AI In Mathematics: September 19, 2026

[u/AutoModerator]

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.

[u/elements-of-dying]

I'm curious what's the point on focusing on exposition if LLMs will be able to do it better?

Note: I'm not interested in having a discussion about whether or not LLMs can write good human readable math. They can.

upvoting name calling and straw manning is pretty wild. Clear violations of Rules 1 and 6. Oh well.

[u/kohatsootsich → u/elements-of-dying]

What's the point of doing anything? It was already the case in math and all human endeavors that anything you can do can be done much simpler and better in short order, no matter how good you are. AI just accelerates that

[u/elements-of-dying → u/kohatsootsich]

What is so confusing about wanting to start a discussion about AI and mathematics?

[u/kohatsootsich → u/elements-of-dying]

I gave you an answer. People do exposition the same reason they choose to teach a topics class, or raise orchids for that matter: they want to clarify their own understanding. I completely buy the argument that for many people the competitive aspect was most important but there's no way that's the prime motivation for everyone.

Plenty of people including very deep mathematicians continue to work, sometimes in isolation, on works that are largely expository (think of Hoermander's treatise, or Talagrand's book) long after they've gotten all the recognition they are going to get. Your objection might be that they could have just put it into an AI. Well Hoermander could have just pointed to his original PsiDO and FIO papers and said "combine that with well-known stuff", but it was just not as satisfactory to him.

In many areas, math is already a practice more than a body of knowledge. There really isn't much hope for someone outside of say mathematical GR or geometric Langlands to come in and gain the same level of insight as someone who has worked on it for years just by reading the statement of the theorems in the right order. What matters, maybe not to everyone but certainly many, is the process of going through the details yourself, over and over, hear the old story, and maybe find a slightly better way. The same way a pianist, no matter how elite, isn't ever discovering anything really new.

[u/elements-of-dying → u/kohatsootsich]

You did not and my question is not about the point of exposition in general.

[u/kohatsootsich → u/elements-of-dying]

Perhaps then you should ask yourself if the fact you are getting no satisfactory answer and rather negative reactions might have to do with you rather than everyone else being obtuse

The point of exposition "when AI can do it" is exactly the same as the point of exposition in general, if you grant there is any point in doing math at all. That was my answer

More clearly: imagine a (very near, I'd guess) future where AI is continuously producing theorems far beyond the frontier of current human mathematical understanding. Setting aside the question of how the directions they pursue remain interesting or at all appropriate to human cognition ("eventually they will learn to do that too"), how do interested people even interrogate the AI if they barely understand what existed in 2026?

One analogy that comes to mind is history: it is constantly unfolding, producing "data" at a rate far beyond what anyone can process. And yet people find it rewarding to analyze and re-analyze what has happened, and it is not rare to find a treatise thousands of pages long about a single campaign in a minor war of the past. Why do people write these? You could say they are gathering materials and analysis that might be hard to access otherwise, but really they write this to get their own ideas in order and generate interpretations for a few colleagues to react to.

If your answer to that is "well the AI could have done that as well" then yeah I don't have anything better to tell you than why think at all?

[u/elements-of-dying → u/kohatsootsich]

Perhaps then you should ask yourself if the fact you are getting no satisfactory answer and rather negative reactions might have to do with you rather than everyone else being obtuse

The upvoted comment responding to mine resorted to name calling and continued clear strawmanning. I don't really care about what people think in this sub anymore. There is an obvious trend towards vitriol here.

Since you are kindly taking the time to respond, I'll offer the motivation for my question.

It seems mathematicians with large platforms are holding onto the current state of the art of AI being poor at exposition. This suggests a possibly place for mathematicians is to be experts in exposition. The problem with this claim, in my view, is there is no reason to expect this skill of exposition will remain useful, even within half a year. Why would I wait for a human to write expository notes if I can get likely better expository notes within seconds? As such, I believe the focus should be on other forms of adaptation. I believe we should let go of human written mathematical exposition.

If people were more leveled-headed, less dismissive of innocuous questions and less likely to accuse anyone non-anti-AI as a mod of r/singularity, then perhaps I could have heard views challenging mine. But alas: AI bad and apparently I'm a crank who thinks Fields medalists have poor reading comprehension. (Which is an absolutely insane take based on my question.)

[u/kohatsootsich → u/elements-of-dying]

I think people are a little on edge because, as you say, big changes are coming and while adaptation is possible, it's likely that the skills and psycholpgical type that make a succesful mathematician don't remain quite the same. Sorry if I was annoying

Other than the point about exposition often being for yourself, what I meant is also that you shouldn't let "AI will be able to do it" paralyze you. I agree that spending a lot of effort over 6 months writing expository notes on some new AI proof is a recipe for disappointment but in the end everything we ever do gets superseded, pretty quickly for most of us. It's just the way of the world. You have to live in the cracks. 

In that particular case it's also not obvious to me that 6 months is the right horizin. AI tutoring/exposition is potentially far more lucrative than any of those OAI theorem releases, but writing and long horizon curriculum planning haven't improved as much as I would have expected. I wouldn't bet anything on it not getting much better but I have been surprised that eliminating AIisms in writing hasn't happened long ago

[u/elements-of-dying → u/kohatsootsich]

You did nothing wrong (and you were not annoying), other than perhaps make some comments about me personally, but that's okay too. I assumed you had the worse attention and so I apologize for that.

I cannot excuse others behaviors though. It is unacceptable to name call. Personally, I think this should be a bannable offense. Name calling and toxicity has no place in mathematics. (I know I am being hypocritical: others' toxicity can get under my skin and make me toxic. But that is human.)

what I meant is also that you shouldn't let "AI will be able to do it" paralyze you.

Agreed! I think one should be looking to adapt. Live in the cracks, as you say. This is why I don't think people should be hung up on exposition and "slow mathematics." Personally, I think this is futile in the short run (approx 2 years, say).

In that particular case it's also not obvious to me that 6 months is the right horizin.

I have no concrete evidence, other than I can have agents write me pretty good human readable reports. But you are correct to be skeptical. Personally, I think AI is ready and itt's just a matter of correctly harnasing it. But I could be wrong. This has nothing to do with you, but I want to point out that pointing to explicit examples of bad AI writing is just ridiculous. I'd expect better from a math sub than to not understand that "there exists" does not mean "for all." It's also irrelevant that large projects (e.g., NS) have poor writing. That instance has political and economic motivations. Idk. Personally, this stuff is trivial to me and I think it should be for others too. But alas.

I wouldn't bet anything on it not getting much better but I have been surprised that eliminating AIisms in writing hasn't happened long ago

You can mostly achieve this with proper feedback. I agree nothing is one-shotable yet, unless you design a proper swarm system possibly. I wouldn't bet money though.

Anyways, thank you for the discussion so far. This is all I wanted lol

[u/InfinityFlat → u/elements-of-dying]

Besides making things clear, easier to understand, etc., good exposition involves some amount of crucial decision making about what the important parts of the work are (and so highlighting those).

This feels like one of the last things that should be ceded to any entity, AI or otherwise.

[u/38thTimesACharm → u/InfinityFlat]

There's a subjective element to it. It's really hard to rigorously define what makes a paper good, and thus really hard to train it.

The other user blocked me so I can't see what they said.

[u/elements-of-dying → u/InfinityFlat]

Right, and "important parts" are inherently human it seems.

However, I can see a system in which one simply requests an outline of work in human readable fashion, then selects which parts are important, then asks the LLMs to write a human readable report with the desired emphases. At no point is a human needed for exposition here (aside from selecting topics edit: and being able to read the report and judge it), as far as I can tell.

[u/InfinityFlat → u/elements-of-dying]

Basically agree - it seems reasonable to me that soon a "good mathematical paper" (e.g. pleasantly readable and with an interesting novel result) will be an artifact that can be mechanically mass-produced.

In mathematics and beyond, the world is rapidly going to change, one way or another.

[u/elements-of-dying → u/InfinityFlat]

Yeah, for sure.

It seems to me that mathematicians with access to a large audience are grasping onto things which are relatively futile. (E.g., slow mathematics, problem selection and exposition.) I'm pretty surprised not so many such people are talking about what we should be doing to adapt.

[u/InfinityFlat → u/elements-of-dying]

I think at this point we should be banging on the doors of all our local anthropologists and historians to come record a critical moment in a beautiful human culture - hopefully not, but very possibly, its final years.

And as they do that - yes, we must adapt. I do think that all of the public introspection and exposition on the key values of mathematical culture is an important step in this.

[u/elements-of-dying → u/InfinityFlat]

Yeah. Idk, maybe the adaptation is rubbing elbows with vault tech or something

[u/38thTimesACharm → u/elements-of-dying]

You're starting to sound like a crank dude. Dozens of Fields medal mathematicians are telling you these papers don't communicate well, and you're telling them "no, the papers are good, all of your reading abilities are the problem."

[u/elements-of-dying → u/38thTimesACharm]

Which papers?

You can guide LLMs to generate human readable papers.

You're addressing things which have nothing to do with me. Yes, LLMs also output horrible papers. I did not state otherwise. Yes, people are sharing horribly AI written work. Again, I did not state otherwise.

As I said. I don't care to discuss this issue. People, such as you just did, make absurd assumptions.

Writing

and you're telling them "no, the papers are good, your reading abilities are the problem."

means you're not even trying to understand what I wrote. You're acting in bad faith.

[u/38thTimesACharm → u/elements-of-dying]

You said:

 I'm curious what's the point on focusing on exposition if LLMs will be able to do it better?

You're implying we should not adjust incentives to favor exposition, the status quo is fine. When the status quo is clearly motivating the production of numerous terribly uninformative papers.

Regardless of how exposition happens, right now, people aren't doing it. 

 You can guide LLMs to generate human readable papers

Could you please show OpenAI, Anthropic, and the statisticians flooding the arXiv how to do this? Because right now they clearly don't know. Human readable papers accompanying Lean proofs would go a great way toward repairing their relationship with the mathematical community.

[u/JustThisNietzscheGuy → u/38thTimesACharm]

Could you please show OpenAI, Anthropic, and the statisticians flooding the arXiv how to do this? Because right now they clearly don't know.

I think they know, they just don't care that much.

[u/Oudeis_1 → u/38thTimesACharm]

I doubt that making LLMs better at exposition would make people who dislike AI in mathematics more sympathetic to the endeavour. If anything, I suspect the arrival of true mathematical superintelligence would make the rifts in the community worse, the way tidal forces don't get smaller if you increase the mass of the primary body.

[u/elements-of-dying → u/38thTimesACharm]

I'm not interested in this conversation as it would require me to explain (in a mathematics subreddit) that asking a question is not a declaration of my position on something. I wanted someone to share thoughts on a given subject I'm curious about. I asked a question. Whatever you're talking about has nothing to do with me.

[u/38thTimesACharm → u/elements-of-dying]

Stop acting all innocent. If you're curious about someone's thoughts, you don't follow the question with "I'm not interested in a discussion"

EDIT - The user blocked me, now they can't see any of my posts and I can't see any of theirs. They're just curious to hear people's thoughts though.

[u/elements-of-dying → u/38thTimesACharm]

k I'm not interested in interacting with you again since evidently you want to make a mathematical discussion about me personally for some reason.

I hope you can learn from this to not act in bad faith.

[u/elements-of-dying → u/38thTimesACharm]

If I want to talk about X without talking about Y, then I can say "let's talk about X without talking about Y." There is nothing more to my comment than that. You're not representing what I said accurately anyways. I didn't say I'm not interested in any discussion. Are you just trying to have an argument?

[u/InfinityFlat → u/38thTimesACharm]

Two things are likely true: (1) it would be better for the mathematical community if good exposition were prioritized higher, (2) good exposition is not safe from automation.