I'm a youngish (recently tenured) faculty member at a reasonably, but not extremely prestigious university in the mathematics department. While I've looked at some graduate admissions files, this is the first year I have been on the actual committee and thus been responsible for reading many files. I feel like most aspects of the application (CV, transcripts, test scores, letters of rec) I understand reasonably well, but all statements of purpose read like meaningless gobbledygook, and I tend to completely ignore them unless there's some aspect of the student's file I'm confused about and hope to find an explanation for (and of course, I often don't).
I've seen a lot of questions on this site about how to write statements of purpose, but not much about how to read them on the other end.
Is it normal/reasonable to essentially ignore the content of SoP unless you are looking for specific information on something unusual in the student's application? What other things should a reviewer look for as positive or negative signs?
I've asked about mathematics in the United States since that's my field, and I want to avoid stupid replies like "But how can you know what lab they want to work in!" but obviously, I am interested in thoughts from people in other disciplines.