I'm not sure about the severity of its impact, but I toyed with the problem when I was learning knot theory. It's a spot where probably hundreds of mathematicians have tried to itch. Advances have been made in attempts to solve it, but didn't quite do the job. Piccirillo's approach is really quite beautiful, and... sorry, this is where mathematics gets weird: the statement of the theorem is what lay-people consume; the method of proof (not even the actual proof, but the ludicrously high-level abstract algorithm that the proof is a concrete instance of) is what mathematicians consume. In that regard, this seems quite buzzworthy.

But if you're a fan of mathematics but still consider yourself a lay person: this stumped John Conway!