It's not that hard. There are several computer-checked proofs of it.
It's hard to explain, because the idea of encoding statements about a system in terms of the system itself is weird if you haven't seen it before.
It's hard to explain, because the idea of encoding statements about a system in terms of the system itself is weird if you haven't seen it before.
That said it can be fully covered in a single semester of undergraduate study, so its not that hard. There are many theorems that couldn't be fully proved in a semester.
“My nose will get longer”