SERIES · AI is making papers cheap to produce but they remain costly to referee. Proofs and Prompts is publishing a series of posts from 26 October on the future of publishing, papers and credit. Questions such as how to disclose AI use, who bears the cost of checking, what authorship means and what papers of the future might look like will be addressed. This post is part of the series. Each is written independently and reflects only its authors’ views. All posts in the series
AI statement: I wrote the initial draft and revised it with ChatGPT’s assistance to polish the English and improve clarity. ChatGPT was also used to screen the arXiv submissions automatically.
The number of papers submitted to the mathematics sections of arXiv is exploding, recently prompting arXiv to impose a cap on submissions per author. As an editor, I also see a substantial rise in submissions to mathematics journals. This is very worrying: the current publication system cannot absorb such a volume of papers. Many will have to remain unpublished. Some journals have even temporarily stopped accepting new submissions.
I took a closer look at arXiv’s “Analysis of PDEs” section (math.AP). The number of papers in this section has increased by a factor of 2.45 in one year: from September 15 to October 14, there were 1,302 papers in 2026, compared with 531 over the same period in 2025. That is 771 additional papers in PDE alone.
Much of this increase is likely due to AI, even indirectly (some authors may be rushing to finish their old-fashioned “brain-crafted” papers before AI supersedes their results). An automated screening of the 1,302 PDE papers found that 493 explicitly disclosed using AI. Most of these, however, reported using it only for language editing and proofreading, which alone cannot explain such a sharp increase. Only 173 papers (13.3%) explicitly reported using AI to generate or develop parts of their proofs.
This is going nowhere. We should use these new AI tools to do new things, rather than ten times more of what we were already doing before AI.
In this post, I will argue that much of the problem comes from our obsession with writing papers, even when another form of publication would be more appropriate. I will propose a new type of technical report, which I will call an “AI proof report.” Establishing guidelines for these AI proof reports is one of our community’s most urgent tasks if we are to prevent our publication system from collapsing. Finally, I will discuss what I believe belongs on arXiv and in mathematics journals.
The obsession with papers
This obsession is already built into the AI models themselves, probably reflecting the fact that we mathematicians do not know what else to do. ChatGPT and Claude tend to present their answers as mathematical papers, complete with a title and abstract, using the amsart LaTeX document class, even when we have not asked for this.
This tendency reached an unprecedented level when OpenAI posted more than 700 “papers” on GitHub on October 6. All were dressed up as mathematical articles, but none could seriously qualify as one in its present form. Even those that resolve an important conjecture would require substantial further work before publication in a mathematics journal. The proofs are largely unreadable. The introductions are generally poor and overlook important contributions to the subject. The choice of references is puzzling. Too little technical detail is provided about how the proofs were produced.
I am deeply concerned to see some of our colleagues also turning to the industrial-scale production of AI-generated papers. I will refrain from naming names, but many readers will recognize the pattern. These colleagues pick whatever conjectures they can find, even outside their own areas of expertise, and race to solve them first, as though playing a video game. Once they obtain a proof, they upload a paper to arXiv, submit it to a leading journal, and move on to the next conjecture. They do not take the time to make the proofs readable, perhaps because they do not understand the arguments themselves.
These AI-generated proofs may have considerable scientific value. For the sake of discussion, let us assume that they are correct (although establishing this for the most complicated arguments may require formalization and verification in a proof assistant such as Lean). Correctness alone, however, does not make an argument a mathematical paper. We still need to turn it into something we can understand and reuse in other contexts. Until that work has been done, these outputs should not be dressed up as papers. Instead, we should treat them for what they are: valuable raw data that require further scientific analysis.
AI-generated proofs as raw data
I have read many blog posts and essays about AI in mathematics, including on this website, and I am surprised by how rarely contributors draw comparisons with other fields. We occupy a small corner of science, both in numbers and in funding (in France, mathematics accounts for only about 3% of public research). I cannot help wondering what other scientists think of our current situation.
Mathematics is unusual in how little its day-to-day practice has changed over the past century. By contrast, most other scientific disciplines rely on experiments, often using sophisticated and expensive equipment. Obtaining good experimental data requires considerable expertise. The data must be carefully collected and organized according to established protocols. Only then can scientists analyze them and draw conclusions.
There are well-established standards for producing, presenting, and sharing data. Data should be structured, clearly labeled, and stored in an open, nonproprietary format. A data report should include enough technical and descriptive metadata to allow others to interpret and reuse the data.
I believe we should take a similar approach to AI-generated proofs. An AI proof report should briefly describe the context and history of the problem, without necessarily providing the full introduction expected of a research article. It should state which parts have been checked and how, identify any known gaps, and provide access to the code, formal proofs, or other supporting files needed to examine the argument. It should explain how the proofs were produced, specifying the model and prompts used and, in the case of a multi-agent system, the number of AI agents, their respective roles, and how they interacted. It should also make the structure of the proof clear. For long arguments, a map showing the logical dependencies between intermediate statements could be useful. The report should make the role of AI explicit, rather than presenting the generated arguments as the authors’ own work. We could develop a dedicated LaTeX class for these AI proof reports and require AI models to use it. Such AI proof reports could also contain supporting computations for a research article.
These AI proof reports should be collected in a community-owned repository where everyone can read, comment on, revise, and reuse the material. They should not be posted to arXiv or submitted to mathematics journals. They can serve as starting points for further research or as supporting material for a paper, without having to take the form of a journal article.
Throughout this discussion, I am treating arXiv as a preprint server for papers intended for journal publication. With that role in mind, we need a separate repository for AI proof reports. The recently launched website hexagonmath.org seems to reflect some of the concerns outlined above and could serve this purpose. For now, however, it accepts “research works of all kinds,” and clear guidelines for presenting AI-generated proofs seem to be missing.
What belongs in journals and on arXiv
Our research papers are already far more technical and less accessible than those in other scientific disciplines. Very few people read the technical parts of a mathematics paper in detail. We should not let AI make this situation worse. We could even use this opportunity to make our papers more accessible.
I strongly believe that research articles should be written primarily for human readers, who should be able to follow the argument from beginning to end. Giving readers greater priority is what will save our publication system.
Experimental sciences offer a useful model: because the full data cannot be included in an article, authors must select and explain the evidence needed to support their conclusions. When the LIGO and Virgo collaborations announced the first direct observation of gravitational waves, they did not reproduce all the data in the paper. Instead, they made the relevant data available through a dedicated website, with documentation and a DOI. Readers could thus examine and analyze the data underlying the published results without those data having to appear in the article itself.
We should take the same approach to AI-generated proofs. Unless they are short and simple, or have been fully rewritten and explained in a way that human readers can follow, they should not appear in our papers. Initially, they might be included as supplementary material. But I expect that they will soon become so long and difficult to read that storing them separately and citing the relevant AI proof report will make more sense.
Like other forms of raw data, AI-generated proofs require careful scientific analysis before they can lead to a research article that humans can fully understand. This takes time and effort. We value simple, general arguments because we can understand and remember them. These are the insights we should try to extract from an AI-generated proof and ultimately present in a mathematical paper.
Extracting an idea does not necessarily mean reading an AI-generated proof line by line, which may be impractical for the longest arguments. And we should certainly not offload the task of checking these arguments line by line onto PhD students or postdocs! In fact, experts may be better placed to spot a promising idea because they know the background and previous attempts. I do not yet know how best to gain insight from a complicated AI-generated proof, such as those OpenAI recently dumped on the mathematical community. We may need help from the AI models themselves in this process. What I do know is that the papers emerging from this material will need to be very different from the texts produced by the models.
I am deliberately leaving open what counts as “human-readable.” It certainly means more than a proof that can, in principle, be checked line by line. Many proofs written by humans are not particularly readable either! As always, referees and editors will have to judge whether the exposition is sufficiently clear. None of OpenAI’s 700 “papers” would pass that test in its present form.
In the future, some steps in our proofs may still require computer assistance, with their correctness certified by Lean or another proof assistant. There is no shame in this: computer-assisted proofs already have a long history, from Appel and Haken’s proof of the four-color theorem in 1976 to Hales and Ferguson’s proof of the Kepler conjecture, announced in 1998. Some areas of mathematics require extensive computations. Wherever possible, these should be confined to a few clearly identified steps, with the code and details of their verification provided separately.
The lengthy and demanding work of analyzing an AI-generated proof need not be carried out by those who produced it. Producing the material and extracting mathematical insight from it can be separate contributions. Anyone can use prompts to generate potential proofs, including people who pursue mathematics as a hobby: this is a form of citizen science. Recognizing a genuinely new and useful idea in the output, however, requires expertise. We may need to form working groups and undertake this analysis more collectively than before, which could be a welcome development.
Even after we have digested an AI-generated proof, rewritten it, or developed something entirely different from it, it may still be worth preserving the original output in an AI proof report. This would make our own contribution clearer and give others the opportunity to draw different insights from the same material.
Final recommendations
Whether we like it or not, AI is already part of mathematical research and is likely to remain so. Many mathematicians already use it daily. My message in this post has two parts. First, we should give greater priority to readability in research articles. I am not sure that banning AI from research papers would solve the problem, since we cannot reliably verify authors’ declarations of how they used it. As editors and referees, we should instead apply a familiar principle more firmly than before: recommend for publication papers that we like and think other human readers will like too. Papers that are original, well written, and likely to have a substantial scientific impact. Papers whose arguments we can follow and understand. The difficulty and technical complexity of a proof should no longer be the main criterion.
Second, we should recognize the potential scientific value of AI-generated proofs, even in their raw form, before the work of analysis and interpretation has been done. We should encourage those who produce them to share their findings as AI proof reports in an appropriate repository, following common guidelines. These reports should be recognized as valuable contributions in their own right, with proper credit given to their authors.
So, if you have obtained an AI-generated proof of an important conjecture but are not prepared to do the hard work needed to turn it into a paper that others can understand, please do not dress it up as one. Share it first as an AI proof report, rather than posting it to arXiv or submitting it to a mathematics journal. Unreadable proofs are likely to be rejected. Establishing that a theorem is true is no longer enough to justify a research article. Deposit the report in an appropriate repository. Then contact experts on the problem and let them know what you have found. They may suggest revising parts of the argument or testing other approaches. Your report can receive a DOI and be credited to you. Good data can attract many citations, bring you recognition, and make a valuable contribution to mathematical knowledge.
Received 27 October 2026.
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