Use of mathematics in economics- My personal views (as on July 19, 2021)

I feel some economists have fallen for an overdose of mathematics.

Every trade/ profession has tools which are appropriate for it. For instance, carpentry requires saw, hammer, nails and similar equipment. If suddenly a carpenter, who has been employed to make a garden chair, says that a digital telescope is required to complete the job then it is natural for one to wonder: what is really going on at the job?*

The same applies to economics with its wanton use of infinite dimensional spaces, differential geometry, martingales and so on.

As far as I am concerned, being within “epsilon” distance of the kind of mathematics Professor K.J. Arrow used in his work (across topics and not just social choice theory) seems to be a necessary condition for the appropriateness of the application of mathematics in economics.

My understanding of Mathematical Economics as a stand-alone subject or a discipline by itself is that it consists of non-trivial applications of mathematics to decision making problems, i.e. Decision Making Theory as well as the development and application of Optimization Theory (e.g. Mathematical Programming) to social and economic problems. Just as writing prose requires skillful use of language but not necessarily a dictionary, similarly good mathematical economics requires skillful use of mathematics- without necessarily having access to an encyclopedia of mathematics. As in the case of language, the requisite knowledge of mathematics (which is essentially a technology) is implied by its requirement for skillful use.

Let us do mathematical economics the Gandhian (as in "Hind Swaraj") way: Using the least mathematical complexity to achieve a desired result. This is precisely what "technological efficiency" requires. 

*Some carpenters may require to refresh their minds by periodically engaging in “star gazing”, in order to apply themselves more productively in mundane tasks.

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