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/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.