Knowledge does not need the guild's permission

There is a sentence that deserves to be read slowly: “Mathematicians did not ask for this work to be done”. The mathematicians did not ask for this work to be done. It comes from the communications group of the Association for Human Mathematics, in a statement published as a guest post on Terence Tao's blog. It is worth being precise about authorship before arguing: attributing it personally to Tao would mean starting the controversy by cheating.

The work in question is what OpenAI announced on 6 October 2026: mathematical results obtained using an internal model. Its repository contains 719 manuscripts, organised into 372 families, with varying degrees of verification; approximately 42% of the main results have been formalised in Lean. Presenting that as 719 definitively solved problems would be misleading advertising. There is still work to be done on verification, assessment and understanding. So far, there is no reason to switch off our brains and start applauding.

But let us return to that sentence. Since when must a discovery have been requested before it deserves to be examined? Who represents all mathematicians? And what right does a profession acquire over the questions to which it has devoted its life?

In my view, a fairly serious confusion emerges here between the authority that comes from knowing about something and the power to decide who may attempt it. A mathematician can demonstrate that a proof fails. They can point out that a result was already known or is of little interest. They can refuse to review a flood of documents for free. All of that calls for arguments we can discuss. The absence of a commission from the guild refutes absolutely nothing.

Nor would it be honest to dismiss all the objections as fear of progress. There are concerns that deserve attention: poor references, review costs, unequal access and an education that could deteriorate if people learn to produce answers without understanding them. The advisory group AGMAI has questioned the testing of advanced problems using inaccessible proprietary models. That distinction matters: questioning the conditions of research allows us to discuss who can check the results and under what conditions.

What strikes me as a protectionist response is the leap from those difficulties to calling on mathematicians to stop collaborating with OpenAI, as AHM does. Everyone will choose their own collaborations, of course. But I do not see how a collective withdrawal, accompanied by such an appeal to the guild's commission, solves those problems. We can demand access, traceability and review without turning the boundary of a profession into a customs checkpoint for knowledge.

Let us try taking the argument into an area where its cost becomes more visible. Imagine, purely as a hypothesis, that Claude helps discover a vaccine against a particular type of cancer. Imagine, too, that clinical trials and the corresponding assessments establish its safety and efficacy. Would it be reasonable to reject it because oncologists had not requested that work, or because it changes the prestige and interests of those who were already doing the research?

Requiring those trials would be mandatory. Rejecting the result, once established, to protect a professional position would be outrageous. The analogy has limits: a mathematical proof and a medical treatment are validated in different ways. What it lets us see is the absurdity of making the value of a result depend on prior permission from those who occupy the field.

There is also the public interest. If any of these results were eventually to enable a practical solution that improved people's lives, that would be something to celebrate, even if the credit changed hands. Here, the application is a possibility, not a benefit we can regard as proven. But protecting professional or individual interests at the expense of that potential benefit would mean getting our priorities backwards.

It would be like a man on horseback protesting against the invention of the car because, on four wheels, his skill as a rider no longer stands out. He can warn of accidents, demand brakes or report a defective vehicle. He has reasons to do so. What he cannot reasonably ask is that everyone else stay on horseback to preserve his advantage.

This issue also concerns us lawyers, translators and designers. We should stop talking about artificial intelligence as though it were a personal insult that someone had yet to retract. If a tool allows us to do part of the job better, we will have to learn to use it and check where it stops being useful. Defending our craft means taking that possibility seriously.

A translator can use it to explore alternatives and pay more attention to the register, intention and ambiguities of the original. A designer can try out proposals quickly and subject them to a judgement that an abundance of images does not supply. A lawyer can test a line of reasoning and look for objections, provided they then check the sources and protect the client's information. A mathematician can explore conjectures, look for counterexamples or work with formalised proofs. In all these cases, professional value depends on what one knows how to recognise, correct and justify.

The urgency of learning does not authorise shoddy work either. Copying a fabricated court judgment because it is written with confidence is still negligence. Delivering an incorrect translation faster makes the service worse. And producing pages of symbols that nobody knows how to evaluate does not deserve a medal either. Adopting these tools seriously means establishing controls, measuring results and retaining the ability to disagree with the answer on the screen.

That is precisely why I have little interest in the worship of technology companies. OpenAI will have to substantiate its claims. So will its competitors. The size of a company and the spectacle of an announcement grant no exemption from rigour. We must be able to hold those who develop the systems to account while making use of what works. Handing our judgement over to them would be a particularly lazy way to modernise.

I understand that all of this is uncomfortable. For a long time, mastering certain operations has required years of effort, and seeing them performed in another way can be demoralising. That effort deserves respect. But it does not create a right to have the world preserve intact the difficulties we worked so hard to overcome. Professional standing will also have to be earned by knowing how to work under conditions that are already changing.

Learning now means trying tools on bounded tasks, comparing their performance with our own work and studying their failures. It means reviewing how we teach a profession so that someone can make use of the technology without being left intellectually defenceless when it gets things wrong. There is an enormous amount to do there. Human understanding deserves all that energy; Tao, in fact, has argued for directing AI towards it and towards useful applications.

I would rather see professionals arguing over how these tools are used. Retreating behind guild boundaries strikes me as a poor response. At stake are the quality of the work we offer and our ability to decide how it is done. If we can be better translators, designers, lawyers or mathematicians, we have a very serious reason to learn. And get a fucking move on.