As much as I like picking on economists and watching them bicker, there's actually a method to the madness. (Except for the shills, I'm looking at you, Krugman[1]). When done correctly, economics becomes kind of a cross between a courtroom and a bullshitting session. People present various theories and sets of measurements. Lots of discussion around instrumentation and epistemology takes place. At the end of the day, the discussion wraps up to be something like "Given that most of us agree that these kinds of initial conditions mostly lead to these kinds of results, do most of us think that these kinds of initial conditions currently exist?" (Note that the "most of us" can very well be different sets of folks)
Oddly enough, it turns out that this kind of discussion has lots of real-world value.
Machine learning and deep learning especially has a pretty cool new role here, but it will never take of this dynamic ongoing discssion.
So no, economics doesn't have a math problem. It doesn't work like that. Perhaps a better way of putting is this: people who expect the world to be deterministic have a problem with economics. That situation is unlikely to change.
[1] I pick on Krugman because his shtick is already knowing the answer, no matter what the question is. He also likes showing us his Nobel. Somebody said once that every Krugman column should begin with "Damn fools!" In this way, this isn't economics; as far as I can tell it's personal aggrandizement using economics as a prop. A huge ego is a terrible thing to waste. But damn, it sure is entertaining!
[Several edits for clarity]