According to OpenAI, their AI models have just accomplished what mathematicians and physicists have been seeking for decades. In one press release alone published on October 26th, OpenAI claimed that an AI proved a renowned computer science conjecture, solved a harmonic analysis conjecture in all dimensions, and created an existence proof for quantum chromodynamics. According to OpenAI, the proofs were formalized using Lean, a machine verification program. None of this has yet been confirmed by an outside expert. This is quite a number of firsts in one blog post alone. This is what OpenAI claims to have discovered and why the hype should be put on hold.
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The Exponential Time Hypothesis (ETH) states that the popularly known Boolean satisfiability problem can only be solved with brute force. ETH is right next to the problem P vs NP and has been used by hundreds of research papers to prove that problems related to graph theory, databases and computational biology do not have any efficient solutions. However, according to OpenAI, their research disapproved of the hypothesis on October 16.
Before getting all excited about fast solutions for everything, note that even OpenAI states that using this research to devise efficient algorithms would require more studies. The panel consists of Russell Impagliazzo and Ramamohan Paturi, who created the very hypothesis. Also, there is Ryan Williams from MIT. Think about that. Two of the people, whose opinions you are trying to get, were the ones who devised the theory that is disproved.
In 1991, Sogge conjectured that waves can not be concentrated for long. At first glance, the local smoothing conjecture looks highly specialized, but in fact, it entails the Kakeya conjecture and Stein’s restriction conjecture – two giants in the field of analysis. In 2019, Guth, Wang and Zhang solved the problem in two dimensions. Wang and Zahl solved Kakeya in three dimensions last year.
OpenAI claims that their models solve the conjecture in all dimensions by leveraging an innovative auxiliary partial differential equation. The company received the solution on October 18, formalized it in Lean on the next day, and uploaded the writeup and proof to GitHub.
And this is the headline grabber. According to OpenAI, the model has provided an existence proof for quantum chromodynamics and a completion of the standard model for quarks and gluons. Existence of pure Yang-Mills, which is part of a Millennium Prize problem, comes as a bonus.
Notice the language used here. “Part of a problem” is not “the solution.” The research relies on an approach pioneered by Balaban. A team of physicists, including Nobel laureate David Gross, has taken it upon themselves to guide the work. This team chose to conceal the artificial intelligence output and write their own paper about it. At the moment there is nothing to verify.
OpenAI labels these papers as raw research data, a nice term meaning that there’s plenty of human labor left to make sense of them. Participants don’t sign NDAs and do unpaid labor in their own name, while OpenAI insists it’s not interested in any academic recognition. It also donated $5 million to Simons Foundation project and is sponsoring an ETH result conference.
But the company realizes the trap: choosing the first shepherds decides who gets to interpret the results. In a community that revolves around peer review and trust, the credentials of the AI are at least as important as the claims of the AI.
Leaning helps: it verifies whether a proof follows from its premises. But it can’t prove whether the premises correspond to the problem. This is where the human experts come in.
The ETH researchers have released all raw data publicly and are inviting the community to assist them with organizing an open evaluation process. And this is where the first credible verdicts will come from, not from the corporate blog.
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