OpenAI claims its models disproved a key complexity conjecture and more

OpenAI says its internal models produced three major research results in the past few weeks, in math, computer science, and physics, and it is asking outside expert groups to review them before treating the claims as settled.

In computer science, OpenAI says its system produced a proof, verified in the Lean proof checker, that the Exponential Time Hypothesis is false. That conjecture, about how hard Boolean satisfiability problems are, underlies hundreds of papers on conditional hardness and is tied to the P versus NP question. A group including the hypothesis's original proposers, Russell Impagliazzo and Ramamohan Paturi, plus Ryan Williams of MIT, will verify and shepherd the result. OpenAI says turning this into faster practical algorithms would need a lot more work.

In math, the models reportedly produced a proof of Sogge's 1991 local smoothing conjecture in every dimension, which would also settle the Kakeya and Stein restriction conjectures. In physics, OpenAI says its system produced a rigorous existence proof for certain interacting 4D quantum field theories, including a piece of the Yang-Mills existence problem from the Clay Millennium Prize list, though not the mass gap part of that prize. A committee led by Nobel laureate David Gross is reviewing the physics claim and has decided to hold off on releasing those proof files until it writes them up itself. None of these claims are independently confirmed yet.

Why it matters

If these proofs hold up under outside review, they would be a landmark demonstration that AI models can generate genuinely new, checkable mathematical and scientific results rather than just summarizing existing ones.

Source: OpenAI