Article 330: OpenAI Says Its Models Proved a Harmonic Analysis Conjecture, Disproved the Exponential Time Hypothesis, and Settled a QCD Proof. Nobody Has Verified It Yet

On Monday OpenAI announced that its models had produced three results: a proof of the local smoothing conjecture in harmonic analysis in every spatial dimension, a disproof of the Exponential Time Hypothesis in complexity theory, and what it described as a "mathematically rigorous" proof in quantum chromodynamics.

Any one of those, if it holds, is a career. All three in one announcement from a company valued at $852B is a thing that has happened before in this industry and has not always survived review.

What the experts actually said

Alex Iosevich, a harmonic analysis professor at the University of Rochester, told Al Jazeera that OpenAI appeared to have "cracked" the conjecture in a "historic development." His personal stake is real: the conjecture was formulated by his PhD adviser, Chris Sogge. Prior work had established local smoothing only in three dimensions; OpenAI claims it in every dimension. Iosevich also said he felt "a twinge of sadness" - theoretical mathematics is about to "change drastically," in his words.

Ryan Williams of MIT, on complexity theory, was more careful. On the ETH: "We are working to verify and examine their proof and determine if it holds up." He confirmed the stakes - the ETH has been believed true since the late 1990s, and a great deal of theoretical computer science was built on it - and noted the proof "proposes a mysterious new method" to solve fundamental problems efficiently. Mysterious is not a compliment in this field. It means nobody yet knows why it works.

The detail nobody is leading with

OpenAI chose a different release methodology per field, decided in consultation with three external expert groups it called "shepherds." The maths and computer science groups published the AI-produced data immediately. The physics group deferred release so it could write up its own interpretation first.

OpenAI's own description of the tradeoff: choosing initial shepherds "necessarily shapes who gets involved first and creates asymmetry of information." That is a company acknowledging, in its own announcement, that it built an information hierarchy around its claims before anyone outside could check them.

And the pattern it fits: last month Anthropic announced a CRISPR-like enzyme system, drew a mix of praise and accusations of exaggeration, and the case is still being argued.

Key Takeaway: The most consequential line in this story is Williams saying they are still verifying. A confirmed ETH refutation would be one of the largest results in complexity theory in three decades. A retracted one would be a lesson in what happens when breakthroughs are announced on the schedule of a funding cycle. The right posture is neither dismissal nor celebration: it is to note the date, note who is checking, and come back when a referee has signed something. AI has earned the benefit of the doubt on writing code. It has not earned it on Sogge's conjecture.

Sources: Al Jazeera, "AI makes discoveries in mathematics, computer science, physics, OpenAI says," 27 October 2026; OpenAI announcement, 26 October 2026