I looked at the paper, and it was impressive, but not as amazing as it sounded. I have a mixed reaction to the God's Number result; on one hand, it's cool that they established a better upper bound (i.e. a better general solution), but on the other hand establishing something is Θ(n^2/log n) is only useful for computability theorists. It's an interesting-sounding result, but doesn't really have much practical use IMO, because saying that some sequence follows a particular pattern of growth as it goes to infinity doesn't tell us anything about individual values, and we only have two values of the series calculated anyway (11, 20, ...) with a third being very far off.

The "optimal solution of a*b*n can be found in polynomial time on n" result is similar; it sounds interesting, but it's only useful in a mathematical sense to establish a bound for the infinite series, and doesn't really make it easier to actually do the solving. The technique used in the proof relies on brute force, and while it is polynomial in n (it looks to be O(n) but I'm not sure) it involves extremely large constants and thus has no real practical use.