The first step was a non-profit program started as part of the Pasadena public school system's offerings that other schools are free to adopt. It's taken students from basic arithmetic to calculus by 9th grade and through a fully undergraduate curriculum by the time they finish high school. His son was one of those students and must be part of why he's been willing to invest so heavily for so many years.
There's now a commercial online version open to the public. The founder hasn't done any marketing of it yet, but I found out about it through a mutual friend / podcast co-host. Math Academy is very comprehensive and the most streamlined way I know of to learn, or in my case, relearn an undergraduate applied math curriculum. It's not as polished, but the content and the actual academic results make offerings like Brilliant.org look like a joke.
I requested a life-time deal last year for access myself and intend to make the most of it, likely in binges between busy periods at work.
https://www.washingtonpost.com/local/education/ap-calculus-e...
The best places that I am aware of for self-studying university-level math are university websites (like MIT OCW) or just going through undergrad textbooks on your own. Someone made an imho decent guide for the latter [0], curious if HN users have other recommendations.
[0] https://www.quantstart.com/articles/How-to-Learn-Advanced-Ma...
Despite studying engineering up to postgraduate level, I tended to avoid any concept that required a deep understanding of the Mathematics behind it. Now, I love Math and feel like I could express most problems using it, as well as make sense of papers and text books that were closed off to me previously.
Start with a book you want to read. If you get stuck, then buy another book (hopefully aimed at a lower level) on that topic and repeat the process with the new book.
Don't be afraid to read "easy" books. You should probably aim to start reading books where you look at the contents page and think you know 80-90% of the material already. I've wasted a lot of time trying to read books that were above my level. The path of least resistance is longer, but in my experience it pays off.
"Do the exercises" is good advice, but don't be too obsessive about it. Be more obsessive about regularly working on the topic, even if that means skipping exercises or jumping between books (on the same topic). You can often find the answer to an exercise in one book in a different book's presentation of the same topic, or on a website or in a paper. As long as you can integrate these discoveries into your conceptual framework of the subject, that's not cheating, it's success.
Writing things out in a lot of detail and working out examples in a lot of detail in a notebook can really help. This is like designing your own exercises and can be better than doing exercises in a book sometimes.
The book starts from axiomatic arithmetic and works all the way up to what you would need as a mathematics major with a focus on pure mathematics. He also manages to touch some beautiful areas like geometry, abstract algebra, symmetry, linear algebra, set theory and more.
There are only a handful of exercises at the end of each section and they are very good at locking in the concepts. I finished a mathematics degree and realized afterwards that there just wasn't enough of a focus on the concepts and beauty. Even with 4 years of math experience, this book still managed to open my eyes
There is an old Schaum's series book on Projective Geometry that was very useful to get the basic ideas quickly. It may not be an elegant presentation of the subject, but it was very quick, and to the point.
All said and done, synthetic geometry (not analytic geometry) is not very easy, and it might help to create models (wire-frame or 3d cardboard or plasticine/play-dough) to visualize things. They may not help to solve the problem rigorously, however.
By coincidence, I am slowly working through another of Stillwell's books, on Reverse Mathematics. You are right, his way of presenting things suddenly makes things you know snap into place.
When it comes to exercises, brilliant.org is lacking in volume. Khan Academy is a great supplement for geometry, single and multivariable calculus although brilliant.org goes a bit further than Khan Academy with Linear Algebra, Group Theory and more.
Khan Academy also has a linear algebra course, but I found it to be kinda crap with no exercises. For linear algebra it's better go with brilliant and 3blue1brown's linear algebra videos, then a good continuation would be Linear algebra done right by Sheldon Axler and also fast.ai's free online course Computational Linear Algebra for Coders.
I am personnaly on a mathematics path, starting with geometry.
Email in bio if you want to exchange.
You can message him on Reddit if you'd like and see if he'd give you an invite: CheapViolin
Forgetting the book, but I have a book on solving problems which I studied from for the Putnam. The premise was to take someone seemingly around your level and build them up to problem solving machines. Probably math competition textbooks would be a good source for you.
If you want to broader review of undergraduate math and physics, then check out the longer book: https://minireference.com/static/excerpts/noBSmathphys_v5_pr...
Both books have hundreds of exercises, which, as other have pointed out, are the most important part of any learning resource. Several readers have said they appreciate how complete the curriculum presented in these books are (based on years of experience helping people review math needed for university-level courses).
It is part of AOPS and it gives step-by-step solutions to problems.
You need to create an account, but it is free.
Here's a good list of books: https://github.com/ystael/chicago-ug-math-bib