OpenAI claims AI-driven proof of local smoothing conjecture and disproof of the Exponential Time Hypothesis

OpenAI's claims are the boldest AI-for-science announcement of the year. According to Al Jazeera, the company says its models produced a full proof of the local smoothing conjecture in harmonic analysis across all dimensions, a disproof of the Exponential Time Hypothesis (ETH) from complexity theory, and a rigorous quantum chromodynamics result. On October 28 OpenAI amplified a statement from a Yang-Mills Working Group convened at UC Santa Barbara's KITP to interpret the physics result.

The proofs were reportedly formalized, which is what makes verification tractable: Lean-style machine-checked proofs can be independently re-run, unlike prose arguments. That is precisely what the community is asking for. ETH is a widely used assumption underpinning many fine-grained complexity lower bounds, so a disproof would ripple through theoretical computer science.

Context matters for calibration. Hacker News commenters agree an ETH disproof would be significant but stress it does not imply P=NP — ETH is a stronger assumption than P≠NP, so refuting it leaves the bigger question open. AllenAI's same-week work on whether LLMs can even judge research novelty is a reminder that AI-generated science still needs human adjudication.

What to watch: whether the formal proofs are released publicly and independently checked, whether harmonic analysts endorse the local smoothing argument, and how the KITP group characterizes the QCD result. Until then, treat these as claims, not results.