So 6 open erdos problems were just solved. GitHub link shows both prompts used and solutions verified by lean. All used GPT 5.6 Sol.

The general way to structure prompts is also mentioned in the twitter thread!

Credits: https://x.com/qiaoqiao2001/status/2080003441821163958?s=46

I recently learned about Shinichi Mochizuki's claimed proof of the ABC Conjecture through his Inter-universal Teichmüller (IUT) theory. From what I understand, the proof spans around 500 pages and introduces a large amount of entirely new mathematics. The main reason it remains controversial is that several experts, most notably Peter Scholze and Jakob Stix, argued that there is a serious gap or flaw in a key part of the argument, while Mochizuki has disagreed with their assessment.

This made me wonder: why hasn't anyone tried to formalize the entire proof in a proof assistant like Lean?

In principle, if every definition, theorem, and logical step were encoded in Lean, wouldn't it be possible to determine whether the proof is logically valid? I realize formalizing 500+ pages of highly abstract mathematics would be an enormous undertaking—especially since much of IUT theory would likely need to be built from scratch—but would such a project be feasible in the long run?

Or is the difficulty not just the size of the proof, but that there are parts of the mathematics that are still too unclear or disputed to even formalize unambiguously?

I'd be interested to hear from people familiar with formal verification or IUT theory.

If anyone knows how to paint a doomy gloomy future it's /r/math, so here's an open ended question for all of you.

No one can predict exactly to which extent the rise of LLMs will change how the workday of a working mathematician. The only thing that is certain is that the future is rather uncertain. The doomiest comments on this subreddit also show that this uncertainty is particularly tough on people who are early on in their studies, and who would probably like to know to which extent it is useful (in the sense of putting bread on the table as opposed to, say, having fun) to pour a lot of energy into learning how to proof stuff.

Now, for even younger people – kids in elementary school or high school say – the future is even more uncertain.

So my question is: has the rise of LLMs changed how you would advise a younger kid to navigate the future? Chances are that it will always be useful to have a good baseline understanding of maths and logic, but would you be less inclined to advise a skilled high school student to pursue a theoretical career? Or would you have more reservations about enabling a particularly gifted elementary school student, so as to not accidentally set them up for a bumpy course?

Or on a more practical level, have you changed your guidance on which skills are the more useful to acquire given that, for example, software development in particular has have its nature completely changed?

I know that this is adjacent to the “Career & Education” thread, but I'm more interested in the high-level picture than in personal advise.

Say I have constructive proof and I want to write a code on Sagemath. I don't know much about coding so I take help from AI. So while publishing the paper what should I do? I'm confused should I add the code or not

AI, for the last year, has been excellent at proving lemmas. I'm beginning to wonder, to what extent hirers should begin to be suspicious as to whether a student/postdoc with good preprints and publications from a minor university - or who had been an unproductive before - is actually talented vs just being early adopter who paid OpenAI $200 in 2025? There are already some young people in my field that I'm a bit suspicious of, as the quality of their publications has no correspondence whatsovever to the ideas they generate during real time discussion. This was historically an issue with collaborations, but we could at least get letters from coauthors there, but now do we need to be similarly suspicious of single author publications?

Is this just eventually going to mean that the only postdocs being hired in 2028 are from the top universities? I believe this is the already the norm in other subjects like English.

For those that celebrate.

I'm still an undergraduate, and I'm not really qualified to decipher what does or doesn't count as meaningful progress in math. Countless papers are put to arXiv every day, but they're not exactly getting posted to reddit and such, there's not a ton of buzz. Meanwhile, it feels like every other day there's some big new AI proof or counterexample of a very significant problem.

I know that people are just focusing on these because it's new and people are interested to see what is happening, but I want to know, how interesting are most of these results compared to, say, the average paper being posted on ArXiv? Or, about how often do humans provide a proof or disproof of a problem on the magnitude of the Erdos unit distance or Jacobian conjectures? Right now it seems like many open problems are being solved by AI in quick succession, and I really hope that humans are doing the same and I am just not hearing about it. Thanks!

I'm entering the fourth year of my PhD and started doing research about 2 years ago. I chose a niche topic that required me to spend a whole year in addition to my course work to get caught up in before even starting any work of my own. My advisor gave me 4 lengthy papers to get through and master their techniques. I got through 3 of them and last semester I gave my thesis proposal and passed. I still have to read the last paper which is the most difficult, but I cannot find the motivation to do it because of the recent AI progress. I am not a very talented mathematician so my only "strength" was spending the time to learn a niche and difficult area. The actual problem that my advisor wants me to solve for my thesis is not terribly difficult and is likely routine for an expert but it will take me close to a year of dedicated work.

The problem is that the last year I have not been able to shake off the feeling that what I'm doing is just a worse version of what an AI can already do. I cannot afford access to any of the top tier reasoning models but I imagine they can read these papers and come up with these extensions in just a few hours. Even just asking the free models questions about the papers it's clear that it has been trained on them and understands them well. Since then I haven't been able to find the motivation to work on my PhD and I feel awful about it. It's not like this type of work will land a postdoc or job anymore.

I don't think this post does any justice to how bad I've been feeling about my future career or my thesis but I don't want it to become a rant. I would really appreciate if anyone has any words of encouragement or validation that my concern is justified. Should I just drop this project and do something quicker to graduate?

There is a big hype over LLMs solving problems in some areas of mathematics.

Now, I'm not here to ask whether this will "replace mathematicians" (whatever that means) or not. That's already being done and a post like that is probably being typed as I'm typing this.

What I'm interested in, assuming that LLMs become better at solving problems than humans, how will we train new PhD students?

This seems like something which could drastically lower the general proficiency of mathematicians. Will a mathematician become just a person who checks LLM outputs to see whether they are correct?

Hey all. I am studying calculus 2 this summer and my professor has put forward a new criteria for getting an A and a quite unrealistic one at that. He said if using chatgpt or any assistance , we are able to create a new convergence test that has never been presented before (works even if it is applicable for even just a few types of series and fails for others) , we can get a good grade. Is it kinda possible that we do this? Has anybody got an idea. HELPPPP

p.s dont mind my english, its my 2nd language.

I’m a programmer with an interest in math so I subscribe here. Seems AI is doing a lot of work in this field and I’m sure plenty of mathematicians are interested in leveraging AI. I and other devs have a lot of experience in how to do so. I was thinking that it might be beneficial to have a thread where we work together to try and optimize your setup so that you can utilize these tools more effectively.

This was motivated by a recent exchange in this subreddit where a mathematician was saying "I’ve never heard of subagents" and I realized that you guys might be able to accomplish a lot more if we put our heads together.

My bro has qualified gate and net in maths both exam. Can anyone please tell me best institute/university for phd(maths) and complete procedure. And when university open their application forms for admission

Chat link is linked. Credit to https://x.com/dmitryrybin1/status/2079904005652893709?s=46

Could someone familiar with algebraic geometry give some insights about this?

Hello! I just got to the ICM and found out that literally no one I know is here. the profs, postdocs, PhD students, and fellow undergrads I know who said they’d go earlier in the year all dropped for various reasons in the last couple weeks :( are there any other younger mathematicians who would be down to meet up at some point in the coming days? Always looking to meet new people!

Assume you have only one month to live, what topic you. want to understand before you die?

algebraic geometry, topology, cohomology, lie group ....etc

recently i studied autostereograms and tried to make them on my own out of curiosity. the outcome was not practically useful at all as there're millions of free resources online that could make autostereograms of high quality. it's the journey that mattered. i learned a lot from it and i'd like to share

at first i was overwhelmed by the amount of variables i had to deal with. the eye separation, the view distance, the background distance, the width of the base pattern, the closest point relative to the farthest point, etc. i got lost. after some struggles i realized it's all about ratio / similar triangles

then everything became simple. we don't have to actually set how far the observer was from the screen, etc. as shown in attached image 1, we let the entire thing to be 1 unit wide and 1 unit high and deal everything inside as ratio

as a math guy i particularly love those variables that lie between 0 and 1. we imagine the observer and the background (the plane containing the farthest point) never move. the screen moves. when the screen touches the background p=0. it's the possible minimum of p. when the screen touches the observer p=1. it's the possible maximum of p. the smaller the value of p, the weaker the 3d effect is

we do the same to the closest point. closest point can be interpreted as the highest point of the 3d scene. we imagine the screen and the background never move. the closest point moves. when the closest point touches the background q=0. it's the possible minimum of q. when the closest point touches the screen q=1. it's the possible maximum of q. the smaller the value of q, the weaker the 3d effect is

let's call p the background factor and q the foreground factor and here's my program. you can run it on browsers. click ▶️ to run. click ⏹️ to exit. when running the program

• press [q] to decrease foreground factor
• press [w] to toggle foreground subject (a disc / a sphere)
• press [e] to increase foreground factor
• press [a] to decrease background factor
• press [s] to change background (4 included)
• press [d] to increase background factor
• press [x] to toggle caption (off / on)

all backgrounds are function generated. if you have any interesting ideas of making background just let me know...:)

Hello all,
I’m currently in the process of enrolling in classes for my first semester in college. I graduated from high school in 2024 and haven’t had much math experience since. Even while in school, I avoided the complex math classes because it was easy to rationalize that I wouldn’t need them for anything I was interested in- plus it was frustrating that missing a day or two meant a complete disconnect from whatever the next section was.

All of that to say, I’m not too well versed in math, and have made no attempt to sustain most of the information I had.

My current situation:
- I moved to Seattle last year and have obtained residency
- I am working 30-40 hours a week and am making enough to sustain myself, but it’s difficult to save up.
- I’ve enrolled for the fall quarter at Seattle central college
- I don’t know what I want to pursue in school, so I want to have general classes that leave wiggle room to make that choice later
- my partner is a math major

Now the question is- should I take MATH 146? Looking at everything I just laid out, the obvious answer to me feels like no. Taking 146 requires me to concurrently take math 46, which I wasn’t planning on because I didn’t want to overfill and exhaust my schedule since I’m also taking english 101. All three of those classes line up to make my in-person schedule MoWe 8:05-11:35 (eng,46,146)

Again, this is my first college experience. I couldn’t find much information on the subject which is why I’m here. My work is able to accommodate my school schedule and express that they want me to succeed; even with accommodations my hours will still take a slight toll.

If you’ve made it this far, I really appreciate it. Please ask any questions that could help. Thanks :)

I'm starting my freshman year at college with a major in mathematics and I cant find anyone with my particular issue. As it says in the title I'm torn between a laptop and tablet as I fully intend to take digital notes as my paper notes are always unorganized and I lose important things often. A issue with a laptop is I would need to get something to take notes on if I got one and a laptop feel like it will be redundant as I am not going to use it at home. I feel like a tablet with a keyboard would just cover all my needs but I would like advice from people who have already gone through this or any recommendations on what to do.

I've seen on other similar posts that a program called LaTeX will require I have a laptop but is this something I need use during lectures or something I can just use my desktop for. Also for reference I live close enough to my school that I will be going home everyday so that's not the issue.

Before I came to this debate I was looking at laptops and found the Acer - Swift Go 16 AI on sale for for 699$ usd. However if anyone has any better recommendations if you think I need a laptop feel free to send them but I would like to say around the 700$ but don't mind going above it if seriously needed. Also I would like to use windows as I'm not a fan of Mac OS. And for tablets I would also just prefer to avoid apple products as I'm not a fan of them but wouldn't mind if its the only good option.

Additionally for classes I'm taking I will have calc 3 in fall and diff eq in the spring if this effects what I should use lmk.

TLDR: just read the title.

Hello!

I am going to graduate in December with a degree in Applied Mathematics. I have had a variety of interests through my classes (cryptography, options, optimization, amongst a few others), but I am unsure as to do what I want to actually do once I graduate. I have started to consider graduate school, but I was wondering if I should rule that out since I’m already unsure on what to specialize in. Any advice/discussion is welcome, just trying to hear others thoughts and experiences.

im sorry if this is the wrong place to ask but what minor did you choose if you did a math major?? Im honestly having such a hard time and thinking about just not doing a minor. (Maybe stats or Econ ????)