TL;DR: On October 26, 2026, OpenAI said its models produced three new results: a refutation of the Exponential Time Hypothesis in computer science, a proof of the local smoothing conjecture in every dimension in mathematics, and an existence proof for quantum chromodynamics in physics. The two math and computer science results come with Lean formal proofs on GitHub, but none of the three has been peer reviewed yet. Expert groups, including the people who first proposed the Exponential Time Hypothesis, are now checking the work.
OpenAI has spent much of 2026 arguing that its models can do original research, not just summarize it. Its latest announcement is the boldest version of that argument so far. In a post titled “Working with academic communities to build scientific understanding”, the company claims its systems settled questions that researchers have worked on for decades, and it describes a new way of handing those results to outside experts.
Below is what OpenAI says it found, who is checking it, and why the honest answer for now is “promising, but unverified”.
The three claims at a glance
| Field | OpenAI’s claim | Released? | Who is reviewing it |
|---|---|---|---|
| Computer science | The Exponential Time Hypothesis (ETH) is false | Yes, paper and Lean proof on GitHub | Russell Impagliazzo, Ramamohan Paturi (UC San Diego) and Ryan Williams (MIT) |
| Mathematics | Sogge’s local smoothing conjecture holds in every dimension, which would also settle the Kakeya and Stein restriction conjectures | Yes, AI-written write-up and Lean proof on GitHub | An outside harmonic analysis collaboration |
| Physics | A rigorous existence proof for certain four-dimensional quantum field theories, including quantum chromodynamics (QCD) | No, held back for now | A group led by Nobel laureate David Gross |
Claim 1: the Exponential Time Hypothesis is false
The ETH is a long-standing assumption about how hard Boolean satisfiability problems are. Roughly, it says that problems like 3-SAT cannot be solved in time that is “subexponential” in the number of variables. Many researchers have treated it as true. OpenAI notes it “has been used in hundreds of papers to derive conditional computational hardness results” in areas such as graph theory, computational biology and databases. If the ETH falls, many of those “this is probably hard” results lose their footing.
OpenAI says its system “recently proved that the ETH is false, a result that was subsequently verified in Lean.” According to a write-up by MACCUS, the 67-page paper was produced by an unnamed internal model, which found the result on October 16, with a Lean-checked version ready the next day.
OpenAI is careful to say this does not hand anyone a fast practical algorithm. In its words, “turning theoretical advances into practical improvements, will require significant further research.”
The reviewers are the hypothesis’s own authors
The most striking detail is who will check the work. Impagliazzo and Paturi, along with Francis Zane, originally proposed the ETH in 1999. They will lead the review with Ryan Williams of MIT, who has previously refuted stronger versions of the hypothesis. Having the original authors examine a claimed disproof of their own conjecture is about as tough a test as the result could get.
Claim 2: local smoothing in every dimension
The math result is about waves. Christopher Sogge proposed the local smoothing conjecture in 1991. OpenAI describes it as the idea that “the most extreme focusing” of waves “must be short-lived.” Larry Guth, Hong Wang and Ruixiang Zhang proved it in two spatial dimensions in 2019, and Wang and Joshua Zahl proved the related Kakeya conjecture in three dimensions in 2025.
OpenAI says its models produced a proof in every dimension, built on “a novel auxiliary partial differential equation,” and that this would also resolve the Kakeya and Stein restriction conjectures in all dimensions. The company says it got the AI output on October 18 and formalized it in Lean the next day.
Alex Iosevich, a mathematics professor at the University of Rochester, told Al Jazeera that OpenAI appeared to have “cracked” the conjecture in a “historic development.” Sogge was his PhD adviser, and he said: “the news was a shock at first.” He also admitted to “a twinge of sadness,” adding that many theoretical mathematicians feel the same way.
Claim 3: quantum chromodynamics, still under wraps
The physics result is the one nobody outside the review group can read yet. OpenAI describes it as “a mathematically rigorous existence proof of certain interacting quantum field theories containing gauge fields and fermions in four dimensions, including Quantum Chromodynamics (QCD).” The Verge reports that David Gross will lead a group including Michael Douglas, Arthur Jaffe, Igor Klebanov and Nikita Nekrasov, and that this group chose to hold the material back and write it up themselves.
This one touches a famous Millennium Prize problem, so it is easy to overstate. MACCUS points out that the Clay Institute’s Yang-Mills problem asks for existence and a mass gap, while OpenAI claims existence only. Until the write-up appears, treat this as the least checkable of the three.
OpenAI’s “shepherd” approach
Beyond the results, OpenAI is trying out a new release process. It picked three expert groups to act as “shepherds” who decide how each result reaches the wider community. The math and computer science groups chose to publish the AI output right away. The physics group chose to wait.
OpenAI admits the setup has downsides. It said choosing shepherds “necessarily shapes who gets involved first and creates asymmetry of information,” and asked for feedback on how to widen participation.
Why this needs a pinch of salt
There are good reasons to take the announcement seriously, and good reasons to wait:
- Formal proofs help a lot. Lean checks every logical step mechanically, which makes an outright error much less likely than in a normal preprint. What it can’t confirm is whether the statement that was proved is exactly the famous conjecture people care about.
- No peer review yet. All three results are company claims until outside experts finish their review.
- AI science claims have had mixed receptions. Al Jazeera notes that Anthropic’s claimed discovery of a CRISPR-like enzyme last month drew both excitement and accusations of exaggeration.
- Practical impact is unclear. Even if the ETH is false, OpenAI itself says faster real-world algorithms are not guaranteed.
What it means for the rest of us
For most people, nothing changes this week. Your laptop won’t suddenly solve hard scheduling problems faster. The bigger shift is in how research could get done. If the reviews hold up, AI systems will have gone from helping researchers read papers to producing results that experts need months to digest. That fits a pattern we have been following, from OpenAI’s new GPT-6.1 Terra model to the rise of reasoning models built to work through long chains of logic.
If you want to try AI on your own research today, our roundup of the best AI tools for science research covers what is available now. We will update this story when the review groups report back.
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