OpenAI Trumpet’s 3 More Math and Science Results, Along With a New Plan for Publishing Them

Most people think that 3-SAT cannot be solved in polynomial time. So when this question comes up, which can happen several times a day, there is a common idea people turn to: the Exponential Time Hypothesis (ETH). This idea has not been proven either, but it gives researchers a useful way to estimate how long problems that cannot be solved in polynomial time might take.

Or is that true? OpenAI claims it has just disproved the entire ETH. If so, everyone will have to rethink what they know!

I'm actually just repeating what I heard in a YouTube video about the ETH, probably not very well, and I don't really understand the topic myself. But for theoretical computer scientists who study optimization and algorithms, this is important. OpenAI is claiming this discovery and two other breakthroughs in its latest release of science results.

Along with its claim that its AI models have disproved the ETH, OpenAI says it has solved a problem called the Kakeya conjecture, which comes from the study of waves and harmonics. It says it found a new proof that works in all dimensions for something called the local smoothing conjecture.

But there is more than just the study of waves. In physics, OpenAI also believes it has proved results about certain interacting quantum field theories that contain gauge fields and fermions in four dimensions. These include Quantum Chromodynamics (QCD) and a unified completion of the Standard Model of particle physics. Yes, that means both gauge fields and fermions!

When OpenAI released 377 math results on GitHub at the beginning of this month, its blog post included some wording that sounded defensive. For example, it said it wanted to “empower scientists with state-of-the-art capabilities” and work to “responsibly release the model that produced these results.“ An advisory group that had worked with OpenAI had already publicly criticized a private company for using unreleased internal AI models to produce major new results. OpenAI had apparently done just that.

This time, OpenAI says it does not “seek academic credit for the discoveries produced by our internal models.” To support that goal, it has a plan to share AI-generated discoveries with the math and physics communities, so those communities can receive the credit. But if taken too far, this plan could resemble Immortan Joe in the movie Mad Max: Fury Road, who controls how much water his thirsty followers receive.

OpenAI is releasing texts created by its models. It says these texts are “best understood as a form of raw research data.” The job of the math and science communities, it says, is to “convert this raw research data into scientific understanding.”

OpenAI says the math results were “formalized” or “verified” using Lean, a tool that helps check mathematical proofs and reduces the need for people to check the same work again and again. But reliance on Lean has already caused problems for OpenAI. People examining OpenAI's supposedly Lean-verified solution to the Navier-Stokes Millennium Problem raised concerns that Lean had verified a weaker claim than the one originally described in OpenAI's published work.

As it works through these early problems, OpenAI says it has already contacted outside experts, often the same researchers whose work its models build on. It wants these experts to act as “shepherds.” They would bring together groups of people to turn the AI-generated results into new knowledge created by humans. However, OpenAI also admits in its blog post that “choosing initial shepherds necessarily shapes who gets involved first and creates asymmetry of information.” In other words, choosing who gets involved first affects who has access to the information.

Some of the supposedly “raw” information is now available on GitHub, but not all of it. OpenAI says the group working on physics has decided “to hold off on releasing the AI-produced artifacts and instead work on writing it up themselves.”