Here is a suggestion: In empirical research, academics should move equations from the methods section to the appendix and, if anything, show the few lines of code used to estimate the model(s) in the software being used (ideally with citations to the software and statistical packages). Preferably, it should be possible to understand the estimation strategy without having to read any equations.
Of course, I am talking about the type of work that is not primarily interested in developing a new estimator or a formal theory that can be applied to a few case studies (or shed light on the limitations of empirical models). I am not against the use of equations or abstractions of any kind to communicate clearly and without ambiguity. I am, however, skeptical towards how empirical research often include equations for the sake of … including equations.
I have a theory that academics, and in particular political scientists, put more equations in their research to show off their skills rather than to help the reader understand what is going on. In most cases, equations are not needed and are often there only to impress reviewers and peers, which of course are the same people (hence, peer-review). The use of equations are excluding readers rather than including readers.
I am confident that most researchers spend more time in their favourite statistical IDE than they do writing and reading equations. For that reason, I also believe that most researchers will find it easier to read actual code instead of equations. Take this example on the equation and code for a binomial regression model (estimated with glmer()) from Twitter:
Personally, I find it much easier to understand what is going on when I look at the R code instead of the extracted equation. Not only that, I also find it easier to think of potential alternatives to the regression model, e.g., that I can easily change the functional form and see how such changes will affect the results. This is something I rarely consider when I only look at equations.
The example above is from R, and not all researchers use or understand R. However, I am quite certain that everybody that understands the equation above will also be able to understand the few lines of code. And when people use Stata, it is often even easier to read the code (even if you are not an avid Stata user). SPSS syntax is much more difficult to read but that says more about why you should not use SPSS in the first place.
I am not against the use of equations in research papers. However, I do believe empirical research would be much better off by showing and citing code instead of equations. Accordingly, please replace equations with code.