How we can win

A blueprint for the mathematical community

In four previous essays, I have argued that the mathematical community must address the crisis of AI-generated mathematics. Using billions of dollars and the collective labour of our community, AI companies have created frontier-level models which threaten to disrupt our scientific practice for the worse. If we embrace the use of this technology in our research, we should expect an explosion of slop mathematics, the exacerbation of all the worst aspects of the publish-or-perish model, and for our field to become financially and intellectually dependent on four companies.

Alignment is a word thrown around a lot in the current discourse.¹ To state the obvious, AI companies are not aligned with us. They have chosen mathematics because it is cheap, uniquely formalizable, and carries cultural cachet. In their effort to increase shareholder value, they tell journalists that mathematicians are replaceable, portray our field as a theorem-proving factory, and presume to offer the public a conceptually incoherent vision of mathematical practice. They claim their models have “solved math”; they enrich themselves on us, instrumentalizing mathematical proofs in order to extract material wealth. We are not the only victims of this parasitic industry. If the AI industry has its way², then essentially all workers will have their labour-producing ability removed by models trained on the products of their skilled labour. There is no attempt at subterfuge here; these companies are ideologically and rhetorically disturbing.

How should our field react internally? I believe the uncritical use of AI tools is not aligned with the goals of our research community. Indeed, increased reliance on AI to understand and generate mathematics may imperil human mathematical understanding, which I take to be the collective goal of the mathematical community. We can look to our friends in software engineering to see the degraded working conditions and cognitive deskilling which await us. Remember: we produce theorems so that we can understand them. The unfettered use of AI tools may decouple scientific production and understanding to a farcical degree, and create a scientific economy in which the incentives are extraordinarily disaligned with the actual goals of our research community. As a community, we want to produce not only solved problems but people who know how to solve problems.³ AI companies have an explicitly hostile stance towards the latter group, and towards skilled labourers more generally.

Thus, we need two types of organizing: external-facing direct action against AI companies, and internal-facing reform to AI-proof our scientific field and align the incentives with the production of human mathematical understanding. For the last 80 years, paper production has been a functional proxy for mathematical understanding; in the current era, this metric is likely to become a very poor one indeed, and evaluating job candidates based on paper production will further encourage low-quality AI-generated mathematics. In the current ongoing “ownership model” of mathematics, LLM tools have placed mathematicians in a field-wide prisoner’s dilemma⁴, and the equilibrium state is not a good one. We should expect defectors when we have field norms that incentivize defecting. Part of the solution will involve an upstream change of this state of affairs so that we are no longer in this prisoner’s dilemma. However, that does not entail ceding the human generation of mathematics. Rather, we must resist the forced uptake of this anti-intellectual technology, stand with our colleagues who maintain an AI-free mathematical practice, and reorient our field to reward mathematical understanding without relying on the production of mathematically correct papers as a proxy measurement.

This will not be easy. This future for our field will not manifest out of thin air; it will require the labour of extremely busy people. Yet we need large-scale coordination to reshape and protect our scientific institutions now that AI tools are capable of autonomously solving mathematical problems. Moreover, these reforms must not only be internal; we need to engage more with the public and our society at large in pushing back against AI companies. We need to bring a political and labour-oriented lens to the question of AI use in mathematics, build solidarity with other workers, and oppose the dangerously unsafe and destructive industry which led to this societal crisis.

External-facing proposals

1. Take back control over our data. We should identify a few potential chokepoints (like the ArXiv, MathOverflow, and Math StackExchange) and begin a protracted legal and technical battle with AI companies to control our data. I am sure this will quickly explode into an arms race; who among us is willing to wade into the fight? Right now, we are providing these companies with a plethora of free training data in the form of papers, chat logs, and forum posts.

2. Mathematicians who use AI tools must switch to open-source (or at least open weight) models as soon as possible. As a first step, LLM users should switch to locally hosted open-source models and retain control of the chat logs in local storage. Stop using proprietary models and feeding these companies valuable training data in the form of chat logs. Stop paying subscription fees to these companies. If you value our independence as a field, do not place yourself in a position of dependence.

3. Do not work with, benchmark, or collaborate with AI companies. It is time to boycott this rogue and dangerous industry. Do not accelerate AI capabilities with your extensive mathematical training, promote their products, accept their funding, or participate in their scientific partnerships.

4. Join the call to regulate the AI industry. Demand a global AI pause. We must add our voices to the political coalition against AI companies. We must stand with other professions in opposing the disastrous societal, environmental, and economic impacts of this industry.

5. Launch a counter-narrative against AI companies. We need a few mathematicians with message discipline and a clear and cohesive counter-narrative to identify themselves as representatives of our community to the media. They should speak to journalists, wade through social media hysteria, and defuse market-driven narratives about “AI solving math”. Already some of us⁵ have stepped up to do this critically important work; more of us should do the same.

6. Stop doing product placements in papers and preprints. Given the fragile position we find ourselves in as a profession, I feel we should not be mentioning specific companies in AI use disclosures. Instead, LLM users should retain all chat logs and products in local storage, so that you can give journal editors access to these logs during the editorial process. Papers in which AI played a coauthorship-level role should be ultimately published in different journals and tagged differently on ArXiv, rather than having AI use disclosures hidden inside the main body of the text. (More on this below.)

We must avoid ceding the independence and autonomy of our research community. We cannot continue to allow AI companies to take over the narrative and mislead grant-funding agencies, governments, and the public about the goals of research mathematics.

Internal-facing proposals:

1. Rate-limit the generation of papers that an individual actor can produce. I believe this is the most urgent and tractable proposal to safeguard at least some good aspects of our mathematical practice and encourage higher-quality work. This policy will prevent human-generated mathematics from being drowned by a flood of AI-coauthored work. It will also prevent us from taxing our refereeing system to the limit. See this essay by Mario Pasquato for further detail.

2. AI-free mathematicians should make that commitment public. We must find each other and form a political coalition; efforts to do this are already underway. My personal belief is that it makes absolutely no tactical or moral sense to use AI tools for research mathematics until a global AI pause has been achieved. Already, many of us have made our commitment public, a non-exhaustive list including: Hugo Duminil-Copin; Max Weinreich; Jonny Evans; Vladimir Lazić; Alexis Marchand; Atticus Stonestrom; and all of the members of the \begin{proof} collective. This list will surely only expand in the era to come.

3. Change our hiring criteria. We need to hire people based on a broader range of markers than just the production of novel mathematical research. This shift is not to imply we should cede ground on human generation of mathematical research: I want human mathematicians to keep generating research math.⁶ But we must disincentivize people from AI use which degrades our collective mathematical understanding, and we must start recognizing that other kinds of labour are valuable and always have been. We should increasingly reward work like:

   1. Teaching, mentoring, and organizing reading groups and seminars.

   2. Participating in scientific outreach (math circles, Youtube appearances, writing in popular science magazines).

   3. Producing expository work which is useful and consumed by others. That includes writing textbooks, producing lecture series, and teaching mini-courses. Here is an example of a model I would like to see grant-funding agencies take up. I would like to see grants, postdocs, or PhD programs which are centred around the production of an authoritative textbook in a given subfield, rather than new research papers. This is especially needed in folklore-heavy fields which have produced spectacular results in the last twenty years but in which the requisite knowledge is diffused across 50 papers or located in the minds of a few subject-area experts.⁷

4. Originality should be given a lower priority when we evaluate high-quality research. Simultaneously, excellent mathematical writing should be increasingly rewarded. We should give less primacy to originality and more to high-quality mathematical content, communication, and dissemination. It is valuable when someone unearths an old, good proof and advertises it. It is valuable when someone reproves a known theorem in a new and clearer way. It is valuable when someone assimilates and rewrites the literature into streamlined and modern prose. We should pay attention when someone adds value to our field, even if they are not the first to invent a piece of mathematics. By devaluing originality, we avoid punishing human mathematicians who are beaten at the last mile by faster LLM users. We prevent the norms of our field from becoming increasingly secretive in the LLM era.

5. Build open-source tools that align with the goals of mathematical practice, and are within the control of the mathematical community. Some of us will have a technological role to play in the days to come. It is past time to consult our colleagues who have built computer algebra systems and open-source software. We cannot repeat the mistakes which led to our community being preyed upon by the scientific publishing industry; we must not depend on four companies for all of our scientific practice. We must thoughtfully design our own tools that discourage cognitive deskilling.⁸

   As an example, I would like to see a literature search tool with the interface of a search engine (similar to MathSciNet) that

   1. uses LLMs as a back-end;

   2. is controlled or initiated at the behest of a public research university or consortium;

   3. is open-source;

   4. and does not summarize or explain other people’s research, but instead refers the user to the right paper and lemma.

   Such a tool could help us preserve our field norms around accreditation and authorship by redirecting us to human-written papers rather than feeding the user a sea of assimilated language slop. Imagine if I could type in “What are the L^2-Betti numbers of H^3?” and be directed to a reference written by humans. If this kind of literature search tool was available, then our field would already have recovered some of its independence, as I know many mathematicians who exclusively use AI tools to assist in literature search.

6. Defend our colleagues who maintain an AI-free mathematical practice. We need to stand by our colleagues who do not use AI tools. They bolster the intellectual, cultural, and political diversity of our field, and their presence helps us maintain our scientific independence. We cannot punish them by maintaining incentives that lead to these colleagues being marginalized and outcompeted. I do not want to see the future of our field become about who has access to most cutting-edge model or which department has the best-funded computer cluster. Rather, I want to retain a fair and equal mathematical playing field for those who abstain from LLMs entirely.

   I believe this should be a popular position. While some mathematicians may want to employ LLMs for literature search or the computation of routine technical lemmas⁹, you should not want your colleagues who have serious qualms about AI to be outcompeted. We must protect those who wish to outsource none of their mathematical work to machines.

7. Value human-generated mathematical work more than AI-generated mathematical work.

   This should be a popular position. First of all, the macroeconomic incentives will lead in this direction anyway, even in a maximal AI uptake regime. Each individually disseminated LLM-generated proof will have low marginal value if any (sufficiently knowledgeable) actor using an LLM can find it; this is already evident in the strange phenomenon in which four papers¹⁰ land on ArXiv in close succession, some using extensive AI assistance, all proving the same result.

   More saliently, we should value human-generated mathematical work more because it required more labour to produce and created more value in the process of production (in the form of internal mathematical understanding). By valuing human-generated work more, we incentivize humans to continue producing research mathematics.

   Such value judgments are often met with concerns about incentivizing lying. I am forced to admit there are no perfect options here. While a maximally transparent and laissez-faire ecosystem does de-incentivize lying, it may still directly punish human-generated mathematics. I do not find that incentive system ideal either.¹¹ While some actors will inevitably engage in deception (and indeed I am already aware of such cases in the current regime), I think we should nevertheless expect the majority of people to abide by the social contract.¹² Creating ethical lines will inevitably be part of establishing reasonable professional norms; implicitly catering to bad-faith actors entails unacceptable consequences of its own.

8. Protect our journal system and the refereeing system. It’s time to state the obvious: LLMs will break the refereeing system. An explosion of AI-generated mathematics will burden this fragile and undervalued system of labour until it collapses. The exponential surge of ArXiv submissions tells us that this phenomenon is already well underway. Journals are some of the only institutions whose incentives are aligned against pervasive AI uptake; thus, we must work with these stakeholders closely and provide journal editors with tools to navigate this crisis. Below, I reiterate and amplify urgent proposals put forward by Atticus Stonestrom.

   1. Proposal 1: AI-generated work should be published in new and separate journals. Traditional journals should either ban AI-coauthored papers or institute quotas in journals for the number of AI-coauthored papers that will be published per year. At worst, traditional journals should create separate subjournals for mathematical work where AI took a coauthorship role. ArXiv submissions in which AI played a coauthorship role should be tagged as such.

      This delineation will make it easier for departments to evaluate hires, journals to apportion editors correctly, and readers to determine whether a work was human- or AI-generated. Furthermore, those who use AI in a coauthorship role should donate their time to refereeing AI-generated work.

   2. Proposal 2: I agree with the Leiden Declaration that we should affirm the humanity of authorship and maintain the social construct of an author. We need a human liability zone around every AI-generated paper; this prevents the production of mathematical papers that no one actually understands. Nevertheless, there is some tension in being the named author of a paper in which one has generated almost none of the mathematical content. We might consider an attribution style along the lines of, “Generated by computer assistant, communicated by Firstname Lastname”.

6. Boycott refereeing AI-written papers. This should be a large public campaign, with the option for signatories to make their views public. Certainly given my serious ethical qualms about AI-generated mathematics and the burden it places on the refereeing system, I will not referee AI-coauthored papers. I think it will be easy to find participants for this campaign.

7. We must not allow LLMs to referee LLM-written papers. We must not end up in the farcical situation where math is being generated by computers, verified by computers, and understood by no one, creating dead ends in human mathematical understanding. Human refereeing must continue.

8. Do not cede teaching to LLMs. This subject deserves far more than a bullet point, but here I will be brief. If we cede teaching, our profession is over. We need to protect the next generation by giving them the same mathematical education we received. We need to safeguard our pedagogical practice and maintain our pipeline of early-career researchers. We must give educators and university professors the tools to navigate the LLM-induced crisis; we owe it to our undergraduate students and graduate students. We must encourage people to continue to study math and explain that our field is more than a theorem-proving factory. My own undergrad mentees tell me that they are unsure if they should pursue research math in the LLM era. We owe it to them to be the adults in the room.

9. Create more open-source educational projects and talk to humans before talking to AI chatbots. As other mathematicians like Jonny Evans have pointed out, even querying LLMs to learn classical mathematics may subtly harm the collective mathematical understanding of our community and make our mathematical practice increasingly atomized and solipsistic. We should instead increase our collective mathematical understanding by talking to each other more. Email each other; ask questions on MathOverflow and Math StackExchange; begin more open-source projects that increase mathematical understanding. Follow the examples of nLab and the Stacks Project.

10. Demand AI proponents take a more active role in the new regime. I understand that some mathematicians are excited by the prospect of new LLM-assisted mathematical breakthroughs. But if you use a technology, you take on responsibility for the social consequences. Everything in this world happens in a sociopolitical context, even the action of typing a prompt into your laptop at home. So, will you agree to referee ten AI-generated papers a year? Will you protect your colleagues who maintain an AI-free mathematical practice, and support hiring lines which prioritize those colleagues? Will you disentangle yourself from corporate AI companies and switch to open-source (or at least open-weight) models? Will you create initiatives that address financial inequities around model access? Will you consider the effect that your own AI use has on our scientific ecosystem? Help your colleagues, and stand with us.

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I think we can win. If we realign the incentives correctly, we can increase human mathematical understanding in the regime to come. Imagine a social ecosystem in which mathematics becomes increasingly social, vibrant, and public-facing. Imagine a world in which we clean up and internalize the mathematical progress we’ve made in the last 40 years, while still pushing the frontier forward collectively. Imagine that we resist a scientific economy in which every mathematician is forced to use AI in their mathematical practice. Imagine that we defy this gross takeover attempt by outside actors. I believe that mathematicians have the power to take back the narrative, realign the incentives, and stand against AI companies as a field. The question is whether we will try.

Acknowledgements. I am grateful to Dylan King for helpful feedback on a draft of this essay. I also thank Atticus Stonestrom for insightful conversations about mathematical journals in the current era. All of the views above are solely my own and do not reflect those of anyone else.

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Further reading:

• Context Widows, by Kevin Baker.

  One might hope that this acceleration heightens the contradictions, that the systems produce so much slop so quickly that the problem finally becomes undeniable. But, as we should all know by now, systems can persist in dysfunction indefinitely, and absurdity is not self-correcting. Whether the acceleration produces collapse or adaptation or simply more of the same is not a question about the technology, and it won’t be answered by debates about capabilities.

• The Least Agentic People Alive, by Ben Recht.

• Knowledge Collapse, by Michael Harris.

• Care for a little more AI? by Hugo Duminil-Copin.

• A proposal for mathematics journals in the age of AI, by Atticus Stonestrom. I also refer the reader to his AI statement.

• On Inevitability, by Fernando Borretti.

1. For my thoughts on model alignment as a cure-all to the AI crisis, see AI Alignment as a Thought-Terminating Cliché, by Fernando Borretti.

2. See OpenAI’s charter.

3. Some thoughts of mine being informed by this post. I should also mention that on a sociological level, unsolved problems are just as important for research mathematics as solved ones; I think of unsolved problems as scarce and finite resources that we burn along the way to mathematical understanding. Consider also mathematicians like Erdős who invigorated fields by creating lots of interesting problems and questions for others to work on.

4. See this essay by Ruodu Wang and this essay about the ownership model.

5. See, for instance, the excellent work of Alvaro Lozano-Robledo about AI and mathematics and this comment of his. Also see Proofs and Prompts.

6. I do not want mathematicians to become reverse centaurs who read and verify LLM-generated math all day.

7. I credit this idea to my friend Caelan Atamanchuk, a PhD student at McGill University and a subject-area expert who could write a sorely needed textbook on scaling limits of random graphs if our profession actually valued that kind of work.

8. For instance, I do not think chatbot interfaces are particularly good at discouraging cognitive deskilling.

9. My personal feeling is that if I cannot prove a technical lemma myself, then that it is useful feedback that I do not understand what I am doing. If I outsourced the computation of technical lemmas in my mathematical practice, I would imperil my own understanding.

10. Links to these four papers. Let me mention that the level of AI use varied across these four papers, and that these four papers employed meaningfully different proof methods at various points. To summarize briefly: Ge did not disclose any AI use; Koirala used LLMs as “an interactive writing and checking aid”; Antonelli said their work “made substantial use of” computer assistant tools; Kong and Zhu said that “essential ideas were generated by AI”. It is not my intention to litigate other mathematicians’ AI use or to degrade any author’s individual contribution, but rather to make a broader point about macroscopic economic incentives in the era to come. I hope that this is clear; I know I could not have proven these results with or without AI assistance.

11. Indeed, this is a primary source of economic anxiety for me as an early-career mathematician who does not use LLMs in research mathematics.

12. After all, why isn’t everyone pumping out papers as quickly as possible right now with the use of LLMs and then lying about it, given that all the incentives reward us for doing so? This is something that actually bears meditating on when we evaluate people’s expected behaviour in the mathematical ecosystems to come. Of course, it could be that this kind of deception is happening frequently and I simply have no way of telling.