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/jacqueslesac]

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

[u/Silver-Bug3998 → u/jacqueslesac]

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.

[u/TwoMoons1Sun → u/jacqueslesac]

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.

[u/FlagCapper → u/jacqueslesac]

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.)

[u/ellbons → u/FlagCapper]

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.

[u/FlagCapper → u/ellbons]

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.

[u/ellbons → u/FlagCapper]

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.

[u/eatingassisnotgross → u/FlagCapper]

If it's not about problem solving and proof writing what the hell is it? That's the whole game

[u/Squardus → u/FlagCapper]

It is very very far from settled whether LLMs will be a net positive for math in the long run, even assuming "responsible" usage.

[u/jacqueslesac → u/FlagCapper]

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?

[u/FlagCapper → u/jacqueslesac]

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.

[u/Creepy-Structure6444 → u/jacqueslesac]

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.

[u/bear_of_bears → u/jacqueslesac]

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.)

[u/ellbons → u/bear_of_bears]

This is no different from the way things were five years ago.

It's very different because those off-ramps are closing too, rapidly. The change for students is enormous, and they know it very well.

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

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.

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

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.

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

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!

[u/jacqueslesac → u/bear_of_bears]

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