Mathematics might force you to be internally consistent, but it also forces you to make bad assumptions. You can prove anything by reasoning from a faulty premise.
And one important thing we learned from those models (which I agree do not work) is that we don't get business cycles from irrationality or from agent heterogeneity -- we get them from the failure of markets to clear. Economists were confused about this for like a century, and thanks to mathematical modeling it became clear.
That seems like a profoundly narrow viewpoint to me. I mean maybe you're right in the sense that there might be an equation that governs the evolution of the universe, but are you really saying mathematical models are the only way to approach research?
If so I strongly recommend you do some scientific reading outside of economics and physics. I think most interesting phenomena in the world are too complex to capture in mathematics. Physics is a profound outlier in that regard.
> And one important thing we learned from those models (which I agree do not work) is that we don't get business cycles from irrationality or from agent heterogeneity -- we get them from the failure of markets to clear. Economists were confused about this for like a century, and thanks to mathematical modeling it became clear.
I really don't think that's clear at all.
Before the 70s/80s, everyone was somewhat confused about what they were arguing, particularly in macroeconomics. Now it's much clearer the kinds of claims we are making about the world.