terrific! thank you.

cool stuff. thank you.

But what should I learn if I'm interested in learning algebra?

N.B. My maturity level is normally only a half step above the average 12-year-old. I can play this game all day ;)

The way you describe it sounds analogous to computers: like saying "you only need to know C, not transistor physics, to program a computer". You can code on an existing machine, port your code to a new machine, but you'll never invent a new machine or architecture.