> The basic concept that people have figured out, so far, is that a number of NP-complete problems can likely be solved if we crack the Boolean Satisfiability problem.
And
> If NP-Complete problems get resolved, it is likely (though nobody knows for sure) that we'll crack every NP-Problem
Isn't the definition of a NP-Complete problem exactly that it is in NP _and_ every other problem in NP can be reduced to it in polynomial time. So we know _for sure_ ([Cook71]), that as soon we have a polynomial algorithm for SAT _every_ problem in NP can be solved in polynomial time, and not just some of them as the excerpt claims.
Am I missing something? Because this seems like a very confusing, if not downright wrong, way to explain NP-completeness and its link to SAT.
[Cook71] Cook, S.A. (1971). "The complexity of theorem proving procedures". Proceedings, Third Annual ACM Symposium on the Theory of Computing, ACM, New York. pp. 151–158.