How can you learn advanced math if you don't have books or a teacher to consult?

Everyone says to read book "xyz", but I have never found books to helpful for several reasons.

1. You can't ask a book a deep question to do with understanding.
2. No book is perfect.
3. I can't afford them.
4. I have ADHD (although I have no difficulty sitting and thinking about math for hours because it really interests me).
5. This might be different with areas of math I'm not used to, but I've always ended up learning things in the past by finding a missing piece in my understanding at which point I can derive most of everything I need, and end up skipping chapters of the book altogether.

Furthermore, I am not connected to anyone I can ask questions to, although I wish I was. Whenever I meet a mathematician, I try to do everything to make the best of the situation. I have tried using Math Stack Exchange, but it just isn't enough to fully teach yourself a subject (and additionally, I don't always feel safe asking questions here). You can visit my profile to see the kinds of questions I've been asking.

I love math. However, after going through all the regular calculus stuff, as well as multivariable and vector calculus as well as a conceptual understanding of linear algebra, I'm pretty much stuck. I've been putting more time than ever into learning math of a wide variety with almost no results.

What I do have is the internet.

What is general advice for learning math from the internet?

• What happens when you read a math book? It isn't easy for anyone. If you're able to think about math for hours, that sounds promising. Are you able to spend hours at a time (or even just a a couple hours at a time) struggling through a book? The questions you're asking look good. I'm not sure that the process of reading books + asking questions on math.stackexchange is actually failing for you. Is it possible that what you think of as "no results" is actually just normal progress? Nobody races through this stuff. Apr 25 '20 at 19:45
• On the point about not being able to afford books, many lecturers make their lecture notes available on their webpages for free. Springer are also currently making a few of their books available for free - see here Apr 25 '20 at 19:51
• If you're looking for some great free Math resources, there's this website I found: realnotcomplex.com
– jl00
Apr 25 '20 at 19:58
• Check out Paul’s Online Math Notes!!! Apr 25 '20 at 20:08
• These are all great points, but one thing I will say is that, when you are doing this on your own, you have a great advantage in that you are not forced to move at any pace. It's okay to put something down and come back to it! Many times, I've had to put a math book down and come back multiple times, until I was finally ready (sometimes years later) to understand it. Definitely move forward, but also don't shy away from giving some ideas time to simmer. That's an advantage many people in the university system don't have, and you will know the material better because of it. Apr 26 '20 at 16:18

What has worked for me is instead of searching for a "$$xyz$$" textbook, search for an online free class with an available syllabus. Preferably a class where you have lectures recorded, exercise lists available and a textbook which can be accessed online via a pdf file. This way you won't be intimidated by the volume of the textbook and things that you need to study will already be pinpointed and highlighted by a professor. I know that MIT and Harvard have a nice open course wares.