Hayek is one of my favorite economists of all time, but I do not consider myself an Austrian economist. To be clear, I have a PhD in econ so I am an economist by training. I have always found their views on the use of mathematics in economics short sighted.
I would argue the paper about complexity science in economics demonstrates this. Effectively they have been so opposed to math in econ for so long that, instead of figuring out how to use math in econ, they more or less waited until others developed a method that fits their worldview. Not only that, they need to convince other Austrian economists it could be useful.
This is a view I've always held, as well. Bob Murphy is one Austrian who I think understands the value of mathematics in economic analysis.
Most of the older Austrians conflated "math" with the kind of real analysis that's so common in mainstream theory. I think many of the Austrian critiques of relying on that type of mathematics are fine.
What they miss is that the kind of work Kenneth Arrow did is also highly mathematical. He was making use of powerful deductive tools that apply to the strict paradigm of ordinal preferences that Austrians rightly emphasize.
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