Today my copy of the recently published book "The Next Generation of Austrian Economics: Essays in Hono[u]r of Joseph T. Soalerno" (edited by Per Bylund and David Howden, Auburn: Mises Institute, 2015) turned up and chapter 7 defends the indefensible: it argues for a mathematical Austrian economics. The chapter is ""Mises and Hayek Mathematized": Toward Mathematical Austrian Economics" by Marek Hudik.
Hudik argues that
At first glance, mathematization of Austrian economics may seem to be contradiction in terms. Yet, at a closer inspection, the idea turns out to be not paradoxical at all [...].Hudik makes the point that there is a communication gap between Austrian economists and the rest of the economics profession. This gap can be narrowed if Austrian economics were to become more mathematised. There are clearly dangers to mathematisation but it must be remembered that maths is just a tool and whether it is good or bad depends not on the tool but on the use of the tool.
While there are dangers to the (over)use of maths, it must also be remembered that there are benefits to the proper use of it as well. Often times people concentrate on the negatives and ignore the positives.
So lets look at the Hudik's plus side. Mathematics can act as a common language helping communication between economists of different "schools". It is a language that most economists speak and thus coordinating on it as a language will help reduce the communication problems between Austrian and other economists. Maths is also a more precise language. Its use forces us to formulate our ideas precise thereby helping reduce any misunderstanding that the verbal presentation of ideas could give rise to. Maths can act as a more efficient language. If is often more efficient than verbal language for both the "producers" of economic ideas and the "consumers" of those ideas. For producers it economises on effort, laborious thought processes can be "embodied' in simple rules for manipulation of mathematical symbols. One can see maths as a "capital good" increasing the productivity of the economist's "labour". As consumers of economics ideas maths can help us economise on time and effort. There is much to be said for condensing wordy volumes into a few precise and understandable pages.