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The TSP (traveling sales person) tells us that computer scientists can construct problem classes in such a way that the construction has a short description, but there is not much structure to the problem: it implicitly incorporates so many different types of problems that we should not expect any one algorithm to solve them all rapidly

A compact description means a verification of a proposed solution will be easy. The question is how to propose a solution. The author's p.o.v is that it is only possible if the problem itself has enough structure to exploit.