At some point, you need people to check your work, though, but you can search for online communities to do that. E.g. a post to mathoverflow asking about whether the following proof is correct, for example. Try to find a community of others online and work with them.
Also remember that math is about ideas. It is not just an exercise in formal deduction. The field is dense with non-trivial, non-obvious, interesting insights, and understanding these insights so well that overtime they become obvious to you is what it means to learn math. Sites like 3Blue1Brown to a good job trying to explain these ideas, but they really put a lot of work into it. Most math texts do not, but you have a professor or classmate you can talk to -- so there is a gap between the text and what you need, but perhaps you can close the gap with online resources.
Agree with that, 100%. Most of my students will, at some point in a course, respond to questions with things that are completely wrong. It's just how people learn. If there was not someone to correct their mistake then they would struggle a lot to find the error and fix it.
One of the most rewarding things about working with students is helping them through tough spots. But it is real work, and takes the time and attention of someone who has training.
> but you can search for online communities to do that. E.g. a post to mathoverflow asking about whether the following proof is correct, for example.
I'll just observe that MO, while a great community, can not scale to helping lots of people check their homework. For instance, in a Linear class session I might have 20 people, each with 12 homework questions. MO is just not set up for that.
Now, sometimes students are sure they got questions right, and usually their certainty is right, so there is no need to ask that one online. And sometimes people can find a relevant previous answer (although learners often struggle to find those, in my experience). Nonetheless, even after taking those out, there are still a lot of people with a lot of questions.
> Try to find a community of others online and work with them.
Yes, very good advice. I just wanted to observe that while it might work for OP (and I hope it does), it cannot work for lots of people. I don't know what the answer is, and maybe MO could help a lot, but it can't be the answer alone.
Homework type questions (anything before PhD student level) are typically asked on https://math.stackexchange.com/
The issues will be the same with self studying anything. Without someone to critique your work, and point out deficiencies you don't even know are a thing, continuous improvement quickly becomes exponentially harder from the bad habits that are holding you back.
Technique totally matters, even in STEM.