TITLE: The Inevitable Wall of the Autodidact
QUESTION [10 upvotes]: I'm a developing mathematician that loves to self-teach when I get the time - unfortunately, I've found a recurrent issue that keeps bothering me.
Often I find myself stuck in this loop:


Become intrigued by a topic (e.g. linear algebra, probability theory, etc.)
Find a book on the topic and dive in headfirst
Make it through the first few chapters
Discover a question or problem with the text that I can't figure out on my own
Ask for help online
Weep silently when the book turns out to be using obscure notation or something esoteric
Choose another book (or another subject) and start again


Needless to say, this is a bit frustrating, and I bet I'm not the only one who has experienced this! Do I need to just start reading more popular books in the subject area? What do you do when you hit a wall in a book and can't find an answer online?

REPLY [3 votes]: Self-study is a really good idea but it can be discouraging quite quickly as you said. If you're in class, then study with a more "formal" and "dry" book is not bad because you listen oftenly the teacher giving explanations and do exercises with friends. Of course, when you're alone it's not really motivating to feel stuck every pages and ask lot of questions about the book you just found. 
My advice would be : choose the right book ! They are plenty of really good PDF online. For self-study, I especially enjoy PDF with little exercises left to the reader : normally they are easy and it's a quick and nice way for learning, in addition of reading proofs, theorems and doing problems. (Of course, it depends of the author. I already saw a book where the first exercise was prove fully the Banach-Tarski paradox, with really few hints, not that easy ...)
Books are rarely clear at the beginning and becoming really obscure at the end. If you are able to understand the first chapters, normally you should be able to understand fair part of the book (with regular work !) Usually, the subject is becoming more difficult, but this is normal to spend more time the more you did advance in your book. That simply mean you are learning something new. You'll never learn anything if everything is clear from the beginning for you ! Learning maths (for me at least) is mainly fail, try, fail, try again (alone if you are motivated enough) and finally understand something new. I don't have motivation everyday but discovering something and feeling you did understood something well is one of the best motivation you can have (for me at least).
Another advice : once you did choose a book, and try a few pages for seeing if you feel comfortable with it, you should keep it until the end. When I try to self-study I was permanently studying with different sources, and thinking "Well, I don't understand so another author probably explain it better !!" and finally I was never making efforts for really understanding the subject.
Hope it helps a bit !