Less than a month after mass-releasing hundreds of manuscripts it claimed contained solutions to long-standing mathematics questions, OpenAI is back with three more “major” discoveries in math, computer science, and physics. This time, the company has decided to let external experts - whom it describes as “shepherds” - guide the results in computer science and physics. For the math problem, OpenAI says it was advised to release the AI output directly so researchers could work through their own explanations. Because nothing says “scientific rigor” like crowdsourcing the peer review.

The math breakthrough, according to OpenAI, is a proof of “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. OpenAI is releasing the model output directly, as it did in its October 6 release. Just a few months ago, NYU professor Hong Wang won a prestigious Fields Medal from the International Mathematical Union for resolving the Kakeya conjecture in three dimensions. Now an AI says it’s done it in all dimensions. No word yet on whether the medal comes with a firmware update.

The computer science result is even bolder: a paper titled “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 (ETH). 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, OpenAI is making the materials public immediately so others can examine them as well. Impagliazzo and Paturi were part of the group that originally proposed ETH in 1999 - so at least someone in the room remembers when the hypothesis was considered true.

The physics information has not been released in full, but OpenAI describes it as 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.” David Gross will lead a group including Michael Douglas, Arthur Jaffe, Igor Klebanov, and Nikita Nekrasov that will shepherd this work. Because nothing says “we're confident” like withholding the full details and calling in the Nobel laureates.

OpenAI admits this approach could have its own issues. 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. In other words: maybe don't treat groundbreaking science like a VIP pre-sale.

The computer science group decided to release the AI output write-up and Lean proof on GitHub today. They also released an open letter to the community asking for input on how to examine the claim and about setting norms for dealing with AI-generated breakthroughs. The letter poses three broader questions: What expectations should govern early access to AI-generated results, disclosure of conflicts of interest, and the use of unpublished material for subsequent research? How should credit recognize both new discoveries and the work of checking, fixing, simplifying, explaining, and extending them? How can we support students and researchers as methods and research directions change, while preserving the understanding and judgment needed to question results and develop new ideas? All excellent questions, and notably, not ones an AI can answer on its own - yet.