Mathematics, papers and archives after AI

日本語

A mathematician at a research university is writing about one 80-page paper a week with AI agents. What limits him now is where he can publish. Preprint servers screen submissions with human volunteers and are turning away papers that look AI-heavy, and journals take a year.

He proposes a new archive: a timestamped, authenticated server where an AI checker verifies one thing, that the paper is true. Joi first argued that a panel of well-known mathematicians would have to stand behind such an archive. By the end of the call he agreed the mathematician was right: AI review will replace human refereeing, initially in the many fields where an AI can computationally evaluate whether a result is true, and since the readers are other AIs, what matters is that they can find the paper.

These notes cover a 40-minute call in late September 2026. The mathematician is not named, and details that would identify him are left out or generalized.

How he works now

His work has always been computational, and he has written his own programs throughout his career. He said the only thing that used to slow him down was the supply of people to make figures and run the supporting work. That constraint is gone.

• Writing. He works mostly with Claude. Agents run day and night on his computer and use his university's computing cluster. A colleague had urged him for a year to run Claude on his own computer, and he started this summer.
• Division of work. Different agents work on different papers and on sections of a paper. Another agent assembles the sections into one paper. The agents have started, without being asked, to point out errors in each other's work.
• Review. When a draft exists he sends it to GPT for peer review. The review comes back, around 100 agents spend the day rebuilding the paper against it, and in the evening he sends it back for a second round.
• Pace. After one or two weeks of this loop the paper holds a result he did not start with. He is producing about one 80-page paper a week.
• Starting point. He often opens a project by handing the agent one of his own programs. The first task is to understand and optimize the code. The mathematics comes after.
• Questions. An open question often gets a bad answer. When he says "here is something I don't understand, do you have a theory?" the agent works for a long time and returns something poor. What works is an ansatz: handing the agent a mostly finished project and asking for an answer in a particular form, which the agent then has to verify. That often yields an elegant answer. Joi's note: this is an interesting prompting technique in its own right, and the same move runs through Terence Tao's published session on the Jacobian counterexample.
• Verification. Much of his work can be settled by exact computation, not simulation, so the agent goes to the cluster and builds a computational verification. The AI referee refuses a paper until it has certificates for the computations. The agents can spend days producing them before the referee accepts.

He described it as 50 people who know everything about his field and other fields, and as more than the best person he has worked with.

He thinks his field is unusually well placed because it is computational. Parts of mathematics have questions that are not yet computational. He expects AI to solve those too, later.

Literature search across fields

A literature agent collects the references each paper has to cite. Once there is an idea, about 50 agents read and return some 260 papers that matter for it. Most come from fields he had never heard of. He no longer reads papers himself, and said he never liked doing it.

His explanation: a mathematical result cannot be found by search unless you already use the name the other field gave it. An agent can match the result itself.

His example was asking whether one of his results generalizes to a wider class of problems. After about an hour and many sub-agents, the answer was yes, with the generalization worked out and a note that the paper now had to cite a paper from the 1960s in a field he does not work in.

He makes a point of this: searching across disciplines and looking for very old papers and theories. A result from decades ago in another field, once an agent has matched it to the problem in front of him, opens a whole domain of understanding that was hard to reach before, because nobody in his field knew it was there or what it was called.

Will mathematics become entirely AI?

Joi asked about the forecast, heard from people in Silicon Valley, that AI becomes recursively self-improving between December and March (the claim examined in the RSI report), and whether mathematics could become entirely AI-driven.

The mathematician thinks it is very likely, and not only for mathematics.

Today the agents do what he asks and write each paper with him. He expects that within months someone could hand a model everything he has published and ask for the next 10,000 papers, and have them a week later. After that, any new idea he brings will get the same answer: this already exists and has been published.

He does not know how long the present window lasts. His advice was that anyone with ideas should work on them now.

The public example of what he means arrived in July 2026. On 19 July Levent Alpöge posted a three-variable polynomial counterexample to the Jacobian conjecture, open since 1939, and credited it to Claude Fable 5. Any computer algebra system verifies it: the Jacobian is the constant −2 and two distinct points map to the same point. The understanding came afterwards from people, with AI as the calculator: Tao's digestion on 21 July, Speyer's geometric explanation on 23 July, and Gao's generalization to every dimension above two on 31 July.

Publishing is the bottleneck

His output is now limited by where he can place papers.

• Journal peer review takes about a year, so he posts to preprint servers first.
• The preprint servers are receiving so many submissions that they are blocking papers. Volunteers screen submissions and reject those that show signs of heavy AI use.
• Single-author papers are filtered harder. One person submitting an 80-page paper every week looks implausible to a screener. A co-author raises the acceptance rate.
• He refereed a paper for a journal by discussing it with GPT. In about five minutes he had a 12-page report with 30 improvements, already worked out for the authors. He then read the fine print: the journal tells referees not to discuss the paper with AI.

He expects about 5 million AI-generated papers within the next month. Many will be better than earlier work and some will be nonsense. He does not think human referees are needed to tell them apart. In his experience a human report rarely goes beyond a complaint about a missing citation, while an AI checks every calculation, improves it, and works out the next steps.

His proposal: a server with a truth checker

He wants a new archive and was specific that it should be a server, not a journal.

• Submissions are timestamped and authenticated.
• There is no human checkpoint.
• An AI checker tests one thing: whether the paper is true. He estimates about an hour for a complicated paper and between one and five minutes for a trivial one.
• Google Scholar and other scholarly search have to index it. Without that the archive does not solve his problem.

He predicts that journals, which he counted at 26,000, will be gone within a year. Nobody will wait a year and pay a fee to publish when 10,000 attempts at the same result can be made in that year.

He also sees the archive as something larger than a place to post papers: an AI-generated library. A mathematician who wants to know something about a field asks their own AI, and it answers from the library.

Joi's objection, and where he ended up

Joi's first reaction was that a system like this needs people behind it. He argued for a review panel of well-known mathematicians, on the reasoning that a university gives a professor's claims standing through its name, buildings and endowment, and an AI-reviewed archive would need an equivalent: people with authority who could carry a result to a court, a legislature or a reader outside the field. He added that AI review works when a person designs it. About 90% of the tokens in his own agent system go to adversarial review, and the result after hours of attack by a model different from the one that wrote the draft is better than a human review would produce, because the review was built that way.

The mathematician disagreed on most of this. The checking has to be automatic and AI-based, and the authority behind it could be another AI. He compared it to two chess programs playing each other, which need nobody watching. In his field there is absolute truth, so a result is not a matter of opinion and the system cannot be "not working."

Two points changed Joi's mind during the call. In this kind of mathematics, and in the many fields where truth can be evaluated by computation, an AI can check whether a paper is true, with certificates that anyone can rerun, so a panel of famous names adds nothing to the verification. Those fields are where AI review replaces human refereeing first. And the readers of the archive are other AIs: what a paper needs is to be findable by them, indexed where their literature agents look. Joi concluded that his panel was an old-fashioned idea, carried over from a world where reputation stood in for verification, and that the mathematician was right.

How results reach people outside the field, a court or a legislature, the mathematician said has to be thought through. It was left open.

Who is using AI

He said the mathematicians and students around him have not worked this way and do not follow what he describes. He was surprised by how few people around him know how to work with agents. He expects every mathematician to be using AI very soon. The slow start is in fields where the work has been paper and pencil, with a computer used only for email.

Joi's reading is that the two of them share the same two conditions: they can write software and they have time.

The mathematician had not realized that public opinion in the US had turned against AI.

Joi's view of universities:

• Universities in the US and Europe are mostly negative about AI, particularly in teaching, on the belief that it makes students learn less. Japan and Bhutan are more positive so far.
• Joi estimates that 10 to 20% of students use AI to learn more and the rest use it to learn less. US universities are blocking the first group. He would encourage that group and work on the motivation of the others, because he sees the difference as motivation and not technology.
• US industry is far ahead, and public opinion has turned against AI and data centers. Joi thinks this gives other countries time to catch up.

After the call

From his messages in the days after the call:

• While the two of them were talking, another paper of his was completed: 120 pages, single author.
• His immediate question is where to put his current preprints so that Google Scholar finds and lists them. He is running out of places. The next day he found that the Royal Society's journals are also restrictive about AI use, which he had not expected.
• He has several hundred papers behind him, many in the leading journals, so his view of the existing system is not from outside it. His reading is that the time is ripe for a new model of science publication, that this is a transitional phase for research, and that the concept of publication and discovery will change dramatically. People do not grasp that yet. He compared the resistance to AI use in journals to resisting electronic calculators or the printing press.

Joi has started working with one of his teams on the archive idea.

Open questions

Joi is working out what such a server would need: a Crossref membership to mint DOIs, publishing metadata, and a host.

• Will Google Scholar index papers whose DOIs are minted this way?
• How do results from an AI-checked archive reach people outside the field, a court or a legislature, when no person has vouched for them?
• Which existing archive will take papers written this way in the meantime?

Substantially AI-generated from the call, with guidance from Joi Ito.