Also, there are almost no implications to real-world applications from this proof because the result has been assumed to be true for a long time. I don't mean t

Also, there are almost no implications to real-world applications from this proof because the result has been assumed to be true for a long time. I don't mean to diminish the value of the proof, which is an impressive bit of work; it's just that the value here is more academic and in the theory realm than in the practical or experimental where the theorem has been treated as true without a formal proof.