I guess I could have emphasized the "problems like this" and the "at least provide insight that helps solve" parts, as I wasn't suggesting that some amatuer wil

I guess I could have emphasized the "problems like this" and the "at least provide insight that helps solve" parts, as I wasn't suggesting that some amatuer will necessarily come along and completely solve this problem. And sure, I agree that in specific instances in which the problem is purely mathematical, outsiders probably rarely have much impact. That being said, it was my understanding that even the most recent paper posted here causing all this stir over the P/NP problem, was using statistical physics, which does indeed make it a somewhat "out of left-field" approach not used by the domain experts that have been traditionally studying this problem.