AI Proved Nivat's Conjecture — and Nobody Read It

A machine-checked proof of Nivat's conjecture went up on GitHub this week, and the repository's own README contains the sentence that makes it a story rather than a result: the proof "has not been mathematically digested by humans." The conjecture, posed by Maurice Nivat in the 1990s, says that a two-dimensional configuration whose pattern complexity on some rectangle is at most the area of that rectangle must have a nonzero period. The formalization is Lean 4 against mathlib — 29 library modules, 377 declarations, first committed on 14 September. The maintainer, Boon Suan Ho, states plainly that the proof was found entirely by GPT-6 Pro in response to his prompts, and that GPT-6 Astra Ultra running in Codex produced the Lean formalization and the documentation around it.

What is left for the human, on his own account, is prompting and arranging verification. He splits the work into three stages — generation, verification, digestion — and says the project covers the first two. The third has not started.

That gap is exactly the subject of a guest post published a day earlier on Terence Tao's blog What's new, by the Northwestern mathematician Bryna Kra. Kra is not a bystander to this particular conjecture: with Van Cyr she proved a partial version in 2012, showing periodicity holds when the pattern count is at most half the window area. Her title is the argument. Deep theorems were scarce and difficult, she writes, and so became an effective mechanism to identify deep thought — and AI has broken that system. Tao, in a short preface, notes that the post itself was converted from another file format using AI, which is either a small joke or the whole problem in miniature.

Kra's evidence is concrete and slightly bleak. In a single week she received several purported proofs of the full conjecture from researchers making their first entry into the subject. Some disclosed AI assistance, described as polishing the English or checking the argument. She invited the authors to explain their proofs to her over Zoom. None accepted. She is careful about what that does and does not establish — silence is not proof that a model wrote the paper, and a proposed proof is not a theorem — but the asymmetry is the point. Producing a manuscript that looks like a contribution now costs almost nothing. Establishing that anyone involved understands it costs the same as it always did.

Her conclusion is not that mathematics should resist the tools. It is that the discipline has been measuring the wrong thing and can no longer afford to. A proof, she argues, is more than a certificate that something is true: it is a story, a picture, an insight, an explanation — a line that runs straight back to Bill Thurston's claim that the product of mathematics is clarity and understanding, not theorems by themselves. If theorem production is now cheap and explanation is not, then explanation is what the profession should be counting.

The proposals follow from that. Disclosure of AI use, in her framing, is not sufficient; authorship should mean being able to explain the mechanism of a proof and answer questions about it. Journals should separate and credit the distinct roles of discovery, proof, formalization and exposition rather than bundling them into one byline. Peer review, already a volunteer system drowning in submissions, needs incentives attached to verification and exposition or it will simply fail under the new volume. And hiring and promotion committees should reward conceptual clarity and teaching rather than theorem counts — the tasks the field has historically undervalued, now load-bearing.

None of this is hypothetical friction any more. BitsMinds covered OpenAI's Navier–Stokes claim last week, where roughly 10,000 agents ran in parallel for 88 hours and a frontier model converted the resulting argument into machine-checked Lean; the same lab spent August announcing ten decade-old problems closed the same way. Formal verification means the community no longer has to wonder whether these arguments are correct. Kra's post is about the question that survives verification: a field whose literature is true, complete and unread is not obviously the field anyone was trying to build.