Feeling a need to include equations may also be a sign that the application is getting too technical and too detailed.
As a reviewer I can't say I have ever encountered an application without equations that I think needed them. I have certainly encountered applications with equations that I think could have done without them.
Most reviewers are asking big picture questions:
- Is the project important and worthwhile and realistic?
- Does the applicant have a track record that suggests they will succeed?
- Is there a concrete plan?
This is where references come in.
Also, you can refer to equations by name (the un-informed will not be put off and the informed will know what you are talking about).
Hence, you can write "our calculations will use the Kubo formula for the conductivity with an electronic self energy calculated by Dynamical Mean-Field Theory (in a manner similar to reference 11)." This is a lot less off-putting and takes up much less space than writing down the relevant equations and defining all the notation.
Having said the above it highlights to me the struggle of writing a good application. There is a hard balance to find between being too generic and being too detailed.
My thanks to Tony Wright for asking me the question.