponential Time Hypothesis. OpenAI published its proof on 25 October in its math repository on GitHub, and Anthropic posted its own, with a machine-checked version, within hours, according to TechCrunch and Engadget.
If the proofs hold, AI has settled a question that human researchers have built on for more than 25 years. Experts are still checking them.
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Anthropic's version says the result "says nothing about solving formulas in practice."
What the Exponential Time Hypothesis says
Russell Impagliazzo and Ramamohan Paturi of the University of California, San Diego, proposed the hypothesis in 1999. It concerns a classic logic puzzle called 3-SAT: given a long list of true-or-false conditions, can you find settings that satisfy all of them?
The hypothesis says that no algorithm can do this much faster than trying a huge number of combinations. As the number of variables grows, the time needed grows exponentially. Hundreds of papers in databases, computational biology and geometry assume it is true, Engadget reports.
3-SAT is not just a classroom puzzle. Solvers for problems like it are used to check computer chip designs, verify software, and plan schedules for airlines, factories and exam timetables. That is why a faster algorithm, even one that only helps in theory, gets so much attention.
What the AI models found
Both labs claim an algorithm that solves 3-SAT in "sub-exponential" time, faster than the hypothesis allows. Anthropic's write-up, published in its formal-math repository, describes a deterministic algorithm that runs in 2 to the power of o(n) time, and says it can even count all the solutions.
The two releases differ in one important way:
| OpenAI | Anthropic | |
|---|---|---|
| What it released | A manuscript on GitHub, alongside a separate result on wave equations | A paper titled "A 2^o(n) Time Algorithm for 3-SAT", credited to Claude |
| Who found it | OpenAI's models | "An internal research Claude model" |
| Machine-checked proof | Not mentioned | Yes, a full formalisation in the Lean 4 proof assistant, written by AI models |
| Review | An expert group that includes the hypothesis's original authors | Anyone can rerun the Lean proof; Anthropic gives the commands |
A Lean proof matters because a computer checks every logical step. Anthropic notes one limit: the computer confirms the proofs, but a human still has to confirm that the formal statement says the same thing as the paper.
What experts say so far
MIT computer scientist Ryan Williams, who is organising the computer science response, told TechCrunch that parts of OpenAI's proof look routine, while "two or three alien-looking parts" stood out. He said the algorithm is probably not the best possible, and that researchers should now take seriously the idea that P could equal NP, the field's biggest open question.
Williams also raised cryptography. A faster algorithm for problems like 3-SAT could, in principle, weaken some encryption. He said OpenAI's science lead, Dan Roberts, told him the company checked and is reasonably confident no codes are broken.
What it means beyond the labs
For most people, nothing changes today. Your bank app, WhatsApp chats and card payments do not suddenly become unsafe, and the result has no practical speed-up yet.
The bigger shift is in how science gets done. OpenAI says it will not seek academic credit for its models' discoveries, and it is releasing results through independent expert groups. For African universities and researchers, these tools could put frontier-level problem solving within reach of small teams, provided the results can be checked as carefully as this one is being checked now.
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What happens next
The computer science working group led by Williams has asked OpenAI to share its proofs publicly and to fund a conference to review them. A third OpenAI result, in physics, is being handled by a separate group that has not published yet. If reviewers confirm the proofs, many papers that relied on the hypothesis will need revisiting.
A 27-year-old assumption may have fallen to AI. Now human experts have to confirm it.
Sources: TechCrunch; Engadget; OpenAI's math repository on GitHub; Anthropic's formal-math repository on GitHub.
