[learnstats2]

I've worked with several adult learners on this but almost no adult is able to learn math just for fun - unless they have a project or crucial examination to work towards. But, you do have a project. You should use that.

I think you're mistaken that your existing tactics won't get you further. This is how most people learn, by trying things out and building on them until they understand what works and what doesn't - standing on the shoulders of giants.

For practical purposes, your satisfactory solutions are a great piece of learning and the start of your understanding. You're maybe experiencing some discomfort about it, but that's normal. Keep going!

P.S. You said "from first principles", which has a specific meaning in math. It's a kind of philosophical ideal in math that you start from nothing (forget about high school math) and carefully and precisely build the subject of mathematics on top. Some of the answers here picked up on that phrase, but it probably isn't relevant to the other interests you mentioned - to do programming or electronics, you will want to build on the knowledge that you have learned already.