At the moment, the mathematics community is facing an unprecedented misalignment brought on by the advent of LLMs. According to the standard telling, the basic tension is between our traditional values (whatever those may be) and those of the corporations that make and market LLMs. The purpose of this brief essay is to point out that some (arguably many) examples of that claimed misalignment boil down to a preexisting mismatch between the values we profess and the incentive structure that we have set up. We are therefore blaming AI companies for something which is our responsibility to fix.
A good illustration comes from a recent petition. The exact content of that petition is unimportant for the present discussion. I want to focus on a single line:
Human mathematicians who are simultaneously proving the same results [as an LLM] may be forced to abruptly abort these research projects, regardless of the additional insights their unique approaches may bring.
Q. Forced by whom?
Of our ostensible traditional values, the most important is supposed to be understanding. Numerous pronouncements have been made that this thing is the true goal of mathematical labor. Moreover, problem solving and the production of novel theorems are necessary but not sufficient steps in this direction. This becomes a criticism of LLMs and the conduct of their makers when it is implied that, by prioritizing answer-generation, they ultimately hurt mathematical understanding. To me, this feels like a case of the pot calling the kettle black. To what extent is our current system really set up to maximize the production of understanding?
Partially, of course. But we cannot reward understanding directly, so instead we reward measurable proxies thereof and incentivize their production. For various reasons, the main proxy has become the research paper, published with the imprimatur of some prestigious journal. Some reasons are good: e.g. the need for an objective metric on which hiring committees can base their decisions.1 Some are not: e.g. the prejudicial view (famously expressed by Hardy) that the expository arts are for “second-rate minds.” The question becomes the extent to which our preferred proxies measure the thing they are supposed to, and that is open for debate.
I believe that most of the misalignment mentioned above has to do with LLMs exposing and widening that gap. Consider the example above, and the question raised. Suppose a human say Buckmaster, Córdoba, or Martínez-Zoroa is carrying out a unique research program along a unique line, via an approach that is expected to bring additional insights. Why should the fact that an LLM had previously proven a big theorem in the domain force them to “abruptly abort” their work? AI companies possess no formal authority to decide what mathematicians spend their time on, nor do they have that inclination. The subtext in the open letter seems to be that, without the carrot-on-a-stick of priority to claim, there will be little incentive for mathematicians to carry on. But if their work really stands to deliver understanding, then our incentives have failed to incentivize the right thing.
Ultimately, it is mathematicians who decide what mathematical activity is worthwhile. Buckmaster and Córdoba both have tenure. Martínez-Zoroa is on tenure track. They are free to work on what they please and we, as mathematicians, are free to reward them for doing so. Mathematicians decide what sort of papers appear in top journals, what sort of work garners prizes, and ultimately who is hired. If OpenAI solving the NavierStokes millennium problem (or prematurely finishing someone else’s research program) decreases our understanding, that reflects a failing on our part, irrespective of any wrongdoing on theirs.
Our emphasis on one particular form of mathematical activity proving novel theorems and the ancillary activity of paper-writing is to the detriment of all others. These second-class mathematical activities include refereeing, code generation and formalization, distillation and digestion, simplification, codification, exposition, teaching, and learning. All are in service of understanding. Perhaps Hardy was right that these activities are for second-rate minds, but the unfortunate reality is, in the age of the LLM and massive agentic swarms (the “Large Agent Collider”), we are all second-rate minds. If we wish for mathematical practice to flourish in the upcoming era, then the responsibility falls on us to redesign our incentive structure to better reward the whole spectrum of mathematical activity. We can do little about the Cossacks at the gates.
We can renegotiate our tradition to better align with our needs. Perhaps the new world won’t be so bad.
- For mathematics, this is the norm of paper strength, for some . For theoretical physics, with a smaller selection of journals to differentiate the strength of individual papers, it is the norm. ↩︎
Received 12 September 2026.
Add to the discussion