On 21 September, OpenAI announced that an internal model, which it began training on 28 August, had solved more than a hundred open problems in almost every area of mathematics. An open problem is a question the community has been trying to answer for some time without success: some have been waiting for years; others, for decades. The figure came two weeks after the company claimed to have solved Navier–Stokes, one of the seven Millennium Prize Problems, which we covered here.
In the same statement, OpenAI introduced a group of nine mathematicians who will advise it on how to review and disseminate those results. It also explicitly cited the letter in which, days earlier, several of the most recognised figures in the discipline had expressed their concern about the direction AI is taking in mathematics.
The debate is no longer about whether these systems can do mathematics. It is about who decides the pace, what happens to the results nobody has time to study, and what happens to the people who devoted their lives to finding them. In this article we go through the controversy, what each side is asking for and how the community feels. Then we explain our position.
Three weeks that turned a result into a debate about the discipline
The sequence helps explain why the tone hardened so quickly:
| Date | What happened |
|---|---|
| 28 August | OpenAI begins training the internal model it will later present. |
| 8 September | OpenAI publishes its Navier–Stokes solution. |
| 9 and 10 September | Terence Tao asks the community to reject “irresponsible and unsustainable” uses of AI. |
| 11 September | The letter “A Severe Misalignment of AI in Mathematics”, signed by Fields medallists, is published. |
| 17 September | Timothy Gowers explains why he did not sign it. |
| 21 September | OpenAI announces the more than one hundred problems and the AGMAI advisory group. |
| 22 September | Martin Hairer explains why he has joined AGMAI. |
Sources: OpenAI announcements, Terence Tao’s blog and the letter’s website. Links at the end of the article.
The Fields Medal is the most prestigious award for a mathematician under forty, and Terence Tao, one of its holders, is among the best-known working mathematicians outside the discipline. He is no AI sceptic: he has spent years using models and proof assistants in his work and advocates bringing them into research. That is precisely why it carried so much weight when, on 10 September, he wrote that the large AI companies are heading towards ever more powerful and autonomous systems regardless of their real value to society, and that the community had to unite around its values.
The letter appeared the next day. As of 25 September, its page lists the signatures of 27 Fields medallists, including Tao, Pierre Deligne and Manjul Bhargava. According to Hairer, some 8,000 more people have endorsed it.
Above all, the letter asks us not to confuse the test with the goal
Anyone looking for a list of demands in the letter will not find one. It is a declaration of principles, and its central idea fits in a sentence: solving problems is a tool and a proxy for something more important, understanding.
For centuries, someone solving a hard problem was a good sign that they had understood something new. Proof and understanding travelled together because the second was almost the only way to reach the first. The signatories fear that this relationship will break: if a system produces the solution without anyone acquiring the understanding that used to come with it, the discipline could accumulate results and grow poorer at the same time.
From there, the letter points to concrete problems: announcements that arrive without sufficient documentation, methods that are hard to separate from the result, prior work left unacknowledged, and the threat to the chain of training, the process by which a mathematician learns to do research by working alongside another. It asks the mathematical community and the companies to act urgently, and for people to decide how this technology is used so that the work keeps serving its purpose.
The most concrete requests come through other channels:
- Tao asks for work to be properly attributed, for the origin of each idea to be known, and for the community to reject uses that harm the discipline.
- Hairer joins AGMAI to establish better standards for how companies publish their mathematical results, and how they present and attribute them.
- AGMAI has opened a form to gather the community’s views on how to coordinate the release of OpenAI’s results.
OpenAI’s response accepts part of these requests. The group, hosted at the Institute for Advanced Study in Princeton, will advise on how to assess the significance of each result, how to coordinate its dissemination and which academic standards should be respected. It may give advice even when nobody asks for it and publish its recommendations, and its members are unpaid. But the announcement explicitly leaves out what worries the critics most: the group will not advise on the pace of the company’s internal progress. Nor does it have decision-making power over any company.
The community does not only fear losing problems: it fears losing the path to them
The mathematical community has not responded with a single voice. Timothy Gowers, also a Fields medallist, did not sign the letter, although he shares much of its diagnosis and admits the discipline is going through a crisis. His objection is that the letter presents one way of understanding mathematics as the only one. Some people solve problems in order to understand, and some seek understanding in order to solve them. Both traditions have produced valuable mathematics.
What worries Gowers most is motivation. Many young people come to research wanting to solve a famous problem. If a machine solves those problems first, some will leave, and with them the chain of transmission between generations may break. Gowers is less afraid of an excess of results than of the social structures that allow them to be digested disappearing with nothing to replace them.
Martin Hairer is more optimistic. He believes that refusing to take part would let OpenAI portray mathematicians as out-of-touch Luddites. And since the letter called for urgent action, he considers it inconsistent to stay out. He also acknowledges the group’s limits: nine people do not represent the diversity of the discipline, they cannot enforce anything, and their statements could be used to improve the company’s image.
In the comments on the blogs where the debate has unfolded, another fault line appears. These are readers’ opinions, not a survey, but they come up again and again:
- young researchers who feel that their years of training may have lost their value overnight;
- distrust of AGMAI’s independence, especially among those who point to some members’ closeness to OpenAI;
- fear that results will be withheld and circulate only among a few. One reader asked whether we were returning to the days when mathematicians hid their solutions to win duels;
- and the suspicion that the debate is led by award-winning professors whose careers no longer depend on what happens now.
This last criticism applies to the signatories and the advisory group alike. The people with the most at stake in this transition are precisely those with the least voice in both spaces.
Three possible futures that depend on decisions, not on the model
Gowers describes two scenarios, to which we add a third that runs through the whole discussion.
An avalanche of results. Models produce proofs faster than the community can study them. Gowers does not consider this necessarily a catastrophe: we could choose which parts to digest. We already explored this scenario in when proving stops being the bottleneck: the scarce work becomes verifying, explaining and deciding what matters.
A coordinated release. Companies, institutions and mathematicians agree on how to publish results, with what information and at what pace. That is what AGMAI is attempting on a small scale. Its limit is obvious: pace, the most contested issue, has been left out of its remit.
A discipline that produces more and trains less. Results keep arriving, but universities, journals and funders keep rewarding almost nothing but being first to prove. Explanation, review and teaching remain unrecognised work, and fewer and fewer young people find reasons to devote themselves to it.
None of the three is settled. The coming months will give clear signals: whether AGMAI publishes recommendations and OpenAI applies them or explains why not; whether results arrive with enough documentation for others to check them; and whether any institution begins to value explanation and review as research work.
What we think at Codin: a result is not delivered until others can use it
We do not share the view that speed itself is the problem, nor do we believe the answer should be to slow down or withhold results. Hiding knowledge to protect a professional hierarchy would be hard to defend. Solving an open problem has value, and a proof being hard to understand does not make it sterile. On this we are closer to Gowers than to the letter: there are many legitimate ways of doing mathematics, and a tool that solves problems can expand what the community is able to study.
Nor are we convinced by the opposite position, that publishing the result is enough and the rest is someone else’s problem. That is where we see the core of the controversy: an asymmetry. The company sets the pace and receives public recognition for the discovery. The work of checking, understanding, explaining and teaching it falls on a community that did not choose that pace and whose incentive system barely recognises that work. An advisory group with no say over the pace can improve how results are presented, but it does not correct that asymmetry.
We see this clearly because it is a problem we know from our own trade. In software, delivering code that works is not enough: if the team that has to maintain it does not understand it, they cannot operate it or evolve it. That is why, at Codin, we consider a piece of work unfinished until it has been documented and handed over. AI makes that difference more visible, because producing has become much cheaper than understanding.
Applied to mathematics, we propose assessing each result with three questions:
| Question | What is needed to answer it |
|---|---|
| What exactly has been proved? | A precise statement, with its assumptions and limits. |
| Why should we accept it? | An argument others can check and a review of what is actually being claimed. |
| What can others do with it? | Explanations, acknowledgement of prior work and materials for further research. |
Framework proposed by Codin. An announcement may answer the first question well and leave the other two pending.
Three concrete demands follow. Whoever announces a hundred advances should accompany each one with enough information to answer those questions. Whoever gains value from announcing them should help fund the work of turning them into shared knowledge. And academic institutions should begin to recognise explanation, review and teaching as part of research, not as secondary tasks.
The question we find useful when the next announcement arrives is what people outside the company can now study, check and use, rather than how many problems have been solved. An advance that only its producer can verify has not yet fully reached the discipline.
Sources
- OpenAI: announcement of the more than one hundred problems and the advisory group, 21 September 2026.
- AGMAI: purpose, members and scope of the group and its announcement on Terence Tao’s blog, 21 September, with the reader comments cited.
- A Severe Misalignment of AI in Mathematics, 11 September 2026. Signatories checked on 25 September.
- Terence Tao: comments of 9 and 10 September.
- Timothy Gowers: Why I didn’t sign the Fields medallists’ letter, 17 September, and its comments.
- Martin Hairer: Why I agreed to join AGMAI, 22 September.
- TechCrunch: OpenAI forms math advisory group, 21 September. Date of the Navier–Stokes publication.
Editorial note: the last section sets out Codin’s opinion. We have not audited any of the results announced by OpenAI.
