The Flood Is Not the Crisis

Key Takeaways

• On 11 September 2026, 25 Fields medallists published “A Severe Misalignment of AI in Mathematics”. Its central claim: solving problems is only a proxy for understanding, and mass-producing solutions could destroy the ground that understanding grows in.
• On 17 September, Timothy Gowers explained why he did not sign. He agrees that learning happens in the attempt. He disagrees about what the crisis is.
• The letter fears a flood of answers. Gowers fears a drought of reasons to try. He thinks the flood is coming regardless, and that the only thing worth protecting is the pipeline of people who still want to struggle.
• Terence Tao signed the letter and then cross-posted Gowers’s dissent on his own blog. That is the more interesting fact about this disagreement.
• The argument is not about mathematics. It is about whether anyone learns from an answer they did not want.

On 8 September 2026, OpenAI announced that an internal system had produced a proof, and a Lean formalization, that a smooth fluid at rest under a smooth external force can develop a singularity in finite time. That resolves the Navier-Stokes existence and smoothness problem, one of the seven Millennium Prize Problems, in the negative. By OpenAI’s own account the run involved on the order of 10,000 concurrent agents, took about 88 hours, and consumed roughly 130 billion output tokens. The company said it does not intend to claim the prize. The Clay Mathematics Institute, which set the problem in 2000, said on 11 September that it “has apparently been settled.”

The same day, 25 Fields medallists published a declaration titled “A Severe Misalignment of AI in Mathematics”. Six days later, Timothy Gowers, who won the medal in 1998, explained why he had not signed it. His post was cross-posted to the blog of Terence Tao, who had.

That last detail is the one to hold on to. This is not a fight between the pro-AI camp and the anti-AI camp. It is a disagreement between people who agree on almost everything, about what exactly is at risk.

What the letter says

The declaration is short. Its argument runs like this. Research mathematics has, over generations, built up “a large corpus of sophisticated ideas, methods, abstractions, and other tools.” Famous problems act as “landmarks and lighthouses.” Solving one “has been a certain sign of new insights and interesting methods, which would then be studied by a community of mathematicians, through a long and arduous process of talks, discussions, simplifications.” At the end of the process, ideally, there is a textbook.

Then the sentence Gowers singled out as the principal claim:

But solving problems is only a tool and proxy for achieving the primary goal of conceptual understanding and insight. Forgetting this in the world of AI may turn the tool against the primary goal. Indeed, the mass production at faster and faster pace of “true/false” statements could destroy fertile ground instead of breathing life into new ideas.

The letter goes on: solutions are “announced in a rush, leaving no time for a proper writeup, the isolation of new methods and ideas, and citing relevant previous work of others.” Without “the willing mathematicians who must take care of their development and integration into the mathematical canon, AI-conceived ideas would never become fully alive and the crucial human transmission chain between mathematicians would be lost.”

The signatories are careful to say this is not only about them. “In many fields and activities, years of training have traditionally served not only to produce a final answer or product, but also to develop understanding and the ability to formulate new questions and ideas.” AI is now producing the final answer directly, and “these goals cease to align.”

If you have read anything else on this site, you will recognise the shape of that claim. It is the reason this site exists. The answer was never the point; the thinking was. Here it is, signed by Deligne, Scholze, Tao, Villani, Viazovska and twenty others.

What Gowers says instead

Gowers opens with a story about being eleven and trying to prove Fermat’s Last Theorem. He failed, obviously. But he discovered difference sequences on his own, and when he was eventually taught them, he understood them far better than he otherwise would have. He tells the story, he says, “as an illustration of the phenomenon that was strongly emphasized in this letter,” that “one learns a lot from thinking about a problem, regardless of whether one solves it.”

So he agrees with the premise. He also agrees there is a crisis. He signed nothing because he wants “to offer a slightly different analysis of what that crisis is.”

His reasons come in four parts.

The letter picks a side in an old argument. A quarter of a century ago Gowers wrote an essay called “The Two Cultures of Mathematics,” describing a spectrum: at one end, mathematicians who mainly want to solve problems and see understanding as a means to that; at the other, mathematicians who mainly want understanding and see problems as a means to that. The letter’s sentence about problem-solving being “only a tool and proxy” declares one end of the spectrum correct. Gowers, who lives at the other end, does not want “to suggest to a large fraction of mathematicians, including myself, that their mathematical temperament is somehow ‘wrong’.”

A flood is not the same as a drought. The letter’s core fear, as he reads it, is that if results arrive too fast, “the digestion process will become impossible.” He does not buy it. What AI produces is not bare true/false statements; the Navier-Stokes result came with a proof that “builds on a great deal of wonderful work done by human mathematicians.” Mathematics is specialised, so digestion runs in parallel: a thousand results a year spread across the field means roughly thirty per subcommunity, “a big task, but not necessarily an impossible one.” And even if the volume exceeds what can be digested, that is not obviously worse than the alternative. His analogy is streaming services: more good content than anyone can watch is not a worse world than less content, all of it watched. “While a flood of ‘big’ AI results would be likely to increase the amount of important mathematics that was not properly digested, it would also be likely to increase the amount that was properly digested, which seems like a pretty good bargain.”

The credit problem is real and temporary. He agrees that AI-produced work is failing to cite the humans it builds on, and that this matters now because careers depend on it. But he expects “the whole ‘credit system’ will surely collapse,” because finding a proof will soon be no more of an achievement than a citizen scientist spotting a comet. He is also puzzled the problem exists at all, since asking a model which ideas in a proof already appear in the literature is a task it should be very good at. His suspicion is that people were simply in a hurry.

He is not sure what the letter is asking for. Models that solve major problems will be released “in a matter of not very many months,” whatever mathematicians think. Once they are, the flood comes from everyone, not from AI companies. Criticising the companies for producing solutions too quickly might bring forward by a couple of months what was going to happen anyway. “Under the circumstances, I think the best we can do is recognise the changes that are coming and try to work out the least unsatisfactory way of dealing with them.”

Where he thinks the danger actually is

None of that is the part of the post that matters. The part that matters is where Gowers says what he is actually afraid of.

My worry then is that we do not manage to transmit what we know to a new generation of mathematicians.

He is candid about why. His own motivation for becoming a mathematician “was the dream that I would solve unsolved problems,” and the more famous the better. He preferred thinking about a problem directly to reading other people’s work. “If the dream of solving a famous problem had not existed, I’m not sure whether I would have become a mathematician.”

So the primary risk, as he sees it, “is that a lot of people who would have done a PhD in mathematics and gone on to become custodians of the mathematical tradition will no longer wish to do so.” Alongside it, a second risk: policy-makers concluding that mathematicians are no longer needed, and the funding going with them.

Read the two documents side by side and the disagreement sharpens. The letter is worried about the supply of answers: too many, too fast, too poorly written up, badly cited, never absorbed. Gowers is worried about the demand for questions: whether, once the answers are free, anyone will still want to spend years not getting one.

Which crisis is the real one

I think Gowers has the better diagnosis, and I think the letter’s own premise is why.

If it is true that “one learns a lot from thinking about a problem, regardless of whether one solves it,” then the learning does not depend on the problem being open. It depends on the person not knowing the answer and wanting to. Gowers at eleven was not slowed down by the fact that Euler had already handled the cubic case two centuries earlier; he did not know, and the not-knowing did the work. A flood of AI results cannot take that away from anyone, because a flood of human results never did. There has always been vastly more proved mathematics than any one person could absorb, and people kept learning by attempting anyway.

What a flood can take away is the reason to begin. Gowers’s satnav analogy is exactly right and slightly understated. Nobody lost the ability to read a map when satnavs arrived. What people lost was any occasion to. The skill did not atrophy from prohibition; it atrophied from irrelevance. You can still refuse to use the satnav, and almost nobody does.

That is the honest version of the crisis, and it is not one that a letter to AI companies can address. You cannot legislate an attempt. You cannot ask a company to withhold answers so that a graduate student in 2031 will have the experience of struggling. The letter’s demand, to the extent it has one, is that the flood be slowed. Gowers’s point is that even if it could be, slowing the flood would not restore the reason to swim.

There is a version of this that sounds like defeatism, and it is worth saying why it is not. Gowers ends with a task, not a shrug: those who supervise PhD students “need to try as hard as we can to come up with imaginative ways for them to use their time productively.” That is a harder assignment than signing a declaration. It asks mathematicians to figure out what a mathematical education is for when its traditional goal, contributing a new proof, is no longer the scarce thing. The letter says the human transmission chain must not be lost. Gowers says: then somebody has to build a new reason to be a link in it.

What Tao did

Terence Tao signed the letter. He then gave Gowers’s disagreement with it a home on his own blog. I do not know his reasons and will not guess at them. But the act itself is a small demonstration of the thing both documents are trying to protect: a community that argues in public, carefully, with people it respects, about what it is for.

That is what the letter calls the transmission chain. It is also what this site has been calling thinking. The Navier-Stokes proof took 10,000 agents 88 hours. The argument about what it means took two mathematicians six days, and it is not finished. That second timescale is the one worth defending, and it will not be defended by asking anyone to slow down. It will be defended by people who still want the argument.

Gowers’s post, the declaration, the OpenAI announcement and the Clay Institute statement are all linked above. Nothing here is quoted from memory.