Note from P&P: On 11 September 2026, 25 Fields Medallists co-authored the declaration “A Severe Misalignment of AI in Mathematics“, which at the time of posting has over 7000 signatures. Below are are two separate and independent submissions we received, respectively, on 15 and 16 September 2026, responding to this declaration. The first one is crossposted from X.
For futher reading, here is another response by Tim Gowers.
The Fields medalists’ objections to AI will not age well.
Yes, the true value of mathematics lies in understanding. But what counts as mathematical understanding, and indeed even a valid proof, evolves. First came geometric construction and thereafter symbolic calculation, numerical algorithms, computer-assisted proofs, and, in cases such as the classification of finite simple groups, arguments dispersed across thousands of pages and decades of work that exceed what any individual mathematician can fully absorb.
Frontier AI systems will be another chapter in this progression.
It may take a village of mathematicians to interpret and understand the mathematical artifacts produced by an AI system, just as with humanly produced ones. But that is not necessarily a bug. It may instead be a useful feature that forces mathematicians to confront more directly what is actually worth understanding.
Even here there is creative license, since understanding is not canonical but relative. Mathematicians stand on the shoulders of those who came before them, routinely invoking theorems they haven’t fully digested. Ultimately, expertise is not exhaustive; it is selective. So that building upon formally verified machine-generated proofs is an expansion of the mathematical toolkit, not a diminishment of it.
Understanding is also, in some sense, a luxury. The natural world is full of objects, structures, and phenomena we don’t fully understand. To the extent that mathematics has value in discovering what is true independently of our ability to understand it, those of us who are Platonically inclined should welcome AI’s capacity to generate and confirm mathematical truths that we find useful.
There will obviously be social consequences with powerful AI. It disrupts the traditional value system that awards prizes and prestige to the first to solve a “difficult” problem. But history is full of once-valuable skills made obsolete by technological progress.
Determining exact time and longitude had been a major scientific and navigational challenge, attracting enormous intellectual effort and institutional rewards. But today, atomic clocks and GPS allow us to measure time and location with extraordinary precision and no expertise. And we do not mourn the convenience that modern technology affords us.
Likewise, if some of the most celebrated problems in mathematics turn out not to be especially difficult in the age of AI, that should not be viewed as a loss. It would itself be a discovery: that what we regarded as requiring exceptional human ingenuity to overcome can, in fact, be solved by machines equipped with enough compute.
The appropriate response is not nostalgia for approaching problems with our unassisted minds, but curiosity about what lies beyond and a willingness to set our sights on new horizons.
On 11 September 2026, twenty-five Fields Medalists published a declaration entitled “A Severe Misalignment of AI in Mathematics”. Within five days, it had attracted thousands of endorsements from mathematicians. By 16 September, the declaration’s website listed more than 7,200 signatories.
The thesis of the declaration is that the goals of AI companies and those of the mathematical community are “severely misaligned.” Mathematics is not fundamentally about producing an ever-growing collection of correct answers. Its purpose is understanding and transmitting this understanding to future generations. If AI companies keep racing to solve open problems, they may undermine the ecosystem from which these problems emerged. The declaration also raises serious questions about attribution, plagiarism, rushed announcements and the possibility that AI-generated mathematics will appear faster than humans can properly understand and check it.
I came away from the declaration completely dissatisfied. The problem is not so much about what it says as what it fails to say. I will argue this in the following three points.
1. The declaration argues that the aims of the AI companies are misaligned with the aims of the mathematical community.
1.1. What can one say to this statement other than “Well, of course”? OpenAI, Anthropic and Google are giant corporations that are not governed by our norms. They have commercial objectives. There was never any particular reason to expect the objectives of a corporation to align with our purposes.
1.2. This is striking given that several prominent mathematicians, most notably Terence Tao, have spent the last few years encouraging us to engage with AI. Tao has spoken publicly about AI as a research assistant. He participated in an OpenAI event on the future of mathematics and AI. Quanta magazine named him “The evangelist for AI in mathematics”.
1.3. The upshot is this: “The companies have different goals from us” is not a serious analysis and it makes the mathematical community look incredibly naïve when its most accomplished members make declarations which complains about why companies don’t care about us.
2. The second major claim of the declaration is that mathematics is about understanding rather than results.
2.1. I completely agree. We have all experienced the difference between knowing that a theorem is true and understanding why it is true. The best papers are the ones that accomplish both the truth of a statement and teaches us new perspectives on why the statement is true.
2.2. But there are two problems with using this distinction as the central criticism of AI mathematics. Our institutions have always systematically rewarded the production of papers. We heard the motto “publish-or-perish” long before we start our academic career. Postdocs are evaluated by publication lists. Departments count papers and citations. Journals compete for results.
2.3. If we now agree that maximizing the number of proved statements is a poor standard for mathematical value, this is very good. But then perhaps the arrival of AI should lead us to examine the incentives we ourselves created. It would be strange to spend decades constructing institutions that reward output and then blame machines for becoming extraordinarily efficient at producing it.
2.4. This seems to be precisely the point where the declaration fails to provide. When twenty-five Fields medalists come together to put a declaration, this would be a great chance to push the community and its institutions towards a necessary change in our values and our reward systems. It seems like this chance is wasted.
2.5. The second problem is deeper. Why should we assume that AI will become extremely good at proving theorems while remaining fundamentally incapable of explaining them? There is an implicit picture behind some of the discussion: humans possess understanding, whereas machines produce answers. I do not think this distinction can simply be assumed.
2.6. Already, one of the most useful things LLM’s do is exposition. They generate examples, compare proofs, do literature search and patiently unpack the steps of a proof. They often make mistakes. But so do they when proving theorems, and nevertheless their theorem-proving abilities have improved dramatically. Are we really sure that their expositional capabilities will not improve over the next few months?
2.7. Dijkstra famously said “The questions of whether machines think is as relevant as the question of whether submarines can swim”. It feels like we find ourselves having arguments over whether a machine “really understands” a proof whose explanation is clearer than ours.
3. The third claim of the declaration is that the mathematical community urgently needs to address these problems.
3.1. Yes. But who is “the mathematical community”?
3.2. This sentence bothered me more than it probably should. The original signatories are twenty-five Fields Medalists. They include some of the most respected and institutionally influential mathematicians. These are not powerless observers, but the people who are in position to influence the norms and values of the community.
3.3. When people with influence say that “the community should act,” it sounds passive. It resembles the familiar sentence from a politician: “We must do something.” But the people signing the declaration are well positioned to begin doing it. The declaration should have been the beginning of this action.
3.4. I believe that the community leaders should urgently propose standards for papers and publications, help establish the new norms for publications and journals, and push universities and funding agencies to reconsider evaluation systems built around publication and reference counts.
3.5. If mathematics is genuinely about understanding rather than output, then this principle should appear not merely in declarations about AI but in hiring criteria, the evaluation process and journal practices. It is imperative to start changing the system now.
3.6. The people with perhaps the greatest stake in these changes are PhD students and postdocs. Yet, we have remarkably little influence over the institutions around us.
I am not worried about what happens to mathematics in the age of AI. I believe it will flourish more than ever.
I am worried about what happens to the mathematicians.
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