I have had a Rubik's Cube since the 1980s and have never figured out how to solve it. At least now I can say I've solved it twice. I looked online and found this great video series that actually made it possible.
It taught me that it gets solved with repeating algorithms, which is something I didn't know. Now, with notes, I can solve it.
Next step is to memorize the algorithms, then figure out why they work. Sadly, I have no idea how I'm solving it.