r/math 4h ago

LLMs have completely my PhD experience

221 Upvotes

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?


r/mathematics 8h ago

Dinitz-Garg-Goemans conjecture is false

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241 Upvotes

r/mathematics 4h ago

6 open erdos problems solved by GPT. 5.6 Sol

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46 Upvotes

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


r/math 12h ago

How are we going to train new PhD students?

176 Upvotes

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?


r/math 17h ago

Image Post Terrence Tao is left scratching his head about the Jacobian Conjecture counterexample. Move 37?

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459 Upvotes

r/math 4h ago

How is the rate of human discovery comparing to the rate of AI-assisted/driven discovery?

17 Upvotes

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!


r/mathematics 8h ago

Prime Indicator Function

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18 Upvotes

r/mathematics 1h ago

What topic you want to understand if you only had one month to live before you die?

Upvotes

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

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


r/math 15h ago

A counter-example to Batyrev’s conjecture on the non-negativity of stringy Hodge numbers

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80 Upvotes

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


r/mathematics 7h ago

Digit Reversal Function

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10 Upvotes

r/mathematics 2h ago

Discussion Laptop or tablet for a mathematics bs degree when I already have a desktop at home

3 Upvotes

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.


r/mathematics 4h ago

what minor did you do as a math major

4 Upvotes

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 ????)


r/math 14h ago

AI and changes to the academic job market?

59 Upvotes

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.


r/mathematics 1h ago

geometry behind autostereograms

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Upvotes

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...:)


r/mathematics 8h ago

Any Applied Math/Statistics majors NOT go CS/finance/medicine route?

6 Upvotes

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.


r/mathematics 23h ago

Discussion What's a Problem Solver to Do? (PhD Student Looking for Guidance)

92 Upvotes

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?


r/mathematics 4m ago

Young people also at ICM??

Upvotes

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!


r/math 1d ago

Why Humans Matter in Mathematics

200 Upvotes

A consensus is emerging among respected mathematicians that there is a decent chance AI will exceed humans in both brute force verification and complex, creative problem solving at the highest levels. Few frontier theorems will be proven by humans alone, perhaps, in a matter of years.

More controversial, AI may also outpace humans in shaping the correct definitions, building theories, and making connections between disparate areas of mathematics, oft considered the peak of human creativity in mathematics. New areas of mathematics may be created without much human guidance.

Perhaps mathematicians become as helpful to AI as toddlers are to mathematicians. One cannot confidently rule out this scenario - Terrence Tao may find himself completely useless in building a rich, beautiful body of new mathematics.

In such an extreme scenario, humans would still matter in mathematics!

Lockhart's Mathematician's Lament argues for the intrinsic beauty of mathematics as being of primary importance. Humans, as knowledgeable appreciators of beauty, thus play an important a role as spectators and enthusiastic amateurs in mathematics, even if they cannot be world-renowned "competitors" in theorem-proving and theory-building. This mirrors the situation in chess, where the vast, vast majority of human chess players and appreciators will never contribute to the frontier of advanced lines, and arguably even the most skilled like Magnus Carlsen rely on AI to develop their strategies, and would be crushed by such AI in competition. Being completely uncompetitive does not make chess playing and appreciation valueless.

Amateur: from French amateur "one who loves, lover"

But there is more beyond this. Mathematics allows you to understand things that are otherwise impossible to understand. Some of these are important for fairness and justice: Arrow's impossibility theorem, statistical bias, observer relatively and other tricky concepts around coordinate systems (map != territory), locally-trivial globally-nontrivial (global obstructions), forgetful maps to extract the essential structure and remove irrelevant details, limits of computation, etc.

Understanding such mathematical concepts allows you to make moral judgements in ways that would be impossible otherwise. Some super-smart machine might tell you Arrow's theorem is true, but internalizing it yourself gives you the rich understanding of fairness in democracy necessary to consciously shape it. As with humans surpassing the capabilities of their own eyes with optical then radio telescopes, we are not impoverished by using tools that allow us to extend our reach into things we can never directly perceive or understand.

It can be frightening because the life's work of someone of the previous generation can be reproduced and surpassed flippantly. Gauss himself spent a significant amount of time manually factoring prime numbers by hand, a tedious exercise upon which his conjecture on the distribution of primes (the prime number theorem) was based. Gauss died before his conjecture was proven. His notebooks full of rote calculations could be reproduced today in a fraction of a second so short you could not perceive it. Anyone today repeating an endeavor like Gauss by hand would be thought a fool, just as an astronomer who refuses to use a telescope.

That doesn't make the pursuit of understanding pointless. As the limitations of our use of AI will stem from limitations of our own minds, it will still be profoundly rewarding to practice mathematics. Indeed, we may spend less time performing rote exercises and miring in false conjectures. Already the body of mathematics is too large for any single person to understand. One can pessimistically reduce mathematics to mechanics, or optimistically find meaning in your particular path through the mathematical version of the library of babel. Because we shape our minds, our society, and our world with mathematics, we will always matter as sentient beings who reify mathematics by subjecting ourselves to reason, and better ourselves because of it.


r/mathematics 1h ago

Statistics College math concerns

Upvotes

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 :)


r/mathematics 3h ago

Number Theory Why hasn't we tried using Lean to formally verify Mochizuki's ABC Conjecture proof?

0 Upvotes

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.


r/mathematics 4h ago

What to do with a bachelors in applied math?

1 Upvotes

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.


r/mathematics 4h ago

Calculus Calculus 2

0 Upvotes

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.


r/math 7h ago

Quick Questions: July 22, 2026

3 Upvotes

This recurring thread will be for questions that might not warrant their own thread. We would like to see more conceptual-based questions posted in this thread, rather than "what is the answer to this problem?" For example, here are some kinds of questions that we'd like to see in this thread:

  • Can someone explain the concept of manifolds to me?
  • What are the applications of Representation Theory?
  • What's a good starter book for Numerical Analysis?
  • What can I do to prepare for college/grad school/getting a job?

Including a brief description of your mathematical background and the context for your question can help others give you an appropriate answer. For example, consider which subject your question is related to, or the things you already know or have tried.


r/mathematics 21h ago

Geometry Happy Real π Day!

15 Upvotes

For those that celebrate.


r/math 1d ago

Notices of the American Mathematical Society: Conversation: Jacob Tsimerman on Getting to the Fun Faster with AI — and Worrying About the Future

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175 Upvotes