In my humble opinion, I would suggest that the highest level of math would be one with both explanatory and preditictive power for how the entire universe works. Of course this is cliche and is the goal of the GUT's and we do not know how simple or complex it might be. Still, if we ever could achieve this goal I think it would qualify. At this point in our search we are not even positive about how many dimensions that we exist in and could we be inside some other "space" that we are not aware of.

I agree that it has to be "turtles all the way down". But, which way is "down"?