A note on proof attempts

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

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

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 ????)

I'm planning my undergrad degree and would love to hear from people who studied Applied Mathematics and Statistics. I love using math to understand complex systems and am most interested in things like space, weather, oceans, history, culture, and languages. Since I obviously can't major in all of those, I'm considering majoring in Applied Mathematics and minoring in Statistics because it seems like a flexible foundation that could be applied to many different fields. Unfortunately whenever I search for career paths, I mostly find people who went into computer science/tech, finance, or medicine which is fine but I'm not interested in those fields at all. Has anyone here used an Applied Math/Stats background in scientific research or other interdisciplinary fields like the ones I'm interested in. If so, what's your profession? If you're in science, what field are you in? I'd like to know more about using applied math/stats in areas like atmospheric science, oceanography, astronomy, environmental science, archaeology, linguistics, history, geography, or the digital humanities. I'm trying to understand how broad the field really is and what kinds of careers people have actually built with this background. I'd love to hear about any less common paths that you've taken.

I'm a PhD student working in probability and analysis, and right now the problem I'm working on could be considered a moderate extension of some existing theory. But it seems like AI is leading to the rapid devaluation of such work and pure "problem solving" as a skill in general (see for example https://davidbessis.substack.com/p/the-fall-of-the-theorem-economy ). If i were to summarize with an analogy - the stock of combinatorialists feels like it is falling while that of people working on geometric Langlands feels like it is rising.

The common sentiment pretty much everywhere seems to be that mathematicians will now be AI guiders and checkers (although the status quo is changing quite literally every day), and those with a wide vision of the entire mathematical "forest" will survive and those who "solve problems for the sake of solving problems" will not or at least will be deprioritized. Honestly, when I think about it, the problem I am working on is small enough in scope that it could probably just be plugged into ChatGPT Pro and solved after some thinking by the model, with no input of my own except a decent prompt. And I have a subscription to GPT Pro, but I still struggle to do that because it just feels so pointless. But at the same time, I feel pointless and obsolete, because - well I am, because my core skillset is problem solving.

Everywhere I look, I see posts stating something to the effect of "solving problems is not the point of mathematics, improving understanding is". And I kind of get it, it's a little evidenced by the counterexample to the Jacobian conjecture, which I saw, and basically said - ok cool, now what? But on the other end, as someone who enjoys struggling with a problem (without thinking about any broader implications), that aspect of math disappearing is deflating. As Paul Halmos famously said:

"Don't just read it; fight it! Ask your own questions, look for your own examples, discover your own proofs. Is the hypothesis necessary? Is the converse true? What happens in the classical special case? What about the degenerate cases? Where does the proof use the hypothesis?"

Sorry, this turned into a rant, but I assume many others are struggling with this transition and I wanted to just get a consensus and some opinions of what people are doing or think is the right thing to do, other than just quit and start feeding questions to AI and become AI guiders. Because if that's what math is going to become, I'd rather not do it and just pursue another field. Literally today, I found a paper on the Arxiv which literally set up a system to autonomously dig through arxiv papers for open problems and then feed them to some kind of LLM to see if it can prove it. Sure, this kind of activity is seeking truth and trying to advance the frontiers of mathematical knowledge - but is this really the point of math? Is this really what it's all about and what it's all going to be?

Here's an example of a non-specialist proving a result which is true just by plopping it into an LLM - it is literally "vibe math":

https://x.com/vikvang1/status/2079370200286433340

The example below is by people who are experts in the field, but basically created an autonomous system to trawl papers for open problems and then feed them into LLMs so that they can find solutions. Big caveat here: I have a lot of respect for the authors - they discuss the impacts of AI in terms of dislocation of early career researchers, and the general societal impacts and how humans are still important. I laud them for that. But still, it's ultimately an automated system to find problems and solve them, almost for the sake of solving them.

https://arxiv.org/html/2607.17388v1

What is the point of working on specialized/non-famous problems and understanding a field deeply if this is what's happening now?

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.

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.

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.

For those that celebrate.

Hypothetically let's assume that a human math researcher had come up with the counterexample (along with a class of counterexamples similar to the one given by Claude) to the Jacobian Conjecture before the AI era. How much recognition would that person receive? Is this an automatic tenure at a top university? Does the person become a contender for the Fields Medal? Or is it just a good CV booster but no major impact on that person's career by itself.

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

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.

The other day, I saw a YouTube video on 1.5! and the Gamma Function, and I understood like half of the maths behind it, but I couldn't really understand why extending the factorial to real numbers and complex numbers is so important. Could someone explain it so a high schooler could understand? Thank you.

I'm a medical doctor in my 50's, a long time lurker here with a passion for math but no mathematical training. I have signed up for a Bachelors in Mathematics (Hons) to be done while continuing to practice medicine. The logistics of completing the course are not an issue. I am doing this purely for the joy of the subject, to have some formalization of learning and maybe then go on to do a Master's or more (i.e. this is not for career development/pivoting - at least not at this point!) What I would like thoughts on is where you see formal training/education going in the coming years. Will having a Master's or PhD in Math lose it's cachet or utility with AI being accessible to the lay public and becoming more adept at solving problems etc (a recent 'theme' here on this forum)? I do realize the study process, learning how to do proofs and think mathematically will be good for my intellectual development. Curious as to some expert perspectives.

Has Anyone read this book Problem Solving Strategies by Arthur Engel? I am a 19 year old pursuing engineering. I love math and programming, I am trying to be better at it.

Greetings.

as you can see in my post, I’m contemplating to switch from Applied math to Applied stat.

the curriculum in two years is the same, but later on specializes, for stat it gets into…well stats in general, while applied math learns more into computional science and modeling&simulation.

my thought is, if I switch would my job seeking would approve?

I choose applied math since I couldn’t get into tech department, and that I’m pretty good at both math and coding.

and the idea of working in a robotics field also makes me interested.