Less than a month after its mass release of hundreds of manuscripts that it said contained solutions to long-standing mathematics questions, OpenAI is back with three more “major” discoveries in math, computer science, and physics. What’s different this time is the choice to have external experts that OpenAI describes as “shepherds” guiding the results in computer science and physics, while for the math problem it says that they advised it to release the AI output for researchers to work through their own explanations.
This time OpenAI says it’s taking new advice from scientists on how to release the results.
OpenAI results added to GitHub today:
Local smoothing for the Euclidean wave equation. The proof uses an auxiliary partial differential equation to establish Sogge’s local smoothing for waves in every spatial dimension at least two. It also yields the Kakeya maximal and dimension conjectures and Stein’s spherical restriction estimates throughout the interior of the conjectured range. We are releasing the model output directly, as we did in our October 6 release.
The Exponential Time Hypothesis is False. The paper gives a deterministic algorithm that exactly counts satisfying assignments of fixed-width CNF formulas in subexponential time and polynomial space. The case of 3-SAT refutes the Exponential Time Hypothesis. An independent working group of computer scientists led by Russell Impagliazzo, Ramamohan Paturi, and Ryan Williams will examine and explain the proof. At the group’s request, we are making the materials public immediately so others can examine them as well.
This approach could have its own issues, the company admits, and the AGMAI panel of math advisers OpenAI put together just said yesterday that “we recommend that AI companies do not adopt” the practices of designating certain people to receive the output first, citing unequal access, borrowed reputation, and biased selection as a few of the issues. Instead, they recommended that in the future, AI labs release output on scholarly repositories, with Lean-formalized proofs, info on how the problems were chosen, funding for people working on understanding the results, and other information.
The physics information has not been released in full, but is a “mathematically rigorous existence proof of certain interacting quantum field theories containing gauge fields and fermions in four dimensions, including Quantum Chromodynamics (QCD) and a unified completion of the Standard Model of particle physics.” According to OpenAI, “David Gross will lead a group including Michael Douglas, Arthur Jaffe, Igor Klebanov, and Nikita Nekrasov that will shepherd this work.”
The computer science collaboration is said to prove that the Exponential Time Hypothesis (ETH), which has been widely believed to be true, is actually false. OpenAI says verification of the result will be guided by a group of three experts that includes UC San Diego’s Russell Impagliazzo and Ramamohan Paturi, who were part of the group that originally proposed it in 1999, with the group deciding to release the AI output writeup and Lean proof on GitHub today.
There’s similar documentation for the math breakthrough, where its model “produced a proof of the local smoothing conjecture in every dimension and therefore also resolve the Kakeya conjecture and Stein’s restriction conjecture in all dimensions.” Just a few months ago, NYU professor Hong Wang was awarded a prestigious Fields Medal by the International Mathematical Union for resolving the Kakeya conjecture in three dimensions.
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