[vouaobrasil]

I love math, completed a PhD, and am very self-disciplined. But even so, I don't think I would have been able to learn much on my own with video lectures, at least not at the start. For some reason, it seems like you need to reach a "critical mass" of knowledge first before you can do that, and I've observed that a crucial component is being in a program with others, and definitely having a very experienced mentor.

Without a very experienced mentor, I think it's very difficult to get to the independent-learning stage with math. That's the key. You need someone to go through your work, correct you, and make sure you don't go off in a very wrong direction.

So my advice is find at least a graduate student in math to help you. It's like a piano teacher, if you've ever taken piano, you know it's absolutely mandatory to have a teacher. People who self-learn from the start end up being able to play but not very well.

Edit: one other crucial component is time. If you're really interested in knowing something like linear algebra, analysis, or calculus with fluency, expect to spend at least 10 hours per week on it for a year. Two hours per week will give you a cursory and very weak understanding only.

[abhink]

> But even so, I don't think I would have been able to learn much on my own with video lectures, at least not at the start.

This was exactly my situation. Videos can give you a lot of structured, well presented information. And for MIT courses you'd get this knowledge from the very best. The problem is that no matter how well the subject matter is presented, I would hit some conceptual snag that I couldn't resolve just by repeating the sections in the video.

Now, years ago, to clear up the concepts, I would go to math stack exchange, write down exactly what I wanted to understand using mathjax and hope that someone will provide a detailed enough explanation. Most of the time I did learn from the answers, but sometimes the answer would be too succinct. In such cases there would be a need for a back and forth and stackexchange is not really designed around that usage pattern. This hassle would eventually make me give up the whole endeavor.

Now however there are LLMs. They don't need mathjax to understand what I am talking about and they are pretty good at back and forth. In the past 6 months I have gone through 2 full MIT courses with practice sheets and exams.

So I would encourage anyone who went through the route of self learning via videos and found it to be too cumbersome and lacking to give it another go with your favorite LLM.

[zehaeva]

My only concern with using LLMs to learn new material is being certain that it's not leading me astray.

Too many times I've used LLMs for tasks at work and some of the answers I've gotten back are subtlety wrong. I can skip past those suggestions because the subject is one I'm strong/experienced in and I can easily tell that the LLM is just wrong or speaking nonsense.

But if I didn't have that level of experience, I don't think I would be able to tell where the LLM was wrong/mistaken.

I think LLMs are great for learning new things, but I also think you have to be skeptical of everything it says and need to double check the logic of what it's telling you.

[hennell]

I have the same doubts, it's like the old rule of reading a newspaper story. When it's outside your area of expertise you think they're a genius. When it's something you know a lot about you think it's an idiot.

But it might still help, especially if you think about the LLM as a fellow student rather than as a teacher. You try to catch it out, spot where it's misunderstood. Explain to it what you understand and see if it corrects you?

[libraryofbabel]

LLMs are indeed excellent as conversation partners for helping with difficult concepts or for working through problem sheets. They’re really opened up self-learning for me again in math. You can use them to go much deeper with concepts much deeper than the course you’re taking - e.g. I was relearning some basic undergrad probability and stats but ended up exploring a bit of measure theory using Gemini as well. I would go so far as to say that an LLM can be more effective for explaining things than a randomly selected graduate student (though some grad students with a particular talent for teaching will be better).

What the LLM still does not provide is accountability (a LLM isn’t going to stop you from skipping a problem set) and the human social component. But you could potentially get that from a community of other self-learners covering the same material if you’re able to pull one together.

[monkeyelite]

When it comes to math and CS, doing exercises is a much stronger indicator of self-learning then reading/watching.

[j7ake]

Like piano it’s important to tackle courses that are appropriate for your level

Self taught people often skip too much of the basics so they struggle to properly tackle the fancy stuff

[vouaobrasil]

Even if they don't skip, they adopt weird hand positions that are hard to correct. There is just too much motor movement that needs to be done right that cannot really be explained or learned by watching a video or reading a book. It's actually similar to math in a certain way, where motor memory is replaced by subtle steps in logical reasoning.

[j7ake]

Maybe what’s common is that self taught people do not even know what to look for to improve on.

They only see the superficial or easy-to-spot goals and lack the eye for detail to build foundations and technique.

[roadside_picnic]

> completed a PhD... But even so,

Not sure why you added "but even so", getting a PhD is fundamentally about believing in the necessity of the mentor/mentee relationship for learning. It's not at all surprising that you would find:

> You need someone to go through your work, correct you, and make sure you don't go off in a very wrong direction.

I've learned enough to publish (well received) technical books in areas I've never taken a single course in, and have personally found that in-classroom experiences were never as valuable as I had hoped they would be. Of course starting from absolute 0 is challenging, but one good teacher early on can be enough.

Though I also don't think video lectures alone are adequate. Rather than focusing on "exercises", I've found I get the biggest boost in learning when I need to build something or solve a real problems with the mathematical tools I'm studying. Learning a bit, using it to build a real project, and then coming back when you need to unblock the next hurdle is very effective.

On top of this, books are just better for learning than videos (or lectures in general). Lectures are only useful for getting the lay of the land, and getting a feel for how types of problems are worked out. Especially with mathematics, you need time to look at an equation, read ahead, flip back, write it in a notebook, etc until you really start to get it.You really can't possibly get any of these ideas in 45-60 minutes of someone talking about it.

That's why, for me, online lectures don't really change the autodidact game all that much. Reading books and solving problems seems to have been the standard way to learn things well for at least the last several hundred years, and lectures don't improve on that too much.

[vouaobrasil]

> Not sure why you added "but even so"

Because the "even so" was for the "self-motivated" part, not the "getting the PhD" part.

> I've learned enough to publish (well received) technical books in areas I've never taken a single course in,

I'm talking about pure math here, not other technical fields which are more hands on and don't require as much mentorship. Programming is easier to self-learn than math for sure, because it is not very abstract compared to math. It's also guided by whether the code works or not.

[roadside_picnic]

> I'm talking about pure math here

Well the post is "Mathematics for Computer Science" which I don't think anyone considers "pure math". Most of my writing has been in the area of applied mathematics, the closest I've gotten to pure math would be some stuff on measure theory.

So yea, it might be a challenge to self teach something like cluster algebras, but at that level much of the work in the field is academic communication anyway.

[ktallett]

I would say that you need to start at a lower level when self learning with a simpler resource. Something like Openstax. People get far too obsessed with the name attached to a resource than whether it is the right method of learning.

[maweki]

I am about finished with my CS PhD and I taught databases at the university during covid. I, personally, would have failed in the remote learning environment we were providing.

I am amazed at those wo fought or even flourished through that.

[odyssey7]

I’m currently enrolled in an online MS program, and I had never struggled so much in courses. The lack of social component might be what’s causing that. The material is mostly a recap of undergrad and things I already knew, so the coursework should not be so difficult for me, but it’s been incredibly difficult.

Then again, William & Mary had some incredible teachers, and maybe the online program through a different school just isn’t very good at designing assignments and teaching by comparison. But I feel that there was a difference in how I could succeed at challenging assignments when I was among other students in a social setting. The work in undergrad was highly rigorous, though exploring it alongside other real-life students made it a very different undertaking.

[sodality2]

I'm a fourth-year W&M student considering an online MSCS program post-grad (possibly the same one you're in) - I'd love to hear more about your experience in it, as compared to traditional undergrad, if you'd be willing to share?

[kindkang2024]

LLM could be the teacher, one of the best already..

[roadside_picnic]

I've found you have to be very careful with LLM as teacher since, especially when it's the one explaining, it is wrong more often then you might think, and there's no way to know.

The best use of an LLM I've found in learning is for when I explain to it my understanding of what I learned and have it critique what I've said. This has greatly reduced the amount of backtracking I need to do as I start to realize I've misunderstand a foundational concept later on when things stop making sense. Often simply having the model response with "Not quite, ..." is enough to make me realize I need to go back and re-read a section.

The other absolute godsend is just being able to take a picture of an equation in a book and ask for some help understanding it notationally. This is especially helpful when going between fields that use different notation (e.g. statistics -> physics)

[AnimalMuppet]

I don't think "one of the best" would be wrong that often.

[kindkang2024]

Sure, it’s not perfect — but most of the time, it gets things right. Also it can answer instantly, and always patiently...

[samrus]

LLMs dont have a deep enough understanding of theory of mind to see how someone is stuck and help them get unstuck.

You need to guide your own study and you might not know what you need to learn to get unstuck

[kindkang2024]

> LLMs dont have a deep enough understanding of theory of mind to see how someone is stuck and help them get unstuck.

Many teachers cannot do that either.

I find ChatGPT and the Gemini model quite good at problems whose solutions are already known. We just need the Wille—the will—to ask it.

[samrus]

> Many teachers cannot do that either.

Of course there are bad teachers out there. The question wasnt "are there human yeachers as bad as an LLM" it was whether an LLM is as good as a good human teacher

> We just need the Wille—the will—to ask it.

Thats the thing. Its is a very good search resource. But thats not what a teacher is. A good teacher will help you get to the right questions, not just get you the right answers. And the student often wont know the right questions until they already know quite a bit. You need a sufficiently advanced, if incomplete, mental model of the sybject to know what you dont know. An LLM cant really model what your thinking, what your stuck on, and what questions you should be asking

[baby]

Says someone who's never used LLMs to learn

[samrus]

This is a somewhat childish comment. You didnt contribute anything to the discussion