Mathematics is the purest form of logic that we have at our disposal. This is because math is derived from the universe. It is the most precise of all the science, and so extensive that it required its own category of study. When a theory is at odds with our mathematical understanding we assume that the theory is wrong. Scientists always differ to math. The dismal science is no exception.
Economics is not as precise as physics or chemistry, but not from a lack of trying. The data that economists deal with is not as refined as that of chemists or physicists. Economists deal primarily with quantitative data such as statistics, trends, surveys. Unfortunately these tools are inexact when they apply to humans. Humans tend to be unpredictable. None the less the tools that economists use are capable of providing us with qualitative information about the economy. With such tools, and a lot of trial and error economists have developed several axioms to be relied upon. When Walter Block talked about a study that concluded that rent controls were beneficial to the economy we knew it was wrong because it broke pre-established axioms. Similarly an astronomist would not give much heed to a study that claimed that the sun orbits the Earth. Once something is graduated into the likes of an axiom in economics, contradictory evidence is disregarded. To the extent that if the contradictory evidence was true, the person who presented it would win a Nobel Prize in economics.
Economics is still not fully understood. The fact that there are still multiple theories as to how the economy works/how it should be treated is a result of this. Chemistry no longer competes with alchemy because chemistry has been proven to be the correct theory. Economics is still in a sort of adolescent phase of understanding. This is because as I have mentioned before it is difficult to apply math to human action. Eventually economists will determine that one school of thought is ‘correct’ and we can finally put old ideas to rest. The prevailing theory will most certainly be rooted in a conclusive mathematic base. If the math does not match up it is because the experiment is faulty or the theory is wrong. You really can’t throw too much math at a problem.