Proofs and Prompts

Rulers of the childless land: A response to the AGMAI

Vladimir Lazić, Professor of Mathematics at Saarland University.

Most days, for the last six months, I wake up feeling shame for the field we have become. Lined up towards a future most of us have not chosen; showing resistance on paper: signing petitions, creating initiatives, shouting in the wind. Led by people with no shame.

A few days ago was such a day, where the Advisors assembled the Advisory Group, advising a company how to eat us slower. So that the generations after us can feel every bite. The strategy is the same as in every occupation: the leaders are assembled and given a choice to collaborate: put your people in order or be removed; make your choice quickly, do it wisely. And so it was done with the Advisors, as it has been done in previous times in different circumstances.

I have written extensively on the futures that await us, and I will not repeat myself: the algebraic geometry community in Europe knows this since two months ago, as do some colleagues outside of Europe and outside of the field. Thus far I have been proved correct, but, as a colleague pointed out to me, I am to suffer Cassandra’s fate: to be right, but not to be believed.

I try not to tell people what to do. But I do tell what I will do: I will not check a paper written by machines, regardless of whether it is put forward by a company or by a prompting mathematician. If such a result in an area of my expertise comes out (and there are a couple of topics where there are no better experts than myself), I will not confirm it correct, and you will have a choice: believe me or believe others.

People join advisory groups for one reason: that in a system that comes next, the advisors remain the elite. But at what a price! Destruction of the discipline; cutting off the lifeline of younger generations so that you can give yourself a lifeline. Pulling the ladder away when it is needed the most: so that you can rule over land with no children and no hope.

To my younger colleagues: the Advisors offer a vision of our profession that you did not subscribe to. They offer desperate, high-paced times. In such times do the opposite: slow down, observe, reflect. And then, after not too long: stand up and fight.

Received September 24.

21 responses to “Rulers of the childless land: A response to the AGMAI”

  1. Mahmut Levent Doğan Avatar
    Mahmut Levent Doğan

    The post makes several points that resonate with me strongly. Advisory board exists to protect the elite status of the elite mathematicians, and early career researchers (like me) should start involving more to the discussion to change the course as much as they can.

    What does not resonate with me, however, is the suggestion of complete abstinence from AI in mathematics. If the academia does not reorganize itself around the question of what it considers to be valuable mathematics in the age of AI, and instead tries to preserve its status, it is clear that complete abstinence will be the most harmful to early career researchers. The problem is that the abstinence is not consistent with the world where AI remains to be a powerful tool in mathematics. Imagine the world where we value human mathematics above all and shame everyone who uses LLM’s in their research. This world will inevitably push researchers to be unethical because it will reward everyone who cheats, uses LLM’s to further their research and try their best to hide the fact that they used it.

    Reply
    1. mhairer Avatar
      mhairer

      You have personally already used this platform to express your opinions and reach thousands of mathematicians in your blog post. I really do not understand how this squares with your rant about not being involved. Also, be careful about generic ranting against “elites”: in the eyes of 90% of the population you are yourself part of the elite.

      Reply
      1. Gary Barlow Avatar
        Gary Barlow

        Writing a post for proofs and prompts is quite different to being on the advisory board to open ai

        Reply
      2. Anon Avatar
        Anon

        Writing a post on proofs and prompts vs being on advisory board to open ai…

        Reply
      3. Anonymous Avatar
        Anonymous

        I’m really not a fan of this response. There may well be something worth discussing in the point that academics themselves occupy a relatively privileged position. But I think the commenter, as a postdoc, is doing something important by expressing a view that many other early-career researchers — myself included — would feel uncomfortable expressing publicly.

        The point made seems quite different to me than a “rant” saying that early-career researchers have no platform. Perhaps its a bit cynical, but a big issue with young researchers is feeling able to criticise existing structures without worrying about professional consequences. Against that background, a fairly dismissive response from someone with the status of a Fields Medallist risks having a chilling effect, even if that was not the intention. I would rather see early-career researchers encouraged to articulate these concerns (even if overly negative) and then have the substance of their arguments engaged with.

        (I must say, this is also why I refrain from posting with personal details…)

        Reply
        1. mhairer Avatar
          mhairer

          Fair enough, it just irked me the wrong way being accused of acting to “protect the elite status of the elite mathematicians” (which in some mysterious way would somehow involve taking part in AGMAI) after spending a week talking to everybody (including *many* early career researchers at the conference I was trying to take part in) to try to figure out the best course of action for the mathematical community…

          Reply
  2. Mister Avatar
    Mister

    Let me quote from your website so that people know how thoughtful and open a character you have: “Prior to May 2026 I had mostly ignored the developments in the use of AI in mathematics, as they used to touch problems which I considered irrelevant for the progress of mathematics in general (such as a plethora of activities related to the trivialities of Erd˝os problems).”

    Reply
    1. anoncstheorist Avatar
      anoncstheorist

      The smugness and arrogance is nauseating.

      Reply
      1. Anon Avatar
        Anon

        Who gave the AI companies the right to “mine” arXiv papers? Their whole business model is based on theft. It is nauseating that you are siding with thieves.

        Reply
    2. Mister Avatar
      Mister

      To be more direct, statements like yours and stances/opinions like this from you and others in your community ripen you as an open target from people wielding these systems. Maybe you too should slow down and reflect on it.

      Reply
  3. Anon Avatar
    Anon

    Excellent post

    Reply
  4. Antonina P. Khramova Avatar
    Antonina P. Khramova

    I was not aware AGMAI are offering anything at this point.

    Reply
  5. betrayed Avatar
    betrayed

    This is a wonderfully brutal takedown of the betrayal we are seeing by the elites. Thank you.

    Reply
  6. Orr Shalit Avatar
    Orr Shalit

    1) I admire your writing and I sympathize with how you feel. Personally, I abhor the idea that elelems can or will “replace” humans (replace us as what? as dust in the wind?). But I think that your powerful metaphor misses the point. It you who is surrendering if you frame our prospective future as a childless world.

    2) I teach my children to use tools. I want my children to thrive in the world that they are born into and not in the (partly remembered, partly imagined) lost world of my youth. I wouldn’t give a cellphone (or a chainsaw) to a baby. Should I give a cellphone to an adolescent? Cellphones are terrible things, and I have choice. I can tell her “Cellphones will destroy you, so I won’t even show you one. If your friends truly cared about you, they would call the landline”. Or I can say to her “I entrust you with this tool, because it will help you connect with people. But you must use it carefully, it is dangerous. These are the dangers (etc) … We are going to have guidelines about how much you are going to use it and what for, and we will probably have fights about this. That’s OK. Even if I am angry at you or scared about the future, I trust you and I love you and I will be there for you no matter what.”

    Reply
  7. Pierre Menard, Author of the Quixote Avatar
    Pierre Menard, Author of the Quixote

    > “I trust you and I love you and I will be there for you no matter what.”

    This is what AI company CEOs hiss to humans while they blink them lizard eyes

    Reply
    1. Orr Shalit Avatar
      Orr Shalit

      Pierre, your logic is backwards. When evil lizard CEOs imitate the behavior of a caring human parent in order to fool everyone, that does not undermine the good intentions or acquired wisdom of actual human parents. To bring the discussion back to track: in light of the emergence of powerful and possibly harmful technology, a nuanced, careful, and clear-eyed approach is called for. People who bear responsibility for the next generation cannot afford to stick to their ideology at all cost.

      Reply
      1. Pierre Menard, Author of the Quixote Avatar
        Pierre Menard, Author of the Quixote

        I do not mean to undermine anything (and I actually admire your attitude as a parent), but to me the time for nuance is long gone. I consider AI corporations an existential threat, and I treat them as such. After the (in)famous OpenAI closed-door meeting in August, Lionel Levine, who was there, tweeted: “To the mathematicians in the room: You should know that AI labs intend to automate AI research” (source: https://x.com/lionellevine/status/2087983775489651193). How much more proof do we need that these marauders are not our friends? They *literally* want to get rid of us.

        Reply
  8. Marcin Kotowski Avatar
    Marcin Kotowski

    ” In such times do the opposite: slow down, observe, reflect. And then, after not too long: stand up and fight.” OK. Stand up and fight how? Be specific.

    Reply
  9. Andreas Thom Avatar
    Andreas Thom

    Vladimir, your claim that people join advisory groups solely to preserve their elite status is a serious accusation against identifiable colleagues. Your post provides no evidence for it.

    The analogy with collaboration under occupation makes this worse. It turns disagreement about how to respond to a deeply uncertain situation into an accusation of betrayal. It leaves little room for reasonable exchange.

    There are substantial questions to ask about AGMAI: whom it represents, how younger researchers can influence its recommendations, whether companies will heed its advice, and whether its members’ reputations will be used to legitimise decisions they oppose. Martin Hairer explicitly acknowledges several of these risks.

    I also take a different view of the prospects for younger mathematicians. I expect efficiency gains to leave little room for avoiding AI in professional problem solving wherever it helps. This applies within mathematics and far beyond it. If mathematicians want to remain among those best equipped to solve difficult problems, we should adapt our practice and our education accordingly.

    Mathematical research has intellectual and cultural value. The immediate demand for the particular results of much pure mathematical research is nevertheless limited. The skills acquired through that research are sought after much more widely. Mathematics provides an exceptionally demanding setting in which to develop these abilities. Working with AI changes how we exercise them and what we need to learn.

    I have great confidence in young mathematicians. Resilience, perseverance, the willingness to endure repeated frustration, curiosity and creativity are qualities they bring, when they are brave enough to study mathematics, and develop through serious mathematical work. These qualities equip them to learn unfamiliar tools and tackle problems we cannot yet anticipate. My confidence rests on their capacity to adapt and contribute, rather than on the preservation of existing career path.

    That confidence places obligations on those of us who teach and supervise them. We should integrate AI into their education, identify what they must still understand and judge for themselves, and teach them to guide, evaluate and interpret work done with AI.

    Reply
    1. Young Mathematician Avatar
      Young Mathematician

      Dear Prof. Thom,

      Having just completed my PhD and only just started my first postdoc a few weeks ago, I would like to give my perspective on your comment “I expect efficiency gains to leave little room for avoiding AI in professional problem solving wherever it helps.” I would also like to emphasize that my point of view is shared not just by myself, but by many of my fellow young mathematicians whom I have spoken to.

      I have never used generative AI and never will. This is due to a variety of reasons, but, if we are sticking just to mathematics, it primarily boils down to the following two reasons:

      1) I simply prefer to do mathematics the “old fashioned way.” I enjoy being stuck, discussing with my friends, reading papers and books from the great men and women who came before me and contributed to the beautiful human edifice known as mathematics, and so on.

      2) I take great pride in my work. I am not delusional as to think that I am some great mathematician like the giants of my field: Mostow, Margulis, Harish-Chandra, Borel, Benoist, to name just a few. I have nowhere near this level of talent. Notwithstanding, I take pride in knowing that whatever little novelty I have contributed to mathematics has indeed been mine, and, quite frankly, it just feels wrong to me to prompt something into an AI, receive an answer, and write a paper with myself as an author. This is just how my heart and mind work — maybe I am wrong, but this is how my inner morality guides me.

      None of us know what the future holds. In the past, I would have imagined that I would have been on track to have a good academic career (finishing my PhD with three strong (of course, in my opinion) solo papers). Maybe I will be much slower than my peers who use AI and will be one of these “dinosaurs” who is wiped out.

      However, I would like to make the following suggestion: I implore the older members of the community, including yourself, to make room for the “old-fashioned” working styles of the younger members of the community. Prof. Jonny Evans did an excellent job articulating this in his previous blog post on proofs and prompts — I admire him deeply for the compassion that he has shown us young mathematicians. Paraphrasing what he said, the community should make room for a plethora of working styles, just as we make room for people who work on a diversity of different mathematical subjects. In particular, I think it is very harmful for senior members to urge junior members who don’t want to use generative AI to do so. In my humble opinion, this will only lead to the extinction of a valuable part of the mathematical community.

      Sincerely,

      A young mathematician with old-fashioned mathematical sensibilities.

      Reply
  10. Michael Rozynski Avatar
    Michael Rozynski

    “People join advisory groups for one reason: that in a system that comes next, the advisors remain the elite.”

    That is quite some logic, and from a Mathematican, to boot. You say: Ed Witten has joined the AGMAI for one reason only: that in a system that comes next (what system exactly, pray?), he remains the elite (must be another elite than the elite of tenured professors, of which you are a member, I assume?).

    I fully support this from your webpage: “I actively resist efforts by corporate interests to co-opt our discipline in order to legitimise their business interests.”

    But does is really help your point if you lash out at other Mathematicians in public?

    Reply

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