OpenAI has made a claim that, if verified, would be one of the most important moments in the history of AI: according to the company, its internal models reached new results on three famous open problems, in mathematics, computer science and physics. The announcement was published on Monday, and on Tuesday it is already one of the most discussed topics in tech. For now, though, these are only claims, and none of them has been peer-reviewed.
The three claims
In mathematics, OpenAI says its models proved Sogge's local smoothing conjecture in all dimensions. The conjecture was proposed in 1991, and according to the company, its proof also resolves the Kakeya conjecture and Stein's restriction conjecture, two well-known problems in the field.
In computer science, the company claims to have disproved the Exponential Time Hypothesis (ETH). Many results in complexity theory rest on this conjecture. Put simply, it says some computational problems cannot be solved much faster than by checking nearly every possibility. If the conjecture is indeed false, some of the results built on it will need to be re-examined.
In physics, OpenAI says its models produced an existence proof for certain quantum field theories in four dimensions, including pure Yang-Mills theory. This touches on one of the Clay Institute's Millennium Prize problems, but the company does not claim to have fully solved it: the problem also requires proving the so-called mass gap, which OpenAI does not claim.
Who is checking
According to reports, the first two claims come with proofs published in Lean, a software tool that lets mathematical proofs be checked mechanically. The ETH disproof is being reviewed by, among others, Russell Impagliazzo and Ramamohan Paturi, the researchers who originally proposed the conjecture. The physics materials have not been fully published and are being reviewed by an outside group of experts.
Why caution is warranted
This is not the first time OpenAI has made big scientific claims. Earlier this month it released hundreds of papers written with the help of its models, and mathematicians raised concerns about their quality and accuracy. Reports on the current announcement also contain inconsistent dates, and no detailed responses from independent experts have been published yet. A Lean proof guarantees that the argument is logically valid, but it still has to be checked that the theorem proved is really the original problem.
What it means
If the claims are verified, it would be a clear sign that AI models can produce new scientific knowledge, not just summarize existing knowledge. For OpenAI, which competes with Anthropic and Google for the title of leading lab, it is also a business statement. In the meantime the advice is simple: wait for the scientific community to check the work, which could take weeks or even months.
