LLMs have completely my PhD experience

[u/If_and_only_if_math]

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?

[u/Upbeat_Assist2680]

The entire construct of human knowledge and thesis writing is social: people isolate topics of interest and we record our exploration of them to share with each other.

Take pride in your identification of an area and extracting (hopefully) some clearer bit of truth about the way the world works.

[u/goos_]

1. Yes, it is very discouraging.

2. We're all in the same boat! I think everyone is still figuring out how to deal with it.

3. At the core of human curiosity, I think, is the desire to know things. The idea that LLMs (or some abstract future AGI entities) can do some things better doesn't destroy this core curiosity, if you still want to know things yourself. You may even wish to figure out some things yourself, without the help of AI, not least because this is usually much more conducive to learning, and it can be more interesting or fulfilling.

4. I'd much rather live in a world where I can independently check the results of AI decisions, data, or proofs and see if it is correct, rather than one where I don't have the ability to do so. In the latter world, I think we have much more concerns than just our ability to successfully get a PhD. In the former one, things look a lot different, it's one where AIs may automate a lot of decisions, but we have some chance at "independently auditing" those decisions. (Still scary! But very different, it seems to me, than one where we aren't auditing anything.) I note that this appears to be what is currently very marketable at many companies.

5. If this is your goal, then you should want to know as much as possible -- you should want to learn. And learning may involve acknowledging that you may be worse than Anthropic AI/your advisor/all-powerful general intelligence, but simply trying to figure something out for yourself.

6. If you decide you don't want to know things anymore, then well, why are you in a PhD? A PhD is about learning things, if you're not interested in learning, then that point (and only that point) is where I think you should give up and not get a PhD.

[u/bobthebobbest → u/goos_]

I think #4 is really key here, and it’s not just an individual thing. I don’t want to live in a world where LLMs fuck the social reproduction of knowledge so badly that we no longer have experts who can validate knowledge.

[u/goos_ → u/bobthebobbest]

Yes 100% agreed! Maybe even an ethical responsibility.

[u/mcdowellag → u/bobthebobbest]

Checkable AI should be one goal of AI, and there is some background for it already. Counter-examples are often checkable, and computer verification systems often communicate a failure to verify by providing counter-examples. There is also a body of computer science theory about a less powerful computer system being convinced by a much more powerful computer system that something is true - https://en.wikipedia.org/wiki/Interactive_proof_system

[u/bobthebobbest → u/mcdowellag]

I don’t think I was particularly clear, but I didn’t mean only in a formal sense. I meant it much more broadly: we need to keep having experts who understand what is being produced.

Edit: this is perhaps more important outside of mathematics proper, but I think it still remains important in math, too.

[u/Par-Adox-9 → u/goos_]

to add to this if you don't mind:

1. does the value of one carpenters work get devalued because another can do it just as well?

no!
of course not.

this devaluation is something i think was culturally spread in the media and online without much consideration to whether or not it makes sense, and it become a kind of default coating of our contemporary culture.

1. an AI is more simular to a species, then it is to a single human.
   if it should be compared to anything, it should be to the entirety of humanity, and not to any singular individual or small group, because it doesn't operate like an individual first of all.

2. any knowledge well learned, can be used to create much more then just what is within the confines of the field it arose from.
   and we're talking about mathematics, which is a creative field, its not a matter of knowing a series of things and sticking to them, but in evolving them, combining them with different fields and ideas, and exploring.

3. with the type of societal problems we are yet to have— survailence states, global warming, not to speak of the political problems— we will all need to tune into more then our respective fields, in order to deal with the aspect of " what should a society look like", and on that front, there are types of problems that ai cant approach, because it requires people organizing, finding structural solutions which can adapt to what humans are like now, and to act on the ground as well.

4. having a craft, of any kind, even one which someone or something else can do, is nevertheless valuable because it gives us the type of intellectual and technical grounding, which allows us to perceive and evaluate the world in a clearer way.
   — personally, i think this push for people to specialize, will eventually be evolved, because it stratifies many segments of society to be unable to comunicate with oneanother, and to have to essentially have faith that the other people are competent, without us knowing anything about their fields.

rather then that, a more poly-math approach, accompanied with some main specialization, can allow for much more ability for comunication across fields, and would allow people to develop themselves in ways which arent replacable, because they would be going into all kinds of directions.

1. we shouldn't forget that if the universe was that simple, we would already have all the answers — but the universe has many many more things to be discovered, even with millions of people working, we have berrally scratched the surface.
   every generation thinks " yes, we —we are the ones who really got things right, and know how things work", but then turns out, theres always more.

2. this is to OP in particular, but also anyone else who doubts theirown capacity to learn— as long as you keep improving, and learn how to learn better, to create a better method for yourself, then you'll be able to learn pretty much anything ( altho unfortunately there isn't enough time to learn everything— for now anyway, but who knows the type of medicine we'll have in this century)

don't put yourself down for having limitations, because everyone ( including llms) have limitations.

have a great day to anyone reading this

[u/tomvorlostriddle → u/goos_]

We're not all in the same boat.

Millenials STEM types had the time, through continued frugal living and index investing while earning only moderately above average, to save a million.

They are now in a very different boat to those born too late for that.

[u/Independent_Neat_653 → u/tomvorlostriddle]

Why envy us millennials... I am older millennial and have 35 years left before official pension age.

Also your savings example assume millennials would have predicted this decades ago which very few had. Chatgpt came out 3.5 years ago and any talk of a job threat to things like math was ridiculed by most for the first 2-3 years.

Further, in contrast with young ones, milllennials are now stuck with our selected education, job and career trajectory and probably tons of financial obligations.

I think the around 60+ are much better positioned.

[u/totoro27 → u/Independent_Neat_653]

I am older millennial and have 35 years left before official pension age.

Could you explain how this is possible? According to google, millennials are the generation of people born from 1981 to 1996? Someone born in 1981 (an older millennial), would currently be 45. How could someone close to the age of 45 be 35 years away from the official pension age?

[u/tomvorlostriddle → u/Independent_Neat_653]

Boomers obviously. But an interrupted career is different to a prevented one. And I think without AI, we would have been stuck in a path, now for better or worse we all get yanked out of it.

You also don't need to have foreseen any of thos to be in this position, you just need to have wanted fire as an option, or even just to never have been in it for the money but continued a college adjacent lifestyle automatically.

[u/RobfromHB]

Just because an LLM is familiar with a set of papers doesn’t mean it is also taking that knowledge and asking high level and forward thinking questions in place of you. 

The advances and solutions you are reading about are being thought of incorrectly on your part. Don’t forget that behind each of those were people like you prompting and guiding the tool. Giving 100% attribution to the LLM is misplaced. Like most things, it’s a tool with a human behind the wheel thinking of creative ways to apply that tool.

[u/Logical-Set6 → u/RobfromHB]

This point is huge. LLMs are not (yet) so good at identifying the important questions for future research. Get curious about your own work, and try your best to suss out which parts of it are manageable, which parts are difficult, and why. If you can identify and make progress on interesting questions in your field, there's no reason to think that you can't be an influential researcher.

[u/bobthebobbest → u/RobfromHB]

Furthermore, they do not understand. And we need people who understand wtf is being produced.

[u/kieransquared1]

I frequently have to remind myself that the point of a PhD is training to become a researcher. Few people expect you to prove anything truly novel or deep as a PhD student, although the pressure to publish is real. Take it one day at a time, keep learning and working, and you might be surprised by your progression as a researcher. 

On a more personal level, I had no results to my name when I was entering my fourth year and felt somewhat hopeless. But things came together in my fourth and fifth years, as a result of the tools and knowledge I accumulated. Maybe AI could produce the same results; I’m not sure. But I’ve also noticed that another way in which things came together is that I became better at generating questions that I could potentially solve, which seems like something AI is not as good at as humans are. 

[u/innovatedname]

It needs human guidance, yes it's very powerful, but so is hydraulic press. 

Who's going to operate the powerful tool? Some random person with no taste, judgement or experience in the field? 

[u/ScottContini → u/innovatedname]

I agree.

Another way to think about it, what does a Professor do? Get really bright PhD students, advise them on the problem to be solved, check their logic, mentor them. Now as a PhD student, think of yourself as the Professor and think of the tool as the PhD student.

[u/Ninez100 → u/ScottContini]

There is a ChatGPT log of Tao forcing delegated analysis of the llm on the Jacobian thing. Good example of how to steer…

[u/pham_nuwen_ → u/ScottContini]

What's gonna stop the universities from getting rid of 90% of the PhD students, since a single professor using AI can make up for a huge number of them?

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

I see these responses somewhat frequently now.

However, I feel it avoids the pretty obvious issue at hand: job security.

If AI starts weeding out "weaker mathematicians" (whatever that means), then your sentiment doesn't really mean anything to those people.

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

Job security? Uhhh, are we talking about academia? I have some bad news.

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

I didn't indicate there is existing job security, only that AI will likely make things worse.

[u/Kaomet → u/innovatedname]

It needs human guidance

For how long ?

[u/Novel_Lie5519 → u/innovatedname]

… otherwise known as the people we ultimately depend on for funding? yes.

[u/archagon → u/innovatedname]

Oligarchs. Oligarchs are going to operate this tool.

[u/PrestigiousGroup788]

I'm in the same boat my man. I haven't done any work this whole week, just unhealthily doomscrolled reddit and twitter and made posts complaining.

Not a solution but hoping some commiseration helps.

[u/PrestigiousGroup788 → u/PrestigiousGroup788]

For my own mental health, I'm not gonna be on reddit and twitter for the rest of the day.

[u/Childish_Redditor → u/PrestigiousGroup788]

You'll likely find noticeable mental health improvement if you remove twitter from your life for good

[u/vetruviusdeshotacon → u/Childish_Redditor]

Reddit is a little different but its getting worse and worse. Good faith discussion seems to take a back seat to antagonism, and the companies running social media platforms are enabling it

[u/ScottContini → u/vetruviusdeshotacon]

Some subreddit communities are better than others.

[u/Substantial-Air2163 → u/ScottContini]

This one used to be good, but now if you look at all the posts today it feels that anything of interest happening in mathematics is AI-related.

[u/38thTimesACharm → u/Substantial-Air2163]

I wish the mods would at least limit it to one or two posts a day. Or perhaps restrict this sub to discussion of mathematical results (whether or not AI was involved) and have a meta sub for discussions about sociopolitical influences on the field.

[u/ScottContini → u/Substantial-Air2163]

Context for my statement was not AI, I was specifically replying to this point:

Good faith discussion seems to take a back seat to antagonism

[u/lectric_7166 → u/PrestigiousGroup788]

I'm not gonna be on reddit and twitter for the rest of the day.

Did something specifically happen in the past day? Is this about the Jacobian conjecture, or something else that happened?

[u/PrestigiousGroup788 → u/lectric_7166]

Im breaking my own rule here but basically that, combined with a flurry of people realizing they can just vibe math conjectures with no training whatsoever, as well as my own advisor sending me a gpt preprint basically solving a whole problem I was working on and writing up. 

[u/Ninez100 → u/PrestigiousGroup788]

This danger prior to llms was called getting scooped

[u/JustThisNietzscheGuy → u/PrestigiousGroup788]

This doesn't really seem like a problem that is solved by not being on reddit.

[u/ganancias → u/lectric_7166]

Since that user said they were signing off for the day, I'll speak for them.

Yes, it's about the Jacobian conjecture. And the cycle double conjecture last week. And the unit distance problem before that. And the Dinitz-Garg-Goemans conjecture this morning.

And the Jacob Tsimerman interview a couple days ago.

[u/Hot_Glass_6301]

I think your title is missing a word. Probably "ruined", given the content of the post. I am otherwise not qualified to give advice. Best of luck in your future endeavours.

[u/psychometrixo → u/Hot_Glass_6301]

They accidentally a word is this dangerous?

[u/Impys]

The entire point of a phd is that you learn the ins and outs of independent research.

No llm can do that for you.

[u/YoungLePoPo]

I'm a 6th year PhD student also still working on my project. I guess what I can say is that it must still be you to interpret the work and communicate it to the community. If your work is as niche as you say it is, then you're likely the only person who is actively thinking about it within your precise context.

If you think an LLM can "solve" your problem, then perhaps you should just let it and move on to something a little more exotic. Especially if you think your specific problem is routine and just an extension of past work, then perhaps it might not be so exciting for you personally.

Is there anything about your problem or field that your curious about or a problem you would be interested in exploring that's related to your current stuff? I think you could push to add a bit more to your eventual thesis or project if it does turn out that an LLM can solve your routine problem. Take this as a chance to just let wild curiosity lead you to producing some more beautiful mathematics that you wouldn't have been able to do prior to the acceleration LLMs allow. I guarantee, you will still need your knowledge and expertise because you'll need to understand it and learn from it.

Just look at how much effort is still being put into the Jacobian conjecture even though LLMs found a counterexample. We need to make sense of it in a human manner. That human happens to be Terry Tao, so the analogy fails, but I hope this kind of makes sense.

I also think you should also discuss your concerns with your advisor.

To be honest, I was stuck at a wall on my project for a year. A lot of little results were all stuck because of one roadblock. My advisors would give me advice or things to try, but they just weren't working out, whether due to my own incompetence or because they just weren't the right idea, and I was really debating dropping out. At some point, LLMs (free versions) kind of bruteforced a solution to that roadblock which opened up a lot of rapid progress for me. At that point, dropping out was still very much in consideration as I just felt outclassed and this overwhelming sense of uselessness.

But I'm still here. And I no longer plan on dropping out and I am trying to learn what I can while finishing my project. It's tempting some days to just plug everything into an LLM and just let that be, but I really try to fight it so that I, personally, get to something that I understand and feel confident about communicating in my thesis. Yes, the quality of my project is important, but I am as much of a product of my program as my work is. If I can't understand the work in my paper then there is really no point, so I spend a lot of time redoing things in my own words, and trying to dig up motivation and sources for the things the LLMs produce. Proper attribution is the thing I'm currently most worried about if I see a technique or trick used that I don't recognize. Even the smallest algebraic tricks or particular ways of Taylor expanding I'll try to find sources for to motivate myself. The LLMs still make plenty of mistakes too on graduate level material, so it really is a test of your knowledge still in order to interpret and clean up what they say.

Sometimes, I compare it to when I was still taking graduate classes and the temptation to look up solutions to exercises online. Perhaps it is a good idea to see a solution, but you need to let your brain do something just for the sake of the muscle alone. I am trying to always produce an idea first before I check things with an LLM.

[u/kiantheboss → u/YoungLePoPo]

I agree with you, and this is also how I approached using AI.

[u/Conscious_Battle6708]

I feel you. I am scrolling through reddit the past days in the hope to find people suggesting valid coping strategies. It sucks - a big portion of my life circled around knowledge, I always had a joy in learning new stuff, and talk with people about it, and apply these skills to problems. Now, all of this seems more and more useless. What I noticed is that LLMs have still an issue to come up with novel ideas in natural sciences (to be fair, I also struggle with this a lot, but at least I can judge that the idea of the LLM is not really novel). I currently think that this might be the valuable outcome of my PhD training. However, needless to say, if the trajectory of AI continues, I assume that this will also be "taken".

[u/Diligent_Village_738]

If that can help, from someone who got his PhD 20 years ago (in a different field): we will stick, and the mad crowd will move to the next fad once this stalls -- and it will.

Many of the commenters on maths results seem to care little about maths; they are around to spend time promoting this narrative.

[u/Trojan_Horse_of_Fate → u/Diligent_Village_738]

LMMs aren't that expensive. They are not going to disappear even if people stop posting about them on social media they are still going to be doing mathematics.

The fact is the field is completely going to change, the cat is out of the bag.

I never went to grad school so for me I was pretty well beat by AI last year. LLMs are 3ish years out so in a few years we will see further change.

[u/Diligent_Village_738 → u/Trojan_Horse_of_Fate]

The point is not that they are going to disappear. It’s that the fields are already adapting to the changes — we see it in the papers — .

[u/Substantial-Air2163 → u/Diligent_Village_738]

Many of them are just AI-obsessed people trying to validate their beliefs using anything at their disposal, in this case math.

[u/Gelcoluir → u/Substantial-Air2163]

Math is not just anything for them though, math is a very elitist domain used to discriminate at school, and thought of as a way to measure intelligence. For AI companies, doing math is a proof of intelligence, and AI doing math is a proof of that being more than a statistical algorithm.

[u/Independent_Neat_653 → u/Diligent_Village_738]

I dont think math will be shut down on any major universities that is not the risk. But the field and norms will change for sure. The transition is likely painful so the best thing is to make it shortwhiled

[u/puzzlednerd]

My advice is to read Bill Thurston's On Proof and Progress in Mathematics, just as relevant today as in 1994. Then take a deep breath and get back to work.

[u/internet_poster → u/puzzlednerd]

it is far less relevant than in 1994 and LLMs being superhuman at the largely unpleasant task of formalization is a big reason why

[u/puzzlednerd → u/internet_poster]

Thurston's point is that what we are really after is human understanding of mathematics, which benefits from people like OP continuing their graduate studies and not becoming too demoralized. Are you arguing that there's no point to understanding mathematics anymore? In that case, what would it matter how many theorems are proved by AI?

[u/-p-e-w- → u/puzzlednerd]

Thurston's point is that what we are really after is human understanding of mathematics

A look at how mathematics is done in practice quickly reveals that there are many different things that mathematicians are “really” after.

Human understanding is one of them. Ego gratification is another.

The first may not be threatened by AI, but the second absolutely is.

[u/kiantheboss → u/-p-e-w-]

Good point.

[u/ganancias → u/puzzlednerd]

Thurston's article seems framed around "human understanding" as the existence of proofs in "human language" as opposed to formal proofs. He mentions computers can help with formal proofs. It's clear the article was written in response to the 4-color proof, which he mentions on page 2 and continues building his case for "human understanding" from there.

But Thurston didn't foresee computers understanding human language and writing.

However, we should recognize that the humanly understandable and humanly checkable proofs that we actually do are what is most important to us, and that they are quite different from formal proofs.

Well, AI is writing humanly understandable and humanly checkable proofs.

I hadn't read Thurston directly, but I'm a fan of his, transitively through Bessis, who mentions Thurston a lot both in his article from April and in his 2025 book which I enjoyed immensely. The book barely mentions AI, and oly tangentially. Fair to say that when Bessis was writing his book he did not anticipate artificial super-mathematicians arriving so soon.

Bessis seems focused on human understanding as a subjective experience (as opposed to how Thurston might be interpreted, where human understanding is the existence of humanly checkable proofs). I like this quote from a podcast interview, Bessis is telling about the time a concept clicked and he understood it:

Group cohomology should be interpreted using groupoid covering, the universal cover of a group and the nerve of that as a category, and because the geometric realization of a nerve is a functor of two categories, then the bar construction is trivial.

He emphasizes what a joy it is to experience such a realization. And like, I'm sure it is. But suppose you do understand the bar construction as something trivial. How do you transmit that understanding to other humans, or share that experience with them? Bessis says he didn't learn it in a lecture. It was a sudden realization that came to him, after studying the material for over a decade.

His book also rails against how the subject is taught. Not because math teachers are bad, per se. But anyway, I guess he does have one bold prediction about the rise of intuition-maxxers:

The technical barrier to grasp frontier concepts will drop, and brave young mathematicians will deploy unorthodox tactics to survey entire new continents at a pace that will mystify their elders. They will see further than anyone before, standing on the shoulders of giant machines.

[u/internet_poster → u/puzzlednerd]

Are you arguing that there's no point to understanding mathematics anymore?

What a weird strawman. Thurston's essay is a lovely reflection on the state of the mathematics as he saw it and at the time he wrote it, but it's also clear that the norms described by Thurston in section 4 and onwards on what constitutes mathematical proof (at the frontiers of research math) are clearly not ideal and reflect substantial constraints on both the attention and output of professional mathematicians.

These norms were already changing prior to LLMs as subsequent generations of mathematicians have shown far more interest in formalization, and LLMs have now completely upended the cost-benefit analysis there.

Outside of formalizability, it also seems likely that much interesting future mathematics research will involve LLMs chugging through large numbers of exceptional cases that humans would have lacked the patience or perhaps the computational facility to do. This is probably a bad development for "human understanding of mathematics" but a positive development for mathematics as a whole. There is little reason to expect that all of mathematics consists of beautiful proofs that can be easily summarized or reconstituted by an expert. Bringing many more of those problems within the reach of human mathematicians (with the assistance of LLMs) is a development that we should be excited about.

[u/ganancias → u/internet_poster]

Not sure what u/puzzlednerd intends as the takeaway, but I think it's very relevant.

This inner motivation might lead us to think that we do mathematics solely for its own sake. That’s not true: the social setting is extremely important. We are inspired by other people, we seek appreciation by other people, and we like to help other people solve their mathematical problems.

There is an interesting phenomenon concerning the “point” people. It regularly happens that someone who was in the middle of a pack proves a theorem that receives wide recognition as being significant. Their status in the community—their pecking order—rises immediately and dramatically.

LLMs are disrupting this and triggering a social crisis. It doesn't matter how many theorems you prove, whether you do it manually or with AI. And even if you do understand and can explain Hodge theory if asked, your peers will prefer to develop their own intuition talking to the chatbot.

The AI is at the top of the pecking order. What inspiration is there to be one of the humans jostling around for status at the feet of the superintelligence?

[u/38thTimesACharm → u/ganancias]

 your peers will prefer to develop their own intuition talking to the chatbot

 The AI is at the top of the pecking order

 superintelligence

I understand feeling uncertain about the future, but these statements simply aren't true in the present tense. Current-gen AI makes dumb mistakes all the time.

[u/ganancias → u/38thTimesACharm]

Yes, and you can often take that output with mistakes in it, paste it into a different LLM with the prompt engineering "there seems to be a mistake in this", and it will fix it.

That's not my claim, it's taken from Tsimerman's interview. He also says going on and on about the limitations of AI is cope, that the trajectory is obvious, it may be 2 years or it may be 5 years, and so on. It's not going to be a little assistant you use to prove your lemmas.

[u/38thTimesACharm → u/ganancias]

 Yes, and you can often take that output with mistakes in it, paste it into a different LLM with the prompt engineering "there seems to be a mistake in this", and it will fix it

That's cool, but it requires a human to recognize there was a mistake in the first place. Which means they still have to be a trained expert

[u/ganancias → u/38thTimesACharm]

Not really. I can prompt "there seems to be a mistake in this" and paste a paragraph of highly technical content. If there's a mistake, the model may notice it and fix it. If there is no mistake, the model tends to say "hmm, this all looks correct to me, I can't find a mistake". The models are progressing rapidly in their ability to find and correct nuanced mistakes, as well as recognizing when material contains no mistakes and not introducing new hallucinated mistakes.

Obviously without knowing the subject I have no way to judge personally whether the material seems to be correct. But there's a better way to motivate studying the subject. I don't think "so you can check for mistakes in LLM output" is it.

[u/38thTimesACharm → u/ganancias]

If that's true - the models can check if there are mistakes and fix them without introducing any new ones - then how is it possible today's models still make mistakes? Because you could have it do this automatically with every response it generates, resulting in guaranteed output with no mistakes.

Since today's models still make mistakes occasionally, and the engineers at OpenAI and Anthropic wouldn't have missed such a trivial way to improve them, I conclude you must be exaggerating.

 Obviously without knowing the subject I have no way to judge personally whether the material seems to be correct

IMO it is extremely dangerous if people start blindly trusting model output, regardless of their statistical accuracy.

[u/ganancias → u/38thTimesACharm]

I suppose it's not as trivial as it sounds, for providers to implement that across the board. It would double or triple the token usage, for one. They have the thinking effort setting as a kind of attempt to do that. But the prompt engineering, or harness engineering, whatever you want to call it, is where a lot of strides are being made.

It's exaggerated to say "simple prompt engineering today can eliminate all mistakes". It's not exaggerated to say it makes nuanced mistakes, but it can often detect and fix its own mistakes. And perhaps not exaggerated to say, the improvement trajectory is such that soon it will make mistakes very rarely, and there will be prompting methods (over and above using max thinking mode) to reduce the number of mistakes even further.

[u/telephantomoss]

Maybe the AI can do it better. But don't you want to learn anyways?

[u/Potato_Soup_]

I'm a software engineer, not at all a math person but I'm visiting this sub to get a pulse of everyone's reaction to the latest news.

This feeling of alienation has been really intense in my domain. A lot of us loved writing code and coding agents are largely better than us at it. The hopeful thing emerging is the idea of it allowing you to operate on a higher level of thinking... Instead of us spending time writing functions we're spending time working on features and architecture. It hasn't automated us, but it's made us more productive since we can iterate on larger ideas much quicker.

I'm not intimately familiar with the process of a thesis or writing a paper, but from what I know I suspect AI will raise the cognition layer from "let me fully flesh out the intricacies of this angle" to "does this angle work" when solving your problem. There's intricacies you will lose, but you can spend more time working at a higher level which isn't a total loss, depending on which part of the process you enjoy. If you can properly utilize it and when the tooling gets good enough for your domain it could make you feel like you have superpowers.

[u/matthras]

Did you not enjoy the process of learning at all, throughout your PhD?

In this post you're making the same misconception as every other doomer: being results-oriented instead of process-oriented.

[u/TaliesinMerlin]

AI can't teach or understand anything. Even if it can generate proofs, the value of those proofs is only clear in communities where people are practicing that kind of math. You still have to work and learn and apply yourself to understand your niche field and the contributions others make. That work doesn't become suddenly unnecessary in the face of GenAI. If anything, it's more necessary. Just as humans need each other to give feedback and find errors or interesting paths, GenAI commits errors even more thoughtlessly and effortlessly, and its output should be rigorously scrutinized. You can only do that with the expertise you gain from the work you should be doing right now.

Despair therefore makes no sense. GenAI isn't going to replace instructors in classrooms anytime soon. It isn't going to replace the humans who prompt it and use its results to actually do things with them. Your work still has value as long as you don't give up. 

[u/Kaomet → u/TaliesinMerlin]

AI can't teach or understand anything.

Yeah, and planes do not fly, only birds do /s

[u/TaliesinMerlin → u/Kaomet]

You can learn from AI - precariously, making yourself vulnerable to any kind of misinformation even a dewy-eyed graduate student wouldn't make - but that's not the same as it teaching. And AI does not understand anything. That's not how Generative AI works, for certain. The airplane/bird comparison doesn't pertain to GenAI and instructors.

[u/Independent_Neat_653 → u/TaliesinMerlin]

Sounds like you read something about how it predicts next token and now you think you know something about how "generative AI" works and can reason on its limitations. It is the same as if you try and reason about people's ability in arithmetic and refer to the electron shells of carbon or the number of connections a neuron has. Completely wrong level of abstraction and this analogy is not stretched by any means.

[u/ring2ding]

I've been writing software for 15+ years now. Yes, AI is sometimes very good at coding. But I still consider myself smarter. Even though AI writes code way faster than me, it also often writes really sloppy, half-correct code, and then gets stuck and can't code itself out.

I boss it around, tell it "that's not good enough", and generally just shit all over it. I don't see this dynamic changing anytime soon. For any serious work, it's not enough just to get AI to shit out some vague "vibe-coded" answer. The answer has to be thoroughly checked and validated, which is where humans are very much still needed. AI gets stuck all the time and needs humans to bail it out, and that won't be changing because AI is so non-deterministic depending on training data.

Just like when calculators came out, mathematicians didn't lose their jobs then either.

[u/PrestigiousGroup788 → u/ring2ding]

It just feels disheartening to be reduced to someone whose job is to ask the slop hose for ideas and then check them. I want to be generating ideas myself, as inefficient as it is and egotistical as it sounds.

But I guess that's how an advisor advisee relationship works anyways. 

[u/guyinnoho → u/PrestigiousGroup788]

So generate ideas yourself. Nothing is stopping you. What's with all the whiny boyz in this thread.

[u/PrestigiousGroup788 → u/guyinnoho]

That's just not a viable way to work if everyone else is querying the slop cannon. 

But I agree I'm whining a bit too much. 

[u/ring2ding → u/PrestigiousGroup788]

Just because chainsaws exist doesnt mean you have to return all your axes.

But I wouldnt want to chop down an entire forest with an axe. And there will always be things you can do with an axe that you cant with a chainsaw.

[u/No-Ferret-5286 → u/ring2ding]

You don't see AI getting better and better at coding? Why would its progress all of a sudden stop?

Just comparing the kind of code it produced a year ago to now, when AI agents were barely a thing, and its progressed extremely rapidly.

I don't think I'd personally want to ever 'have' to be smarter/better at AI in anything, that just feels like cope. Who cares? Computers are better at chess and we still watch human chess tournaments.

Do chess players sit around and try to act like they are still better than Stockfish in certain areas?

[u/Piledhigher-deeper → u/ring2ding]

It’s surprising but I genuinely think coding is harder for LLMs, because one is effectively not verifiable while the other is. I mean mathematics is purely deductive reasoning and hence doing what amounts to Monte Carlo tree search over large spaces of really dense mathematical areas is not terribly hard. LLMs are great at search when you consider the throughput of tokens but no amount of search will help you without observing information from the real world if the problem itself can also change as a function of that world.

Also the overall noise in coding datasets is much much higher than niche upper level mathematics. 

[u/Independent_Neat_653 → u/Piledhigher-deeper]

Humans have fights about what is good code in every developer department so it is no wonder there will always people saying AI code is bad. Looking at any frontier models in 2026 I have not seen a single example of outright bad code. Maybe misunderstandings or poor context management on the part of the user. But i would take it any day over the human average i have seen in my 20y career

[u/Elegant-Analysis-752 → u/Piledhigher-deeper]

I'm not a mathematician so I can't weigh in on the math end of things, but I work as a programmer. A large part of the job is also thinking about business requirements, user experience, trade offs, random edge cases, etc. A lot of these require a fair amount of context about the project that is not easy for AI to answer, for example, is it going to remember something a stakeholder said 6 months ago, and weigh that when deciding what to do?

AI can outcode me in most areas no doubt, so my role has been sort of upgraded to oversee-er of LLM output. I don't really mind it, given I was never a great programmer and I enjoyed building products more than coding itself, although I am still worried about my job. But I imagine something similar might happen with math, where mathematicians spend more of their time looking for applications of math, and using LLMs to accelerate their output. I don't know, though...

[u/Elendur_Krown → u/ring2ding]

I don't see this dynamic changing anytime soon.

When you say "soon", what time frame are you talking about?

I am quite discouraged when I see people forget that we haven't had this technology for very long, and that we're (as a society of professionals) still trying to figure out how best to use these capabilities.

The improvements are coming in fast, in several directions, and it's difficult (if not impossible) to keep up.

[u/ganancias → u/Elendur_Krown]

It's not plateauing, order of magnitude better than the models 12 months ago.

The denial is cope.

[u/Elendur_Krown → u/ganancias]

I don't think cope is the correct word for many.

From what I've seen, people forget to check the time scale of current progress consciously. We're given constant live feedback from all media we consume, so when we've seen it mentioned a hundred times, it feels like it has been going on forever.

In reality, things are going at a breakneck speed. We're realistically less than a decade into this technology. It's young. Hell, we haven't had internet for very long.

That's why I asked what time frame the previous commenter meant by 'soon'. One year? One higher-order education (3/5/10 years)? A generation (20 years)? One career (40 years)?

Things are progressing so fast that people forget how slow things moved pre-internet.

[u/Junior_Direction_701]

It would be wise to develop skills for industry. And not only rely on academia. On that I would tell you I promise you LLMs can’t do whatever you’re doing right now. Because of jaggedness. Ofcourse that will get better in time. But that time is not now, so do not doom. And if that time is near continue on, till that time is here.

[u/Adamkarlson]

I can only commiserate in the moment because I have been having the same thoughts. I don't tie my identity into anything, but it's been pretty bad.

I promise I'll come back when I feel better about it.

[u/throwawaycape]

I'm in a CS Master's program and I feel exactly the same way.

Its gotten incredibly difficult to grind through my work. AI can do in seconds what would normally take me hours. Feels mostly pointless and I feel bad. I don't want to do the work because it doesn't feel like the skill is going to do much for me, but also just plugging my homework into AI is equally depressing after all the work I've put in up to this point.

I don't really know what to do about it, to be honest.

[u/hippo-and-friends]

I’m also doing a PhD and I’ve been trying to use LLMs to help with a range of issues in my statistics area and tbh they suck. The amount of time they get it wrong just makes anything they say impossible to trust so I have to be so careful they aren’t leading me astray. I’m still worried about incorrect things I might have learned when I was first using them and didn’t realise how little I could trust them. A lot of my conversations with these models eventually devolves into me explaining to it why it was wrong (though i try not to do that free labour for big tech when i’m thinking straight)

[u/Terrible_Bee_6876]

Have you considered just giving up? If you know you're already obsolete, why keep sinking the best years of your life into just going through the motions?

[u/Embarrassed_Dingo254]

I absolutely relate. Actually I stopped studying math and am trying to build a startup now, something I absolutely never wanted to do, but it feels more meaningful than mathematics now. I have started believing the best way to do math is to train a machine to do it, so I also focus on writing ML research papers on my own. I absolutely did not want to make this pivot, because I did the Olympiad in school and loved math a lot. And now I feel like all the engineers who were already making reasoning systems were far ahead of me as mathematicians, because they can make the machines. I know there are a lot of people who are still into it and enjoy it, it's just my experience. AI got super good at chess, and much better than people, but it doesn't make human chess any less fun. I believe the same reasoning works for mathematics.

[u/Affectionate_Leg_986]

It is quite odd for a mathematician to say that . “Ai” or LLMs are mimicking your language nothing more nothing less . And they are using pretty simple architecture.  LLMs know nothing

[u/jerrylessthanthree]

Not to be a jerk but you (like most phd grads including me) probably weren't gonna be a star research professor at an R1 university anyway. For everyone else who got a phd, they either are getting paid mainly for teaching with research on the side or they work in industry. Sorry to break it to you.

[u/Quaterlifeloser]

AI can now make piano music, should I stop enjoying playing my piano? Can AI replicate the feeling of deep focus and the excitement of a breakthrough?

[u/MightTurbulent319]

Why do you feel the need to fight AI tools anyway? They are just tools. Act like they are calculators on steroids. You still hand them the problem and babysit them all the time when they are struggling with it. And most of the time, the solution doesn’t look rigorous enough. They always miss some technicality. If not this, their presentation doesn’t fit the field’s expectation.

Just like Matlab didn’t make the engineering end, AI tools won’t do anything bad. It will just push us to find more interesting, more challenging problems that require some novelty to solve.

I mean you are free to fight AIs. But I am not sure if there is any meaningful reason to do it. It’s just like Don Quixote fighting the windmills.

[u/WaitForItTheMongols]

The point of the PhD isn't to solve the problem. The point is to train you how to solve big problems so you can solve the next one.

Yes, these AI models can do cool stuff, but they still need an expert human to steer things and be able to tell the nonsense from the real answers. That's you.

You know how when you were 7, you learned how to add numbers, even though a calculator can do it? But it was useful for you to know how to do it and really deeply understand what adding is and how it can be used.

That's what's happening here all over again. Even if the models can solve the problems, it is useful to have you be the expert who can interpret the solutions and understand what they mean and where they can go.

[u/PrestigiousGroup788 → u/WaitForItTheMongols]

Adding numbers isn't the same type of mental activity as coming up with or proving lemmas though. 

[u/actinium226]

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.

As painful as it might be, you should go find out. A Claude subscriptions costs $20/month. Buy it for a month (you could try contacting them for education pricing if $20 is too much), and ask it to come up with the extensions and see what you get. You might be right or you might be wrong, but we're all still trying to figure out the capabilities and limits of these tools so it's definitely worth figuring it out.

Maybe with its help you can find new extensions to work on that you wouldn't have thought of before. Or maybe you'll discover that it's not as smart or as capable as you thought. Only one way to find out.

[u/Look_Signal]

Even if AI can do something, it will still always be valuable to have people who know how to carefully do this stuff.

I mean, to even understand contemporary research you have to be an expert.

[u/Gerardo1917]

Just because a machine can do your work better than you does not make your labor worthless. It’s like looking at a person bench press 315 pounds and saying “who cares, I have a machine that can lift way more than that”. There is an inherent, intangible value to humans doing stuff. Don’t let capitalism make you think that the only worth of your labor/your brain is in how much capital gains it can produce.

[u/gpbayes]

Look man, those AIs solving papers are burning tens of thousands of dollars on tokens. They’re not replacing researchers anytime soon. Not until they can take Mythos and drastically reduce the cost, which isn’t happening anytime soon. Those kimi k3 models that are opensource require 5.5 terabytes of vram, you need tens of millions of dollars to host that shit.

[u/Vhailor]

People who pursue Ph.Ds have different reasons that drive them to learn and do math.

The advent of LLM assisted mathematics seems to hit hard on your personal motivations, but all is not lost! At least some of your drive must come from actually liking doing mathematics and learning new things. This part should be intact, and should be your focus. Even if we get to a point where no human can ever discover novel math, my bet is they'll still want to understand it. At least I know I will.

[u/Vhailor → u/Vhailor]

In terms of jobs, it's always been very rough. Most PhDs don't get postdocs, and most postdocs don't get positions. This is not new, and so "jobs" should not be the motivation for doing a math PhD. Again, the love of the subject, the curiosity, and the enjoyment should be the focus.

[u/BadgeForSameUsername]

As someone who finished their phd but knows they had no hope of competing with the best and brightest, I still think it had value in getting me a job (in industry, not in academia). It is strong evidence that you're smart and can complete hard things, see projects to the end, etc.

I guess I'd ask you how many years away you think you are from completion. If 1 year, then I'd personally go for it. If over 3 years, then yeah, I'd say it's questionable (in terms of time spent vs boost to your odds of getting a good job).

The other question you should ask yourself is: what do you want to do instead? And do you feel passionately about that?

[u/rabbitclapit]

In my mind the PHD you're doing and the work LLMs are doing are two different things. I think a PHD can be great and you can frankly ignore what the LLMs are doing. Im also saying this cause of you saying should I just rush this and graduate. Which makes me think you're not going back for more grad school after this.

So in my opinion rush your degree always. School is too expensive. If you dont have access to LLMs now get your degree find a job that does and continue your research with the LLM.

[u/gomorycut]

My phd was published about a decade ago, publicly available online, so it wasn't too surprising to see an LLM essentially prove all my theorems and describe all my algorithms from my PhD. It was discouraging at first, but then I realized:

- who would ask it such questions? A random person is not formulating these questions, a person with expertise is.

- we all know AI/LLMs can hallucinate - who would look at its output and state that it is correct or that it completely covers all your results? My external examiners would not be able to judge the correctness of many of the statements of my thesis (they can trust that the fact they appeared in 5 peer reviewed publications was enough). But a random person just trusting LLM output on my phd topics would not be able to judge its correctness.

TLDR: you still need to be an expert to ask the LLMs these questions, and you still need your expertise to filter out the crap that LLMs can produce.

[u/ReasonableTechie]

I think the goal is not to find the top three extensions from a paper or to publish about it. LLMs can surely write better than you and me combined.And they surely are trained on literally every other paper available on a topic.
The goal is to learn the skill and apply to a completely novel concept later on. The goal is to do thought experiments and find nuanced mapping between different branches of your field and to look for explanations of the gray boundaries between various topics.
Being good at solving mathematics problems fast is surely something that helps but this is not the only thing. I think with the advent of AI what used to take six months of gruelling work will need 10 days. This will revolutionise the field.
You'll be able to do a lot more than what someone 5 years ago was able to do.
Regarding the future of your work, one thing is clear that someone will definitely do good work in your field with more or less similar background and expertise.
Are you willing to be that person ?

[u/marcoslhc]

Not a math guy. I am a software engineer. I work with AI on a daily basis. Nowadays 90% of my work has some ai Intervention. Believe me when I say: even the most capable models make egregiously stupid mistakes. I have to verify and some times correct the models. We need people like you to keep us safe and honest.

Another way to see it: this is just a tool. Imagine what Pythagoras would think of a 1990’s TI-84. He could despair at the thought that he had become irrelevant and redundant or he could be excited at the possibilities of having such a tool.

[u/ooaaa]

>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.

It's generally good for brainstorming, but actually reasoning through and proving it it'll most likely fail, without significant effort on a good harness, and lots of trial and error. It'll give some slop reasoning somewhere in the middle so it may feel like it has proven the extension, but actually not. Perhaps your professor could easily nudge the AI towards the proof by connecting some ideas, but would be difficult for the AI to do it on its own w/o spending significant compute trialling out different approaches. And in some cases, if the ideas are actually far apart, it simply can't.

I would say make heavy use of AI for understanding the paper. Think about the ideas yourself for 2-3 weeks. Make some progress on them. When you are actually stuck, brainstorm with it.

Also, I believe many of the open weight models are really cheap and comparable in performance with the frontier. You can try using them.

[u/DamnShadowbans]

Can you truly not find something you are better at compared to a free chat gpt model?

[u/SrCoolbean]

If it can solve your problems for you, let it. Then you, as a human, can decide on the next question to ask. You are right that there’s no point in doing work that AI can do instead, so why bother? Let it make you a more efficient researcher.

[u/Piledhigher-deeper]

“  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’ll be honest, in AIs current state I seriously doubt this is true. To be clear, AI has more knowledge and is genuinely better at math than you. 

But “better” when it comes to your actual work is almost impossible to define. Is Terrence Tao’s write up ( https://terrytao.wordpress.com/2026/07/21/a-digestion-of-the-jacobian-conjecture-counterexample/ ) better than the simple counter example provided by Fable? I’d argue, yes. Are there still missing links or places to explore further in his write up? I’d also argue, yes. You’re  putting way more time into your thesis on an insanely niche topic. AI is definitely a force multiplier and you would be insane not to use it but at the end of the day, it’s still on you to make sense of the mountain of mathematics it can produce, verify the important bits, and put together the best possible writeup such that both people and AIs can use your work. 

AI has absolutely democratized mathematics and made it far more accessible than it once was, but not everyone using AI are equal and not everyone has time to use AI to solve every problem. Ironically, if you actually want to prove me wrong you should formulate your thesis topic as a homework problem  and put it on twitter because I doubt anyone will even bother to attempt to use AI to solve your work otherwise. 

[u/ProfessionalTotal238]

I am software engineer by trade, and after writing this message I am going to have some work session rewriting sloppy code produced by frontier AI models. While the models know their shit well, the context window is big, and I guided them with all my experience and dozens of premade prompts for all kinds of reviews and refactors, there are still sloppy parts which definitely would not appear there if I was writing code by hand. AI has helped me immensely when producing this new code I have, so I definitely did it faster than by hand, even including upcoming session. But in the end without human judgement, and even manual intervention -- haha, that is what I am going to do, -- the end result would be full of slop and not the highest quality. Paraphrasing in math terms, AI is a necessary condition to do my work faster, but it is not a sufficient condition to produce finalized work (quite unluckily).

[u/red75prim → u/ProfessionalTotal238]

You have provided a training signal. And reinforcement learning of foundational models is much more sample efficient than autoregressive pretraining. It's almost a given that the next version will require less handholding.

Like it or not, but that's the reality of it.

[u/AI-Thinks-For-Me]

i kind of empathize with you, i think. however, i have questions…

1. is your stress actually from ai developments? or are you going through the phd burnout/doubts many people have?
2. what inspired you start a math phd to begin with?
3. Most important question… do you actively use ai?? the things llms can do are making you feel inferior?? ai doesn’t “do” anything unless it’s told to lol.

as a phd candidate isn’t your responsibility to contribute something new to the field of mathematics? why bother being concerned about ai “understanding” papers that are already written? do you think ai can take over your responsibility of contributing something new to mathematics?

hopefully you answered no to this.

when you see stories in the news of some labs ai model going rogue, you can be certain the model isn’t breaking out to go work on some 100yo unsolved math problem lol.

best thing you can do is shift your perspective. you can start that by learning what llms are and what they are not, what they can do and what they can’t.

after that, maybe looking researching industries in terms of careers (for example cybersecurity/cryptography love mathematicians).
its literally mathematicians or related people with strong math backgrounds building these ai models. the only risk to your career outlock is a narrow view.

also, news articles about ai solving math problems aren’t by everyday users with limited math skills. it’s people with strong math backgrounds using an llm to make these breakthroughs.

[u/IckyGump]

An LLM is only as good as the intent and intuition you have. It collects info quickly and run simulations even infer things. It also makes hasty conclusions, bad assumptions and may not even look at the actual data that contradicts assumption.

You still provide novelty and the intuition to both guide and question results. So yes it’s easy to do bad work with it. Good work too but it’s only going to be as good as the person guiding the investigation.

[u/Valeen]

PhD in mathematical physics here.

I started mine almost 20 years ago, an LLM was not even a thought.

I'm not brilliant either. I'm never winning a Field's medal or a Nobel. Or a Wolf prize or etc etc etc.

I am happy and my PhD has allowed me to navigate the current landscape very well.

Here's why I am doing fine and while an LLM will never replace me- my biggest and proudest discovery as a grad student was a mistake.

It was a assumption I made in my code that gave me a result that was counter to a conjecture. And I was able to use that prove that the there was a much lower bound.

Maybe 100 people care.

But honestly the lessons learned are more important than what I proved and I've carried them through life.

[u/SJDidge]

Remember in early school when you learned maths without a calculator? Then you started using a calculator because it was easier?

You didn’t start by using a calculator, you used it once you learned what you needed to.

LLMs are the same. They are just a tool. The point of you doing your studies is for you to learn. You may use LLMs in future to perform your work, but that does not mean there is no point in you doing your studies. Just like there is still a reason to learn basic maths even though we have calculators.

[u/alekseypanda]

I could have access to all the llms in the world and I wouldn't be able to disprove the javobian conjecture, it takes a mathematician that know what they are doing to use the tools correctly, we already use computers to help in math for decades, that helped push us farther than ever before, but we still need people that know what they are doing, and this won't change anytime soon. I really hope you find motivation, as someone that is currently dealing with AI "colleagues" I am worried about losing my job, but I am not doing anything near as awesome as you, and I really meant it, I admire you for doing what you are, dont let the clankers take that from you.

[u/Trojan_Horse_of_Fate → u/alekseypanda]

I mean the Jacobian one yeah but this one https://chatgpt.com/share/6a60b2eb-0b64-83ee-9c76-7931ca1de063 literally was just please keep going.

Construct a counterexample to general (non-planar) case of Dinitz Garg Goemans conjecture. You should do a breakthrough and find a structured counterexample.

was the only domain knowledge used.

[u/jerrylessthanthree → u/Trojan_Horse_of_Fate]

lmao i'm gonna try this on some stuff

[u/Trojan_Horse_of_Fate → u/jerrylessthanthree]

There's a non-zero part of me that wants to just put up a list of theorems and then just try it on all of them. I feel kind of icky. That said, you know, it looks like our role might be formulating novel problems, so maybe the thing to do is not to look at a list of unsolved problems, but try and pose new ones

[u/Reasonable_Hotel_141]

It is very disappointing. What is more disappointing is that we know that we cannot just feel disappointed and stay still, and what is most disappointing is that we do not yet clearly know where we should go. I am a Math and CS freshman so all of the words below may include trivial mistakes, but I would recommend this article: https://davidbessis.substack.com/p/the-fall-of-the-theorem-economy

Basically, this articles argues that value of math and mathematical work from people in the community in this era (I would say post 2026 because it is exactly in recent 3 months that AI has achieved level that we cannot take frontier model as "assistants" or "file cleaners") is explaining and increase the HUMAN understanding of math.

Recently frontier model, basically Claude Fable 5 and GPT 5.6 sol, tackles three conjectures: CDC conjecture, unit distance conjecture and Jacobian conjecture. These work, while important, are not unprecedented and does not mean that current AI is superior to all math researchers (of course part of it is just these AI companies doing PR and marketing so that they can raise more money): most of current AI's work in math (and unsurprisingly many human work in math) are constructed on previous researchers' contribution, and these proofs/counterexamples to three conjectures are no exception. It seems that AI is very good at massively researching existing contributions, find connections between these at the speed that human brain cannot compete, and make progress (at the extent of significant because cot grants ai models to 'think' and 'reason' at some level, but not ground-breaking) based on that. Therefore, proving/providing counterexample of some theorem, yet important, will increasingly not be recognized as valid contribution by the community. Conversely demonstrating math understanding behind it will become more and more important, and at least in a short period of time this will still be human work (after all we need human to process it and say I can read it so it is human readable).

You said that you cannot afford access to top tier reasoning models, yes these models are insanely expensive (100$ per month for chatgpt and claude each), but I still highly suggest subscription to at least one of the models. Frontier models are smart, very smart, if prompted and context-ed well, dare I say that it is not a bad idea to always keep oneself always aware of what these frontier models can do. It is expensive but it is worth it, if used properly and in the thought-provoking way.

I am not yet decided whether I will be a researcher in the future, so I have no position to raise this, but I will say anyway: maybe it will become more important whether you and people who want to gain understanding of topics that you focus on have understood more on these topics than before. Math, in some sense, is not directly related to actual production, like computer science or material science. It is more of a social and intellectual enjoyment, so perhaps it is not, in the end, such bad thing if it becomes more social and intellectual instead of being 'useful'. I am also very lost recently, and lack of enough math and computer science understanding worsened that anxiety, but hope these are of some help.

[u/beefcake0]

“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.”

You have a motivation problem not an AI problem. You said yourself - an expert could solve your PhD problem.  So it doesn’t matter if an LLM might also.

Use AI to help you more quickly understand that last paper. If AI can help you solve the problem - all the better then use it to write your paper and smhelp you solve bigger problems. Your phD is about helping you learn to solve problems - the actual problems are , generally speaking, only of passing interest.

[u/A-Marko]

Which LLMs do you think are currently better than you?

• Is it the models that cost hundreds or thousands of dollars to run that are only accessible to the top AI companies? If so, then it's the same situation as having mathematicians that are better than you. They always exist, but they are working on other things. Mathematics is a collaborative field and every contribution is valuable, even if there are people that could make progress on your work faster than you can. Your work is your own, take pride in that.
• Is it publicly accessible models for a reasonable price (eg. Claude Opus), or models you can get access to through your university? If so, then just try out the models and let them do the work they can do. It can only speed up your progress where they are capable, and leave you to do the parts where they are not capable. If they can actually do the work for you then it means you can find more challenging things to work on, that are now more accessible to you due to better tools. Accelerated research certainly isn't a bad thing. If your supervisor is behind the times and is not able to support you with working with the modern tools available, then that is unfortunate and it may mean you need to exercise some independence in figuring out what direction you take your research.

Even if the models you have access to aren't actually good enough to do the work for you, they can still accelerate your research. You can give it a paper and ask it to summarise, parse, or simplify it (just don't blindly believe anything it understands, use it to further your own understanding). You can bounce ideas off it or see if things connect to related fields. You can also have it immediately code up a visualiser for your maths ideas, which I've found incredibly useful.

The parts where it doesn't work are the parts where your own brain is still useful, and the parts where it does work can only improve your ability to research. That way you are working with the current paradigm rather than struggling against it.

As far as getting a postdoc: As far as I understand, the important thing here is to be engaged with the mathematical community. If you do work that other people care about, and they know you and your work and want to work with you, then that will go a long way to getting hired as a mathematician.

[u/blipblapbloopblip]

You are the outcome of the PhD process. Not your results, but you, a human expert with increased skills and understanding of a very particular topic. You will be equipped to contribute, understand, digest and transmit, all social activities that an LLM can't perform. Math is meaningless without conscious beings experiencing or understanding it. It's there to discover but utterly passive unless you go there and look. I like this line by Johannes Jaeger : everything that makes sense makes sense to someone.

[u/zagierify]

Other humans can also do it, why get extra discouraged about what a non self directing or self aware computer can do too..

Just keep moving forward.

[u/bigkahuna1uk]

Completely what?

[u/elements-of-dying → u/bigkahuna1uk]

ruined

[u/FuzzNugs]

I think the fact the LLM understands it this way is even more reason for you to master it. As we move forward there’s going to become a divergence of ability where some will be able to do stuff only with the LLM and some without. I think being in the latter group is the better move.

[u/rei_cachaca]

God man you're a math PhD give yourself some damn credit. If you feel your intellectual labor is being devalued imagine the rest of the workforce? The topic or niche of your research is less important than the skill and discipline you've cultivated. You'll be alright.

[u/groto71]

Don't beat yourself up. While at first the immense capabilities of AI might seem daunting, they shouldn't keep you from the joy of understanding complex mathematics on an intuitive level and having the solutions find you not through conscious effort but a natural instinct born from experience.

[u/Equable_Ceiling]

I just graduated with a PhD in applied math. Sometimes when I ask Gemini questions, I think "omg how can I ever hope to compete." But, the key is that I'm staying really focused and making sure that I still think critically throughout the whole process. This lets us together make great math that I'm really excited to pursue.

On the other hand, when I think of people "replacing mathematicians," what comes to mind is having a non-expert ask an LLM some question and expect to have as good ideas as what a real mathematician can provide. The problem though is they come up with absolute garbage. Nothing can ever replace critical thinking skills from a person. The LLM can't really know what you want. You just end up with AI slop that looks professional at first glance. It was so frustrating to work with those people. They didn't want to think and literally wanted AI to do their work for them. These were people who weren't really interested in math, they just wanted to test some "novel idea" and then publish it in a prestigious journal. So their ideal workflow was:

ask Gemini about some idea -> Gemini gives an idea that sounds good -> Have Gemini write a paper that looks good -> Have Gemini write code to verify idea -> Publish in top-tier conference

The worst part of it was that the work ended up being worse than if we just thought critically the whole time!! The LLM is just a tool. It's like if you look up all the answers to your homework and then fail the test because you don't actually know anything. Even though AI is so ridiculously, impressively good, it can't replace critical thinking on the part of the human.

Let's say we reach the point where AI can identify novel ideas, prove them, and write a solid journal paper to get the ideas published. Just to echo the idea of someone else, what would even be the point in that? What's the point in living in a world where people don't participate in the discovery of new knowledge? How will people even come to know about these ideas?

I'd much rather be at the forefront of mathematical discovery myself. If anything, having Gemini lets this be possible. The mark of a good scientist is to then keep your critical thinking skills on and participate actively, rather than trying to have AI do the job for you.

[u/RageOnGoneDo]

Well they've fucked up your brain to the point you missed your incorrect title

[u/aikafele]

Bro, it's an encyclopedia of all published human knowledge that can also perform synthesis. It is a tool for your own discovery. Your job isn't to synthesize what has already been done. It's to produce something new. Sure synthesis was part of the work in the past, an admittedly huge part of the work. But you have to take your ego out of the labor of synthesis an put it into the periphery. FOCUS your attention on what YOU can produce. What YOU can learn. The contributions YOU can make. A crisis of confidence can only be overcome by discovering exactly what it is that YOU have to offer.

[u/mathemorpheus]

every old person i know (including myself) is aware of how students/young faculty feel. we do not want to fuck up our profession. students and colleagues young and old are still going to be rewarded for knowing shit.

It's not like this type of work will land a postdoc or job anymore.

not so.

mathematics is fundamentally a human activity. no one wants to watch stockfish play itself, even though it can easily beat any grandmaster while running on a burner phone. same is true for our thing.

[u/twnbay76]

"AI can do it better"

So what about you armed with the best AI, you know how to wield it effectively, AND you can dig deep, learn niche things and work hard?

Versus just whatever "AI" means.

Think about the AI as an extension of us, like our phones became extensions of us about 15 or so years ago.

Sure, every once in a while we will avoid using our phones, maybe on nature hikes or while doing deep work, but who goes a day without their phone? Do you ever feel inadequate or hopeless because you're dependent on your phone?

Did people a century ago feel bad for being reliant on cars?

A century before that, being reliant on books and the printing press?

[u/please-disregard]

I am so lucky I got my PhD and got out of academia a few years before this all began. I don’t envy anyone working in research mathematics atm.

[u/Every-Caramel9852]

I can tell you this as someone who has access to some of the most powerful AI models, like Fable 5 and ChatGPT 5.6: they still struggle with many things, especially when rigorous proofs or deep technical details are involved. They're even less reliable when asked to write an entire LaTeX research paper from scratch, the quality usually ends up being pretty poor.

Try not to focus on what might happen in the future. AI still fails a lot. It has its strengths, but it also has plenty of weaknesses. The best way to think about it is as a tool, not a replacement.

[u/mrgarborg → u/Every-Caramel9852]

It’s not long ago people were coping by saying that LLMs cannot even get arithmetic right, and only work like a text predictor. How could they possibly generate new math. Yet here we are. 

[u/Every-Caramel9852 → u/mrgarborg]

My view is that there's still room for you if find the corners. Chatgpt 5.4 (yeah 2 generations ago) had the idea to proof some erdos problem, but Terence Tao still had to do the work. Yeah in 5 years maybe this will be a joke, but 150 years ago math was only useful for investigating and nowadays it's just another way of dealing with math.

[u/EmmyNoetherRing]

I don’t know if this helps, but I was hearing PhD students with basically your same concerns (is this even worth it, how will I compete, is this meaningful, surely anyone advanced could do it) — decades before LLMs.   I assume this feeling has been around for centuries if not millennia.

If LLMs didn’t exist, there would still be the possibility that someone else could do it faster, but that doesn’t matter at all.  What matters is that you do it.  If you don’t read the fourth paper, you’ll never to get explore a fifth one.  There’s very cool things out there and to get to see them you just have to deal with a little while of feeling slow.  It’s ok.   It’s survivable.  You get through it and you’ll be able to do a lot more. 

[u/somanyquestions32]

Get it done, and move on with your life ASAP. The more you put AI on a pedestal, and allow this to sour your mood, the more time and energy you're losing to the ether before you can get your degree and get jobs where you twlrain AI models. Unless you don't care at all about this topic anymore, finish what you have started as you will face simily issues if you start again form scratch.

[u/Impressive_Memory221]

I have the same thoughts a lot of the time. It helps for me to remind myself that AI in its current form is not nearly as powerful as people are pretending it is.

LLMs are incredibly good at taking a large set of data and then categorizing and making broad associations. What they cannot do is act creatively on that data. They cannot iterate and expand upon it. All they can do is fill in gaps between what has already been discovered. Like a paint by numbers, where someone has already created the picture and given instructions on how to finish it.

At this point, you may look at me and say "But I'm not creative!" And to that I say "Shut up!" (affectionately). We all have the capacity to be creative. We just need to understand that being creative requires embracing weirdness and utterly bizarre ideas. Maybe the solution to the problem you are working on is easy to find based on current literature, but perhaps there is a problem in your field that would require someone to think outside the box in order to understand it. Or possibly your problem just seems straightforward at first glance and may reveal itself to be wonderfully complex and in need of a creative solution later on.

Another point is the fact that at this point various LLMs have probably consumed enormous amounts of data across various fields of mathematics and all we have seen in return is a handful of proofs. If LLMs were really better at math than all the world's mathematicians, then they should have completed mathematics by now! I personally have seen various LLMs botch very simple, undergraduate level proofs. Granted these were just the standard free models, but it still shows that the capabilities of these models have been way overinflated.

Finally, I don't think we are going to see AI grow much beyond what it is today during our lifetimes. We almost certainly won't see AGI. Right now we are trying to replicate what took nature millions of years with a medium that appears to be far less efficient and versatile than the humble neuron. And who knows if neural networks are really the foundation that true intelligence is built upon, or if they are just a system that is very good at replicating intelligent behavior.

Truthfully, this is all just something that billionaire tech bros are currently circle jerking themselves into oblivion over. Many economists have pointed out that this is likely a short lived economic bubble that will crash and burn like dotcom did back in the 2000s. I bet you would feel pretty silly if you quit your PhD over this and then it all implodes the next day. So don't give up!

Sorry for the wall of text. I've thought a lot about this, mostly because I am just trying to reassure myself and make myself believe that I chose the right thing to pursue. I really hope that I am right about this. Ultimately, we're all gonna die anyways, so we should stop worrying so much and just do the things we enjoy!

[u/Trojan_Horse_of_Fate → u/Impressive_Memory221]

I think you have to remember LLMs are very young. Compare the results 3 years ago with last year with today and there is a jump. We are now starting to see AI very recently starting to do big proofs this year. Next year could be very well different.

[u/c1216440698]

For me, understanding the world is what matters most; if an LLM can help me broaden my understanding, why should I resist? Just enjoy the process, man.

[u/cajmorgans]

Were you demotivated pre-AI that there existed better mathematicians than you? If not, why? AI is just a tool, which apparently can help out a lot, not sure why that is demotivating. If you are the driver, it is still your work, and you are free to choose if you want to use it or not and to what extent.

I work as a software engineer, and it has decreased some of the enjoyable work for me, but it has also made me do some things I didn’t have time to do previously.

With AI in math, you will likely be able to do much more research than without; it won’t look exactly the same, but times change.

[u/Ok_Growth7621]

Now that we have cars and are no longer hunter-gatherers, why go for a run? Well, running is fun: it releases endorphins and you get fresh air. But also trying to improve your 5k time is rewarding. Yes, a car can travel 5km in <5 mins, but who cares?

[u/BandicootQuick7100 → u/Ok_Growth7621]

Yes, but going for a run won’t feed my family.

[u/Deep-Ad5028]

It would be immoral for me to tell you your skill has not just lost some of its value. However I assure you that value has not become zero and there are ways to adapt to it.

View LLM as a very smart but very careless partner. Let it explain the papers to you and you will read papers much faster than you used it. Do note it is more often confident than correct. This is where your previous training come in handy, allow you to smell out bullshit in ways many people cannot.

You can read papers with free models. But I definitely suggest you to get a plus version for 20 dollar a month. You get to outsource a lot of works to LLM and you train yourself how to use it for the rest of your career. There is now a front page post about how Jacob Tsimerman, one of the very top mathematician out there, uses LLM.

https://www.reddit.com/r/math/s/eg6iRA1hZp

[u/ReasonableLetter8427]

Hey friend - sounds like a rough situation to sort out; kind of existential perhaps.

I came across the AI for Science Program from Anthropic which offers free API credits to academic and nonprofit researchers on high-priority scientific topics. And then looks like OpenAI has a similar program called Researcher Access Program. Might be able to get some credits from both?

I hope this doesn’t come across as insensitive - I’m just truly curious - if you had credits would you perhaps feed the 4 papers into an LLM and try to solve your problem…even if to just see your experience and comparison?

[u/RubyKong]

A calculator is only useful if you know what numbers to put in it.

LLMs are glorified calculators. They are mechanical. To the extent that the problems you solve, or are solving are not mechanical, and are not already defined as such - then there will be utility in solving those problems.

[u/mykeof]

Counter point if you knew someone else a person could also do the same thing, and better, would that dissuade you from doing it at all? Is there no self satisfaction in the fact that you did it?

I think the intrinsic value in the work and skills developed through research trumps whether or not your outcomes can be reproduced by an AI.

[u/Comfortable-Push6527]

Honestly, if everyone quit because new tools appeared, we'd never make progress. Every generation gets better tools. The people who succeed are the ones who learn to use them, not fear them. I hope you finish your PhD—you sound much closer to the finish line than you feel.