New to this? Read it in simple words
- OpenAI says its AI showed that a widely used idea about hard problems is false.
- The proof is public, but no outside expert has confirmed it yet.
- Three experts will lead an open check and say this does not mean the claim is right.
- OpenAI also claims proofs in maths and physics; the physics one is not released.
- Exponential Time Hypothesis
- An assumption that some logic puzzles always need a huge number of steps to solve, however clever the method.
- Lean
- A computer language that checks a mathematical proof step by step, so a machine can confirm each step follows.
- Conjecture
- A statement that experts believe is true but that nobody has proved yet.
In September, OpenAI said a model had solved over 100 open maths problems without naming them. This time it has published a proof that anyone can examine.
The claim
The Exponential Time Hypothesis, or ETH, says that some logic puzzles cannot be solved much faster than by trying a huge number of options. OpenAI says it has been used in hundreds of papers, in fields from graph theory to biology and databases.
OpenAI says its model found a disproof on October 16. The next day, OpenAI checked it in Lean, a computer language that tests proofs step by step. The write-up, dated October 25, and the Lean files are on GitHub.
The Lean statement describes a method that counts every solution of such puzzles in less than exponential time. Turning this into faster methods for real use “will require significant further research,” OpenAI wrote.
From OpenAI’s announcement of October 26, 2026, and early reports.
Who will check it
A group led by Russell Impagliazzo and Ramamohan Paturi of UC San Diego and Ryan Williams of MIT will examine the result, OpenAI says. Impagliazzo and Paturi, with Francis Zane, first proposed the hypothesis.
“Our involvement should not be taken as certification of the claim,” the three researchers wrote, as quoted by TNW. They added that a correct claim would change an important part of theoretical computer science.
OpenAI says members are unpaid, sign no nondisclosure agreements and speak only for themselves. It agreed to the group’s requests to publish all raw data and to fund a conference about the result.
Maths and physics
OpenAI also says its models proved the local smoothing conjecture, a 1991 idea about how waves focus, in every dimension. That would also settle the Kakeya conjecture in all dimensions, it says. It published the write-up and a Lean proof.
Alex Iosevich, a mathematician at the University of Rochester, told Al Jazeera that OpenAI appeared to have “cracked” the problem. He called it a “historic development”.
The physics claim is a strict mathematical proof that certain theories of particles, including quantum chromodynamics, exist. A group led by the Nobel laureate David Gross will write it up first, so nothing has been released yet.
Sources
Every fact in this story comes from the sources below. Open them to check our work.
- 1Primary source · October 26, 2026Working with academic communities to build scientific understanding OpenAI
- 2Primary source · October 26, 2026The Exponential Time Hypothesis is False: scope of the Lean formalization OpenAI (GitHub)
- 3Research · October 26, 2026OpenAI says its AI model has disproved the Exponential Time Hypothesis TNW
- 4Research · October 27, 2026AI makes discoveries in mathematics, computer science, physics, OpenAI says Al Jazeera
- 5Research · October 27, 2026OpenAI announces new discoveries in mathematics, computer science and physics Engadget
All three results are OpenAI’s claims. The Lean check was OpenAI’s own, no outside expert has confirmed the proofs, and the physics work has not been published.
OpenAI says its AI proved a famous computing idea wrong. Silicon AI News, October 27, 2026. https://siliconainews.com/stories/openai-eth-disproof-claim
OpenAI claims its AI disproved a famous computing hypothesis and proved maths results, but no outside expert has confirmed them yet. How we rate the mood
The mood shows how the news frames the event for the tech and AI world: as an opportunity (6 and above) or as a loss (below 5). It is not our verdict on who is right.