As a former cognitive neuroscientist with a master's in psychology, I will just point out that psychology departments look at the massive amount of data demonstrating human irrationality, and conclude that economists are mistaken or wildly naive to extrapolate from "rational actors" human beings.

You don't have a "math problem", you have a "data/science problem". And saly, at least at the micro-level, economists could have disabused themselves of the accuracy of rationality decades ago (e.g., Kahneman and Tversky's work in the 70's).

Much modern economics is like the elaborate math of epicycles, close enough, but still missing key insights. And this won't change until data is valued more.

The issue is that assumptions such as perfectly rational actors can diverge so far from reality that it renders the resulting idealized conclusions meaningless from the perspective of actual human economies. The abstract study of incentives is of course interesting in its own right, but may have little to do with economics in practice -- i.e. the important practice of how actually should we run an economy.

What theoretical economists do is not 'nonsense' but can become nonsense when it naively forms the rationale for real-world policy.

Rats are, in some ways, very different from humans too. But if it's impossible to run human trials, or there are severe deficiencies in the way we are able to execute them, studying rats is still the best argument.

If there is a convincing empirical economic study that widely contradicts a theoretical consensus---yes, that evidence should be preferred. But that is not often the case, and otherwise the theoretical argument is simply the best argument there is.

What drives me bonkers, though, is the people who dismiss the math and its conclusions as being 'meaningless', but then what they substitute is not superior empirical arguments of their own, but their own emotional sentiments and undisciplined intuitions (typically decorated by cherry-picked historical observations).

The "rat is to human" (from a pharmaceutical perspective) as "rational actor is to human" (from an economic perspective) I think is a very fragile analogy. Rats and humans are very similar in their response to pharmaceuticals (and so serve as reasonable first model), but the difference between rational actor and human is so vast (at least in terms of how the real world works) that it calls into question the value of rational actor models for real-world policy.

In that case, the "theoretical argument is simply the best argument" is wrong; we should study economic history and human behavior rigorously and let that inform our policy. Theory can serve as a useful model when it is validated by some sort of observation and data -- but even when we cannot perform controlled studies there is not a knock-down argument that "theory" must be our best guess.

I agree that a person's interpretation of economics is very likely to be influenced by their idea of how the world should work; but this is more a problem of our characteristic lack of critical self-reflection. And of course, we should have cogent arguments for our interpretation of economics, ideally rooted in objective evidence.

mathematical formalism was introduced precisely to allow the formulation of "cogent arguments". you can't evaluate the evidence without economic theory