I need to perform several text reviews, each of them containing lots of equations. I need some methodology for proof-reading the equations. The context is not really academic, but I believe a similar situation happens for peer-reviewers in scientific journals, or when some one proof-reads a book before publication. I'm not allowed to contact writers directly.
In general, I can try to "read paying attention", just like someone would read an english text searching for grammar and spelling mistakes. I believe this would be tiresome and prone to error.
Some equations are "practical", such that I can place numbers on them and test consistency of results. Most are not. A few of them might have quantities associated with physical dimensions, such that I can check for errors in the physical dimensions.
A few equations could be tested by implementing unit test-like software that would simulate them, but this would be a long, time consuming process which itself is also prone to error.
Some equations are referenced in the literature, but the notation is quite different.
I have at least to assume that for any equation:
1-The writer might have come up with something that is just plain wrong.
2-The writer might have misspelled something, and this error may propagate to later equations
3-There might be errors in the derivation of those equations.
My performance guidelines are:
1- I'm expecting around 5% of the equations to have some issue, but If I tell some equation is wrong, I'm allowed to be myself mistaken less than 5% of times. But out of all wrong equations, I need to point out 95% of them. The idea is that after 3 reviews by different people, the chances of any mistake having slipped through are negligible.
2- I need to present my reasoning to tell why an equation is wrong, at least to the point where if I'm wrong myself, my own mistake can be pointed out to me.
Are there rules or best practices used in academia for this purpose? Are there other assumptions one could/should make when performing such kind of review job?