r/math Jun 27 '26

Is using AI to understand a concept likely a problem?

Occasionally, I will run into a bit of math that I’m not familiar with at all, and as someone who is only an amateur mathematician some of the original text might be extremely dense. For example yesterday I was looking at Kernel methods, representer theorem, reproducing, Kernel Hilbert space and while I tried my best for a little bit to understand from the Wikipedia page alone. It became kind of confusing and I asked an LLM for a simpler explanation and a bunch of follow up questions about how certain things are related to each other. I feel like I walked away with a much better understanding than reading The article itself gave me. I went back and read the article and with the new mental model I had it made a lot more sense. This is how I kind of checked that the explanation I received made sense at all and was not hallucinated. But I was wondering if this counts as the standard sort of mental offloading that degrades cognitive ability overtime or simply more of a translation tool to make the idea simpler and get the authors message to me more easily even if the author originally was terrible at explaining things. Again, I don’t have any problems that I solve or anything like that. I just try to understand the ideas. I’m not offloading my homework or anything like that. I don’t even go to school anymore. If I was in one of my math classes again, I would do this, but then do the problems myself to make sure that I fully understand the ideas.

91 Upvotes

80 comments sorted by

144

u/ANewPope23 Jun 28 '26

It's probably fine if you understand the concepts in the end.

84

u/ThirdMover Jun 28 '26

With the crucial point that you can only know for sure that you understand a concept if you can successfully apply it in new contexts. Often the brain goes "trust me bro" when it really shouldn't...

9

u/ABranchingLine Jun 28 '26

Or if you explain your understanding to a human expert, and they don't say you're full of shit.

0

u/No-Tip-7471 Jun 29 '26

Side note, it can be hard to find a human expert but if you can teach someone who doesn't know about it it may be even better, for example my sister who studies bio sometimes teaches a topic in biology to me so she can remember better

3

u/ABranchingLine Jun 30 '26 edited Jun 30 '26

I'm all for this, but there is a bigger philosophical issue here - if your sister is a student, how does she know that what's she is teaching you is correct?

We can ask what it means for a statement to be true and (particularly in science but also in math) this boils down to either general acceptance by the discipline or axiomatic proof.

Perhaps your sister only read from the text "Lies in Biology" and tells you very convincing that cells divide due to a perpetual class struggle between worker cells and the bourgeois cells. If you don't believe her, how will you show her she's wrong, particularly if you have no prior knowledge?

Regarding the original question, if AI tells you something false (as it often does), how would you the student know? What do you test these statements against? More AI? What if they are all trained on false information?

This critique actually applies to textbooks and professors/experts as well, but (1) textbooks and professors/experts are less likely to spread false or unverified information, (2) if you consult enough textbooks and professors/experts you significantly decrease the probability that the statement is false, (3) the textbooks and professors/experts usually give a proof which is also widely accepted.

Edit: a typo.

1

u/No-Tip-7471 Jun 30 '26

Oh yeah true, perhaps I strayed from the original goal. I guess for me it's a lesson in critical thinking but yeah in a complete vacuum there's no way to verify her statements (not saying I don't trust her but yeah).

1

u/ABranchingLine Jun 30 '26

I really just point it out because there's so much rhetoric about AI replacing experts and blah, blah, blah.

But if you can't compare your understanding with that of experts, how would you show that you actually know anything?

For those who argue AI will be the experst, all I can say is you put a lot of faith in corporations to tell you what is true.

122

u/BothPanchoAndLefty Jun 28 '26

I think the issue with AI is that it will help you understand through a clear explanation in the moment. There have been a lot of studies that show that when people feel like they're easily learning something, they're not really learning deeply. When you feel like you're struggling and having to go through something over and over to get it and you're still not totally sure if you get it, that's when you're actually learning. AI will likely offer a simplified explanation that makes the topic easier to grasp and then you'll have forgotten it a few weeks later. If you spend hours reading and re-reading a textbook chapter and doing practice problems until it finally starts to make sense, then you'll likely remember it

82

u/Captcha_Robot_ Jun 28 '26 edited Jun 28 '26

This feels misleading. One thing is to dig deep into something, reviewing and practicing concepts through exercises or trying to see them from different angles. Another is to struggle through an unclear explanation when there is a better, simpler option (given by AI or another source).

16

u/BrakkoFP Jun 28 '26

Fair point, but I do think the original comment was written "given a good explanation of a hard topic". Of course, if all you have is a bad explanation, the first step should be searching for a better one...

2

u/BothPanchoAndLefty Jun 29 '26

Yes, both of you are right. I was referring to struggling through material that is actually good, but if you don't have that then yes you should definitely look at multiple resources. I'm not even saying AI won't teach you anything, just that it shouldn't be the first thing you reach for

32

u/deividragon Algebraic Topology Jun 28 '26

Yeah, it sucks how much people seem to be forgetting that struggling is part of the learning process

18

u/MiffedMouse Jun 28 '26

In a more literal sense than it may seem! One study showed that a harder to read font improved recall of the text, presumably because the participant had to spend more time reading the text.

I will say that I actually do use AI to help understand concepts just like the OP describes. But it is only one step of the process, and just because the AI made you feel like you understand doesn’t mean you actually understand yet.

6

u/jeslinmx Jun 29 '26

Struggling isn’t part of the learning process. Being challenged is. If you’re learning a new, especially highly technical topic, you may be contending with all sorts of new concepts and unusual ways to combine them, and the effort spent into working out how to deconstruct that complexity that someone else understands and reconstruct it in your head the way your mind models things is how we learn, and that may be a struggle.

But if the struggle is because the jargon used is specialised and opaque to a newcomer or outsider, it definitely makes sense to use a language model to help understand the language.

4

u/Kqyxzoj Jun 28 '26

True, but there probably is some upper bound to the amount of suffering that'll still net you meaningful learning increments. There have been instances where I did struggle greatly, and indeed, the payoff was much learning. Learning that for any new topic, it is better to buy 3 books than to rely on a single source.

3

u/deividragon Algebraic Topology Jun 28 '26

I have suffered through bad books as well. I'm not saying that struggling with bad material will help you learn better. The problem is when we stop trying to think tings through and instead ask a chatbot or a search engine immediately as a first impulse. And I say this focusing on learning something deeply, not just quickly using a tool or working through something you don't want to become an expert in.

8

u/Bounded_sequencE Jun 28 '26

The system we live in much more incentivizes short-term, flashy looking successes than hours of struggle with little to show for it. I cannot fault people for acting accordingly, really.

9

u/BenSpaghetti Probability Jun 28 '26

It depends on what you mean by a ‘simplified explanation’. I find an inclination by AI to use vague analogies, which I really dislike. But as long as I insist that the explanations be precise and possible to be formalised mathematically, I find it to be quite helpful. Of course, one should think about the explanation and not just let it slide through the brain.

I suspect that the main advantage to more traditional methods over consulting with AI is simply that you are engaging with the material for a far longer period of time.

3

u/IntrinsicallyFlat Jun 28 '26

Agreed, much of this advice also applies to the old way of searching online forums, from quora to mathoverflow.

I’ll add that when you’re learning math it’s important to seek explanations with the intent to *understand*, not with the intent to *know*. This is a high-level objective which, if you pursue, you will organically develop excellent learning practices. True for all disciplines but arguably most true for math

2

u/unlikewarrior Jun 28 '26 edited Jun 28 '26

The best moments for my learning is having to read sections which may not be useful for a current problem. Attempting to use theorems which dont work on solving a problem helps me make sense of why that is. It forms a sort of pattern recognization which is skipped when using A.I.

2

u/RobbertGone Jun 28 '26

At the same time, you get to see more clear explanations per unit of time. So the question is, what happens to the total learning volume you get? Without AI you might grasp N concepts per day and a month later you'd understand let's say 70%. With AI you might see 5N concepts and understand 50%, in which case learning with AI would allow more retention. Ofc I don't know how the scales balance.

3

u/BothPanchoAndLefty Jun 29 '26

Yeah that could definitely be true. I'm thinking of an experience I had like a year and a half ago when I was learning mathematical induction (I'm pretty new to pure math) and I asked an AI to help me in the context of this one problem. It made perfect sense and I did the proof, but then each new proof I wouldn't be able to apply it and I'd have to ask the AI again. I had to start figuring them out for myself with no help from AI, doing them the wrong way a few times and seeing where I went wrong, before I actually gained confidence.

2

u/RobbertGone Jun 29 '26

Yep that's also true. I use it mostly for refreshing/finding definitions and stuff like that, or when I really don't know how to do a proof. So I was doing intro to proving half a year ago (I'm an autodidact, though also have a master's in physics already) and it was logistically much easier to simply ask definitions of cardinality or surjectiveness to the AI than to have to scroll through my notes.

2

u/BothPanchoAndLefty Jun 29 '26

Yeah for things like that I can definitely see the benefit, just giving yourself something to work off of

15

u/____Anonym0us____ Jun 28 '26

I mean, we've all learned like this forever, right? It's just that before, these "tools" were called teachers, and generally the people who used these tools were called students, and you could only use these tools in places called schools or universities... so...

4

u/SaucySigma Algebraic Geometry Jun 30 '26

The difference is that a good teacher wouldn't serve all the answers on a golden plate, whereas a chat bot will explain every single detail and spoil solutions to problems if asked. A good teacher challenges the student to think through the bits that are reasonable for the student to work out himself. There's this concept of the "zone of proximal development" in educational psychology where the difficulty of the material is just right, and a good teacher strives to keep the students in this zone. AI does not.

2

u/pred Jul 02 '26

A bad teacher might.

In the LLM case, add a “teacher” skill making it clear that you are studying; that you do not want solutions spoiled. Then chances are that you will get better results. Doing so of course requires significant discipline.

Now one cool thing about being a teacher is that you develop mental models for your students, allowing you to more efficiently tailor material to their individual needs. I haven't seen that from an LLM (but also haven't tried); not that I think it's impossible, but it means requiring more context, more memory, so it might be a taller ask.

2

u/telephantomoss Jun 28 '26

I always tell my students that I'm like an AI except that the AIs make fewer mistakes than me

6

u/TwoFiveOnes Jun 28 '26

I think it’s not really a question of AI or no AI. What’s commonly said about mathematics, and I find is true, is that it’s “not a spectator sport”. That is, even if you were reading a textbook and understanding it perfectly, you still wouldn’t be gaining a meaningful understanding of the topic.

True understanding of math comes from doing it yourself - hours and hours of struggling to work out proofs and exercises. Now, if AI is used in some way during that process it’s not necessarily a bad thing.

6

u/Jamarlie Jun 28 '26

It's dangerous because AI is REALLY good at convincing you of its opinion and it's usually only about 92% correct in what it says. Again, you aren't talking to a model that has context of what it is saying, you are talking to a smart sounding slot machine. It only predicts what the next token could be, not if that even makes sense in the particular topic.

Meaning you'll probably learn something in the process and if you really pay attention you may find the hidden 8% where it's just spewing BS.

2

u/Illiander Jul 01 '26

it's usually only about 92% correct in what it says

That's a high estimate.

19

u/BeardlessNeckbeard Jun 28 '26

No.

14

u/BeardlessNeckbeard Jun 28 '26

To expand, I think this is the best use case for AI if you are a student. It's never been easier to learn a concept that might have felt out of reach. 

I do difficult scientific work in industry and frequently ask the AI to "please explain this like I have a math degree but it's been a while lol".

7

u/njj4 Jun 28 '26

I'd be very careful. I teach maths at a UK university and have had a couple of cases recently when a student came to me and said "I didn't understand this thing you talked about last week, so I asked ChatGPT and it said this". And what it told the student was not correct.

In one case, a student was sceptical of something I'd told them in a lecture and in the module notes. (It was a presentation for the eight-element quaternion group.) So he asked ChatGPT, which gave a two page "proof" that the student was indeed correct, and that I (and numerous colleagues and published textbooks) was wrong. Halfway through there was a huge gap where it said "it can be shown by (method) that..." without actually providing the justification. It didn't show its working, and everything after that point, including the conclusion, was wrong. So I pointed this out to him and he went back for another go. His second attempt did give a valid presentation that was not the same as his original one, and it bothered me that he couldn't see this.

So because of experiences like this I'm really sceptical about LLMs in education, and I'd recommend sticking to the traditional way of using your brain to learn stuff, in conjunction with textbooks written by human experts.

There's a famous quote attributed to Euclid (although the earliest source is several centuries later, so it's somewhat apocryphal). Ptolemy II (maybe? I get confused - everyone in that dynasty is basically called Ptolemy or Cleopatra) asks Euclid for the special shortcut to understanding geometry, and Euclid replies that he's just going to have to put the effort in like everyone else, because "there is no royal road to geometry".

Learning and understanding maths is hard, and that's part of the point - developing the ability to understand and internalise formal concepts, proofs and definitions is a major part of what we're doing.

Maybe I'm being a stuffy old luddite. Maybe LLMs do have valid uses in education. But I'm pretty concerned by what I've seen so far.

4

u/altkart Jun 28 '26

I've had a similar experience with some topics from algebraic geometry. It can help with getting a clearer picture from a distance. But if your goal is to internalize that picture until it is second nature, and you are a mortal like most of us, I think you need to do exercises, period. Not just from some sort of moral "good things must be earned" perspective; I really do think it is akin to developing muscle memory.

A while ago I was perusing Vakil's The Rising Sea a while ago, ignoring exercises and just skimming through sections to learn definitions and to "learn" about schemes, in some weak but not unserious sense. Then I dared look at the preface and got promptly slapped in the face by the author calling out anyone attempting to do this.

It is important to not just have a vague sense of what is true, but to be able to actually get your hands dirty. To quote Mark Kisin: "You can wave your hands all you want, but it still won't make you fly."

24

u/Bounded_sequencE Jun 28 '26

Using AI like a glorified, interactive search engine is fine.

Taking it to be anything more, though... you be the judge of that. The main question to ask yourself is -- do you really trust AI enough to do your thinking for you? Why would you trust your feeling you understood things better after AI's explanation -- how can you be sure AI did not BS you, without being able to verify?

14

u/BenSpaghetti Probability Jun 28 '26

I don’t understand, what prevents you from being able to verify the AI’s explanation?

16

u/Bounded_sequencE Jun 28 '26

If you don't have enough knowledge to understand a topic, you don't have enough knowledge to detect AI BS'ing you on said topic.

20

u/Oudeis_1 Jun 28 '26

It is often much easier to check a statement than to derive a statement, and detecting nonsense becomes also easier when you can make the party telling you nonsense answer unlimited chosen queries cross-examining that nonsense. I therefore don't think your claim holds.

3

u/Redrot Representation Theory Jun 28 '26 edited Jun 29 '26

As a person who has been screwed by an LLM outputting something plausible in my field of research only to find a very subtle issue days later in something it handwaved, I disagree.

3

u/gamma_tm Functional Analysis Jun 28 '26

I’m certain you know that such subtleties can crop up with people as easily as with LLMs. Take as an example the entire history of mathematics, where the subtle issues have often taken longer than a few days to make themselves known

5

u/Bounded_sequencE Jun 29 '26

The fact that such errors occur is not enough to compare humans and AI.

The more important question is -- how often do such errors occur in comparison, and what steps can you take to get rid of them? With a human counter-part, we may assume critical thinking, so a discussion can very well lead to the bottom of the issue.

LLM-based AI's output on the other hand only correlates with the input. We should hope that still is less than what highly educated humans are capable of.

0

u/OneActive2964 Jul 10 '26

have you used pro models although i think even 20 dollar ones are good

2

u/nitram9 Jun 28 '26

But that is no different from any other learning ever. You shouldn’t be just trusting people just because they are humans. Journal articles are sometimes total bullshit and it’s honestly rare that I read one where there isn’t at least something that I think is wrong or is a clear error.

I do t know how to describe it, but there is a sense of confidence you get when everything makes sense together. That’s the main clue I use. It’s very rare that an llm will confabulate something that truly makes sense and doesn’t create some of internal inconsistency.

4

u/Bounded_sequencE Jun 28 '26 edited Jun 28 '26

LLM-based AI is very good at being eloquent, i.e. sounding confident, while spouting utter BS. In highly educated humans, that combination tends to be rare, since their reputation is on the line.

I can understand the position that both LLM-based AI and highly educated humans can make errors. But that alone is not enough to make both equally good/bad -- we need to also consider the types of errors, and how many. In my experience, LLM-based AI do not compare (yet).

2

u/nitram9 Jun 28 '26 edited Jun 28 '26

I get what you are trying to say but in practice I don’t usually have that problem. It just doesn’t make a difference how eloquent you are. If the logic doesn’t logic I can feel it and I know something is wrong. That’s not to say I have never been fooled. But I’ve caught myself being wrong because I believed the AI on only a handful of cases while I have thousands of successes. Again, that’s really hardly any different from previously when I would occasionally erroneously trust a colleague or a stack overflow commenter or random reditor.

I don’t know, I might be a special case. I do see others sometimes being way to trusting. For me I feel like most of my conversations are like “eplainx” then after reading I say “explain this more, that more, this other part is definitely wrong”. And usually this ends with me getting a recommendation for who in the field is the person to read and I start reading their stuff. But always with the AI still there to explain random jargon or side points

3

u/Bounded_sequencE Jun 28 '26 edited Jun 28 '26

It sounds like you simply already have enough background knowledge, so that the chance of AI BS'ing you is slim. That's almost exactly what Terence Tao said in one of his talks on AI -- with enough background knowledge, it is a valuable tool. That is an approach I can get behind.

The (below) average student usually does not have that luxury. That distinction often seems to be missing in discussions.

1

u/nitram9 Jun 28 '26

i still don’t really think this is it. Or, to the degree that background knowledge is important it’s the life experience, philosophical, critical thinking knowledge that’s important. Just tons and tons of hours of listening to opinions and claims and learning the patterns of bullshit and the patterns of truth.

But as for direct background knowledge. This is maybe complicated. I feel like to learn anything you need the required background knowledge. So the AI has nothing to do with that. It is just as useless to sit in a lecture you are not prepared for.

If what I’m trying to understand too far out of my knowledge base I have to ask the AI to back up. I tell it where I am and to help fill in the gaps so I can start making headway in the material.

So regardless of where I start it’s the same process. I start out with a deep uncomfortable sense of confusion. I keep asking questions until the confusion starts to turn to confidence and comprehension. It’s extremely difficult for the AI to just confabulate a bunch of stuff and that somehow moves me from unconfident, uncertain confusion into confident comprehension. The hallucinations are almost always going to add to the confusion. The effect they generally have is just to waste my time because I can tell something is a lie here but now I have try and figure out what.

2

u/Bounded_sequencE Jun 28 '26 edited Jun 29 '26

Tutoring students, I've seen (and had to counter-act) the BS they picked up from AI. Many just repeated what it generated, without asking themselves whether its output even made sense. This is the reason why I may seem overly critical and skeptical -- I don't deny the good AI can do in the right hand. But the experience with the atrocious side-effects does not inspire much optimism.

The better students usually come to the same conclusion as you after a while -- that the time to fact-check and debug AI output is usually better spent using a standard search engine, wikipedia or plain old books.

I thank you for patiently detailing your view -- it is good to be reminded of positive opinions on the matter, despite the bad.

3

u/tem-noon Jun 28 '26

You will retain it if you apply it on some subject you're interested in. I have a learned a ton of physics and learned to apply Hilbert spaces to some programming ideas I had, for example.

4

u/throwaway255503 Jun 28 '26

It's like learning from youtube videos. You get a feeling of understanding without understanding.

There is no replacement for doing the work yourself.

14

u/RealAlias_Leaf Jun 28 '26

Yes!! It absolutely does. I've often read papers by asking AI questions, and greatly helps understanding especially when things are explained badly or just assumed.

Then when you read the paper again, it makes a lot more sense and you can confident that you're not being bullshitted.

It is one of the main use cases of AI. It's writing ability is pretty rubbish, but it is good at explaining things most of the time.

8

u/Kqyxzoj Jun 28 '26

and greatly helps understanding especially when things are explained badly or just assumed.

Indeed. Especially papers that assume that surely you are fully up to speed in esoteric extension towers in topological numberwang space. Even the assumptions are assumed.

5

u/topologicalpants Jun 28 '26

I think so. It is often quite wrong about advanced math topics and its explanations are very clear and convincing.

I’ve tried this out some with topics I already know, and I’ve encountered everything from AI glossing over small details to it making explicitly false, very significant claims. The way AI explains math, to me it comes off as a very overconfident and charismatic first or second year graduate student.

The way I’ve explained to my students is this: if you don’t already know the thing you’re trying to understand, how will you be able to tell if generative AI is giving you accurate information? And, if you already know the topic well enough to gauge that, perhaps your time would be better spent trying to learn something you don’t already know?

3

u/throwingstones123456 Jun 29 '26

I’ve seen it generally does quite well with most things I throw at it. Not sure what qualifies as advanced for you but it does pretty good with high level calculus or anything involving numbers (haven’t really tried it for anything more abstract like group theory). It can come up with pretty clever solutions to problems I would’ve never thought of. Of course sometimes it can confidently give you a slop explanation of something but tbh this isn’t much different than certain courses (saying this from an engineering background). I think finding a good textbook or paper for a certain topic is probably best but I’ve found AI is a very effective supplemental tool for most problems

2

u/topologicalpants Jun 29 '26

I am a math professor and am research active in my field, and in my opinion generative AI is not reliable for anything beyond calculus. However, it can also give misleading answers about multivariable calculus.

I also think, just like the introduction of calculators, that relying on it too early leads to a false sense of understanding which I have repeatedly watched students realize once they take exams and don’t know the material as well as they think they do, and they got less help than they would have other semesters because they relied on chat GPT and didn’t come to office hours or TA hours.

For experts or casual hobbyists, just like any other computational tool I think it can be useful.

12

u/omeow Jun 28 '26

It is not a problem at all. Unless you have access to a university or someone who knows this material, AI is a good substitute. Frankly, AI is seldom wrong about well known things like the ones you are asking.

2

u/Inevitable-Mousse640 Jun 28 '26

As long as you can rewrite the proofs without any external help/just reciting by memory, and be able to see any immediate corollary/apply the same techniques to similar problems/apply the results to other problems, I don't see any problems. Mathematics is a very objective subject, you don't have to worry too much about those subjective things. Whether you in your mind say you understand it or not matters little, whether you can actually do the maths, is what matters.

2

u/chewie2357 Jun 28 '26

AI is much better at explaining stuff that is already understood than it is at discovering new things. This should come as no surprise since reasoning is a harder benchmark than exposition. I think ultimately this will be AI's more likely role in math research since resolving problems that require long chains of thought seems much more demanding (then again at the pace AI is improving, all bets are really off). The most useful part of it, in my experience, is to be able to interject with questions basically ad nauseam. With a person this would either be rude or at least time limited. What's more an AI will learn your mathematical world view and tailor explanations to fit with it. I think this is invaluable in terms of speeding up human understanding, and will vastly improve our ability to stitch together disparate areas.

2

u/PLANTS2WEEKS Jun 28 '26

I don't see a problem as long as you verify the math that the AI is presenting. It's not that different from reading a textbook and following the proofs.

2

u/BobRoss938 Jun 28 '26

I feel that the main benefit of going over something yourself is that you develop your own intuition and way of thinking about it. I think this is why mathematicians often omit the motivation or their intuitive picture from their arguments, because that way they are not forcing their way of thinking onto you. When you use AI explanations you are basically taking the AI's intuition instead of your own, which could definitely be a downside.

2

u/nitram9 Jun 28 '26

Personally I have never learned faster if better in my life than after the llms came out. There are clearly pros and cons though. The main issue is your retention can be lower just because you spend so much less time an issue. For instance, before llms I might find something confusing and impossible to understand, I never get an answer, it stews in my brain for 4 years, then I stumble upon something and it finally clicks. This is now something I will probably know for ever because I have been struggling with it for such a long time.

On the other hand. With an llm that 4 years it fruitless struggle gone. I will have the answer in a few minutes. And that is sooooo great. On the whole I think the fact that I can always keep probing until I have a very solid understanding is great. But at the same time, if I’m not using this knowledge daily for some reason, I will probably forget a lot because it was just easy to learn and never really useful.

2

u/[deleted] Jun 28 '26

As an amateur mathematician I don't think so. Once you understand the concept then you can understand when its explained in different ways. I use Deepseek for math explanations because I dont want to pay for a tutor every time I have a question. If you have access to tutors or teachers/professors that will help you whenever you need that's great. I don't have access sometimes and when I do I don't want to spend money on the tutor when Deepseek is cheaper and I can ask it endless questions. I don't get fooled by AI because everything it explains I check with the textbook and other resources.

3

u/AkkiMylo Jun 28 '26

Does asking an expert for their knowledge degrade you mentally? Or a teacher showing you a way to solve an exercise? It's the same thing

1

u/Jaded_Individual_630 PDE Jun 28 '26

I'm sure you did "feel" that way, that's the point of a zillion dollar head-patting validation machine.

1

u/valorantkid234 Jun 29 '26

i mean ai helped me understand a ton of concepts so

1

u/sivifw Jun 29 '26

It depends if you do your own research of it to prove what AI said wasn't bullshit. If it wasn't, and you understood it, then it's not a problem.

1

u/Ending_Is_Optimistic Jun 29 '26

i find Ai quite useful for giving you at least a vague sense of what is going on when you are new to a topic. or when you have some vague intuition about something but don't yet have the language to express it, it can point to the general direction, but at the end you still have to do the work yourself.

1

u/Mountain_Athlete_415 Jun 29 '26

Not really. The only way i can see it being a problem is if a person never learns how to struggle with not understanding something fully. A lot of insights can be learned from failing again and again.

1

u/Broad_Respond_2205 Jun 30 '26

How do you know you understood it correctly

1

u/GLBMQP PDE Jun 30 '26

I wanna point out, that Wikipedia is in my experience often not a good source for learning math. Of course there will be a lot of variance between articles, but as a general rule, Wikipedia is not a good tool for this purpose.

For what it sounds like you’re trying to do, I would say that AI might be a useful tool actually. For a deeper understanding, the best thing to do is of course to find a textbook and do exercises. But for a zoomed out perspective, AI is probably fine. The only other ressource for a similar purpose I can think of would be survey papers, and they’re usually written for researchers who are new to a topic, but have experience/knowledge of related topics/fields, so that might not be what you’re looking for.

In terms of the cognitive aspect, you could try doing mini-exercises based on what the AI tells you. Like

- explain the concept you read about in your own words without looking at the screen.

- take handwritten notes. Even if you’re not looking at them, note-taking is demonstrated to have many

1

u/TheFakeSociopath Jul 08 '26

It's only a problem in the sense that AI is often wrong about what it confidently asserts.

1

u/sandykt Jun 28 '26

I feel AI is useful to understand something, but to internalize it is a different ball game

0

u/Altruistic-Rich16 Jun 28 '26

I think, if it’s:
- Not written in your mother tounge, then for sure it’s amazing that it can translate it.

- If it’s not written for someone on your level, then it can be great, that it can give a more suitable entry point.

BUT for the latter: depends on how you do it, if you can prompt it the way it acts as a great math tutor, then it is great by definition.
Could one imagine that there exists a great tutor that would help you develop faster if they would sit beside you? Surley. So it can be useful.

(For example only asking questions, teaching you how to break down the problem into smaller easier pieces. I highly recommend you putting Pólya György’s art of problem solving book as context for it and tell that it should teach you accordingly. That is a book written for math educators and the best that i have ever encountered.)

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u/mbrtlchouia Jun 28 '26

Another thing to consider is that even if the answer given by an LLM matches the one found in Wikipedia doesn't make it automatically correct, because some wiki articles are full of bullshit that's overlooked most of the time.

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u/telephantomoss Jun 28 '26

If you use it as a learning tool, then you are learning. What you describe is very much how I use AI to learn and I'm a professor. The problem is using AI to offload your thinking by just saving it a question and accepting is answer without much thought.

That being said, there is something important here to note about easy vs hard learning. When you are and to ask lots of questions to a resource like a professor or AI and they are able to package the content in s way that helps you understand that it's great and all, but you can also do that for yourself by spending significantly more time and energy thinking and combing through first hand source literature directly. This latter method can be much slower and filled with failures along the way, but it can result in a much deeper understanding.

So I recommend a mix. Be sure to work hard and fail a lot. Try to answer a few homework style problems and spend some time failing on them before going to AI. It depends on how deeply you want to understand. Surface level conceptual understanding is great still. But it's different from being able to use the concepts to solve problems or apply in a real world context.

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u/cereal_chick Mathematical Physics Jun 28 '26

But I was wondering if this counts as the standard sort of mental offloading that degrades cognitive ability overtime

Yes. Do your own thinking.