On September 8, OpenAI said 10,000 of its agents, running for 88 hours, had produced a 166-page proof regarding the Navier-Stokes equations — which describe fluid movement and have remained an open question since 1934. It’s one of the seven Millennium Prize Problems established by the Clay Mathematics Institute in 2000, each carrying a $1 million prize; only one has ever been awarded.

OpenAI has said it won’t be claiming the money, which is just as well, since outside estimates put the compute bill between $10 million and $40 million .

Clay now says the problem has “apparently been settled,” while the formal evaluation proceeds. The institute calls that process “deliberately unhurried.” Before Clay will consider paying, a proof has to be published in a refereed journal of worldwide repute and then survive two years of mathematicians trying to break it. If you check Clay’s website, it now labels Navier-Stokes “Active”: neither unsolved nor solved.

Those conditions were written in 2000, and you’ll notice they don’t ask whether the argument is formally correct; they ask whether mathematicians have read it, argued with it and failed to break it.

It seems the machine has produced the proof much faster than the mathematical community can absorb it, and while the cost of producing the answer is visible, the cost of turning it into understanding is only starting to be calculated.

Navier-Stokes is the sharpest case so far, but it isn’t really a story about fluid dynamics. The interesting story is the gap between a result being correct and a result being understood.

Earlier this week on September 11, 25 Fields Medalists signed a declaration saying the way AI labs chase mathematical problems is damaging mathematics. The next day Terence Tao, who signed it, gave his blog over to two philosophers of mathematics, Silvia De Toffoli and Eamon Duede, who explained the claim.

They separated two concepts that had rarely needed separating before: a logical proof (deductive validity, which a machine can verify) and an intelligible proof (understanding why something is true in a form humans can explain and build upon). Historically, these came together because no human could construct the first without possessing the second. AI pulled them apart. Their verdict on the Navier-Stokes result: “What OpenAI has given us is an answer. But it is not clear that they have delivered a fruitful solution.”

Your Company Already Has This Problem

A Q1 2026 survey by Digital Applied of 2,847 developers who actively use AI coding tools found that they spent 11.4 hours a week reviewing AI-generated code and 9.8 hours writing new code. LinearB, analyzing 8.1 million pull requests, found that agent-created pull requests waited 5.2 times longer for their first review than unassisted ones.

And it isn’t just engineers. In January, Workday reported on a survey of 3,200 employees and business leaders. While 85% of employees said AI saved them between 1 and 7 hours a week, 37% of that time went back into correcting, rewriting and checking its output. Only 14% said they consistently achieved a clear positive net outcome. The most interesting number in the report is that 77% of daily AI users review AI-generated work at least as carefully as work produced by a colleague.

AI hasn’t eliminated the work, it just moved it from production, which companies measure, into verification, which they largely don’t. The output appears in the productivity dashboard; but the effort required to make it trustworthy disappears into the working day.

Explainability Is the Wrong Test

Companies already have a term for making AI outputs understandable: explainability. But explainability and intelligibility answer different questions. Explainability asks whether an output can be traced, interpreted or justified. Intelligibility asks whether the people responsible for acting on it understand it well enough to challenge it, defend it and build on it. An organization can easily satisfy the first while completely missing the second.

Levent Alpöge and Tristan Buckmaster, two mathematicians who published AI-assisted proofs of their own the same week, called their first writeup of one “the worst writeup we had ever seen in the history of mathematics.” A proof assistant called Lean had confirmed every line of it, but making the argument readable took weeks, and they were still working on it when they published.

That translation phase is where the time actually goes, and where AI’s theoretical efficiency dies in practice. In academia, that effort is called scholarship; in a business, it’s your most expensive people spending their days translating machine output instead of building new value.

I ask founders a version of this question every week: once the model produces the answer, what must a human still do before a customer can use it? Few can put a number on it.

First, measure the reading as well as the writing. Companies track what their AI tools generate: code, reports, analyses and resolved tickets. Far fewer track the expert hours required to check, rewrite and approve that output. But without that number, output is a measure of throughput, not productivity.

Second, stop accepting explainability as the answer to an intelligibility question. Ask something different during the review: who here understands this well enough to challenge it, defend it and extend it? If the answer is nobody, you own an artifact, not a capability.

Third, treat reviewers as the scarce asset. They’re the people with enough domain depth to catch a confidently wrong answer; and they are frequently the same people an efficiency case says the company will need fewer of. Generation scales with compute. Judgment does not.

Mathematics has spent centuries building institutions around the gap between an answer and accepted knowledge: journals, referees, public criticism and time. Most companies just built a dashboard to track the speed of generation—and missed where the year actually went.