OpenAI and Anthropic both say an AI model broke the same decades-old computer science rule this month. Both set the discovery date at Oct. 16, 2026. Each lab moved on its own timeline.
Dan Roberts, an OpenAI scientist, posted his lab's claim on X at 21:36 UTC on Oct. 261. Levent Alpöge, an Anthropic researcher, posted his lab's version six hours later, at 04:00 UTC on Oct. 273. Both proofs still await a mathematician's line-by-line check.
Same Rule, Broken Twice
The rule is the Exponential Time Hypothesis. Russell Impagliazzo and Ramamohan Paturi proposed it in 19997. It covers 3-SAT. A computer hunts for one combination of true-or-false switches that satisfies a list of conditions.
Every algorithm for that puzzle, the hypothesis says, stays exponentially slow as its list of conditions grows. Hundreds of later papers built their own results on top of that assumption2.
OpenAI's model wrote its own disproof on Oct. 16. A Lean check cleared it the next day. Lean is software that checks a proof's logic, step by step2.
Claude, Anthropic's model, found a separate algorithm for the same job that same day. "The core algorithm was found on October 16 by an internal Claude research model with 14M output tokens and no human input," Alpöge wrote. "Anthropic researchers worked with Claude to improve the presentation, resulting in this paper"3.
Anthropic's paper lists Claude as its only author. It also solves a harder version of the puzzle, counting every satisfying combination instead of finding just one4.
Dario Amodei, Anthropic's co-founder and chief executive, met Prime Minister Rishi Sunak in London in May 2023, three years before this claim. Anthropic's own paper lists Claude alone as the result's author. Amodei and every other employee stay off the byline4.
Six Hours Between Two Posts
Roberts signed OpenAI's post under his own name. Anthropic let Claude take the only byline on its paper. That gap says something about how each lab wants its claim read.
OpenAI's post pulled 5,765 likes by Monday morning. Anthropic's pulled 1,793, less than a third as many3. Readers on X flagged the overlap before either lab explained it.
OpenAI's Post Draws More Than 3 Times Anthropic's Likes
Likes on each lab's X post announcing an Exponential Time Hypothesis disproof, as of Oct. 27, 2026
Each column is one lab's post. OpenAI's taller column drew more than three times the likes Anthropic's post did for the same hypothesis.
Sources: Dan Roberts on X [1]; Levent Alpöge on X [3]. Chart by Kelly Dennis.
The numbers behind this chart
| Item | Value |
|---|---|
| OpenAI's post | 5,765 |
| Anthropic's post | 1,793 |
Hacker News readers pushed the story past 700 points within a day6. A Digg writeup flagged what many caught first: both papers used the identical exponent bound, filed by labs that say they worked apart9.
OpenAI and Anthropic Both Date Their Proofs to Oct. 16
Discovery and announcement dates for each lab's Exponential Time Hypothesis disproof, October 2026
Both discovery marks sit on Oct. 16. The two announcement marks sit six hours apart on Oct. 26 and Oct. 27.
Sources: Dan Roberts on X [1]; The Next Web [2]; Levent Alpöge on X [3]. Chart by Kelly Dennis.
The numbers behind this chart
| Date | Event |
|---|---|
| Oct. 16, 2026 | OpenAI drafts its proof |
| Oct. 16, 2026 | Claude drafts its proof |
| Oct. 26, 2026 | OpenAI posts on X. 9:36 p.m. UTC |
| Oct. 27, 2026 | Anthropic posts on X. 4:00 a.m. UTC |
levent@__alpoge__“The core algorithm was found on October 16 by an internal Claude research model with 14M output tokens and no human input. Anthropic researchers worked with Claude to improve the presentation, resulting in this paper.”https://t.co/rZLajqbVH8
Who Is Checking Which Claim
OpenAI handed its computer-science claim to outside referees before it posted. Russell Impagliazzo and Ramamohan Paturi, the hypothesis's own authors, agreed to check it. Ryan Williams, a complexity theorist at MIT, joined them2.
"An internal model at OpenAI has produced a claimed refutation of ETH! Russell Impagliazzo, Mohan Paturi, and I have been asked to help organize an open and independent examination of this claim," Williams wrote on Bluesky2.
The three went further in a joint letter. "Our involvement should not be taken as certification of the claim. A result of this significance requires careful, independent scrutiny," they wrote2. They also asked OpenAI to release its raw data and fund a conference on the result, and OpenAI agreed to both requests.
Anthropic's version stops at two automated checks. One is Lean's own kernel. The other is a second tool, nanoda, built to catch what the first one might miss4. Its byline lists Anthropic's researchers and Claude, with an outside mathematician absent from it.
Andrew Sutherland, a mathematician at MIT, set this bar three weeks earlier, after OpenAI's October math release drew its first wave of complaints. "Until and unless they release the model and people can replicate their results, I think you should treat any claims about one-shotting problems with a single agent as unverified," Sutherland said. "We should ask for receipts"8.
Your Passwords Stay Safe From a Broken Rule
A disproof of the Exponential Time Hypothesis sounds like it should break something big. Both results stay purely asymptotic, Anthropic's own paper says. The advantage only shows up once a problem grows larger than any computer could hold4.
The hypothesis sits inside a bigger question computer scientists call P versus NP. Breaking it narrows that question by one assumption. The larger puzzle stays exactly as open as it stood on Oct. 157. Mathematicians still rank P versus NP as the field's biggest open question.
Beating brute-force search on paper differs from beating it on a laptop. Anthropic's algorithm needs problems far larger than any machine could run before its edge appears. The passwords, bank transfers and messages that lean on hard math stay exactly as safe as they did a day earlier.
What to Do
Treat both claims as leads. A settled result waits on a human's own check, done apart from Lean's output, line by line.
Watch Impagliazzo, Paturi and Williams' public channels for the first outside word on OpenAI's claim. Anthropic's version still waits on a comparable group to step forward.
By the Numbers
- 27 years: how long the Exponential Time Hypothesis stood before this month, counting from Impagliazzo and Paturi's 1999 paper7.
- Six hours: the gap separating Roberts' post on Oct. 26 from Alpöge's on Oct. 27, by posting time13.
- 14 million: the output tokens Claude used to find its algorithm, on its own, Alpöge says3.
- 5,765 likes to 1,793: how Roberts' and Alpöge's X posts compared by Monday morning13.
- 15,847 stars to 357: how OpenAI's and Anthropic's math repositories compared on GitHub the same morning54.
- 718 points: the Hacker News thread on OpenAI's three claims earned by Monday morning6.
What to Watch
Watch for the first outside mathematician to finish checking either proof line by line, apart from any machine's word. Impagliazzo, Paturi and Williams signaled their review of OpenAI's claim would run for weeks. A second marker: whether Anthropic names its own referees the way OpenAI did, or leaves Claude's paper standing on Lean's word alone.
Sources
- Dan Roberts (@danintheory), post announcing three new discoveries in mathematics, computer science, and physics, X, Oct. 26, 2026, https://x.com/danintheory/status/2114833682469122314
- Ana Maria Constantin, "OpenAI says its AI model has disproved the Exponential Time Hypothesis," The Next Web, Oct. 26, 2026, https://thenextweb.com/news/openai-exponential-time-hypothesis-false-kakeya-yang-mills
- Levent Alpöge (@alpoge), post on the provenance of Anthropic's 3-SAT paper, X, Oct. 27, 2026, https://x.com/__alpoge__/status/2114930095009968506
- Claude (Anthropic), "A 2^o(n) Time Algorithm for 3-SAT," anthropics/formal-math repository, GitHub, Oct. 27, 2026, https://github.com/anthropics/formal-math/tree/16a5ce41304fcdaea4e0be7c132e1c361dc26da5/eth
- OpenAI, openai/math repository, GitHub, accessed Oct. 27, 2026, https://github.com/openai/math
- "Three new discoveries in mathematics, computer science, and physics," Hacker News, accessed Oct. 27, 2026, https://news.ycombinator.com/item?id=50251344
- Wikipedia contributors, "Exponential time hypothesis," Wikipedia, accessed Oct. 27, 2026, https://en.wikipedia.org/wiki/Exponential_time_hypothesis
- Joseph Howlett, "OpenAI unleashes hundreds more math results upon a field already in shock," Scientific American, Oct. 6, 2026, https://www.scientificamerican.com/article/openai-unleashes-hundreds-more-math-results-upon-a-field-already-in-shock/
- Digg, "Claude-discovered 3-SAT algorithm reportedly refutes the Exponential Time Hypothesis," Digg, accessed Oct. 27, 2026, https://digg.com/ai/fihxyqj1