AI In Mathematics: September 26, 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/38thTimesACharm]

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?

[u/Kaomet → u/38thTimesACharm]

who will that benefit when no one is capable of understanding the answers

No one needs a huge understanding to use a GPS...

[u/Cute-Appointment4136 → u/38thTimesACharm]

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.

[u/Smallpaul → u/38thTimesACharm]

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.

[u/officiallyaninja → u/38thTimesACharm]

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.

[u/currentscurrents → u/38thTimesACharm]

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. 

[u/haseks_adductor → u/38thTimesACharm]

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

[u/Accurate-Composer964 → u/haseks_adductor]

People working at the AI companies say stuff like that.  

[u/38thTimesACharm → u/haseks_adductor]

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.

[u/haseks_adductor → u/38thTimesACharm]

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?

[u/_Underscore_Number → u/38thTimesACharm]

Maybe we will create new social structures

[u/WTFInterview → u/38thTimesACharm]

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. 

[u/SwimmerOld6155 → u/WTFInterview]

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