OpenAI’s proof that QCD exists is not out yet
Three AI results in math, computer science and physics, each released the way its community advised
We reached out to external experts and asked them to act as shepherds, organizing groups to understand the new results. They advised three different release strategies:
- For the math result, release the AI output, leaving researchers free to organize their own efforts to explain the result.
- For the computer science result, form an external group of collaborators to explain the result, while making the AI output publicly available for anyone to examine and build on.
- For the physics result, form an external group of collaborators and defer to them on the release of materials.
This is short, but big: a proof of the local smoothing conjecture in every dimension, and with it the Kakeya conjecture and Stein’s restriction conjecture; a proof that the Exponential Time Hypothesis is false; and an existence proof of quantum chromodynamics.
Three communities, three different ways, and OpenAI tries to honor what each one wants. Only yesterday I said the math community seems to reject progressive disclosure, as AGMAI recommends labs stop designating mathematicians to see the output first. The math result follows that: the expert they reached out to recommended releasing it publicly, the same way as the October 6 release.
The physics result is the closest to my progressive disclosure idea. The circle starts with the lab, widens to a group of experts known to be working on the problem, and the public comes last, when the group decides:
For the physics collaboration, the group has decided to hold off on releasing the AI-produced artifacts and instead work on writing it up themselves.
The computer science result is in between. The shepherds are designated, but the natural language proof and the Lean formalization are public immediately, and the group asked OpenAI to fund a conference and “invites the community to help organize an open examination of the ETH claim”. So the data is open to everyone at once, and only the explaining is led by a designated group.
OpenAI also names the cost AGMAI is worried about:
On the other hand, choosing initial shepherds necessarily shapes who gets involved first and creates asymmetry of information.
QFT, much earlier than I expected
Just a week ago I asked whether a network of agents could formalize QFT. And this is it, much earlier than I expected:
The physics collaboration will understand and explain a result that gives 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. […] As a subproblem, this work also includes a proof of the existence of pure Yang–Mills theory, which is part of the Quantum Yang–Mills Theory Clay Mathematics Institute Millennium Prize problem.
The timeline and the way it is handled are interesting:
Our models produced a natural language proof for Yang–Mills existence on September 9th, 2026, and then subsequently produced a proof for QCD on September 18th, 2026. Given the length and complexity of the work, we postponed release until the Lean formalization completed. We finished our formalization of Yang–Mills’ existence on October 16th, 2026, which led us to develop the collaboration described here.
The proof is not even out there yet. This is an interesting take on progressive disclosure: progressively review what’s proved, but take more time to digest it, to publish it properly. It also means the Yang–Mills proof existed inside OpenAI more than a month before I asked, which is the lab’s early access by construction, as I argued in the economy post.
Because of that, it is not clear what has been proved. My reading is this:
- It is an existence proof, that these theories exist as rigorous mathematical objects. The Millennium Prize problem asks to prove that Yang–Mills theory exists and has a mass gap, which is why OpenAI says “part of”. The mass gap is not claimed.
- “A unified completion of the Standard Model” is “the simplest grand unified theory that includes the gauge fields and fermions of the Standard Model”, which is probably the SU(5) of Georgi and Glashow. So SU(5) is proven to be consistent as a QFT, not that a GUT for our current Standard Model is discovered. Minimal SU(5) is ruled out as physics, since the proton does not decay as fast as it predicts. And the quote mentions only gauge fields and fermions, no Higgs, so as I read it, there is nothing in the proven theory to break SU(5) down to the Standard Model.
- If it is SU(5) with the fermions of the Standard Model, those fermions are chiral, and that would be big on its own. Balaban’s approach is on a lattice, and chiral fermions are notoriously hard to put on a lattice (the Nielsen–Ninomiya theorem). As far as I know, a rigorous construction of a chiral gauge theory in four dimensions has never been done, so I’d like to see how the proof handles them.
- The Lean formalization OpenAI mentions is for Yang–Mills existence only. What is formalized for QCD and SU(5) isn’t said, and since nothing is released, we can’t read the Lean statement either, which is what a Lean proof actually proves.