Mathematics is the field where AI’s wins are easiest to prove. In September, 25 winners of the Fields Medal, the closest thing mathematics has to a Nobel Prize, signed a declaration saying those wins miss the point.
AI wins there for a simple reason. In most fields, its weak spot is the mistake you can’t catch: a memo can sound right and be wrong. A mathematical proof, the step-by-step argument that a statement is true, can be checked line by line, even by a computer. As Terence Tao, a UCLA mathematician widely seen as one of the best alive, told Nature, “in mathematics, almost uniquely, you can automatically check the output.”
In a controlled test called First Proof this year, AI systems solved 7 of 10 new research-level problems at publication quality, for $10 to $1,000 of computing each. Then, on September 8, OpenAI announced that its AI had solved Navier–Stokes, one of the Millennium Prize Problems: the most famous open questions in mathematics, each carrying a $1 million reward. Thousands of AI agents produced a 165-page proof in about 88 hours. It hasn’t been independently verified yet, but the argument that follows doesn’t depend on it holding up.
The Medal Fields declaration came 3 days later: “A Severe Misalignment of AI in Mathematics”. The signatories, Tao among them, grant that AI “can solve major outstanding problems.” Then they name what those problems were for: solving them “is only a tool and proxy for achieving the primary goal of conceptual understanding and insight.”
In plain terms, solving problems was a stand-in, and the real goal was understanding. As long as humans did the solving, the two came as a package. AI pulled them apart.
Days before the announcement, Tao had described this exact scenario: an AI lab cracking one of these famous problems with “almost no value added to mathematics as a consequence.” The prize goes to the answer. The field grows from the attempts.
How understanding gets lost
Tao splits mathematical work into 3 parts: finding the proof, checking it, and what he calls digestion (understanding the result and explaining it to others). For most of history, digestion came free. You couldn’t spend months fighting a proof into existence without understanding it by the end. Let a machine find the proof and it lands on your desk, correct and undigested. AI can explain it to you, of course. Whether you understood is another matter.
Hence his rule for students: if you couldn’t present the AI’s output in class and answer questions about it without AI help, “it should not be part of your workflow.”
The loss scales up. Each researcher’s output can improve while the field gets worse: more correct results, fewer that anyone has digested. A group can lose its shared understanding even when every single output is correct. The declaration calls what’s at stake “the crucial human transmission chain between mathematicians”: the way understanding passes from one person to the next.
None of this makes Tao anti-AI. He expects humans to “still be driving,” with AI speeding up the exploration. The line he draws is between 2 kinds of difficulty. Tedious repetition can go to the machine, as long as a human stays in the loop and can check the result. Real conceptual difficulty, which he calls natural friction, is where the learning happens, and a tool that smooths it away takes the understanding with it. Call that augmentation: the machine carries the tedium, you keep the hard thinking, and the journey gets better instead of shorter.
He keeps what he calls a “mindful cognitive diet”: choosing which skills to let lapse and which to keep in practice.
The handover came fast
Mathematicians have handed work to machines before without protest. As Tao likes to point out, in the Age of Sail mathematicians computed navigational tables by hand; in the Second World War, ballistics. Computers now do both, and nobody misses it.
Call it the difference between outcome work and journey work. In outcome work, what matters is the right answer, whoever finds it: solving equations. In journey work, the doing is what builds the value: proving theorems, it turns out.
This time the handover came fast. In late 2024, Tao called one AI model a “mediocre, but not completely incompetent” research assistant. By early 2026, he rated it “on par with” a junior human co-author. Much of his field went through what he calls “the five stages of grief,” and the declaration went out in a rush, “sooner rather than later.”
A test for any automation
This debate is what made it click for me. I was formally trained in Mathematics, and I’ve always seen mathematics as a craft of beauty. Shortly after the declaration, I heard Cédric Villani, the French Fields Medallist and one of the signatories, on Radio Classique (in French). “The path is often even more important than the result itself,” he said. He remembered writing his big textbook holed up for days with soup and a fresh baguette: “it was pain, it was happiness.” He has told his new PhD student not to touch generative AI for the length of the thesis. I came away feeling he was afraid of losing his art.
The theorem is what makes a mathematician famous. The search for it is what they love. Automate the theorem and you risk emptying the craft.
That gave me a test I now apply to any automation: if you automate the outcome, does the journey still have value? For a good life, philosophers have answered that since Aristotle, who held, as C. Thi Nguyen put it to Derek Thompson, “that meaning in life comes from activity, not just outcomes.”
Companies follow the same rule, for a harder-nosed reason: their competitive advantage gets built in the journey work. Every company has both kinds of work, the outcome work and the journey work. The expense report is the equation solving, it’s an outcome work. The budget meeting is a theorem, it’s a journey work.
What a company can lose
Start with the expense reports, because outcomes are good. Expense claims, invoice chasing, spreadsheet reformatting: what matters is that they’re right and on time, so hand them over without guilt. And if AI finds a cure for a disease, take it with both hands.
Your budget meeting is different. It produces a spreadsheet, but its real job is alignment. Swap it for an AI summary in every inbox and everyone gets the information. Nobody gets the common knowledge.
Michael Chwe’s Rational Ritual (2001) shows that public rituals exist to create exactly that: everyone knows, and everyone knows that everyone else knows. That shared awareness is what lets a group act together. Every summary can be accurate while the alignment evaporates. AI can still augment the meeting: let it prepare the numbers and scenarios, so the room spends its time arguing about choices instead of reconciling spreadsheets.
The same holds for one person. Take the analyst on your team who runs a customer panel or a social-listening report. The report is the proxy. The product is her feel for the market, built by pulling the numbers herself: the kind of knowledge Michael Polanyi had in mind when he wrote that “our body knows more than it is capable of saying” (a line Richard Bordenave puts at the heart of his case for intuition).
Automate the panel and the report still arrives. The feel doesn’t. Keeping the old routine out of loyalty misses the point. Rebuild the feel deliberately, with AI on her side. Let it do the pulling and cleaning. Then have her write down what she expects before she opens the report, read a sample of raw customer comments, and ask the AI to argue against her read.
This is the new job for leaders: keeping people learning when much of the work that taught them is automated. A company needs the same kind of cognitive diet Tao keeps for himself, chosen skill by skill, on purpose.
The tempting shortcut is the headcount line. If AI does the junior work, why keep juniors? Because the junior work is how seniors get made. Give them AI that checks their work and pushes back on it, the way Tao prefers to use it, rather than AI that does it for them. Cut the journey, and in a few years nobody left can judge what the machine produces. More results, and fewer people able to produce the next ones: the mathematicians’ problem, on an org chart.
Strategy lives here too. Your competitors can buy the same outputs from the same models, so outputs stop being an edge the day everyone has them. What’s left is what can’t be bought: judgment built over years of doing the work, and the alignment a team earns by arguing in the same room. Both are built in journey work, which makes it the last place a company should cut. (I made versions of this argument in When AI Turns Secret Sauce Into Ketchup and Outsource the Slop, Not the Soul.)
Automate or augment: sort your work first
The declaration treats mathematics as an early case of a threat to intellectual work in general. The task, it says, is to make sure “we do not lose sight of what that work was meant to achieve in the first place.”
Mathematicians had to answer that under pressure. Companies have one advantage they didn’t: they can see it coming. How much time that leaves is anyone’s guess. Use it to sort the expense reports from the budget meetings before the automation is already done.
Take every good outcome AI offers. Then, for each piece of work you hand over, ask which kind it is. Is the result the whole point, or was doing it building something: understanding, judgment, alignment, the next generation of seniors?
If you’re unsure, borrow Tao’s class test. Could the person who shipped it present it and take questions without the AI? (Worth running on the last AI-drafted memo you sent.)
Most of the time, it’s an expense report. Let it go. Sometimes it’s a theorem, and you keep it on purpose.
Villani reached for The Little Prince to make the same point. As the fox tells the prince: “It is the time you have wasted for your rose that makes your rose so important.”
Mathematicians found out what their rose was after the fact. You still get to choose: automate the outcome, augment the journey.