Comment by ghm2180
3 days ago
The current cycle of AI and mathematics gives me great hope for ordinary people like myself to try and attempt learning some mathematics and try and see if I like the experience. Has any one tried that or is trying that? How are you approaching it? I would like to know - you can DM me - I would love to have a conversation if this excites you :)
I think the _key_ to knowing if I can do it has to come from the fact if my intuition about a problem helps me make progress. I would use AI to learn the parts I did not know and engage a community of people to ask questions. Both are key.
Also I am not 100% sure, but me beginning straightaway with lean to try something — like an engineer would — does not seem like the right approach before building some critical mass in the subject. It feels kinda wrong like building the cart before the wheel would.
The problem with trusting AI to learn a complex subject, which I've tried multiple times, is it will always at some point confidently give you the wrong explanation for something important and you will have no way to detect it. Its quite frustrating and that realization might not come for hours or days and you've built lots of false mental models that can be hard to untangle.
You have to do it along with some sort of ground truth, like a book, and you have to be able to understand that book in order to be able to see that bad advice immediately.
Alas, there are no shortcuts in life. You still need to very eagerly read and understand the source materials you're studying as you would have before AI and to the extent which AI is helpful for that is debatable. Your brain still has to do the thinking.
I agree with the sentiment of mixing up sources. However there are not really many textbooks that rise to the level of "ground truth". Plenty of times that books give wrong explanations as well.
Well I said sort of, but I'd argue most significant works in significant fields do not give completely incorrect explanations, and if they do there's usually versions of those works and they are updated. Your llm conversation is not versioned, there is no consensus built around its correctness.
In my experience learning with llms is the equivalent of doing (bad) tutorials, and you end up in tutorial hell where you feel like you're learning but you find it hard to implement said thing without that guide. It creates surface understanding thats not really worth the effort. Its better to dive deep on your own.
We're all looking for that shortcut, myself included, but as the saying goes, "there's no free lunch".
So... use a RAG trained on the books you care about?
>The problem with trusting AI to learn a complex subject, which I've tried multiple times, is it will always at some point confidently give you the wrong explanation for something important and you will have no way to detect it. Its quite frustrating and that realization might not come for hours or days and you've built lots of false mental models that can be hard to untangle.
This is an amazing problem to have! Often, preAI, I'd reject models flat out since they weren't even convincing on their face. There is value to this even if it's not correct. How long were people stuck with the aether? a few days or months is nothing.
I can chime in about this. I’m a software engineer and about 7 years ago I decided to get a masters in pure mathematics. Because I was working full time, I could not attend any class so I self studied from textbooks and it worked well.
When I would get stuck, I would struggle with the problem, ask around, ask on Math Stackexchange and along the process I would end up learning a lot more.
With AI now, it’s like having your own tutor: you can ask personalized questions and it would answer it very well.
But that would also mean the amount of time I would spend struggling would go down considerably.
So you really have to be self disciplined and struggle with the problem a little bit before asking for help. You can also ask it to give hints only.
Do not mistake understanding the answer with learning something rigorously.
So if you are curious and doing an exposition, use it as you would normally and it will work wonderfully.
But if you want to learn it rigorously, our usual present habits with AI spitting out answers and us reading them will not work at all.
I wonder: can you get the AI to give you exercises that, when solved, would illustrate a point? This might require more theory of mind than they have.
I've tried to do this but with learning poker, and it's sort of a mixed bag. You kind of have to know what you don't know before you can get anything useful out of it. It can sort of help going from "I understand this concept, but not instinctively" to "I've drilled this enough that I could do things like this in my sleep", but it takes a lot of iteration and asking questions before it can settle on a series of instructive examples that each build on top of each other. You're still much better off with a well-written textbook.
Claude Code will make Bartosz Ciechanowski-style [0] explainers for me in about 3 or 4 hours. Here is an example of converting waveforms into spectrograms to train a model to associate sounds with words or classifications. [1] Or, it will take the research paper for Data Lake and convert it into animated, step-by-step visualizations explaining how the data store works. [2]
It is still work! And, I have to struggle to get it to make sense and look nice. This means I'm interacting with the code and system which is how I learn!
[0] https://ciechanow.ski/sound/
[1] https://adamsohn.com/clap/
[2] https://adamsohn.com/algoviz/?algo=delta-week
In my experience AI is a very bad teacher. It mumbles in AI-ish, a dialect of English which is difficult to understand without reading things twice. Also, it uses concepts before they are defined. And doesn't have a good mental model of what the reader knows. Stuff like that.
AI labs definitely should work on it.
I think AI is more effective as a tutor than as a teacher. The student sets the curriculum and does the work up front (e.g. writing up LaTeX notes) then the AI checks it and answers questions with the notes as context. I've had some success with this approach for theoretical physics, but it is clunky and maybe there's a better solution.
If you want to learn a mathematical topic, I would recommend reading textbooks instead. They are expressly designed for the purpose by experts on the topic.
I might suggest also trying to find online a syllabus for a course that taught that topic using that textbook. That can give you an idea of a reasonable pace to learn the material. If you can't find one using the same book, you still can get some idea of pacing based on the topics listed.
A good textbook will be designed so that you can move on when when you just have a decent understanding, and your understanding will deepen and complete as you gain experience from the material being used to help teach the new material in later chapters.
At the point where it is OK to move on most students feel like they are nowhere near ready. If you just move on when you feel ready it is easy to find yourself a few months later wondering why it has taken you several months to get to chapter 3 when you know that in college students finish the whole book in that amount of time, which taking several other classes.
It is OK if you go slower than the college classes. If you can't put in as much time per week as college students do you would be expected to go slower. Just use the college pace, adjusted for how much time you can put in, to help know when it is OK to move on so you don't get stuck due to thinking you aren't ready.
It can also help if you can find a list of assignments for a class that used the same book. That can give you an idea of a minimum number of exercises you should be doing. It is ok course OK to do more.
For many STEM subjects, MIT OpenCouseWare [1] is a good place to find syllabi and often much more for free.
[1] https://ocw.mit.edu/
"Reading" a textbook is very different from reading a novel, that should be noted. You gotta do the exercises.
I would think the exact opposite. I always lacked academic rigor and I own that.
How could you come in with less rigor and claim to understand things because you're using AI?. Sorry for the aggressive tone but is there an answer to that questipn?
Use a good (human-written) textbook and solve the exercises. Use AI to ask clarifying questions when necessary.
> - you can DM me -
...how?
HN profile.