Twenty-five Fields Medal winners — the closest thing mathematics has to a Nobel — co-signed a warning about AI. The internet's reflex wrote itself: the old guard is scared. Experts defending their authority. Luddites with tenure.
Then you open the statement, and the reflex dies.
It begins by crediting AI. In the past few months, large language models have solved significant open problems across multiple fields of mathematics. No hedging, no denial. The people best qualified to check the work are the ones confirming it stands.
The warning comes after the win, not against it. Their own word for the problem is in the title: a serious misalignment. AI companies are optimizing for answers. Mathematics exists to produce understanding. Those are not the same product.
TL;DR: The statement is not anti-AI — its lead signatory tests frontier models for a living. The actual claim: famous unsolved problems are lighthouses, not summits. Their value is the navigation they force and the tools built along the way — Fermat's Last Theorem produced 350 years of number theory machinery we still run on today. AI now solves the problem and skips the journey, delivering proofs that add roughly zero knowledge. The scarcest resource is "students and ideas" — in that order — and apprenticeship collapses when answers are free. This is Goodhart's law applied to a whole civilization's scoreboard, and the same misalignment is coming for every knowledge industry. Including mine.
I am James, CEO of Mercury Technology Solutions. From Cyberport, Hong Kong — 15 September 2026. My company builds AI-to-human bridges for enterprises, so a statement from the world's best mathematicians describing the gap between machine output and human understanding is not an abstraction to me. It is the product spec. More on that below.
The man who posted the alarm
Terence Tao put the statement on his blog on September 11. Remember who you're dealing with: Tao has been invited into frontier AI labs to stress-test their strongest models on mathematics, and he has sat on YouTube walking through how he uses AI to solve problems live. He is more AI-native than most of the people building the models.
And on the same blog, the same day, he posted a second thing: the announcement of an open challenge around a decades-old unsolved problem — the Andrews-Curtis conjecture — which he helps organize, and whose rules explicitly welcome AI tools.
Same man. Same day. An alarm in one post, an invitation to the machines in the other. "Guarding territory" cannot explain that combination. What explains it is a distinction: he is welcoming the tool and rejecting the scoreboard.
The first twenty-five signatories are all Fields Medalists, the list is open for more, and the names include 2026 medalist Deng Yu of China. These are not people whose relevance is fading.
What are famous problems actually for?
Outsiders see the famous unsolved problems as summits. Fermat's Last Theorem, the Riemann Hypothesis, the twin prime conjecture — mountains, and whoever plants the flag first wins. Question closed.
The statement calls them landmarks and lighthouses. That metaphor is the whole argument, so take it slowly. A summit is a destination. A lighthouse is a direction. It stands at the edge of water nobody has crossed, and its entire function is to send ships there — and on the way, the ships build things.
Fermat's Last Theorem took three and a half centuries. Wiles closed it in 1994. But the flag is not what we kept. What we kept is the machinery — entire fields of algebraic number theory developed on the way, still in daily use across mathematics and cryptography. If you only stare at the final proof, you cannot see how far the discipline actually moved. The problem was never the point. The journey was the point, and the journey left infrastructure.
照著燈塔找路，和直接把燈泡擰下來，是兩回事。 Navigating by a lighthouse and unscrewing the bulb are two different things. The bulb gives you light. The lighthouse gives you a coastline.
The ten-million-line proof nobody needed
The clearest explanation I found came not from the twenty-five but from a mathematician in the comments. Take the twin prime conjecture — still unproven, yet everyone in the field believes it true and roughly knows why. Now hand that mathematician a ten-million-line, machine-verified proof of it.
His knowledge increases by approximately zero.
The only new fact is that AI has now proven it. "And then what?" Even with every step machine-verified, a human still has to read it, digest it, understand it — before anyone can build on it. That work does not compress. It is not a receipt you collect; it is the product itself.
We already ran this experiment. In 2002 and 2003, Grigori Perelman posted three brutally terse preprints proving the hundred-year-old Poincaré conjecture — no journal, no polished argument, steps skipped. The answer sat on the public internet, free and correct, for three years while multiple teams of mathematicians filled in every gap, produced hundreds of pages of detailed argument, and ran seminar after seminar. By around 2006 the result finally belonged to mathematics.
Notice what that means: the answer existed in 2003. The understanding arrived in 2006. Only the second one counted, because only understanding can carry the next result. A proof nobody understands does not enter mathematics. It enters the archive.
Students before ideas
The statement's most quietly radical line: the field's most precious resource is "students and ideas" — in that order.
Here is the practice behind that line. Mathematics advisors deliberately assign students problems where the answer is already known — sometimes problems solved and printed in the literature decades ago. The answer was never the assignment. The assignment is the three days stuck at a wall, the wrong turns, the 3am moment when two ideas finally weld together. That is how the tools get learned — under load — and those tools have to carry forty years of research.
AI now places the answer on the table mid-struggle. Students take it. Of course they take it; I would too. Stuck for three days while a correct hint sits one prompt away, and the sensible move is to refuse? No.
The statement does not blame the students. It blames the scoring system. When an entire industry grades AI by how many famous problems it solves, everything downstream optimizes toward the announcement and away from the understanding. Leaderboards can measure fast, correct, comparable. They cannot measure "written so others can follow it," "methods others can reuse," "a student who came out the other side stronger." That is the misalignment: the thing being optimized and the thing that is actually valuable have come apart. Goodhart's law, scaled up from one metric to a civilization's.
Why an AI company should listen
Mercury's founding premise is that the last mile of AI is human — that a huge share of value is lost in the gap between what the machine produces and what the human absorbs. Mathematicians are simply the purest case: their answers take the longest to digest, so they feel the gap first.
But the pattern is not theirs alone. The report nobody reads. The dashboard nobody trusts. The AI analysis the executive cannot defend in front of the board without an interpreter. Output is not understanding — in any industry. As models deliver answers at machine speed, comprehension becomes the bottleneck of every organization that touches them. What we measure for clients is essentially answer yield: how much of what the machine produces converts into human decision and capability. The Fields Medalists have been living at the hard end of that curve all year.
And they close with restraint. They don't accuse anyone of being wrong. They say: what this technology becomes depends on where the people who control it point it — and mathematics is only the first trade where answers started arriving faster than understanding.
What to do about the misalignment
For AI builders: stop benchmarking answers alone. Add the comprehension metrics. Can a competent human verify the output in reasonable time? Did a non-expert learn anything reusable from it? A model that proves what nobody can digest has optimized for a press release.
For leaders: protect apprenticeship on purpose. Keep known-answer problems in the curriculum — the struggle is the content. Grade teams on what they can explain, not what they can prompt.
For anyone procuring AI right now: ask the mathematicians' question before signing. When the machine is right, what does my team actually gain? If the vendor's answer is only "speed," you bought a bulb, not a coastline.
Stop scoring answers. Start scoring understanding.
Twenty-five medalists will not stop the benchmark race — mathematics is too good a gym for machine reasoning, and the labs know it. But they have written the sharpest description yet of the trade the entire economy is about to make. The ships just learned to unscrew lighthouses. Whether anyone still knows the coastline is now a management problem.
Mercury Technology Solutions: Accelerate Digitality.