Probably not - in applications, heuristics/approximations and "probably true" are king. And in this case the relevant approximations have been known for decades

Probably not - in applications, heuristics/approximations and "probably true" are king. And in this case the relevant approximations have been known for decades at least. That's a very different beast to the game mathematicians play, which demands rigorous proof (or at least a fairly close social version of it, it's turtles all the way down).