I also very much enjoyed: "In this section, we verify that our proofs aren’t circular."
Didn't have the motivation? So what? They did.
The things they did seem obvious? Yes, I bet they do in hindsight. Touch screens on cell phones seem obvious today too.
I don't try to discredit this stuff, and probably couldn't come up with similar proof myself since I'm not that interested in mathematics in general, but I am personally getting kinda tired of all these "child discovers x" stories where x turns out to either be something this is already well known or it turns out that they've just restated something that was well known in a somewhat trivial way. I'm not saying that's what happened in this case, but it is what happens in most of these sorts of stories that get published anytime it's a slow news day.