This note is based on the assumption that the adoption of AI in mathematics is already inevitable. To paraphrase the principle of Chekhov’s gun, if we strive to resolve a conjecture while inhabiting a world that contains a button that, if pressed, will promptly resolve said conjecture, someone will indeed press the button. Maybe AI will become unaffordable for mathematics, but I do not see this happening very soon. This is not to say I do not find the rapid development of AI that we are witnessing deeply unsettlingquite the contrary. I simply believe that we will need to grapple with it one way or another.
With that in mind, let me outline a few problems that I believe we need to tackle together.
The spectre of nihilism, or the crisis of the human contribution
Until recently, we had some shared understanding of what counted as a valuable human contribution in mathematics, if only because, with the exception of a few automated proofs, mathematics was a purely human enterprise that took place for the most part in our minds. We might have disagreed on the details, but few would have denied that settling a conjecture, developing a new theory or discovering a connection had shaped much of our intellectual efforts. It is therefore not surprising that, now that AI can make significant progress on all these fronts at surprising speed, our faith in what makes a human contribution to mathematics valuable is called into question. This is no minor problem, as any significant human enterprise requires deep commitment, determination, and sacrifice, all of which are difficult to sustain unless we truly believe in the value of what we are pursuing.
I am writing about this because I could not help noticing that AI-generated proofs of long-standing conjectures do not seem to elicit strong emotions in many of us (not uplifting ones, at least). In the worst case, we may even learn that a problem we found interesting was resolved by AI, feel no excitement at the news and, at the same time, feel thatas a communitywe were deprived of something fundamental, namely, the possibility of discovery. If this becomes the norm, we may simply lose interest in our work as prompting becomes a simulacrum of what mathematical creativity used to be. In this case, we may slowly but steadily surrender to the conclusion that no valuable human contribution to mathematics is possible anymore in a sort of nihilistic doom for the discipline.
This need not happen, and I believe there is still a lot of room for valuable human contributions to mathematics, including (at the time of writing) the following:
- Community interaction: seminars, conferences, discussions, collaborations.
- Exploratory projects that cannot be pursued through prompting alone (as opposed to “yes or no” questions).
- Comprehension and carefully crafted explanations of deep phenomena.
- Investigation of problems beyond the range of frontier AI models.
Prompt or Perish, or a race to be the first to do what exactly?
As demonstrated recently, a few dollars can buy you the solution to a famous conjecture. Maybe that is not true yet for a problem in the league of Navier-Stokes, but one generic prompt may still settle a problem that was a highly regarded within a field. We need to reckon with this as a community and act accordingly.
Traditional mathematics was based on the competitive assumption that whoever proves a conjecture first takes all the glory. There were plenty of reasons already to question the fairness of this criterion, as Perelman famously observed. However, today this practice stands as the relic of an old ethos which has lost its meaning: when a proof can be obtained by simply pressing a button, being the first to obtain it is no evidence of a distinctive intellectual contribution. Are we still going to praise that? I hope not: if there is a single thing that is clear to me in these confusing times, it is that we should abolish “priority of proof” (from now on simply “priority”) as an independent source of merit.
A failure to come to terms with this reality would be detrimental to our community, for in that case there would be strong incentives (even existential ones for young researchers) to race and be the first to prompt AI about any possible problem. This is no exaggeration and in some form it is already happening. Again, although prompting conjectures is not my cup of tea, I welcome the fact that some are doing so and made clear that this issue should be addressed swiftly by our community.
If we do not let priority go, I am afraid that “Prompt or Perish” risks becoming the norm. We will then be overwhelmed by an avalanche of poorly written papers, many of which will not be read, maybe not even by their authors (though they may claim verification in Lean).
But even if we are lucky and our discipline is able to adapt, racing to prompt as fast as we can stands in stark contrast with the emerging consensus that careful explanations will play a fundamental role in the new mathematics: as we all know, good writing takes a lot of time, a resource that will be scarce in a world in which we constantly worry that someone might be prompting on the same topic. Incidentally, if not contained by the demise of priority, this worry also has the potential to turn mathematics into a rather secretive activity: after all, who would be so naive as to present a partial result or an intriguing route to the solution of an open problem at a seminar or a conference, if someone else may learn about it, fill in the gaps with the aid of AI, and get away with the credit?
At this stage, it is tempting to contemplate the possibility that the prize for priority might still make sense for problems beyond the range of frontier AI models. Leaving aside the fact that the latter concept is very volatile (as we have witnessed over the past year), it is worth observing that these harder problems are not immune from the demise of priority as a meaningful metric.
As made apparent by the Navier-Stokes controversy, it is not clear whether an AI model may return an answer that is tacitly informed by the prompts of other mathematicians. After proving a result with the aid of AI, we may become aware that another group of people was working on the same topic and speculate on how to interpret this news. However, the model might also have learnt from a group of people working on an apparently different problem. In this case, we will have no means of learning about their contribution. In other words, Perelman was able to recognize the fundamental role of Hamilton in the solution of the Poincaré conjecture because, in the past, there was a clear (though maybe tortuous) way to track the history of a problem. But today tracking the prompts that may have informed the reply provided by a model is impossible, another indication that priority is turning into a paper crown.
AI disclosures, or the road to hell is paved with good intentions
When we reflect on the current crisis in mathematics, a nostalgic solution often comes to mind: maybe human proofs should be valued differently than AI-generated ones. There are plenty of reasons to believe so: after all, aren’t the former evidence of creativity, knowledge, and scholarship, while the latter might have been obtained by a rather naive prompt? These considerations led to the introduction of current AI disclosures, which allow authors to describe the use of AI in their work. In other words, if we could judge the extent to which our papers were produced with the help of AI and state this clearly in an honest disclosure, we would have effectively unscrambled our egg, and the challenges that AI poses to mathematical practice (such as the demise of priority) might be kept under control.
While I share the emotional attachment to human proofs, I believe that this hope flies in the face of the hard reality that there is no way to distinguish between human and AI-generated proofs, at least when presented by capable mathematicians. This brings us to the main problem: AI disclosures are strikingly unverifiable claims. In other words, if we follow the path of attaching greater value to human proofs and adopt AI disclosures as the gatekeepers of superior human achievement, we will create a system in which the value of a paper is based on a few unverifiable statements that we are expected to believe blindly. In a competitive ecosystem such as the academic one, this looks like the perfect recipe for nurturing distrust among colleagues, rather than a way to restore a lost order.
We may, of course, keep our heads down and press on with AI declarations as a meaningful source of information about the human contribution. As in the case of priority, there will then be great pressure to lie about the use of AI and embellish one’s contribution (was it 40% human and 60% AI or the other way round? What does this even mean?). The high price of writing candid declarations will be unaffordable for many young researchers, paving the way for a culture of concealment. Such a system will be detrimental to our community, spark doubts about one another’s credibility and, above all, be terribly ineffective in achieving its stated purpose: distinguishing between more and less valuable contributions to mathematics.
Instead of clinging to unverifiable claims, I believe we should simply reckon with the fact that there is no systematic way to distinguish between human and AI-generated proofs, which means that otherwise comparable contributions should receive the same professional recognition, regardless of whether they were produced with AI assistance (professional reward should not depend on claims that cannot be assessed reliably, especially when that dependence rewards concealment). This does not mean that AI disclosures should go completely. On the contrary, they will be very useful when they provide, for instance, a description of a clever new way in which AI was employed to overcome an obstacle. We should simply resist the temptation to adopt them as a means to distinguish between human and AI-generated proofs.
Lastly, while it is perfectly understandable that some may be less inclined than others to adopt AI in their work, offering an institutional reward for abstaining from AI in a discipline in which this technology is performing incredibly well does not seem to be a wise choice (plus, the lack of a sensible way to “police” the use of AI makes such an enterprise rather futile from the start). Is it really worth spending hours and hours on some finite combinatorial obstacle with no independent interest that could be resolved swiftly by AI for the sake of keeping our research untainted by the sin of prompting? I am not sure. I believe that everyone should be free to decide what best suits their research. Some might abstain from AI completely, others intermittently, and others will turn it into a fundamental part of their research. In a world in which priority is not crucial anymore, there might be room for all tastes.
Hic sunt leones, or navigating without a compass
If neither priority alone nor AI disclosures can provide a reliable basis for assigning credit in mathematics, we are in uncharted territory, as our competitive system requires us to assign credit to scholars in one way or another. Given the pace at which AI models are advancing, one may sense that any practical recommendation may become obsolete in a matter of months. However, if you have been patient enough to follow me this far, I owe you a few concrete proposals. Some of these will already be familiar to those who have engaged in the discussion on AI in mathematics.
Perhaps the most pressing practical problem is that of hiring, which understandably worries many young researchers. A way of evaluating researchers consistent with the demise of priority and the difficulty of verifying claims that proofs were produced without AI would be to reduce the weight given to publication counts and priority and instead focus on the candidates’ ability to explain advanced mathematics clearly, draw connections with neighbouring areas, and discuss sensible directions for the future both in general terms and in great detail. Consequently, seminars and interviews with various members of a department or research group should become a core aspect of any hiring procedure and receive greater weight. The old-fashioned recommendation letter can also be rescued as a meaningful source of information if we abandon the widespread exaggeration of candidates’ abilities and strive for honest, informative assessments instead (plus, some of the content of the letters can be corroborated in interviews and seminars). There are certainly other contributions that can merit recognition, such as participation in a significant research programme, but a detailed list will have to wait until we adjust to the presence of AI in our scientific ecosystem.
The elephant in the room is, of course, that such a change in hiring culture is possible only if we also replace the current “publish or perish” system with one in which priority is less central by design. I suspect that we might soon have a clearer picture of what such a new order will be. However, a road map for the interregnum in which we happen to live would be as follows. First, we identify some interesting exploratory programmes in each area.1 Then we send a message to those we believe may be willing to join the project and ask them to express their interest if they have the time and ability to contribute to the research. We then organize our work as a group and carry out the research under the direction of a few more experienced researchers.
The aim of this deliberate shift from collaborations among a small number of people to work within larger groups would be to make priority, AI disclosures, and competition less central to the discipline in the immediate future. Larger collaborations may also work well in a culture which attaches greater importance to observable contributions and recommendation letters. Lastly, such a shift will strengthen the sense of community, which is probably the aspect of current mathematics we most want to preserve.
- “Yes or no” questions may work equally well, if the road to their solution is amenable to teamwork. ↩︎
Received 21 September 2026.
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