Cherry picking a controversy doesn't do much to generalize an entire field (if you want I can find some Freud controversies and say that psychology is hocus pocus). By the way, I'm not american.
Funny enough, that one you picked is exactly the opposite from here. The authors were harshly criticized for NOT applying "mathy" rigor. The conclusion from "This time is different" is exactly what common sense would tell you, don't get too much debt or else you might grow less in the future and they got crushed because they did not entered in the extreme math/econometrics analysis. What the article criticizes is exactly what "This time is different" did, it applied less data rigor to point out almost a common sense and yet it backfired, so what is it? Should economists apply more or less "math"? I guess either way, this misses completely the point about economics and dismissing the entire field because of it is ridiculous.
I am not American either. I pointed this out because you seemed to imply that USA was the best example of how to properly use a mathematical approach.
Also, I think it is appropriate: what we had here was someone "demonstrating" why a specific policy works: "it works because our math model proves it works".
So instead of going for an empirical proof everybody was expected to be ok wih this because, look, we have math. Also, if it is not working for you it's because you are not doing it right.
In a proper scientific discipline you design experiments to verify if your formulas are correct: if you send a rocket to Venus and it crashes back on Earth you can't just say "you didn't it right, I have an Excel sheet that says it should have reached the target"...
http://www.newyorker.com/news/john-cassidy/the-reinhart-and-...