There has been a lot of negative talk about the maths in economics – like a huge amount. Just look at these links, some of them are poor and reactionary, but some of them are excellent and the last two are my favourite (*, *, *,*,*,*).
Now although I believe much of this attack is excessive, and I believe the role of maths in economics is very very important, like all protestations there is a grain of truth to be found.
The way I see it, the role of maths is as a language – Mario Rizzo covers that off in more detail here. Now, maths is not the only language that can provide clarity and solidity to the discussion of a given issue – words are still effective if treated with the same structural integrity. The prime example of this is the work of Spinoza.
Maths was useful as it helped to drive structure and clear up arguments. It helps to clarify thoughts, and acts as a clear linguistic device.
However, as with any language the main issue with maths in economics is when it loses its ability as a clear linguistic device, namely when:
- people using it become overconfident of their assumptions, thereby missing some implicit assumptions in their modeling
- people use mathematical notation to hide their results.
However, both of these errors aren’t a problem of too much mathematical use in economics – they are an issue of too little concentration on the formal, logical, elements of using maths as a language!
The lesson here is that economists have to be aware of exactly what the elements of their models represent, and should be able to evaluate these elements when moving on to make recommendations – at least in some sense. The maths is not the problem, and an arbitrary crusade against mathematics would only serve to reduce the usefulness of economic analysis.
An economist with a strong eye for mathematics and a strong nose for elements of reality can overcome these issues and use mathematics to provide a clear, incisive, and valuable contribution to the study of the economy and society as a whole. I am glad to say that I believe many theoretical economists do possess these traits – hence why I am confident about the future of the discipline.
Note: I am not a theoretical economist, and spend most of my time using words and numbers – not maths. Even from my position of weakness I can see the important role that mathematical rigor plays in economics.