Well hell. A friend of mine (Thanks Ange!) pointed this out to me this afternoon.

Very neat, and the really interesting part is how linked together many of the main problems in number theory are and how they relate to the ABC Conjecture. The profoundness of this in mathematics was only just revealed after looking up a bit on what the ABC conjecture means and its implications here.

But essentially, this proof would give mathematicians a means to more easily arrive at proofs for other open and solved conjectures in the field of number theory. The practical implications are, well, not obvious to me. But some things don’t require utility to be beautiful.