OpenAI says its models have produced three research results, and the boldest is a proof that the Exponential Time Hypothesis is false. If that survives scrutiny, a belief that hundreds of computer science papers lean on gets knocked out. Nobody outside OpenAI has confirmed it yet, and the company says so itself: in a post on its own site, it describes recruiting senior academics to examine the work.
The Exponential Time Hypothesis, or ETH, is a long-held bet about how slow a certain kind of puzzle must be. The puzzle asks whether a logical formula can be made true, and it sits next to the famous P vs NP question, the best-known open problem in computing. Researchers have widely believed the ETH, so they have used it as a starting assumption in work on graphs, computational biology, databases, and geometry. OpenAI says its system found a disproof on 16 October and that a Lean formalization followed the next day.
Lean is software that checks proofs step by step, which makes it a strong filter against a wrong argument. It does not settle every question, though. People still have to confirm that the formal statement says what the headline claims it says. That job now falls to three algorithm experts: Russell Impagliazzo and Ramamohan Paturi at UC San Diego, plus Ryan Williams at MIT. OpenAI says it agreed to publish all the raw data on GitHub and to fund a conference on what the result means for the field.
Even if the disproof stands, nothing gets faster tomorrow. OpenAI says the result reopens questions about how far such tasks can be sped up and may steer the search for better algorithms, but adds that practical gains will take significant further research.
The other two results are harder to judge from outside. In mathematics, OpenAI says its models proved the local smoothing conjecture, which Sogge proposed in 1991 and which concerns how sharply waves can focus. Guth, Wang, and Zhang proved it in two dimensions in 2019. OpenAI claims every dimension, and says that also settles the Kakeya and Stein restriction conjectures. The company obtained that output on 18 October and had it formalized in Lean a day later. On an outside expert’s advice, it released the writeup and proof publicly and left researchers to organize their own effort.
In physics, OpenAI claims a rigorous existence proof for Yang-Mills theory and for quantum chromodynamics, the theory of the strong force. Yang-Mills existence is part of one of the Clay Mathematics Institute’s Millennium Prize problems. Nobel laureate David Gross heads a five-person group examining it, including Arthur Jaffe, who helped formulate the Yang-Mills prize problem. That group has chosen to hold back the AI-produced material and write the result up themselves.
Those three handoffs are the quieter story. OpenAI tried a different release approach for each result and says it does not yet know which will work best. It also concedes that picking the first reviewers decides who gets to see the work first. Participants sign no nondisclosure agreements, are unpaid, and speak only for themselves, and OpenAI says it is not seeking academic credit for what its models produced. It has also pledged $5 million to the Simons Foundation for workshops and conferences on understanding AI-made results.
Treat all three as claims until the reviewers report. The ETH verdict is the one to watch, because the answer will arrive from named experts at UC San Diego and MIT rather than from a company announcement, and every field that borrowed the hypothesis will have to decide what it still stands on.
Published by OpenAI on its own website; the source gives no publication date.
