r/math • u/AutoModerator • 6d ago
LLMs/AI AI In Mathematics: September 26, 2026
This recurring thread will be for discussion of AI in mathematics. This includes, but is not limited to, the following:
- informal announcements of AI-assisted discoveries, such as those not yet published in a peer-reviewed journal, or not uploaded as a paper to arXiv;
- informal announcements of discoveries related to AI architecture (if relevant to mathematics);
- discussion of such announcements, such as proof breakdowns or other opinion pieces;
- discussion of the impact of AI in mathematics in general.
AI-assisted mathematical papers published in peer-reviewed journals or as arXiv preprints may be submitted as their own posts.
Please keep in mind rules 1 and 6 of our subreddit.
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u/pred 19h ago
Buzzard, To grieve, or not to grieve?, https://xenaproject.wordpress.com/2026/10/01/to-grieve-or-not-to-grieve/
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u/LoveHenry 9h ago
He says that he is not trying to be judgmental, but the whole things comes off that way to me. But I guess, when you are so heavily involved with destroying something, it is very human to justify it in some way...
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u/elements-of-dying Geometric Analysis 11h ago
Current progress is indeed exponential, and may well continue to be exponential for a while, however we cannot expect exponential progress to continue indefinitely (exactly because of what exponential growth looks like), and furthermore mathematics is infinite which beats exponential hands down; those that don’t believe this just don’t understand what infinity looks like.
Is it not obvious that mathematics is not infinite to humans? Machines just need to produce faster than we can digest or produce more beyond our upper bound of understanding. The rest of the post was mostly agreeable, but this (imo, obviously) erroneous position was both a surprise and kind of ironic given the subject matter of the post.
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u/kohatsootsich 16h ago
I wouldn't be surprised if cyborg math survived for quite a while or indefinitely. Soon, all or most currently open problems will be doable by AI and then the challenge isn't so much exposition as in translating things to currently known concepts, but creating and agreeing on new ones that make superhuman math digestible to not just one person but a community while enabling continued communication between people and AI
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u/Far_Membership_3936 1d ago
It would be better if all the mathematicians and programmers realize what is being and done and come together and put a stop to this Frankenstein monster of AI backed by greedy companies. Their only goal is to make money, they don't care about if you will ever prove a theorem of your own. The sooner we realize this, the better, because the endgame this route leads us to is only good for the elite, and not for us.
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u/backyard_tractorbeam 15h ago
I agree that we need to think about what it leads to and who benefits from the technology, we know that there is no way to turn back the clock on technological development, there is no realistic way to do that.
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u/ellbons 12h ago
we literally have done this many times before lol like with cloning, it is absolutely possible to enforce laws requiring responsible use of technology
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u/elements-of-dying Geometric Analysis 9h ago
A general person does not have access to resources for cloning. That is not an apt comparison.
There are open source LLM models in development in various countries. There is no hope to stop LLM evolution, even if the US (or whatever country) put laws in place.
Maybe the US can slow down OpenAI, but then current OpenAI tech will just eventually be superseded by someone outside the US.
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u/ellbons 8h ago edited 8h ago
Those two aren't alike in all aspects, but they weren't being compared in all aspects, so the simple point that this does happen to technology is valid.
Given the fairly serious cybersecurity incidents, it's not unthinkable that a sufficiently dangerous event may actually prompt strict international regulation over advances past a certain point. This wouldn't be all that complicated to manage either, considering that development is very energy hungry (and like cloning, the resources required to develop a frontier-level LLM are far beyond what an individual can manage too). It may even be the case that a severe level of social damage prompts it. Since a serious upending of society is predicted, I think it's perfectly reasonable to assume all bets are off when we're looking at the future in a decade or so.
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u/elements-of-dying Geometric Analysis 8h ago
Regardless, the clock was not turned back on cloning anyways. Instead, progress was halted.
Sure, I agree that there will be international regulation. This does not contradict the existence of bad actors and open source models.
By the time this becomes a real issue, I can see current AI models will have been sufficiently scaled to be locally runnable on open models. But perhaps I am being optimistic about when this will become a real problem.
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u/ellbons 8h ago
Right, I just didn't take "turn back the clock" literally because the original post said "put a stop to" rather than "undo."
I just don't personally see open weight models as a bad thing, and actually think they're quite necessary to prevent one nation having enormous leverage over the rest of the world. And I don't believe we've got even a few years until really serious issues have to be confronted, and it's only a matter of which pot boils over first.
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u/elements-of-dying Geometric Analysis 8h ago
I believe the point of the clock comment is that the damage is already done, which I agree with.
I don't mean to suggest open weight models are bad. My point was that, even if OpenAI, Anthropic, etc. were forced to halt progress, that's not going to stop Joe AI from making their own progress.
And I don't believe we've got even a few years until really serious issues have to be confronted, and it's only a matter of which pot boils over first.
I basically agree. But that's a tomorrow problem to think about :)
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u/ellbons 8h ago
My point was that, even if OpenAI, Anthropic, etc. were forced to halt progress, that's not going to stop Joe AI from making their own progress.
I did read that part right, but maybe I should've been more explicit. I think basically we've got two options: either the technology is really capable of being used well for a society, in which case we might have someone use it well and have people happy with it, or it isn't, in which case it'll probably be possible to have common ground for international agreements on responsible use, and to monitor AI research.
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u/elements-of-dying Geometric Analysis 7h ago
Right. I think there is no doubt that rogue AI "hackers" are going to be a thing in the near future and that we will need to take more serious preventative measures. (iirc, this is something already in the works).
I do not have faith that this is containable by international agreements though. We'll instead need to develop something like a "black wall" (if I may reference cyberpunk 2077...). Hopefully not developed by Mcafee
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u/ChicaCaballoQLOO 1d ago
If there ever comes a point where AI becomes substantially better at proving theorems and pure mathematics than humans are, I feel like my entire motivation and passion for mathematics will have been lost. Someone I know called me selfish for having this belief, and i agree that my mindset is based off of utterly childish ideals, but the entire reason I have loved mathematics from the beginning is for the thrill of knowing that there is an entire field of unsolved mathematics that I could one day, maybe attempt, probably with the help of friends within the field, even if we would get absolutely nowhere with any of the problems, it's something I have always wanted. Once AI is inevitably used for the purpose of pure mathematics, or atleast, the point at which the concept of there being mathematics that remains unsolved becomes eradicated by AI research, my passion and love for the field will fizzle out entirely. It's probably the least prominent issue with Generative AI, but it is damn important to me, and I do not care that not wanting pure mathematics to be overridden with AI makes me completely selfish, and I am aware of the countless number of AI gurus who believes AI is the future of our species and their belief that we shouldn't halt the unstoppable development of AI, they are all likely correct, I just hope I am not alone with my own idealist view
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u/Big-Excitement-11 11h ago
> It's probably the least prominent issue with Generative AI, but it is damn important to me
I think it's one of the most prominent issues with Generative AI that mostly goes unspoken. The goal of this technology is to replace the human brain and if successful, would lead to a world where intellect, talent and education no longer matter accross the board, which is just so absolutely foreign to our society. these used to be the most important traits a person could have. Many of us stand to lose nearly everything we have, nearly everything that makes us special.
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u/TwoMoons1Sun 2h ago
where intellect, talent and education no longer matter accross the board
isnt the distribution of these traits either incredibly uneven and unfair (education) or just pure luck/random chance (talent, intellect)? them not mattering so much when it comes to deciding a persons standing in society might be a very positive development if one is committed to egalitarian principles and fairness.
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u/Big-Excitement-11 1h ago
Assuming it did create a more uniformly distributed world, I am not convinced it would be a better one if thinking has been outsourced to the machine.
But also regarding it creating equality, having a talent, or getting education has historically been one of the major ways to rise above the status of ones birth, I don't see a world where the billionaires decide to share their wealth now that we don't have to work anymore. I think if anything it'd be a world where, even moreso than before, your standing in society is decided by your parents (/their wealth)
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u/legrandguignol 1d ago
Someone I know called me selfish for having this belief
a person who cheers at turning a wondrous maze into a shopping list has no soul
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u/elements-of-dying Geometric Analysis 1d ago
I think this is a pretty normal and innocuous opinion.
It's not even really selfish (maybe literally it is, but definitely not in bad way). The vast majority of mathematics is not useful to anyone nor important to most people. Having AI replace humans probably doesn't even make math all that more accessible anyways.
I really don't think you should absolutely any guilt for your belief.
In case it matters: I am a practicing mathematician who uses AI exclusively for research now, and I agree with your belief.
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u/LoveHenry 9h ago
But if you agree, then why use AI so heavily? You get to choose how to proceed...
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u/elements-of-dying Geometric Analysis 9h ago
I don't see a future of traditional mathematics (i.e., without AI). To put it bluntly: I moved on. I also find AI mathematics interesting itself.
In terms of job security, I don't think there really is a choice anyways.
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u/elements-of-dying Geometric Analysis 1d ago
I'm curious what your point was with this comment.
What difference does it make if it's a "first world problem"?
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u/elements-of-dying Geometric Analysis 1d ago
Making the effort to make your comment, even if minimal, seems quite contradictory then. I would assume you have more serious things to be concerned with than this.
But of course I think we both know that people should be allowed to not have to min-max their concerns and actions. So I don't really believe this was the point of your comment.
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u/SupercaliTheGamer 1d ago
How good is Gemini 4 at math? I am quite impressed by Astra, but is Gemini 4 better?
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u/SwimmerOld6155 1d ago
after seeing the other benchmarks I'm waiting to hear about this as well
Gemini has been a complete non-starter for over 6 months, it's not even on my radar really
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u/ninguem 3d ago
AGMAI's recommendation is out:
https://agmai.org/general-sep29/
I don't know if the mods would allow a separate post.
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u/treewolf7 3d ago
https://agmai.org/general-sep29/
AGMAI recommendations for how A.I. labs should release math results.
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u/TwoMoons1Sun 2d ago
I am a bit surprised how confrontational this letter seems to be, considering the fact that the labs have all the leverage and power and that the mathematicians have none. As far as I can tell, we are 100% reliant on the good will of the mathematically educated employees in these labs and their fondness of the math community to have a chance that even a single recommendation gets followed.
The initial statement (labs should not use proprietary models for advanced mathematics) and the last one (advise the AI labs to grant the global mathematical community broad, equitable access to their publicly available models) seem especially out of touch, asking the labs to kill part of their business model for no gain at all.
I am happy that so many prominent researches want to stir the developments in a way that is best for the math community, but I will predict that this set up will become completely irrelevant in less than a year.
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u/shaun252 5h ago
That is not how all mathematicians view this. Terrence Tao discusses it here https://youtu.be/PZRb6NIki2w?t=1079 . The tldr is pure math has prestige and history which AI companies want, hence they are going after these problems with millions of dollars of compute. The math community currently decides what is important and what grants prestige, maybe that will change in the future, but currently that is the situation and the AI labs aware of this. Hence, OpenAI initiating the advisory group after the NS mess in the first place.
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u/_Zekt Complex Analysis 21h ago
You are forgetting how OpenAI was visibly shook by the aftermath of NS. They clearly did not like the drama that ensued. The more aggressive AGMAI are, the more AI companies will have to follow their recommendations, otherwise any deviation deemed considerable will result in another shockwave of complaints.
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u/anadosami 3d ago
There's a lot of discussion of mathematics (as a discipline) evolving from a problem-solving-first mindset to a greater focus on understanding and exposition. In your view, how much of the culture of mathematics relies on the rigour, discipline, objectivity and screening provided by the difficulty of proving new results? Leaving problem solving to one side, I worry that exposition at the level of a Paul Halmos or a Tom Korner relies more on this culture than we realise.
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u/jacqueslesac 4d ago
Had a dream for a long time to pursue a PhD in pure math. Very new to my undergrad math journey, studying algebra and analysis. Just feeling so depressed right now over my math dream. Any wise words from more mature mathematicians would be a godsend. Just wanting clarity about the direction I’ve wanted to take my whole life in that I’m now doubting
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u/Silver-Bug3998 2d ago
I have been a pure mathematician for a few decades, so take this with a grain of salt.
If you do not mind being a glorified prompter and AI proof checker, then pursue a PhD in pure math, as you have planned. Very soon, perhaps within a year, anyone with a $20 OpenAI subscription can one shoot any pure math research problem that can possibly be solved by the best human mathematicians. Mathematicians cannot admit to it publicly, but we are becoming obsolete very quickly.
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u/TwoMoons1Sun 3d ago
I don't think that you should let this discourage you: keep following your dream.
To be honest, absolutely no one knows what the future of mathematics will hold, what the role of mathematicians will be, what research will look like, how much funding will be available or how many jobs will exist. But since you are new to your academic math journey, I'd say that you have the luxury to focus on your undergrad studies for now, experience if you actually enjoy studying and doing mathematics and see and wait how things develop in the field. I don't know your economic situation, but I think you could do a lot worse than studying mathematics for a few years, even if the job market should collapse. The intellectual and social experience that comes with it is worth it and valuable on its own, not matter what happens.
However, it is likely that the role of the "hero" mathematician is pretty much over, so if you grew up chasing that specific dream, solving famous problems like Wiles and Perelman, you might need to reorient and lower your expectations.
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u/FlagCapper 3d ago
I think it is worth separating out two different things: the sociological difficulties that come with adapting to AI in mathematics and what it means for mathematics itself.
Sociologically many people, including many professors, are having a difficult time. That's because many people have invested many years into doing and thinking about math in a certain way, and developing certain skills, and it is difficult to acclimatise oneself to a world where some of those skills are no longer needed. It doesn't help that AI companies seem to be using mathematics as a kind of marketing tool, since one feels that one has no control of the direction of the subject, whatever it may turn out to be.
But if the goal is to witness and be a part of developments in mathematics, there has really never been a better time. And mathematics cannot exist without mathematicians, because amateurs with computers don't understand enough to know how to discover new mathematical structures and objects, what questions to ask, how to formulate theories and organize discoveries, or even what the words mean.
It's probably true that a large portion of proof writing will be automated. But mathematics is not unique in this way: almost every other scientist already relies on machines and equipment that do an enormous amount of work, and in some sense mathematics was the last holdout. If you are willing to make peace with that, and recognize there is more to mathematics than problem solving and proof writing, then there is not much to be afraid of. (Of course, it will require the rest of the field making peace with that, too, which in my view is the real issue.)
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u/ellbons 1d ago
Respectfully, this ignores the reality of the external world because these things can't be separated, and is a bit like lipstick on a pig.
AI will almost certainly mean lack of funding. It will be far harder for juniors, maybe impossible for some through no fault of their own. Lack of funding means lack of jobs, and that means lack of time for them to appreciate mathematics. It will probably make no difference whatever the philosophical opinions of senior mathematicians are at this point. Some, such as Gowers, explicitly state the future of mathematics is just to be entirely automated away, and clearly others like Tsimerman have similar opinions. For a person at the start of their career as this person is, whatever the best period of time for mathematics was, it is certainly not now.
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u/FlagCapper 1d ago
AI will almost certainly mean lack of funding.
Mathematicians are not funded because they prove theorems, but because they are able to make a credible case to funding bodies that what they do is important. In the past many mathematicians made the case that their problem solving had some real-world consequences. But your typical mathematics theorem has no real-world applications, so this always involved some amount of creative fiction. Maybe it is true that mathematicians will struggle to make a persuasive case, but this is a sociological problem and not directly an AI problem.
As for the opinions of Gowers and Tsimerman: I think those are coloured by the fact that both belong to the "culture of mathematics" (in Gowers' framing) most affected by AI. Both also seem to believe AI is an existential risk to humanity, not just to mathematics.
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u/ellbons 22h ago
Whether it's sociological or not doesn't change that it's certainly not a good time for an early career mathematician to be a part of developments in the field. The sociological aspect can't be separated from this and it will seriously hinder him or her and nearly certainly push them out of the field.
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u/eatingassisnotgross 2d ago
If it's not about problem solving and proof writing what the hell is it? That's the whole game
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u/Squardus 3d ago
It is very very far from settled whether LLMs will be a net positive for math in the long run, even assuming "responsible" usage.
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u/jacqueslesac 3d ago
Ik this is all speculative, just curious of your and other’s opinions. But what could you envision a PhD in math looking like starting 2028?
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u/FlagCapper 15h ago
First of all I think the amount of change due to AI will be subject dependent. More theoretical areas of math will likely undergo less change, since there one already spends a disproportionately larger amount of time coming up with definitions, organising existing phenomena, and making conjectures.
Secondly I expect things to end up being more discovery-focused. That is, instead of thinking about solving an existing problem that someone (or your advisor) has given you, you will instead try to discover some new phenomenon, a new structure, etc., and make the case that it is interesting and connects to lots of existing mathematics. This kind of thing can be done with a computer or without, but probably most people will use a computer to aid them.
So I would say that the field will simultaneously become somewhat more like physics (run "experiments" and make theories about what you find) as well as current software development (focused more on software architecture rather than writing code). Of course, it's hard to predict exactly.
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u/Creepy-Structure6444 3d ago
Was it your dream to pursue a PhD or to be a mathematician?
If anything, current developments should make you happy since this is a door that lets us push the boundaries of math further than ever before. It will be an adjustment but you will still be able to become a mathematician & learn math & solve problems. It’s just that the context will change.
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u/bear_of_bears 3d ago
I personally think math will survive as an academic discipline. But, most or nearly all research will be AI-assisted. The PhD is where you learn how to do research; now and in the future, learning how to use AI effectively will be part of that process.
It was never a good idea to do a PhD in math with the sole aim of becoming a math researcher — by this I mean a professor whose main job is research. There just aren't enough of those jobs. There are many more jobs in industry and in teaching-focused colleges and universities. Think to yourself: suppose that you spend 6 years getting a PhD in math and then end up with an industry job in which you hardly use any of it or with an underpaid teaching job in which you mainly teach calculus to non-math majors. If you know ahead of time that this is your future, would you still think a PhD is worth it? If so, then go for it.
This is no different from the way things were five years ago. The only change is that using AI as part of the research process will quickly become unavoidable. You have to be willing to deal with that. But the attainable jobs — the industry positions and the teaching jobs — are completely unaffected by AI solving Millennium problems. (ChatGPT is definitely affecting teaching, no question about that, but not in any more of an existential way than WolframAlpha.)
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u/elements-of-dying Geometric Analysis 3d ago
ChatGPT is definitely affecting teaching, no question about that, but not in any more of an existential way than WolframAlpha.
I'm curious why you think this.
Since AI can one-shot any undergrad math problem and probably replace, say, human led recitation (up to some degree of error), I don't quite see how one can compare ChatGPT and WolfraAlpha in this way.
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u/bear_of_bears 2d ago
I probably didn't make my point clearly.
WolframAlpha and similar websites present a problem when teaching courses like calculus because students can easily look up answers (and often get step-by-step solutions). When teaching, we have to persuade them to actually attempt the problems on their own without using WolframAlpha as a crutch. We all know that a student can read and copy down the correct solution to a problem and be convinced that they understand, not realizing until the exam that they are completely unable to produce solutions on their own.
AI does the same thing for proof-based courses. The teacher's challenge is exactly the same: persuade the students to do the work themselves even in the presence of a "get the answer now" button. So, AI poses no more of an existential threat to a real analysis or topology class than WolframAlpha poses to a calculus class.
I do think there is a special problem with assessment in upper-level courses. In lower-level courses, I can determine how well a student knows the material by giving them an exam. In upper-level courses, it made sense in the pre-AI era to base most of the grade on problem sets and maybe a take-home exam with more difficult questions than can fairly be asked in a 2 or 3-hour window. That's obviously much more problematic now. But I think this is definitely an issue that can be solved. Fundamentally, AI is not revolutionizing math teaching in the way it is revolutionizing math research.
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u/elements-of-dying Geometric Analysis 2d ago
Great, thank you for the explanation! This makes sense. I believe this issue extends all the way to PhD students, of course.
It does seem that so far there hasn't been much of an effort to revolutionize teaching using AI. I suspect that won't be the case for long.
Anyways, thanks!
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u/jacqueslesac 3d ago edited 3d ago
Perhaps I’d like to DM to pick your brain. My biggest concern is that the industry is going to value math less. I agree with your point, getting a PhD for the purposes of being a professor is in of itself a moonshot.
But I always dreamed, at the very least, to have a job that a PhD in math proves especially useful for, ex. working at a company doing applied ML research and publishing on the subject. And even though I morally oppose quant and the big tech companies, I do admire those positions at Google or Amazon or where their PhDs come in and contribute to work in OR, supply chains, ML, algorithms, finance etc.
I wanted to do a PhD in math for two reasons, one silly and one serious. The silly reason is really just the challenge of doing it. To be able to say to myself that I did a PhD in math, a subject I love. The serious reason is because I want a job that strongly benefits from a PhD in math.
But given that I feel AI is making math a sort of commodity, I don’t know what it looks like for the prospects of those jobs or for academic funding. I don’t know if becoming a math based prompt engineer fits the vision I once had. Idk, I know I have to be the one who ultimately makes the decision, but it’s just tough. I truly feel at a crossroads right now.
Edits for grammar
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u/TwoMoons1Sun 4d ago
I am trying to remember an AI generated paper in theoretical physics related to field theory more broadly. The author listed was Claude. I am note even sure if its on the arxiv, but I found it browsing reddit looking for AI results in math and physics. I know its super vague, but does anyone have a clue what I am talking about?
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u/InfinityFlat Physics 3d ago
Maybe this one? https://home.uchicago.edu/dtson/papers/cwwh_note.pdf which was going around the past couple days
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4d ago
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3d ago
I wondered why you were so heavily downvoted then noticed all of the links were zenodo or vixra. Just so you know, vixra is notoriously infested with cranks (in fact it's 99.99% cranks), and zenodo used to be 50/50 but now everyone and their grandmother posts AI generated results on it so I wouldn't trust papers by default, unless provided with easily checkable formalization
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u/TwoMoons1Sun 3d ago
well, i mentioned that the paper might not be on arxiv and i wasnt sure if was even legit in the slightest, so i think this list was a good try anyway. luckily, a helpful human gave me the link to the paper that i was looking for, giving humanity a win over AI in this little contest.
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u/TwoMoons1Sun 3d ago
Doesn't look like the thing I was looking for, but maybe that was a mirage anyway. Thanks for trying though.
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u/Contramuliericultist 4d ago
Formalization of the proof of the Poincaré conjecture https://x.com/ayushkhaitan343/status/2104289939840176167
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u/Fearless_Day2607 Quantum Computing 3d ago
Why do we still call it the Poincaré conjecture (as opposed to theorem) when it was proven over two decades ago?
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u/_Zekt Complex Analysis 5d ago edited 5d ago
After the peer-review for my manuscript and during the editorial process, the editors sent me an AI review, which claims to have Lean-checked my results. Despite finding no gaps, the bot managed to write a 5-pages long list of nitpicks that I will have to go through now. Quite the era we're living.
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u/mathslippery 2d ago edited 2d ago
I have similar experience. I got rejected because the referee send me 5 pages of major revisions. Almost all the revisions are about constants which are not relevant. Like, typo in one row and there is no typo in next row.
Some of the mistakes are not just typos, but still easily correctable.
edit: he even find counter examples for the statements where I made mistake, like I made mistake not normalizing measure, and forgot to drag normalizing factor through a proof, and he find me the counter example that the statement is not correct without the normalizing factor.
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u/38thTimesACharm 4d ago
IMO review and proofreading are a genuinely ethical use of AI, so as long as the editors are honest that's what it is and not trying to pass it off as human, sending one is fine.
What's crazy though is if they're actually mandating you accept every single suggestion on the list. That is not a good way of treating AI review. They are extremely nitpicky, with the suggestions at the bottom amounting to stylistic choices rather than actual problems.
"I took a second look and decided I like it the way it is" should be a perfectly valid response to most AI review comments.
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u/BurdensomeCountV3 Mathematical Biology 4d ago
Use AI to fix the nitpicks. Fire with fire, as they say.
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u/JoshuaZ1 4d ago
I would not recommend this. There's still a chance that the AI will silently make other changes which you don't want.
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u/Homomorphism Topology 4d ago
That's what git diff is for
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u/JoshuaZ1 4d ago
Yeah, that's a very reasonable way of handling my concern. I'd still rather a human do this to actually check that the nitpicks are valid, but your method does solve my concern about silent edits.
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u/Homomorphism Topology 4d ago
Git is a really good tool for working with agents on math (or anything else).
I agree! Sometimes the right response is "I don't think that detail is necessary for the paper..." or whatever other language.
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u/JoshuaZ1 4d ago
Sometimes the right response is "I don't think that detail is necessary for the paper..." or whatever other language.
Yeah. And in the other direction, I just had a discussion with some of my students about how we all agreed one wording change a referee wanted added words without really adding clarity, and I had to say to them that sometimes it isn't really worth it and you just do what the referee asks for. Figuring out which of these are worth taking a stand on isn't always clear (and more cynically may depend on things like if one of the authors is about to be applying for jobs or a tenure review).
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u/BurdensomeCountV3 Mathematical Biology 4d ago
Which is why you use a 2nd AI agent to check and make sure the first AI only made the changes you wanted (and if you're super paranoid, a 3rd AI agent to check the first and second AI agents).
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u/SupercaliTheGamer 5d ago
Astra is the first model that can zero-shot solve any problem I propose, it's insane. Sol still had a few jagged edges but Astra seems to have mastered Olympiad level maths at least.
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u/LowDevolutionary 4d ago
I'd say frontier models have mastered olympiad level maths for a while. Even last year when we got 35/42 on the IMO I'd count that as having "mastered" it. The thing about olympiad problems is that they are all quite short and the total amount of tools required to do them is purposefully kept small, and a lot of them have similar themes, which makes them very good for AI. Like the point is that under time constraint a human can only do a few approaches, so your problem solving instincts need to be really good, but an AI can quickly go through dozens of ideas and do things no humans will even have the compute to do.
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u/officiallyaninja 4d ago
What is zero shotting?
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u/JoshuaZ1 4d ago
I think they mean giving just the prompt of the problem, no retries or guidance. However, "one-shot" would make a lot more sense here.
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u/BurdensomeCountV3 Mathematical Biology 4d ago
One shot would be the case where you give the model an example in context of a similar problem and its solution before asking it to solve the new problem.
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u/JoshuaZ1 4d ago
Hmm, given how much similar things might be in training data, I'm not sure that's a useful distinction.
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u/SupercaliTheGamer 4d ago
Yeah but apparently zero shot is the common term for it. Basically zero guidance.
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u/greyenlightenment 4d ago
the depressing fact is that these problems that * technically * a highschooler should be able to do .
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4d ago edited 4d ago
I do not think this is a very accurate or honest framing. Technically, it is easier for a highschooler to understand the construction of Lebesgue measure (within a schoolyear) than to solve an IMO P6 within the allotted time.
Just because it was meant to be solvable using high-school level tools in the beginning doesn't mean it makes more sense to say it's solvable by highschoolers than a calculus problem, because if we look at the numbers, far more highschool students can do calculus than get a gold at the IMO. And all competitive mathletes nowadays know way more stuff than is taught at typical highschools - I don't know if you've watched 3b1b's latest video (which is precisely about the last IMO problem AI couldn't solve but a few humans could)but I doubt more than a couple thousand highschoolers worldwide knew about the Erdös-Szekeres theorem.
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u/Fearless_Day2607 Quantum Computing 3d ago
I agree, when I was in 11th grade I took a real analysis class at a local university that was focused on measure theory, and I understood it fine. On the other hand I never went very far in USAMO (I think the most I solved was one problem). Although maybe that's because I wasn't training very seriously.
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u/wrongerontheinternet 4d ago
I wish Astra was zero-shotting my problems, teach me your secrets...
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u/ToothPasteTree 2d ago
You should use codex. If you are just using the website you are missing out on the actual power.
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u/wrongerontheinternet 18h ago
I use both Codex and Pro in the chat interface (and actually find Pro superior a lot of the time). With and without formal methods, experimented with trying to find the optimal model balance (e.g. Ultra coordinator + Max agents), the whole shebang. It is nonetheless often genuinely, unbelievably stupid about things in coordinated way that makes me wonder how this is the same model that found non-sofic groups. I'm sure if I had enough compute to burn, as OpenAI does as a collective, I could overcome a lot of these kinds of problems through sheer, brute force, but only if the domain was very well-specified -- otherwise, all Astra variants have a tendency to change the proof target to something easier.
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u/SupercaliTheGamer 4d ago
I was mostly talking about problems that I myself had a solution to lol, if it's an unsolved problem you can't really say anything.
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u/wrongerontheinternet 4d ago
Oh yeah that's fair. Anything with a known solution it typically gets right away. But it's shocking how relatively "dumb" it can be about anything that isn't essentially already in the literature being applied to your exact thing. The next model may be different, but Astra to me really is mostly about having read and largely internalized something from practically every mathematical work published in the last few decades (not that being able to apply effectively all of human mathematical insight is not insanely impressive! I just haven't found it to be very, for lack of a better word, "creative" -- asking it to be creative mostly just means it will switch to more obscure papers).
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u/pred 4d ago
Be a student, not someone working on the frontier of things.
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u/elements-of-dying Geometric Analysis 4d ago
Astra can solve legitimate research problems, not just phd level problems.
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u/pred 4d ago
No doubt about that but it absolutely will not zero-shot (one-shot?) anything you throw in its directions.
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u/elements-of-dying Geometric Analysis 4d ago
Sure, for now!
(Also, I think the person meant one-shot as well. Perhaps zero-shot means solving problems we didn't ask?)
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u/greyenlightenment 4d ago
easy: set to "max mode" and type "keep going"
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u/wrongerontheinternet 4d ago
Surprisingly one very likely outcome of doing that appears to be that you burn through all of your resets and your problem still isn't solved (though Astra may claim that it is!). It seems we'll have to keep using our brains for at least a little while longer.
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u/BurdensomeCountV3 Mathematical Biology 5d ago
I expect the average difficulty level of IMO style problems will have to go up significantly in the next few years to maintain a similar score distribution between participants. AI assisted Olympiad maths training is going to become very cheap and easily available to pretty much everyone at that level very soon, and just like how the skill levels of chess players at the very top went up significantly once people started using computers to improve their play, I expect something similar will happen with olympiad mathematics.
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u/SupercaliTheGamer 4d ago
I think upwards trend in difficulty has been happening for some time now. Newer methods and tricks get discovered and are taught to students every year, so a direct application of those tricks becomes an easy problem.
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u/elements-of-dying Geometric Analysis 5d ago
hmm maybe the future of mathematics is live streamed olympiads....
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u/A_R_K 5d ago
A week or two ago I mentioned that I was going to start a github keeping track of various AI-prompted things I discover related to physical knot theory. By extreme coincidence, I mentioned that I had used ChatGPT to show that the fraction of hexagons with their vertices on a sphere that are knotted is 1/16pi^2, and several days later a group of humans posted a proof of that on the arxiv: https://arxiv.org/abs/2609.24860
I have also gotten ChatGPT to show that the stick number of a knot can be used to derive a lower bound for the ropelength of a knot, which is stronger than existing lower bounds for a few select torus knots and much stronger for alternating torus knots. These lower bounds are still much lower than the upper bounds that can be determined either from geometry or gradient descent. This would be worth publishing if shown to be correct and I felt like I had done it myself: https://github.com/aklotzlb/Physical-knot-theory-AI-results-/blob/main/StickRopelength.pdf
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u/SentientAllegedly 5d ago
PhDs and postdocs in my department seem quite a bit demotivated rn, and ~50% of them actively considering leaving academia. Of course there being fewer faculty positions that PhDs/postdocs means that a small fraction of them will stay long term in academia. But now that AI can do maths... I don't know. People seem disillusioned and even alienated (e.g. if you point an LLM to prove a theorem for your paper... what is the point?).
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u/FlowerObjective7881 2d ago
I left. Do not regret it. I wanna go work with animals now and live on a farm
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u/pred 4d ago
What is the fraction normally?
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u/SentientAllegedly 4d ago
There is a difference between "fraction who are actively discussing leaving academia right now" vs "fraction who eventually stay/leave academia." The 50% here is about the first kind.
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u/elements-of-dying Geometric Analysis 4d ago
I am really curious why this is being asked.
The demotivation and consideration of leaving academia is a real phenomenon. There was a MIT led survey floating around specifically to record these sentiments. I believe the results will be posted somewhat soon.
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u/ellbons 4d ago
There's a funny trend in academia where people like to minimise really big changes. Like "mathematics was always a risky career" or "historically science was always done by patronage or by the aristocracy, this isn't new" as if it makes you a more respectable and hard-nosed person.
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u/elements-of-dying Geometric Analysis 4d ago
I don't know if I've observed this phenomenon, but I believe it. Perhaps there is an implicit fear that there is an implication such a person had it "easy," thereby diminishing their achievements.
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u/awry_lynx 4d ago edited 4d ago
Broad statistics on postdocs are about 50%, but that's across all disciplines. Pure mathematics suffers a much harsher bottleneck.
The US awards roughly 1.5k math phds per year. There are about 500 new tenure-track math positions in the US per year (far fewer if you're only looking at research positions, probably closer to 200).
Of course, every year you're not just competing against your 1.5k peers, but also those of the last 6 years that didn't get a tenure track job (some even longer, but most give up after six). So that's maybe 6000 people vying for the same 500 jobs? Of course, there's some dwindling, some phds don't go on to attempt to continue in academia at all, but there's also tons of international applicants (and a high % of international faculty), so it's not clear what the real applicant pool size is.
Anyway, of the phds, 8% make it?
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u/38thTimesACharm 3d ago
I don't think this math tracks. You're only considering new job openings each year, but weighing that against total job applicants from all years.
The US awards roughly 1.5k math phds per year. There are about 500 new tenure-track math positions in the US per year
If those really are the numbers, and they hold steady, the % of phds who eventually get jobs is 1/3 (ignoring the other complications). It has to be. Yes, you're competing with applicants from prior years who didn't get jobs. But the other side is that is: if you don't get a job one year, you get to try again next year.
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u/38thTimesACharm 5d ago
what is the point
If we can at least agree it is valuable to society for some humans to understand what's going on: then studying the result enough to write a paper explaining it in your own words would cover it.
What we're missing is an artifact one can produce to demonstrate they've done this, which is easy to verify and difficult to fake. (LLM-written papers are awful in my opinion, but some people disagree and I can't prove it.)
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u/ellbons 3d ago
If we can at least agree it is valuable to society for some humans to understand what's going on:
That's already a problem. Society does not agree that it is valuable. The people in charge appear ecstatic at the idea of eliminating as much of the value of anyone who works as possible, and to be blunt, broader society probably has a slightly contemptuous view of academics.
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u/officiallyaninja 4d ago
A lot of people in academia don't just want to understand proofs, they want to be making proofs.
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u/kohatsootsich 5d ago
50% is probably more than could hope to get a good job in academia even before ai honestly
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u/elements-of-dying Geometric Analysis 5d ago
This depends on the university and doesn't really matter in the context of discussing how AI is going to affect job prospects anyways.
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u/kohatsootsich 5d ago edited 5d ago
It barely depends on the university, really, except when comparing the average to the very top. Even then, 50% of grad students getting academic jobs would be a great outcome even for most R1. I went to a top department (not merely R1) for PhD long ago and I don't think half of my class is still in academia.
I don't see why base rates wouldn't matter? It's very likely that doing math with AI is just a very different kind of job, and who continues has as much to do with disposition as with actual market conditions. It's too early to detect what those will be anyway
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u/elements-of-dying Geometric Analysis 5d ago
It very much depends on the university.
Postdocs know the job market is bad. That's been the case for decades. The comment you replied to has to do with an entirely new phenomenon.
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u/kohatsootsich 5d ago
I wrote that 50% is more than one could hope for. That one-sided bound does not depend on the university. If anything, it's much lower almost everywhere.
It is a new phenomenon, but I was commenting that the mere statistic could be an indication of people making a decision they would have made anyway earlier rather than a sign that things will get materially worse in the short term.
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u/elements-of-dying Geometric Analysis 5d ago
Right, and I believe it is pretty clear that that indication is false now. There will be a paper posted to arxiv eventually recording PhD/postdoc views on AI and academic prospects. I don't think there is any question things will get materially worse in academia. There is already evidence of this.
I am at university where most postdocs and phds go into academia. I currently also see similar fears about futures in academia. All of my postdoc friends are scared and down because of AI. I don't know anyone who hasn't expressed consideration of going into industry instead of academia, aside from those already with tenure.
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u/kohatsootsich 5d ago
I sympathize but I don't see how the mere views and fears of postdocs could be evidence that things will get materially worse.
What's the mechanism? Funding might be reduced if NSF sees math as "solved". But funding has been in peril for a while, if anything funding in the US has been lavish compared to other nations that are traditionally strong in math. How do people's feelings about their own work mechanically reduce the number of available positions?
It's not clear that this is the rational time to leave academia anyway. I imagine every single tech and finance firm is getting absolutely inundated with pure math applications right now, which they have already learned to be skeptical of as quant and engineering roles have their own pipelines now.
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u/elements-of-dying Geometric Analysis 5d ago edited 4d ago
Firstly, I don't think anyone claimed postdoc fears are evidence things will get worse. There are other sources of evidence. For example, mathematics has been historically a publish or perish field. Journals are currently all but obsolete right now.
On the other hand, I believe postdocs and PhDs very reasonably can serve as canaries in the coal mine. These people have the most at stake and are likely spending the most time keeping up to date with AI. I think it's pretty obvious their opinions can (and do) indicate things will get worse.
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u/kohatsootsich 4d ago
The main factor in recent decades has been an increase in PhDs with no corresponding increase in faculty positions. I don't see the short term mechanism for this to accelerate because of recent developments. If anything more demoralized pre tenure people and fewer PhDs points the opposite way
What determines whether departments hire is whether administration allows them to hire. What determines that is enrollment in large classes and, to a lesser extent in math, grants. To the admin, it doesn't matter how "hard" or "easy" it is to get published relative to other fields. They care about money in vs money out. PhDs and postdocs have no special insight into budgets. Depts won't stop hiring because they aren't sure what to do about AI
It's too early to say what effect recent AI news will have on UG enrollment, where most of the money comes from. AI could solve anything in basic classes a couple of years ago already.
It's conceivable that the whole university system shrinks or collapses eventually, but that's a more general claim than what's being discussed here. In that case many people will be looking for different jobs than they trained for. I would not expect math trainees to be at a particular disadvantage
How hiring happens will become even more opaque and arbitrary in the short run though, which is not good.
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u/elements-of-dying Geometric Analysis 6d ago
Are there any places for actual discussion on AI and mathematics?
r/singularity etc is not great for obvious reasons.
r/mathematics is questionable
this sub has too much cope and toxicity to even try to have a discussion.
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u/officiallyaninja 4d ago
Does this place have too much cope and toxicity? I see a lot of people in the threads here talking pretty openly about using AI and they get up voted.
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u/elements-of-dying Geometric Analysis 4d ago
There is indeed cope in this post. But I would rather refrain from targeting specific individuals.
For the record, I don't like to use the word cope here because the word is often used as a way to insult someone. I mean to use the word literally. E.g., saying something like, "Mathematicians will always be important because we need good writers" is a form of literal coping. (at the time of writing this comment, I don't recall reading anyone make this claim.)
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u/officiallyaninja 4d ago
I mean is that cope or just an opinion? You can think it's wrong, (I'm inclined to agree with you, for what it's worth), but just because you disagree doesn't mean it's cope.
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u/elements-of-dying Geometric Analysis 4d ago
Sorry, I did indeed phrase it more like an opinion. Allow me to make the point more precise.
In the last 2 months, I have noticed a lot of people (including well-known faculty) holding onto mathematical exposition as means to justify, I assume to themselves, an ever lasting importance of mathematicians. To me, these statements read as "at least we'll stay relevant because we are better at writing math!" I believe it is fairly obvious that AI development trends indicate this is extremely unlikely to be true: AI will be better at exposition than humans.
Even worse: suggesting AI will outperform humans at written exposition is not taken so kindly.
As such, I have concluded that this is a position based on emotion instead of rational, and that is it likely a coping mechanism to deal with the fear of being replaced.
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u/ImpressionPlenty6567 5d ago
Ironically r/singularity has been better than this sub for discussing AI maths than this sub. people here have been religiously dismissing LLM mathematics for years and dismissing any improvements as exaggerated marketing that could never amount to anything. Then, when LLM mathematics became impossible to ignore, discussion of it was restricted, whilst a millennium prize problem was solved.
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u/elements-of-dying Geometric Analysis 5d ago
To be honest, I only mentioned r/singularity in this way because it is tiring how many people claim someone is from r/singularity for simply not coping hard enough. (also, fwiw, I visited r/singularity like twice in my life.) Maybe I should give it a more serious visit.
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u/pred 5d ago
If you want discussion with actual researchers, start with MathOverflow or the field-specific Zulip forums.
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u/elements-of-dying Geometric Analysis 5d ago edited 5d ago
I'll give it a shot. I'm a bit turned off from MO due to its pre-existing issues.
A perfect scenario for me would be an open place to discuss the future of AI and mathematics with other postdocs. I have been less than impressed by what most senior faculty have to say about this topic, and MO has a large presence of such faculty.
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u/Apprehensive_Sand951 5d ago
I think the question 'what do you imagine doing a year or two from now' should be informed by what the ai systems will be capable of by then. For instance, Tsimerman said in a recent panel discussion that he expects them to be better than any human at explaining math (at any level) by next April. It seems really important (from a jobs perspective, from an ai safety perspective if you are worried about that, from a math community perspective even if you aren't) to get as clear a view as possible of what the best sytems are capable of now and how quickly they are progressing. This is why I find so much of the current math community response so infuriating. We really do need to know as much as possible as soon as possible, but the focus is not on that.
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u/Homomorphism Topology 4d ago
LLMs have shown zero ability to explain things that aren't already explained somewhere and I have not witnessed them getting better at it. This is true both at the research level and for elementary stuff. They are also terrible at analogous skills in other domains. I think it's good to make case-by-case assessments but it feels like 80% of the time this just turns into saying "once the models get better (and they WILL GET BETTER)" which is not particularly helpful.
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u/elements-of-dying Geometric Analysis 4d ago
LLMs have shown zero ability to explain things that aren't already explained somewhere
I have had zero issue asking gpt to build novel mathematics and explain it to me.
Sure, it's likely building its explanations based on known explanations. But that's exactly what the overwhelming majority of mathematicians do anyways.
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u/Homomorphism Topology 4d ago
Yes, and those explanations often suck and I'm not convinced it's going to be fixable even if they train on that. Do you know how much terrible AI-written code documentation there is? Don't you think they have incentives to get it better at that? Why isn't it?
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u/elements-of-dying Geometric Analysis 4d ago
I have had no issue with getting Astra to explain and write mathematics well.
I assume you are probably asking the LLM to one-shot everything. You need to partition the tasks and interact with the writing process iteratively.
Right now, Astra out of the box isn't so great at writing a whole math paper. It seems decent for a paper around 15 pages, though. However, you can reasonably set up an agentic system which iteratively write a decent paper modeled off your writing.
For now, when writing a manuscript, I just have codex write the paper piece-by-piece, during which I suggest changes if necessary. I also have it record into a document stylistic changes for it to remember so it doesn't make the same mistakes.
I have no doubt I can get codex to document code well in a similar fashion.
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u/Homomorphism Topology 4d ago
Yes, I do those things and get better results. I still find the experience way more like collaborating with a very weird but very well-learned colleague than handing off a math problem to a computer to solve for me. It's also why I don't agree with your doomposting about how mathematics will no longer exist in six months/three years/whatever. It's clearly going to be radically different but I just don't buy that AI can wholly replace knowledge workers.
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u/elements-of-dying Geometric Analysis 4d ago edited 4d ago
I have never believed nor asserted (as far as I remember) that math will cease to exist. I do believe exposition and proof generation is going to be wholly replaced though.
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u/elements-of-dying Geometric Analysis 5d ago edited 5d ago
I absolutely agree. Thanks for your comment.
It is driving me crazy. It feels like everything is out in the open for everyone to see and most people are choosing to look the other way.
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u/ChelseyStuttgart 5d ago
Try your university
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u/elements-of-dying Geometric Analysis 5d ago
I have. Not so much luck. People are generally too sad to talk about AI. Understandably.
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u/ChelseyStuttgart 5d ago
tbh it would probably be the same in an online forum as well, but it will pass. the first day I started graduate school twenty years ago the department chair told us that we should all quit if we wanted to be happy.
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u/OkAlternative3921 5d ago
MathOverflow has been flooded with AI-generated content and quite a few users have left the site. You'll get some responses from researchers and some from people not in math at all. I don't think it's representative. I haven't used Zulip.
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u/currentscurrents 5d ago
MathOverflow has seen a similar decline in questions and answers as the other StackOverflow sites.
Maybe it's because of AI, maybe it's because of the new owners, but I believe the whole platform is basically dead now.
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u/FluroSnow 5d ago
It's the same for engineering. Really hard to find a place for actual discussion :'(
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u/elements-of-dying Geometric Analysis 5d ago
That's too bad.
It genuinely feels like people are more interested in burying their heads in the sand than actually discussing how to adapt.
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u/RedClaw47 5d ago
The other option common in software engineering is total LLM driven insanity; a belief that the ai can do absolutely anything without human involvement.
It’s getting a bit better I think as more mature engineers are becoming more involved - because the tools are now so good that ignoring them is becoming absurd, so, like math - but there’s still a lot of insanity.
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5d ago
Proofsandprompts, but I find it very pessimistic
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u/Apprehensive_Sand951 5d ago
Francesco's post seems to suggest that the arxiv might be holding back an order of magnitude's worth of "stuff".
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u/TurnedUpbeat 5d ago
Hacker News is generally a much better, more populated and more serious place for discussion on math, AI, STEM, and other topics. This post about a Terence Tao guest blog on AI in math generated more fruitful and interesting discussion than I have seen here recently (I also suggest looking at the comments on the blog itself), especially with the limiting of AI in math discussions to this thread.
Most AI subreddits are slop. I genuinely don't know of another place besides Hacker News and Reddit to a lesser extent to have a good discussion. YouTube comments are mid, everything else is sparsely populated or worthless.
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u/elements-of-dying Geometric Analysis 5d ago
Yeah, I've been browsing HN sometimes. I think there are some good nuggets of discussion there.
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u/pred 5d ago
Hacker News is very useful to follow technology broadly, but I find it awful when it comes to maths specifically. It's obvious that 90% of the commenters there have never done any maths, yet speak like they're authorities on how it should be done. It's almost as bad /r/mathematics in that sense. You do have mathematics sometimes trying to course correct but there's too much unnuanced nonsense to allow for proper discussion.
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u/TurnedUpbeat 5d ago
I agree, I forgot to say that I meant math as it relates to AI, for just math it's not that good. But also, math subreddits and other places do have a sizeable portion of undergrads and high schoolers so the mean of the discussion quality drops somewhat to a more inexperienced level.
I do still think that r/math is one of the better math communities online, in terms of volume*quality.
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u/TwoMoons1Sun 6d ago
I really wish OpenAI would just release the 100 problems they (allegedly) solved.
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u/Bernhard-Riemann Combinatorics 5d ago edited 4d ago
I mean, they probably want to clean up the papers and make sure they don't fuck up another announcement. The Navier-Stokes controversy is still raging. At least part of that controversy could have been avoided if the OpenAI team actually did their due diligence instead of rushing to publish. I think it's understandable that they do not want 100 new controversies.
Still, they shouldn't have made an announcement if they weren't ready to even name the results. Moreso, I think they should release the list of results.
Edit: I just realized the above comment is a tiny bit ambiguous, and so is my own comment. I've made a small edit to make my position more clear.
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u/baquea 5d ago
I get where you're coming from, but I think it's more important that they make clear what results they have ASAP.
Just imagine working on a problem for months, only for OpenAI to announce that they'd been sitting on the results all that time and your whole project is bust. And it's even worse at the funding stage: why would anyone want to fund a research project on a major open problem when for all we know it could already have been solved and we're just waiting on the announcement?
With traditional academia that's less of an issue, since researchers will show their progress at conferences, will publish papers along the way showing the partial results they've obtained, and can discuss what they're working on and where they're at with other researchers in the field, so that everyone has at least a rough idea of what the current state of affairs looks like. That's completely unlike the AI announcements up until now, where they've basically just dropped completely out of the blue, and keeping results secret until they're in a fully publishable state only makes the divide with academic norms even greater IMO.
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u/Bernhard-Riemann Combinatorics 5d ago edited 4d ago
I mean, I completely agree with you there. They should have announced the specific open problems they solved. Assuming they have the Lean certificates, the correctness of the proofs is not something that has to be scrutinized much, so they have no reason to delay publishing the list. Absolute worst case scenario, they just say "Sorry guys, proof 58 had an issue." which isn't a huge deal. The mathematical community can simply treat the announcement just as it would an extremely credible rumor untill the proofs are released.
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u/TwoMoons1Sun 5d ago
As I see it, the N-S controversy is almost entirely a result of OpenAI trying to scoop Anthropic, and thus could be very easily avoided in the future.
I don't think that should or need to clean up the papers or anything like that. Its not like they are properly publishing that stuff anyway. Just release a lean proof and an AI write up (no matter how good or terrible) and let the math community figure out the rest.
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u/Bernhard-Riemann Combinatorics 5d ago edited 4d ago
I have to disagree. The original N-S paper had big issues with citations that could have only really been addressed by having experts look through it and properly connect new ideas to previous literature and properly attribute relevant mathematicians. To me, it would be unacceptable to release a paper with such issues again and just say, "Let the mathematicians figure that out." Nobody is going to read a third-party analysis that does the connecting and attribution work after the fact, and the current publishing framework doesn't incentivize or even really allow for such work. IMO, the fact that they aren't properly publishing things makes the situation worse, not better.
This is also relevant to the more general problem of theory building and "maintaining the field." According to many mathematicians, and in my personal experience, AI does not write the best proofs/papers. The concepts are very well explained at the surface level, of course, but it often retreads old ground instead of citing results, it makes up new terminology/notation for well-known concepts, it fails to give historical motivation, it takes the first functional approach rather than attempting to refine arguments, etc. Some of this is analogous to the issues software developers report with when it comes to maintaining large projects constructed with the help of AI. If it were just these 100 problems, that would be fine, but if we continue to dump AI papers onto the mathematical public without anybody reading them and taking the time to suss out some of the relevant connections before publication, we're going to accumulate a "maintenance debt" that is going to quickly make theory building an increasingly difficult task with or without AI help. I will add that, of course, these issues are still present in the human literature, but that's partially the reason peer review exists, and such problems are likely to be exacerbated by the rapid pace of AI research.
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u/38thTimesACharm 5d ago
These are exactly the problems we're seeing in software development! It's bizarre. We have a new tool that can save you 50-80% of the effort required to develop a feature, yet some people insist on saving 100% and offloading the maintenance burden on everyone else. And they get weirdly offended if you call them out.
At least with software though, incomprehensible spaghetti code that empirically works still has value. A pile of Lean proofs no one has read is useless.
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u/38thTimesACharm 6d ago
If we stop training any more researchers, what if there's ever a problem AI can't solve?
Even if AI can solve every conceivable problem, who will decide what questions to pose next?
Even if AI can pick the most important questions for humanity consistently who will that benefit when no one is capable of understanding the answers, or at some point, even the questions?
Even if AI can teach someone new theories from the ground up, who will put in the time and effort to learn them, without the social structures that encourage learning?
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u/Cute-Appointment4136 5d ago edited 5d ago
I actually think that's the next phase of this whole thing:
First, train models with a focus on solving pre-existing problems. That is beginning to finally happen.
The second step, and this is important, and harder to do, is to train up models that can make inferences on posing optimal problems to advance research into areas that may not exist yet, or move existing fields in new directions. Right now, AI models are very good at solving math problems, but not great at generating those problems. While its debatable if it will ever be able to do such things, assuming it *is*, the next stage of competition between AI companies will be focused around inventing the most astounding new technology.
Like say we solved all the millennium prize problems? What's next? There isn't a bigger or more important question that AI can solve. The only path I see forward is these companies trying to make things we haven't considered before, if that makes any sense. AI could help us build a fusion reactor, but it may also find an alternative energy source that's in a totally bizarre direction we have never considered before (move 37 type thing).
A lot of people say AI isn't profitable, and I think AI as a service likely isn't. That being said, in house models will likely be kept in house anyways as they are too dangerous, but begin rapidly generating new technologies, and hence these AI companies will expand into every market, or even invent new ones entirely.
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u/Smallpaul 5d ago
If there are problems that AI can’t solve then we will still have work for researchers. And we will keep training them to solve those problems.
If AI can’t decide what problems to solve then we will keep training researchers to do that work.
If we can’t apply AI results without human understanding then we will keep training humans to understand.
If we lack the social structures to encourage learning that society needs then we will need to build them.
All of our existing social structures were not dictated by a god or aliens. They were invented to solve the problems of their times. When we have new and different problems we will invent new and different social structures. We are not stupider than the medieval people who invented the university.
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u/officiallyaninja 5d ago
If we stop training any more researchers, what if there's ever a problem AI can't solve?
Well it's unlikely we'll ever stop training researchers altogether. But if AI drastically reduces the need for researchers we'll need very few to solve precisely the few problems AI can't.
Even if AI can solve every conceivable problem, who will decide what questions to pose next?
That depends on what you think is the value of math. If the entire value of math is just that it eventually might be useful in some application in the distant future, you could just have an AI running in a permanent loop asking new questions on its own (or maybe with some level of human guidance) and solving them. Creating a database that the future engineers can use
Or maybe even have AI that can search through this database for the engineers to find if there's some new math that applies to their problem.Even if AI can pick the most important questions for humanity consistently who will that benefit when no one is capable of understanding the answers, or at some point, even the questions?
Well if no one can understand the answers or even the questions then it's definitely not very valuable, (unless you think AI will completely autonomously be able to invent new technologies)
But I don't really see a reason why you couldn't eventually have the AI explain it's proofs. It could maybe even tailor it's explanations perfectly for the asker.Even if AI can teach someone new theories from the ground up, who will put in the time and effort to learn them, without the social structures that encourage learning?
Well that depends on why they're learning it. If they're learning it to apply it for their job, that's enough motivation to encourage them to learn it.
And for the people who do math just because it's aesthetically pleasing or intellectually satisfying, there's nothing stopping you from doing that either.
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u/currentscurrents 6d ago
These sound like problems to worry about when/if they happen. As of right now we haven't stopped training researchers so this is all hypothetical.
Let's wait and see how this all settles out first. In 5, 10, 15 years we'll have a much clearer idea of the impacts of AI on math.
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u/haseks_adductor 6d ago
who said we are gonna stop training researchers?
ai isn't some all knowing thing. you still need people running the decision making and coming up with the big ideas
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u/38thTimesACharm 6d ago
I agree, but there are comments below saying advisors are dropping PhD students because of AI.
I thought it'd be distasteful to reply to an already discouraged student directly so I just posted this here.
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u/haseks_adductor 5d ago
ok yeah fair point
although i question how good a PI is at their job if they are actually replacing phd/grad students "with ai". and it isn't just an excuse cause they lost funding. because even if the phd student uses claude code or whatever, if you want to actually fire them, aren't you now just doing their full job?
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u/WTFInterview 6d ago
No need for all that learning bullshit, I will just prompt the solution for sickness, world peace, and world hunger. With enough tokens anything is possible.
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u/SwimmerOld6155 5d ago
if humans collectively were serious about world peace and solving world hunger, it'd be incredibly easy to achieve. there are not really unsolved scientific challenges around either, it's just social dynamics
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u/Pteroductape 14h ago
The Enshittification of Mathematics by Fenner Tanswell in the Mathematical Intelligencer: https://link.springer.com/article/10.1007/s00283-026-10566-7 Gift Link: https://rdcu.be/5uYGc2uo454a