The wording in the article also makes it sound like the existence of a faster algorithm for edit distance would imply P=NP ("Most if not nearly all computer sci

The wording in the article also makes it sound like the existence of a faster algorithm for edit distance would imply P=NP ("Most if not nearly all computer scientists believe the P equal to NP problem is false", although later a variant of the problem is mentioned), but that's not the conclusion of the theorem. A more accurate wording would be that the existence of a fast algorithm for edit distance implies that P is "close" to NP, because there would exist a sub-exponential algorithm for SAT (but not necessarily a polynomial algorithm).