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
At the end of the Royal Society’s recent conference on AI and mathematics, Professor Ben Green said, “The vibe today has been a lot more positive and sort of forward-looking,” and I found myself thinking, “Did we just attend the same meeting?” It didn’t feel very positive to me. The optimism was quite cautious, while the atmosphere of panic was shrill.
There was a session on publishing in that meeting and I asked a question. The question was whether perhaps we could split the mathematics journals into a flagship and daughter journals, like Nature. At coffee someone told me the question was provocative. It was not meant to be. It seems to me to be a very natural idea: if the publication system is under strain, we could expand it by having more journals. Encouragingly, someone else said to me also at coffee that it was a very good idea.
A lot of people seem to think that it’s a good idea to just destroy the publication system and try to do something better. Politicians do say, “Never waste a good crisis.” But we are not politicians. We are in a crisis, but we don’t have to use this revolutionary time, which is profoundly changing how we do mathematics, to also revamp the publication system at the same time. An alternative is to bolster the publication system as it is. The new generation will be writing and publishing their research probably in larger quantities, and so will we, the more senior academics. Then, once the AI crisis is weathered and the dust settles a bit, we can go back to having those slow deliberate discussions about revamping the publication system that we’ve been having for a while.
There is this idea floating around that we are seeing the death of mathematics. I think that we are not. I hope we will be instead seeing an acceleration and flourishing of mathematics. The purpose of this essay is to defend the value of incremental research even if it is easy and to flesh out some details of the idea that I suggested in the question at the Royal Society AI meeting as to how all the worthy incremental research might be published. A deep philosophical existential crisis that has a practical solution that maintains the status quo and just takes a bit of money, as this one does, is not quite as poignant as crises could be.
Why the problems we work on are important
In every paper and every grant application, I write why the problems I work on are important. Here is a paragraph from a grant application from last spring:
“We know from numerics and experiments that many complex physical systems demonstrate the same behavior independently of the precise details of interactions among their constituent elements. This phenomenon, called universality, is conjectured to hold more generally. In the context of random matrices, the universality conjecture asserts that various properties of large random matrices are independent of the precise probability densities that govern their stochastic behavior. This conjecture has deep philosophical and practical consequences, allowing random matrix theory to be applicable in a wide variety of contexts. Two well-known examples are in data analytics (e.g., Principal Component Analysis), where both data and noise come from an unspecified non-Gaussian distribution, and in nuclear physics where the randomness models the complexity of a large atomic nucleus. Thus random matrix universality fulfils one of the central objectives in mathematical physics: the derivation of macroscopic properties of large systems, despite unknown or random specifics of interactions.”
In this paragraph I set out why the problems I study are important: the philosophical question of why large system behaviour doesn’t depend on nitty-gritty details and how someday this kind of thing may be applied. None of these justifications are impacted by the fact that the research will now be easier to carry out.
I believe the importance of mathematical results comes from understanding, but that’s a rather overused word. What exactly is meant by understanding? There are a few things that make mathematics and mathematical results important. One of them is shining light on the structure of various mathematical objects. We may think of the themes of structure and randomness in Prof. Terence Tao’s blog and eponymous book: what is structure, what is randomness, how one turns into the other, and finding structure in various interesting and unexpected places. The second is to tell apart—and this is done by rigorous proofs—what is always true, what is sometimes true, what can be true and in what pathological cases it is true, and what is always false, and also to tease out which aspects contribute to a behaviour and which don’t, i.e. which assumptions are used and which are not necessary.
Mathematics looks very far forward. If it was cancer research thus accelerated, there would not be so much gloom. While we are not curing cancer, the technologies we now use are based on mathematics developed decades, if not centuries, ago. Mathematics is very forward-looking. In 500 years, maybe, the technology humanity will be developing will be based on the mathematics done now.
Incremental research
Incremental research is important for various reasons. I don’t believe that breakthrough research is truly possible without the availability of wide variety of results and methods. Consider Perelman’s proof of the Poincaré conjecture, announced in 2002–03. It followed the Ricci-flow programme that Richard Hamilton had begun in 1982. Between Hamilton’s starting point and Perelman’s breakthrough lay a growing body of results: existence and uniqueness theorems, Shi’s local derivative estimates, Hamilton’s compactness theorem and the Hamilton–Ivey curvature estimate. Among papers on these subjects many were incremental. These gave mathematicians tools for controlling the flow and understanding its singularities. Perelman built on this accumulated theory.1
For most of us, while we mustn’t tell this to our funders, we may honestly say that a lot of papers we write are incremental. I think of breakthrough research like spires on a church, which is built upon the little bricks, brick by brick, of incremental papers. For those bricks to be useful, there needs to be somewhere for them to be placed. The way we publish incremental research will affect all of us, but particularly early-career researchers, PhD students and undergraduates, who usually start with high-quality incremental research. They used to take joy in it, get credit for it and get training from it. If all of that research just collects dust in people’s hard drives, that will be a profound loss to mathematics.
More research needs more capacity
I am finding myself two to three times more productive now that I use ChatGPT than I used to be and solving problems I tried and failed to solve before. If this gain is generalised to the community, we can expect two to three times more papers to go through the publication system. The publication system is under strain.
Professor Martin Bridson, speaking in the afternoon of the same meeting, was talking about cups. He was saying that there are cups that go into museums, and then there are cups that we drink coffee from. I think, in his analogy, the cups we drink coffee from were the kind of incremental research that I am talking about here. He said they’re very important, and they are very important. But it’s even more useful to have these cups if they’re organised into cupboards. Currently, the journal system organises these cups by field and by quality, one way or another. It tells us where the cups from a particular field are, which cups are good, which are mediocre and which are bad. That is important for hiring, promotion and evaluation of people’s work. It is also important for readers.
Daughter journals and paid refereeing
A practical idea to expand publishing is to split high-profile math journals: use the big-name journal as a flagship and add five electronic daughter journals. The flagship would retain its present form and standards; the daughter-journals would provide homes for sound but more incremental work. They could be organised by subject, with their own editorial boards and shared administration. Nature provides a precedent. An early attempt to divide it into three publications in 1971 was reversed in 1974. The lasting expansion kept the flagship and added specialist titles, notably Nature Genetics in 1992, Nature Structural Biology in 1994 and Nature Medicine in 1995. The daughters inherited the Nature name and, with it, some of the prestige and confidence built up by the original brand. They did not have to attract authors and readers entirely from scratch. Historians of this expansion describe precisely this transfer of reputational capital through the shared name.23
The question voiced often is why not just use the arXiv? The answer to that is peer-review. ArXiv doesn’t have it. With the expansion of incremental research, can we find the capacity to peer review it? Thus a key to this idea would be paid refereeing. Right now, refereeing carries a cost and no benefit aside from some moral satisfaction. I believe that, with the cost-of-living crisis and housing crisis, there will be many more takers if the task is paid for. The advent of AI also makes refereeing easier. Part of the referee’s job is to verify that the arguments presented are correct and that the calculations presented are correct. The AI can do this quite well now. The human just needs to check whether the paper constitutes an advance, is important enough for a particular journal, and is well written.
Therefore, I believe that the use of AI in refereeing, as well as monetary incentives, can allow us as a community to cope with the reading and processing of papers and the sorting of them into cupboards, and thus building our field brick by brick but quicker and further.
What it would cost
One may ask about money. I had ChatGPT Astra cost an expansion of the Annals into one flagship and five daughter journals, with the daughters being online. The working assumption is 30 papers per daughter each year, or 150 additional papers per family. For the Annals, allowing 30 flagship papers gives 180 published papers annually across the family.
The report budget assumes two initial reports at £100 each per fully reviewed manuscript, a 50 per cent acceptance rate after full review across the whole family, and one revision report per accepted paper. That is five reports per published paper on average, including reports on rejected manuscripts. We then allow another 400 preliminary or additional reports per family each year. For the Annals family, this gives 1,300 reports, costing £130,000. The 50 per cent assumption is a family-wide rate after transfers, not the flagship’s overall acceptance rate.
Daughter-journal operations add £55,000 per family annually: £25,000 for a shared office and platform, plus £200 for light production on each of the 150 new papers. Adding a 10 per cent contingency gives £203,500 a year for the Annals family, with a further £50,000 to launch it.
For ten leading journal families (Annals of Mathematics, Acta Mathematica, Inventiones mathematicae, Journal of the American Mathematical Society, Publications mathématiques de l’IHÉS, Duke Mathematical Journal, Journal of the European Mathematical Society, Geometric and Functional Analysis, Annales scientifiques de l’École normale supérieure, and the CPAM/Courant family), the plan therefore creates 50 new electronic daughters alongside ten existing flagships: 60 journals in total. With 445 flagship papers and 1,500 new daughter papers as the planning volumes, the annual allowance is 13,725 paid reports. The totals are as follows.
| Additional expenditure | Annals family | Ten families |
|---|---|---|
| Referee payments each year | £130,000 | £1,372,500 |
| Daughter operations each year | £55,000 | £550,000 |
| Annual contingency | £18,500 | £192,250 |
| Total additional annual cost | £203,500 | £2,114,750 |
| One-off launch cost | £50,000 | £500,000 |
| Total additional cost in year one | £253,500 | £2,614,750 |
So the answer is about two million pounds a year, with half a million to get started. It is not that much on the scale of research funding. Various foundations, like the Simons Foundation, governments and AI companies are plausible supporters.
Conclusion
Of political slogans, my preferred one at this interesting time is “Keep calm and carry on.” The research we have always been doing just got easier but, in my opinion, no less important. There have been discussions about improving on the journal system for a long time now, and we do all realise that it is not perfect. But it has functioned reasonably well for a long while and, with a little bit money and a dose of caution toward radical change, could function qualitatively in much the same way in an age of AI as it always had, but simply with expanded quantity. An acceleration of mathematics need not mean the end of the institutions that have served it.
AI Declaration
AI has been used to help polish and research this essay. Ideas are my own. Costing is fully AI generated.
- John Lott, The Work of Grigory Perelman, especially the account of earlier Ricci-flow results on pages 2–3. Read source ↩︎
- Nature, History of Nature. See the 1970s and 1990s sections for the early split and the later specialist titles. Read source ↩︎
- Mahdi Khelfaoui and Yves Gingras, Expanding Nature: Product line and brand extensions of a scientific journal, Learned Publishing 35 (2022), 187–197. DOI: 10.1002/leap.1422. Read source ↩︎
Received 3 November 2026.
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