A 30-year-old open problem in combinatorics just received several purported full proofs in the same week, and the mathematician who spent over a decade chipping away at it says that volume, not any single result, is the real story. Bryna Kra, writing in a guest post on Terence Tao’s blog, argues that mathematics built its entire reward system on a false assumption: that deep theorems would stay rare because deep understanding is hard to fake. AI proof generation, she says, has severed that link.
The test case is the Nivat conjecture, a question about whether a simple cap on the number of local patterns in an infinite grid of colored tiles forces the whole grid into a repeating structure. Kra and Van Cyr proved a partial version in work first circulated in 2012, showing periodicity holds once the pattern count drops below half the window’s area. A separate team, Jarkko Kari and Michal Szabados, later attacked the same question through algebra rather than dynamics. Specialists in the field spent years looking for a bridge between the two methods and never found one.
Kra’s point is that a large language model does not carry the years of specialization that made the search slow. It can hold both frameworks at once, test combinations without fatigue, and turn out something that looks like a finished paper. The Nivat conjecture had already been proposed for Google DeepMind’s Formal Conjectures project, a repository that turns open problems into targets for automated reasoning, which put the question in front of far more potential solvers than before.
What arrived this week, in Kra’s account, were several claimed proofs from researchers new to the area. Some disclosed AI use, limited to language polishing or proof checking. When she asked the authors to walk her through the argument over a video call, nobody accepted.
Kra is explicit that declining a call does not make a proof invalid, and that a correct result is still a contribution regardless of who or what assembled it. Her objection sits elsewhere: correctness was never the whole point of a proof. She quotes the topologist Bill Thurston’s 2010 answer on MathOverflow, that “the product of mathematics is clarity and understanding. Not theorems, by themselves.” A manuscript that proves a statement without anyone able to explain why it is true transfers a fact without transferring the understanding the field actually trades in.
That gap matters because mathematics’ hiring, tenure, and prize systems were built to reward theorem production as a proxy for exactly that understanding, on the assumption that faking the proxy was too expensive to attempt at scale. Kra argues the field’s peer review process, already strained by a small pool of unpaid reviewers, cannot absorb a volume of submissions that no longer costs years of specialized labor to produce. She proposes that journals start crediting discovery, formalization, and exposition as separate, individually valued roles rather than folding them into a single publication credit.
Her closing argument extends past mathematics: she calls the field a canary for any discipline that depends on scarce expert output as its quality filter, and names science, law, and public policy as the next fields that will need new ways to separate abundant machine output from work worth trusting. For any research organization currently treating publication counts or proof counts as a hiring or evaluation signal, Kra’s argument is a warning to build a second signal, one based on demonstrated explanation rather than output volume, before that volume arrives in your own field.
Bryna Kra, professor of mathematics at Northwestern University, wrote this argument in a guest post published September 13, 2026 on Terence Tao’s blog.
