Recently, every mathematician has heard lots of news on LLMs’ achievements in mathematics. After being shocked for a few days, one may wonder: what exactly is the limit of its ability? Can it really keep producing works of this level (say, disproving Erdős’s unit distance conjecture and the existence of non-Sofic groups) at the same pace for maybe 20 years and evolve without human mathematicians? (I do not count those works done by humans but with LLMs’ assistance).
Mathematicians—especially those working in highly abstract areas—seldom meet people who know more than they do about their own subjects. Sometimes, it even happens that the others are not concerned or knowledgeable enough to judge if one top mathematician’s works are true or false. This makes it unusually easy for us to be impressed with (or even afraid of) the apparent mathematical abilities of LLMs. However, part of this impression comes simply from the fact that LLMs have absorbed far more literature than any individual mathematician could possibly read. Many recently solved problems do not require fundamentally difficult new techniques to be developed: the real obstacle is that nobody has noticed that the relevant techniques already exist somewhere in the literature.
I do not think mathematicians should compare their own accumulated knowledge and techniques with that of LLMs, just like people should not compare that with Google or MathSciNet. The more meaningful comparison concerns what mathematicians can do beyond retrieving and recombining known information. Humans still have important advantages in deciding which problems are worth studying and, more technically, in developing genuinely new tools for genuinely difficult problems. After looking carefully at the recent mathematical progress made by LLMs, there’s no convincing evidence that they currently possess this latter ability—e.g., the ability to attack problems like the Kakeya conjecture.
All in all, what I want to express is: LLMs, just like computers, are becoming a powerful tool for mathematical research. Mathematicians should definitely use it and keep learning at the same time, since our job is to discover mathematical truths, not to protect a monopoly by ourselves. But human mathematicians should really insist on their right to remain the authors of mathematics, and should not transfer the authority to evaluate mathematical works to LLM companies. The LLMs are not strong enough to force mathematicians to give up these rights. I see no evidence yet that the dependence of LLMs on human mathematicians’ work is about to disappear.
The Sendov’s conjecture was recently proved by Lech Mazur with GPT 5.6 Pro assistance. This is in fact good news for human mathematicians. It suggests that the ability to solve problems like those demonstrated by the internal models is also accessible to individual researchers using publicly available models. And in fact, I seriously suspect that OpenAI stored more than 10 problems to announce later (possibly including Sendov’s conjecture), because for their benefit, the narrative they would like to describe is that “they are improving the models and solving the list of problems one by one” rather than “they have a limited list that can be solved but cannot do more”. For this reason, people who care about mathematics should use publicly available LLMs—through APIs or simply several independent chat sessions—to search systematically among established open problems and try to resolve them. But for sure, before publishing, people should really check and understand the arguments by themselves, take responsibility, and declare the use of LLMs. This is at least better than waiting for the LLM companies to announce the solutions of these problems, which would further help their promotion. Once this list is exhausted, people will see the true roles between human mathematicians and LLMs.
For a related reason, I would be cautious about sharing genuinely new mathematical ideas with AIs before those ideas are made public. Companies may promise that users’ inputs will not be used for training, but if a user’s work (let’s say, one of the works that will be awarded Fields medals) is highly useful for their promotion, they’ll have high motivation to claim it as their own. If the AI companies really take over mathematics, I’m afraid that this subject, which has lasted thousands of years, will become a place full of misleading or wrong advertisements (there are already too many wrong advertisements about mathematics on the internet). Even formal verification would not completely solve this problem. In that possibility, humans may lose their interest in studying advanced mathematics, and which problems are important will depend on LLM companies’ promotional needs.
I have paid attention to the recent discussions on the Jacobian conjecture (and also the recent progress on ratios of zeros of Riemann’s zeta function on the critical line, but maybe not worth speaking here). I found that the most historically concerned version n=2 remains open, while Anthropic claimed that they “resolved the Jacobian conjecture”. This is highly misleading, because it is mostly dimension-indexed, just like the Kakeya conjecture or generalized Poincaré conjecture; also, at least for a group of mathematicians, this name only referred to the 2-dimensional case (since there’re many positive results/evidence in this case), and the higher-dimensional versions were frequently labeled with “almost no evidence“. Some media also mentioned the Chinese mathematician Yitang Zhang. On one hand they claimed “Claude disproved JC”; on the other hand, they said “the study of JC led him to scrape by doing odd jobs for many years.” But this is wrong, since Zhang worked only on 2 dimensions, and this JC is not the one disproved. One can argue that such distortions are the fault of the media rather than of AI companies themselves. Sometimes that is true, but the distinction is not always so clear. Technology companies possess extraordinary resources for shaping public narratives, and a proportion of modern media’s reports are in fact advertorials.
This creates a particular danger when large technology companies enter mathematical research. The companies can create the impression that a result must be Annals-level, or Fields medal level, while thousands of results of comparable or greater mathematical depth in the same year may receive almost no public attention. Mathematical importance has never been identical to publicity, of course, but this kind of noise can also affect mathematicians, since most of us are not polymaths. Mathematicians should be especially wary of allowing this noise to distort their own standards of judgment.
Mathematicians may worry: what if AI eventually becomes capable of doing mathematics autonomously, improving its own mathematical abilities without human assistance, inventing fundamentally new tools, and solving problems such as the Millennium Prize Problems? This may happen someday, but I’m not sure that, if it happens, it will be a problem specific to mathematicians. From my perspective, such abilities would represent a more advanced level of intelligence and be applicable far beyond mathematics. At that point, people in many other professions—including people working for AI companies themselves—would have reasons to worry about their own roles. If that happens, insisting on the above rights for human mathematicians may not make much sense, and human “mathematicians” would become learners rather than researchers. But we are not there yet. Until then, it’s still important that mathematicians make use of AI without surrendering responsibility to determine the direction, standards, and intellectual values of mathematics itself.
Received 15 August 2026.
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