This text was originally an e-mail I wrote to a bunch of people, hence the pretty colloquial style. AI use: none (see the author’s note at the end).
I am sorry but I just wanted to bombard a bunch of random people with a few thoughts about the AI thing.
To be clear, although I find a lot of the reactions understandable, although it is clear that this changes what math is, and although it is clear that this touches (some) people’s sense of relevance, I personally find this panicky end-of-the-world atmosphere kind of incomprehensible. It seems to me a proof that if one is looking for emotional maturity, there are better places to look for it than among mathematicians. I also find really weird that, although mathematicians are normally pretty good at keeping the different parts of a problem apart, here a salad is being done. The things I see mostly being mixed are the following:
- fear that in the future there will be less/no jobs
- the fact that now anybody can produce in a week enough good papers to have gotten you hired in Princeton
- the fact that nobody knows what to do about graduate students and what to tell them to do
- the doubt whether math will be fun, and if people will want to do math
- whether the world or society will collapse and we will become pets to AI
I will not say anything to that last point, because it is clear that if society collapses and AI takes over, then the fate of math is the last of our worries. So, let’s suppose that the world does not collapse and focus on the other things.
Well, when it comes to whether there will be jobs, I think that mathematicians have in general not asked themselves why they are being paid. I mean, if it were because of the cultural value of math, somebody should tell me why mathematicians in the aggregate are being paid so much more than poets or theologians. Now, if we are being paid because of teaching, are we really afraid that because AI can prove Cannon’s conjecture biology, economics or physics students are not going to be required to take calculus? And yes, one could be afraid about AI also taking over the teaching, but I would not put my money there. At the end of the day MOOCs were some times ago the threat because why would you go to Juan’s class if you can attend a lecture by the best of the best. Then, during COVID we also saw the effect of not having in person teaching (you cannot imagine how much furniture I built during online seminars, and you can take my word that I don’t remember any of what went on – at least for me, unless I am incredibly motivated, the discipline of having to sometimes show up seems crucial to follow lectures, and there is also the fact that human communication is much more than what AI offers and will be able to offer unless it can decide that I am not saying anything because I went to the loo or because I am thinking). Anyways, besides culture and teaching, some people do actually claim that we are paid because math is where the human intellect conquers the highest points or some bullshit like that – here I guess that I say bullshit because I never thought that my scientific work had anywhere close to the social value as the burgers being flipped by those guys in McDonald’s. So, why are we paid? If you ask anybody outside of math, it is because we do really useful things. We all know that, when it comes to our own work, this is bollocks. But math regularly produces, by sheer random, things that happen to have enormous economic value. Now, I am not much of a politician, but if I were talking to somebody deciding how money gets allocated, I would be making the case that we now have this super duper tool that will make progress much faster, and that therefore one should expect that more and faster progress is achieved, producing more high value advances. At the end of the day, if the NIH got a great machine that allowed them to find really fast cancer cures, instead of sending the people running the machine to sell ice-cream cones, you would tell them to see if it also helps to find cures for Parkinson or Alzheimer. Anyways, the main reason I see to fear that we are going to have less money is that a bunch of mathematicians go around crying and saying that math is over.
Now, it is clear that many things will have to change. First and foremost, how we give jobs and decide who is “high status” and who isn’t. Nobody is going to deny that when it came to hiring what we wanted was to hire “good mathematicians”. The issue is that in the moment of making a decision this was often set as being equivalent to publishing many and good papers journals (I would say that we were measuring these things by weight of the papers together with a factor for each journal) and that currency has been incredibly devalued. But also before AI, that currency was nowhere close to absolute because if you wanted to be hired somewhere you had first to convince somebody (local, or somebody writing a letter) that you were a good mathematician, and then that somebody used your papers to defend your case. That second step will be much harder, but everybody knows that if you keep Mladen B. and me around for a week, both armed with as much AI as we want, you will decide at the end that Mladen is a better mathematician than me (or you are out of your mind), and that you will not need to compare publication records to get to that same conclusion. I don’t know how are we going to decide as a community how we will decide who is a good mathematician, but it is clear that arguing that it is not possible to distinguish because now AI can write 10000 papers a minute is kind of silly (in countries like Spain or Italy it was decided, until not long ago, by having people solve exam problems in different areas of math – I am not advocating for that, but it shows that the system has not been stable since the Palaeolithic).
Now on to training of graduate students. Let me start by saying that I am glad to not have any graduate students starting this year, because I would not know what to tell them. The usual thing would be to give a problem one would like to work on oneself, but where one knows that if one does something, then something comes out. That is nowadays a 5 minute AI problem, and so that route seems closed. But the issue is that graduate students have been trained to write papers, because this is how we decided who is a good mathematician. When we have a clearer opinion about that, we will know how to train students.
Now about whether math will be fun or not. I guess that for some people math was a competitive sport, and these people are fucked because now that thing can easily beat you. I guess that this is the people who did math to climb the highest peaks of what human intellect can achieve, or some nonsense like that. Also, in the math bubble people’s perceived status was largely determined according to what they proved, and that has been incredibly devalued. I guess that this must hit some people really hard. Luckily for me, I was always aware that what I was doing was climbing heaps, having fun with it, finding new heaps to climb, and that while climbing around I was understanding math. I have always had a hard time answering why I did something, because I do whatever I do because I feel that there is something interesting to be understood. I don’t see how this changes now. The way I work might change (more about that below) but I am pretty sure that I will not wake up in the morning and get from AI a 15 minute summary telling me in what random directions it has been working and what random questions it has asked. It will be us who continue asking the questions. I mean, I am spending a month surrounded by statisticians who talk about Frechet means in Riemannian manifolds, and today it occurred to me to start thinking about what subsets of the round sphere can be realized as the Frechet mean of a measure—the Frechet mean is in this sense the set of global minima of the function . I am not sure if this is a good or a bad question, but I am sure that AI will not propose it to me, and that if I think about it I will understand something new. Even if I use AI. I really do not understand people who think that math stopped being fun. For me the fun is in the understanding, and I understand by climbing the next heap, and by looking from there for the next one to climb. At least for me, it is there. In my shallow mathematics.
I am a bad vegetarian. I mean, I don’t eat meat but I eat fish and lots of cheese and eggs. Not very logical, I know. But I think that I will also be a bad vegetarian when it comes to AI. I will use AI to explain things to me. I will use AI to answer random silly questions I have and that I know I would never pursue. But if there is a question I care about, for example one I discuss with somebody else (I never work alone: my mother used to say that otherwise I would never be able to write papers in English, but it is that math is for me a human endeavour, and that what I like is to talk math), then I will first think and proceed as if AI didn’t exist, and only when it comes to actually proving the painful lemma that always is there, once I know “why” that lemma is true, once I see how I would approach it, I will maybe/probably let AI do it for me. In other words, I will let AI break stones for me, but I will want to tell it what stones to break, and I will want to understand why they need to be broken, and why they can be broken. The point is that I want to understand. And I do not only want to understand because I like that, but also because I believe that this understanding is what leads me to see the next heap I want to climb. If I just went now and asked AI all the questions I might have collected over the years, then it would be done in no time, and I would have not learned anything (other people might learn by reading, but I learn by doing) and I would be afraid of not seeing anything else to do.
Something that really bothers me about the arrival of AI is that something I really value (valued?) about math is the openness of the community. The fact that mostly people shared freely what they were working about, and what problems they found cool and worth investigating. I am afraid that this will change / has changed and that given that questions are the new gold, this will largely stay like that. Even when it comes to writing research proposals. I mean, usually a research proposal would contain a combination of feasible and unfeasible questions. If you wanted to evaluate one now, you could just feed it to an AI and it could tell you how long it took for each problem, and so you could decide if the proposal had been a good one or not… I mean, while I don’t think that people are going to go total secretive, I am not sure how many people are going to send their “gold”, that’s their questions, in their applications to 50 universities. I also don’t see who is going to go and say “I think that this is a good problem” in a talk, knowing that it suffices for 2 people to talk about it for 5 minutes afterwards and decide to ask AI. That bothers me, and I hope that we as a community we will find some decent ethical standard to deal with these issues. I assume that once we have a clearer idea on how are we going to decide who is a good mathematician, we are going to also come closer to solving that problem.
Okay, if you made it here you are probably tired of reading. And I am tired of writing. But I still want to say something. People with permanent jobs can be as panicky as they want, but who are really freaking out are postdocs and people graduating this year. Somebody should tell them that the MPI, the IHES, ICMAT, NSF, most universities, and so on, are going to hire in the next year, and probably in the subsequent years, as many people as they hired before. I mean, the Max-Planck-Gesellschaft will not decide: “OpenAI proved the Cannon conjecture, and we can now close the MPI and make a haircutting saloon out of it”. Besides, contracts are signed for years, grants are valid as long as they were. All of that might change at some point, but it is not a question of a few years, the time scale at what postdocs think. So, somebody should tell them, because they are freaking out even more than the rest.
Anyways, sorry for the long rant, but I am sick of the doomsday attitude.
Juan (no AI was used here.)
Received 14 October 2026.
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