What a signature is worth

A mathematical problem should not have to wait for its author. If we can solve it today, with the means at our disposal, it would be strange to prefer that it remain open so that someone has time to attach their name to it. Yet this is the question the Navier–Stokes affair leaves me with: what are we trying to preserve when discovery comes sooner than expected?

In early September, OpenAI announced a solution to the problem, in a formulation involving an external force. The company says it deployed around ten thousand agents for eighty-eight hours before obtaining its result. Two mathematicians, Tristan Buckmaster and Levent Alpöge, were working on related problems, notably the Euler equations. They too were using AI. A controversy arose over the competition between these projects, how credit should be assigned and whether unpublished data had been used. OpenAI denies such use. It has not been established.

The validity of the result requires mathematical scrutiny. The question this affair raises for us can already be asked. If the proof holds, if it can be checked, understood and passed on, we know something we did not know before. That is what research is supposed to produce. The conditions under which it does so have just changed abruptly.

I understand what such an announcement might mean to someone who has spent years working on a subject. There are the abandoned approaches, the months without progress, the funding to secure, the conviction that one is onto something. Being overtaken can hurt. But the time devoted to a question does not confer a right to its answer. It brings experience, sometimes exceptional understanding, and contributions that deserve recognition. It does not reserve the final line.

A signature has its place in all this. It identifies those who contributed something, those who can explain it and take responsibility for it. It also provides the means to pursue a career. So I am not asking researchers to become indifferent to recognition. I am asking what happens when recognition becomes so closely tied to finishing first that faster progress in knowledge begins to look like a threat.

Buckmaster himself acknowledges that a genuine advance by OpenAI would be remarkable. He asks that the history of the contributions be respected and that the proofs be made intelligible. That is a sound requirement. A proof that no one can understand remains difficult to build on. Scientific work continues after the result is obtained: its ideas must be brought out, the conditions under which they hold understood, and their uses elsewhere explored.

We therefore need to reconsider what we reward. Choosing a good question, developing a method, making an argument understandable or enabling others to build on it should count in a career. We cannot celebrate science as a collective endeavour while judging those who practise it solely by their position in the finish-line photograph.

When it comes to governance, however, I find the naivety troubling. It lies in believing that the tool's provider will remain in the role we have mentally assigned to it. We buy a service and imagine that the provider will be content to supply it. Yet that provider has its own teams, research objectives, competitors and commercial interests. It can help you in the morning and work on the same problem in the afternoon. Its ability to do so should be part of the calculation from the outset.

This obviously does not entitle it to make improper use of confidential work. Power does not exempt anyone from their obligations. But it changes the relationship one is entering. Entrusting an essential part of one's work to an industrial player requires understanding what it can see, what it can do and what one will be able to verify. Enthusiasm for the tool's performance settles none of these questions.

In this case, the two researchers describe a personal collaboration, with no institutional agreement between their employers. That does not mean that no protections applied to the tools they used. It does, however, reveal the possible gap between the ambition of a research project and the arrangements supporting it. A team may aim for a major advance with arrangements that seem adequate as long as no one else takes an interest in the race.

Universities and funders have work to do here. The conditions for access to data, the preservation of records, the attribution of contributions and the handling of disagreements need to be considered before the discovery. It must also be possible to have a concern examined by someone who is not a party to the dispute. A company may be acting entirely in good faith; its assurance alone is not a system of oversight.

Even well-managed confidentiality does not resolve everything. By its own account, OpenAI launched its effort after hearing a rumour of a scientific breakthrough. Knowing that an approach is becoming promising may be enough to trigger a decision to devote considerable resources to it. A researcher is then no longer competing only with other researchers. They face an organisation capable of rapidly concentrating resources to which they have no access.

I see no reason to look down on those resources because they produce the result faster. Computing power can be fruitful. A proof obtained with substantial resources is not inherently less interesting. The question is how this capability can become useful beyond a handful of announcements, for many teams and for subjects whose importance cannot be measured by the attention they attract.

This is where public funding and cooperation between institutions matter. If we want research to pursue questions that are useful, difficult or still overlooked, we must give those who pursue them the means to work. We cannot allow the choice of problems to depend entirely on what a company wishes to demonstrate about its own model.

Seen from Valais, this shift concerns us too. A small team can now access capabilities that were previously beyond its reach. That is a possibility I believe in. It requires knowing what we retain: our results, our methods, our ability to change tools and our freedom to choose what comes next. A team that works faster but can no longer decide the conditions under which it works has gained on one front and ceded ground on another.

The purpose of research remains to advance our understanding of the world. A signature should recognise those who contribute to it and give them the means to continue. When tools change at this speed, researchers need institutions that support them and a clearer understanding of their partners.

I want science to advance faster. I also want enough researchers to remain free to decide where to look.