OpenAI announced on Monday that one of its internal AI models has allegedly refuted the Exponential Time Hypothesis, a conjecture that underpins hundreds of papers across computer science. The same day, the company revealed two additional breakthroughs: one in mathematics and another in physics.
The Exponential Time Hypothesis concerns the computational difficulty of Boolean satisfiability, a problem intimately connected to the P versus NP question. Researchers have relied on this conjecture to establish hardness results across graph theory, computational biology, databases and numerous other domains.
OpenAI's model arrived at the alleged disproof on 16 October, with the company verifying it using Lean, a proof-verification language, the following day. Both the model's explanation and the formal Lean proof are now available on GitHub.
Independent verification from the conjecture's originators
Russell Impagliazzo and Ramamohan Paturi of UC San Diego, alongside Ryan Williams of MIT, will lead the independent examination. Impagliazzo and Paturi were among the original proposers of the Exponential Time Hypothesis, along with Francis Zane.
In an open letter to the research community, the three scientists emphasized the limits of their involvement.
https://x.com/rrwilliams/status/2114833319431209352?ref_src=twsrc%5Etfw
Our involvement should not be taken as certification of the claim. A result of this significance requires careful, independent scrutiny.
Russell Impagliazzo, Ramamohan Paturi, and Ryan Williams
Williams disclosed on X that the verification group signed no confidentiality agreements and will receive no compensation. The researchers requested that OpenAI make all raw data on the Exponential Time Hypothesis result publicly available and fund a conference for the broader research community to discuss the findings. Both requests were accepted, according to Williams and OpenAI.
Mathematical and physical breakthroughs
On the mathematics side, OpenAI claims its models have proved the local smoothing conjecture—originally posed by Christopher Sogge in 1991—across all dimensions. This proof would simultaneously resolve both the Kakeya conjecture and Stein's restriction conjecture in every dimension. Prior to this, mathematicians had established local smoothing in two dimensions in 2019 and the Kakeya conjecture in three dimensions in 2025. OpenAI has made the model's explanation and Lean proof available, consistent with its release of 722 mathematics papers on 6 October.
In physics, OpenAI reports that its models have produced a rigorous proof demonstrating the existence of certain quantum field theories in four dimensions, including quantum chromodynamics, which governs the strong nuclear force between quarks and gluons. The work encompasses a proof of pure Yang-Mills theory's existence, which represents one of the Clay Mathematics Institute's Millennium Prize problems. OpenAI noted in September that it would not pursue the prize money associated with its Navier-Stokes proof.
The physics verification team is headed by Nobel laureate David Gross, with Michael Douglas, Arthur Jaffe, Igor Klebanov and Nikita Nekrasov as members. This group has decided to withhold the AI-generated material for the time being and will prepare its own write-up of the findings.
The question of attribution
OpenAI has stated it does not seek academic recognition for these discoveries. Instead, the company maintains that the researchers in each verification group should receive credit for the explanations they produce. Additionally, OpenAI has donated $5 million to the Simons Foundation to support workshops and conferences focused on AI-generated research results.
The three computer scientists have raised a broader question in their letter: how should attribution function when artificial intelligence identifies results before humans do? They caution that recognition may disproportionately favor those who publish first or possess the most advanced computational resources, while the labor of verification and explanation receives less acknowledgment. Similar concerns were articulated by mathematicians in the Leiden declaration released in June.
If the claim is correct, it will change an important part of theoretical computer science.
Russell Impagliazzo, Ramamohan Paturi, and Ryan Williams
Source: The Next Web
