I think you are right about mathematics, but wrong about logic. I think economic theory is very logical in almost all classes . . . except when they get to monetary policy and government spending. Then suddenly the clarity of microeconomics and logical thinking goes out the window and economics becomes incomprehensible. I suspected either I was stupid or my professor was incompetent when I took a course on monetary policy. Now I realize that it is political and clarity would hurt the agenda.
I took only a macroeconomics class in college so maybe that explains it.