Recently one of the most prestigious schools of economics, London School of Economics, held an interesting debate between economists who prefer historical retrospective and economists who prefer mathematical modeling. Interestingly enough both sides of the debate agreed that neoclassical economic theory doesn't work well. But the answer why and its implications differ. Below you should see a YouTube video with the recording of the debate. We invite you to listen.
The discussion might be summarized as follows. "Historians" are highly convinced that neoclassical economic theory has failed due to its intimate relationship with math and lack of historical insights. Neoclassical economists obtain nice mathematical equations, but fail to learn from the repeated financial crises. "Historians" suggest that there should be less math in economics and that the math should be replaced with historical analysis. As the debate goes on this rather radical suggestion grows milder and is developed into a rather reasonable proposal, but its essence remains the same.
"Mathematicians" on the other hand subtly pointed out that "historians" fail to see what mathematics truly is and why it is actually used. "Mathematicians" agreed with the "historians" that maths for sake of pure maths (as "historians" imagine applications of mathematics in economics) is not (or should not be) of interest to economists. Yet maths and computer modeling is an excellent tool to test general insights about how economic systems work. The data may be interpreted wildly differently and it is completely unclear which of the interpretations is correct one. Maths, and computer modeling, helps narrow down the set of possible interpretations. It is like filter, or more like reality check.
I believe that the outcome of debate was somewhat "rigged" (see the title of the debate). One side has demonstrated significantly more understanding of the other side's position, while the other side stubbornly defending their beliefs. It wouldn't be too much of a problem, if not for the mistakes of formal logic (especially Straw man), which significantly weakened the grounding of claims by a certain side.
To conclude, it is evident that we do support "mathematicians" in this case. Though insights gained from pure observations should not be forgotten as well.