No, that's basically it.
The reason for all this work is basically the concept of a currency that isn't backed by and dependent upon governments while also being impossible to counterfeit, hence a lot of encryption because it fundamentally says that you can't trust the other computers that you're talking to. Everybody holds a ledger that says that you have $5, so you can't suddenly say that you actually have $10. And all the math is to prevent inflation by limiting the amount of currency that exists at any time. The more currency there is from solving the math, the harder the math gets to slow down the creation of new money.
It all falls apart, though, because the only value that crypto has is what it's worth in traditional fiat currency - the very thing that it's supposed to replace.
So it's just a bunch of computers doing a lot of math to make funny money that's supposedly worth something because...of reasons?