5 ms·

I personally don't get this attitude. For one thing, nobody on earth can give you a 500-word summary of quantum physics in a way that lets you internalize even

I personally don't get this attitude. For one thing, nobody on earth can give you a 500-word summary of quantum physics in a way that lets you internalize even a tiny bit of it. That's not how you learn anything. Here's how I do it: I open Baby Rudin (3rd ed.), second chapter, and read the main text - absolute brutality. I unpack almost every sentence with Claude/GPT until I finally get what's going on. No ELI5 nonsense, just examples and counterexamples galore while absorbing the techniques and the way of thinking in analysis/topology. How do I know I've learned the material? By solving every single problem in that chapter. Here's the thing, though: the problems in Rudin can be brutal and decoupled from what's in the text, so if you can handle them, you've definitely mastered the material. No 500-word summary of analysis here.

sublinear 2mo ago
Is that meaningfully different from the study methods of the past? That doesn't require an LLM, and using one risks correctness in exchange for speed. You might not even get that speed if you're stuck in the weeds often enough. A decade ago, a google search for study guides written by another professor would have been slightly slower. A decade before that, you'd be even slower fumbling through several books. Every single word could at least be trusted. You don't get that from an LLM.
- winnit 2mo ago
  When studying a mathematics text, it is good practice to question what you are reading, trying to prove things to yourself etc., which IMO makes the problem of trusted sources much less than it is in things which you are not able to verify e.g. historical accounts.
- Jtarii 2mo ago
  If you have an actual mathematics professor to ask questions to then sure do that, but most people don't have that luxury. Also the error rate of frontier LLMs on textbook highschool/college level mathematics is going to be extremely low. It is also significantly more engaging and fun.
  - tcp_handshaker 2mo ago
    >> the error rate of frontier LLMs on textbook highschool/college level mathematics is going to be extremely low. The scientific basis for this statement is unclear.
    - refactor_master 2mo ago
      AIME and HMMT are high school math olympiad competitions now used to benchmark AI. Frontier models score 95-99% https://benchlm.ai/blog/posts/aime-hmmt-competition-math https://benchlm.ai/blog/posts/aime-hmmt-competition-math
      - batshit_beaver 2mo ago
        They score 99% but then can’t explain _why_ their solution works with any accuracy. Not as useful for learning as one might think.
        fl4regun 2mo ago
        are you referring to this section? > Verification is different from generation: Models scoring 98 can solve problems but can't always explain why their approach works at the level a human mathematician would. It doesn't say it can't explain why with any accuracy, it just says it can't *always* explain at the level of a mathematician, but most of us don't have such a mathematician at our beck and call to answer our questions anyways (thinking of the perspective of a self-learner outside of formal education)
        batshit_beaver 2mo ago
        It’s not just math. Anecdotally, LLMs struggle the same way with software engineering where the code they write is correct (compiles and passes tests), but reasoning is wrong often enough to eliminate most trust in these models’ ability to explain codebases or even features they themselves produce. It’s not about the _level_ of the supposed intelligence where a model struggles to summarize things succinctly or simply enough (responding to the “pocket mathematician” comment) or can’t grasp certain concepts at all (if so, how tf is it able to apply them?). It’s that by their design LLMs have no concept of truth and no concept of causality. They guess with every single inference and it’s very hard as a user to understand which guesses are more or less certain, since, you know, confidence ratings aren’t part of these models’ design either.
- cornholio 2mo ago
  > Is that meaningfully different from the study methods of the past? The fundamental service a teacher provides is personalized feedback, quickly identifying where you are stuck and focusing the explanations and exercises on that area, drastically increasing the speed and quality of learning versus the self-supervised route. The lack of this closed loop effectively killed the high hopes that were placed in e-learning and MOOCs 15-20 years ago, TV learning in the 1960s and many other failed revolutions, seems every generation has its own version. It appears to me LLMs have a real potential to close this loop and become the failed educational revolution of our own generation.
  - alper 2mo ago
    > personalized feedback, quickly identifying where you are stuck and focusing the explanations and exercises on that area, This has been a huge blocker when I tried to study advanced math myself. Many of the exercise books don't have worked out answers, so often you're either stuck or you have to hunt a variety of sources online for solutions and advice. It kills flow.
- defmacr0 2mo ago
  I certainly would only trust my textbook as the authoritative source, but i can see that in the absence of an expert teacher it's nice to have something that can critique a proof. Imo the fact that it's hard to verify that your own proof is correct is one of the main barriers in self-studying math, especially if one is at a level where one is not completely fluent in applying the various techniques. This also applies to judging answers to open-ended questions in any other field.
  - nicf 2mo ago
    I'm a private math tutor specializing in exactly this sort of material, and I agree with this very strongly. Knowing what "counts" as a proof is one of the most common gaps I see in students who come to me after self-studying, and most students do need some back-and-forth with an expert to really get that skill down. I imagine that LLM's could be very helpful for this if they were used judiciously!
turzmo 2mo ago
Baby Rudin is a special textbook: it comes from a time when mathematics textbooks were not at all judged by their pedagogical value, but instead by their aesthetic appeal to mathematicians (a la Bourbaki). If you actually want to learn analysis, there are a nearly infinite number of friendlier resources (e.g., Understanding Analysis by Abbott). Learning to unpack difficult text on one’s own is a valuable skill. Research papers often require a similar amount of suffering, and at the frontier of knowledge, despite all the advances we’ve seen, LLMs seem to have absolutely no understanding or intuition. They are much better at things that have been expounded at length by humans before. I would argue that if you’re going to use an LLM to make Rudin easier to understand, you are not learning how to absorb difficult material, nor are you learning analysis efficiently.
- engineer_22 2mo ago
  Your argument sound remarkably familiar. Humor me: "For this invention will produce forgetfulness in the minds of those who learn to use it, because they will not practice their memory.“ -Socrates, on writing. From Phaedrus Secondary source: https://www.historyofinformation.com/detail.php?id=3439 https://www.historyofinformation.com/detail.php?id=3439
  - ethbr1 2mo ago
    ChatGPT also offered this: "For the correct analogy for the mind is not a vessel that needs filling, but wood that needs igniting - no more - and then it motivates one towards originality and instils the desire for truth. Suppose someone were to go and ask his neighbours for fire and find a substantial blaze there, and just stay there continually warming himself: that is no different from someone who goes to someone else to get some of his rationality, and fails to realize that he ought to ignite his innate flame, his own intellect, but is happy to sit entranced by the lecture, and the words trigger only associative thinking and bring, as it were, only a flush to his cheeks and a glow to his limbs; but he has not dispelled or dispersed, in the warm light of philosophy, the internal dank gloom of his mind." -Plutarch, on listening https://books.google.com/books?id=0U-hsAonP1AC&lpg=PA50&dq=plutarch%20mind%20vessel%20igniting&pg=PA50#v=onepage&q&f=false https://books.google.com/books?id=0U-hsAonP1AC&lpg=PA50&dq=p... I didn't read the whole passage, but it seems to be talking about the same thing.
uncivilized 2mo ago
Feel free to share your chat that has explanations for Baby Rudin. I’d like to see what you consider helpful in this context.
hackrmn 2mo ago
There's been research done (I know, big words -- don't have any links readily available), where it was pointing to the fact that what goes easily in (into the brain) also goes easily out, and conversely, what the brain requires effort and literal calories and energy to understand, stays there longer (investment must be rewarded / recouped somehow). So while there's no doubt that facilitating learning is a net-positive, at some point it becomes a net-positive, I suppose -- your brain just chucks it out faster because it knows you can re-obtain the same information again since it worked so easily the first time. It doesn't know the difference between easy and hard, all it knows is how much effort it takes and how much reward (hormones) was generated for it all (to cement the habit/result).
- bryzaguy 2mo ago
  Spaced repetition could address this, no? Also, the right example or metaphor can make a difficult concept both easier to understand and stickier in my mind which I think is different than something easy to learn.
  - runarberg 2mo ago
    Spaced repetition is a good way (perhaps even the optimal way) to get large amount of trivial memorization into your brain, but it not a good way to understand a complex subjects. Memorizing one word in a foreign language is not that complex, nor hard. The tricky part about learning a language is that you have to memorize thousands of words, and the trickier part is that you have to retain most of those words over a long period of time. Spaced repetition helps by finding an optimal schedule to for the exact same activity as you would otherwise.
  - hackrmn 2mo ago
    I agree regarding metaphors, I myself aggressively utilise analogies with both myself and others, as a "digestive", but I feel like with LLMs we're treading on thin ice as it's not straightforward to classify a particular use case as one scaffolding learning with a metaphor, or just having the opposite effect where your brain "sails" in a faulty sea of "learning" while in reality there's no real work being done, not of the kind the brain needs to do in order to re-order all the synapses and own networks that ends being "knowledge" eventually.
deleted 2mo ago
[deleted]
the_gastropod 2mo ago
Your obvious use of an LLM to write this comment isn’t exactly confidence-inspiring that it’s helpful for learning to do things on your own. Seems like it’s evidence that LLM’s quickly become a crutch for even trivial efforts like posting internet comments.

sublinear 2mo ago

Is that meaningfully different from the study methods of the past? That doesn't require an LLM, and using one risks correctness in exchange for speed. You might not even get that speed if you're stuck in the weeds often enough. A decade ago, a google search for study guides written by another professor would have been slightly slower. A decade before that, you'd be even slower fumbling through several books. Every single word could at least be trusted. You don't get that from an LLM.

winnit 2mo ago
When studying a mathematics text, it is good practice to question what you are reading, trying to prove things to yourself etc., which IMO makes the problem of trusted sources much less than it is in things which you are not able to verify e.g. historical accounts.
Jtarii 2mo ago
If you have an actual mathematics professor to ask questions to then sure do that, but most people don't have that luxury. Also the error rate of frontier LLMs on textbook highschool/college level mathematics is going to be extremely low. It is also significantly more engaging and fun.
- tcp_handshaker 2mo ago
  >> the error rate of frontier LLMs on textbook highschool/college level mathematics is going to be extremely low. The scientific basis for this statement is unclear.
  - refactor_master 2mo ago
    AIME and HMMT are high school math olympiad competitions now used to benchmark AI. Frontier models score 95-99% https://benchlm.ai/blog/posts/aime-hmmt-competition-math https://benchlm.ai/blog/posts/aime-hmmt-competition-math
    - batshit_beaver 2mo ago
      They score 99% but then can’t explain _why_ their solution works with any accuracy. Not as useful for learning as one might think.
      - fl4regun 2mo ago
        are you referring to this section? > Verification is different from generation: Models scoring 98 can solve problems but can't always explain why their approach works at the level a human mathematician would. It doesn't say it can't explain why with any accuracy, it just says it can't *always* explain at the level of a mathematician, but most of us don't have such a mathematician at our beck and call to answer our questions anyways (thinking of the perspective of a self-learner outside of formal education)
        batshit_beaver 2mo ago
        It’s not just math. Anecdotally, LLMs struggle the same way with software engineering where the code they write is correct (compiles and passes tests), but reasoning is wrong often enough to eliminate most trust in these models’ ability to explain codebases or even features they themselves produce. It’s not about the _level_ of the supposed intelligence where a model struggles to summarize things succinctly or simply enough (responding to the “pocket mathematician” comment) or can’t grasp certain concepts at all (if so, how tf is it able to apply them?). It’s that by their design LLMs have no concept of truth and no concept of causality. They guess with every single inference and it’s very hard as a user to understand which guesses are more or less certain, since, you know, confidence ratings aren’t part of these models’ design either.
cornholio 2mo ago
> Is that meaningfully different from the study methods of the past? The fundamental service a teacher provides is personalized feedback, quickly identifying where you are stuck and focusing the explanations and exercises on that area, drastically increasing the speed and quality of learning versus the self-supervised route. The lack of this closed loop effectively killed the high hopes that were placed in e-learning and MOOCs 15-20 years ago, TV learning in the 1960s and many other failed revolutions, seems every generation has its own version. It appears to me LLMs have a real potential to close this loop and become the failed educational revolution of our own generation.
- alper 2mo ago
  > personalized feedback, quickly identifying where you are stuck and focusing the explanations and exercises on that area, This has been a huge blocker when I tried to study advanced math myself. Many of the exercise books don't have worked out answers, so often you're either stuck or you have to hunt a variety of sources online for solutions and advice. It kills flow.
defmacr0 2mo ago
I certainly would only trust my textbook as the authoritative source, but i can see that in the absence of an expert teacher it's nice to have something that can critique a proof. Imo the fact that it's hard to verify that your own proof is correct is one of the main barriers in self-studying math, especially if one is at a level where one is not completely fluent in applying the various techniques. This also applies to judging answers to open-ended questions in any other field.
- nicf 2mo ago
  I'm a private math tutor specializing in exactly this sort of material, and I agree with this very strongly. Knowing what "counts" as a proof is one of the most common gaps I see in students who come to me after self-studying, and most students do need some back-and-forth with an expert to really get that skill down. I imagine that LLM's could be very helpful for this if they were used judiciously!

turzmo 2mo ago

Baby Rudin is a special textbook: it comes from a time when mathematics textbooks were not at all judged by their pedagogical value, but instead by their aesthetic appeal to mathematicians (a la Bourbaki). If you actually want to learn analysis, there are a nearly infinite number of friendlier resources (e.g., Understanding Analysis by Abbott). Learning to unpack difficult text on one’s own is a valuable skill. Research papers often require a similar amount of suffering, and at the frontier of knowledge, despite all the advances we’ve seen, LLMs seem to have absolutely no understanding or intuition. They are much better at things that have been expounded at length by humans before. I would argue that if you’re going to use an LLM to make Rudin easier to understand, you are not learning how to absorb difficult material, nor are you learning analysis efficiently.

engineer_22 2mo ago
Your argument sound remarkably familiar. Humor me: "For this invention will produce forgetfulness in the minds of those who learn to use it, because they will not practice their memory.“ -Socrates, on writing. From Phaedrus Secondary source: https://www.historyofinformation.com/detail.php?id=3439 https://www.historyofinformation.com/detail.php?id=3439
- ethbr1 2mo ago
  ChatGPT also offered this: "For the correct analogy for the mind is not a vessel that needs filling, but wood that needs igniting - no more - and then it motivates one towards originality and instils the desire for truth. Suppose someone were to go and ask his neighbours for fire and find a substantial blaze there, and just stay there continually warming himself: that is no different from someone who goes to someone else to get some of his rationality, and fails to realize that he ought to ignite his innate flame, his own intellect, but is happy to sit entranced by the lecture, and the words trigger only associative thinking and bring, as it were, only a flush to his cheeks and a glow to his limbs; but he has not dispelled or dispersed, in the warm light of philosophy, the internal dank gloom of his mind." -Plutarch, on listening https://books.google.com/books?id=0U-hsAonP1AC&lpg=PA50&dq=plutarch%20mind%20vessel%20igniting&pg=PA50#v=onepage&q&f=false https://books.google.com/books?id=0U-hsAonP1AC&lpg=PA50&dq=p... I didn't read the whole passage, but it seems to be talking about the same thing.

uncivilized 2mo ago

Feel free to share your chat that has explanations for Baby Rudin. I’d like to see what you consider helpful in this context.

hackrmn 2mo ago

There's been research done (I know, big words -- don't have any links readily available), where it was pointing to the fact that what goes easily in (into the brain) also goes easily out, and conversely, what the brain requires effort and literal calories and energy to understand, stays there longer (investment must be rewarded / recouped somehow). So while there's no doubt that facilitating learning is a net-positive, at some point it becomes a net-positive, I suppose -- your brain just chucks it out faster because it knows you can re-obtain the same information again since it worked so easily the first time. It doesn't know the difference between easy and hard, all it knows is how much effort it takes and how much reward (hormones) was generated for it all (to cement the habit/result).

bryzaguy 2mo ago
Spaced repetition could address this, no? Also, the right example or metaphor can make a difficult concept both easier to understand and stickier in my mind which I think is different than something easy to learn.
- runarberg 2mo ago
  Spaced repetition is a good way (perhaps even the optimal way) to get large amount of trivial memorization into your brain, but it not a good way to understand a complex subjects. Memorizing one word in a foreign language is not that complex, nor hard. The tricky part about learning a language is that you have to memorize thousands of words, and the trickier part is that you have to retain most of those words over a long period of time. Spaced repetition helps by finding an optimal schedule to for the exact same activity as you would otherwise.
- hackrmn 2mo ago
  I agree regarding metaphors, I myself aggressively utilise analogies with both myself and others, as a "digestive", but I feel like with LLMs we're treading on thin ice as it's not straightforward to classify a particular use case as one scaffolding learning with a metaphor, or just having the opposite effect where your brain "sails" in a faulty sea of "learning" while in reality there's no real work being done, not of the kind the brain needs to do in order to re-order all the synapses and own networks that ends being "knowledge" eventually.

deleted 2mo ago

[deleted]

the_gastropod 2mo ago

Your obvious use of an LLM to write this comment isn’t exactly confidence-inspiring that it’s helpful for learning to do things on your own. Seems like it’s evidence that LLM’s quickly become a crutch for even trivial efforts like posting internet comments.