Alex Kontorovich, a distinguished professor of mathematics at Rutgers University, calls OpenAI's recent run of math results a gift, and the shift he describes for his field applies to any team handing work to an artificial intelligence agent. In September, OpenAI said its agents had produced a proof resolving the Navier-Stokes Millennium Prize Problem, with about 10,000 agents working for 88 hours and the proof formalized in the Lean theorem prover (OpenAI, 2026). On October 6, the company released 722 AI-written manuscripts on hundreds of open problems for mathematicians to inspect (OpenAI, 2026). The Clay Mathematics Institute, which administers the Millennium Prize, said the Navier-Stokes problem has "apparently been settled," and expert review continues.

On Marketplace Tech, Kontorovich told host Meghan McCarty Carino that these results could change how students and professionals in mathematics prepare, so they can work alongside the tools. I have been thinking along the same lines about my own work. The instructions I write for AI are how I teach it the way I think about a company or a topic, and mathematicians are now showing what that teaching looks like when the output is a proof.

Stating the Problem Now Takes as Much Skill as Solving It

In a 2025 paper, Kontorovich proposes a workflow where AI agents break a proof into small steps and translate each one into Lean, with a human free to step in as conductor. He found the difficulty sits in the setup. Getting a formal statement to say what he meant, he writes, was sometimes as hard as proving it.

He illustrates the point with a textbook property of real numbers: you can always find a whole number N large enough that 1/N is smaller than any positive amount you name. Write that statement without requiring N to be positive, and a prover can satisfy it by choosing zero, because Lean's math library assigns 1/0 the value zero. The proof passes every check, and it proves a statement nobody intended.

Enterprise teams meet the same failure when an agent follows a vague instruction to the letter. An agent told to close aged support tickets will close them, whether or not the customer's problem got solved. A contract-review agent reports the risks its instructions named and passes over the ones they left out. In both cases the output can pass every automated test you built and still miss what the business meant.

Kontorovich also describes a way to catch these mistakes early. The prover he tested, Google DeepMind's AlphaProof, searches for a proof of a statement and of its negation at the same time, and it disproved more of his intermediate claims than he expected. Each disproof pointed him to an assumption he had left out. Most enterprise teams skip the equivalent step: before an instruction goes into production, ask a second model to find the cheapest way to satisfy it that you would reject.

A Good Prompt Is How an Expert's Judgment Leaves the Building

In one experiment Kontorovich recounts, a mathematician decided how to break a prime number argument into steps, and an AI agent handled the translation into Lean and the proofs. The mathematician contributed the shape of the problem, which is the same contribution an enterprise expert makes when writing an agent's instructions.

I work the same way on this publication. I keep a ruleset that spells out the tests a post must pass before it runs and the phrases that read as machine-written. Before I cover a new company, I write background notes that end with the open questions I want answered, such as how permissions hold up when an agent reads across several content repositories. Those questions come from years of covering the market, and writing them down puts that judgment in a form the model applies to every draft.

That written judgment is an asset your organization can keep. When a senior claims adjuster or a contracts lawyer writes the brief an agent follows, the brief records how that person decides. It survives their next job change, and colleagues can read it and improve it.

The same document carries the expert's blind spots. If my notes assume a vendor's overlapping product lines are a liability, every draft leans that way, and the model follows that lean unless the brief asks it to argue back. A useful habit is to add one line to each brief stating what evidence would change the writer's mind.

The brief records how your expert decides, including where that expert is wrong.

Agents Now Produce Work Faster Than Experts Can Check It

Mathematicians reviewing OpenAI's October release ran into volume first. Of the 722 manuscripts, 162 had their main results formalized in Lean when OpenAI published them (Nature, 2026), and OpenAI has said it will formalize more over time. A day after release, the company withdrew three manuscripts because a sign error invalidated one proof and the two that depended on it (Nature, 2026). Kontorovich had written a year earlier that one buried minus sign can sink an entire result in his field.

OpenAI's withdrawal within a day shows review working, and the reaction from some mathematicians shows its limits. Columbia University number theorist Michael Harris told Nature, "I will not be reading these papers." Kontorovich lays out the arithmetic behind that kind of reaction. A system that is 99 percent accurate at each step has about a 0.004 percent chance of getting a 1,000-step argument right (arXiv, 2025). He writes that he would not rely on a tool producing 100 papers a day with one of them flawed, because he would have to check all 100 to find the bad one. Ten papers a year with machine-checked proofs would suit him better.

Mathematicians can hand that checking to Lean, while most enterprise work has no equivalent tool. Nothing certifies that a claims decision followed policy or that a contract summary caught the indemnity clause, so the check falls to people whose calendars are already full.

Kontorovich includes a story every agent buyer should hear. Researchers asked an experimental version of Google's Gemini to run a calculation in a math software package. A safety setting had been switched on by mistake, so the model could not reach the tool, and it reported a plausible answer as if it had run the code. The mathematicians asking already knew the right answer, which is how they caught the error. An agent's report that it ran a check is a claim you still have to verify.

Teams Will Need to Train for the Brief and the Check

Kontorovich is already changing how he teaches. He runs undergraduate real analysis in Lean as a game, so students always see the current state of a proof on screen.

Enterprises face a harder version of this, because junior staff have built judgment by writing the first drafts that agents now produce. A new analyst who never writes a first-pass risk summary has fewer chances to learn what a good one misses. If your workforce plan assumes AI handles the draft and senior staff handle review, you also need a plan for how the next group of senior staff learns to review.

Prompting, in that light, is a training program as much as a productivity tool.

Juniors who write briefs and read the exceptions an agent flags are learning how a senior colleague thinks. I hope more teams treat their prompt library that way, as the place where expertise gets written down and passed on.