What should one look for in a statement of purpose (from the admissions side) in mathematics?

Question

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.

Answer 1

Good question. I worked on graduate admissions at my math PhD program (at UGA, in the US) for several years, and after a few years off I am the new Graduate Coordinator, so I will shortly be wading through a sea of applications and personal statements. Here is how I see things at the moment. I'll modify my answer if upcoming experiences change my mind.

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?

You could put a more sugary coating on that for public consumption, but: quite reasonable and probably rather normal, I think.

What other things should a reviewer look for as positive or negative signs?

1. A statement of purpose is a great place to address things that are out of the ordinary. It's really the only place for that. There are a lot of math PhD programs in the US, and most of the applicants to most of the programs (i.e., not Harvard/Princeton/Berkeley/Chicago/UCLA...) have applications which are "uneven" in some way. Giving context and explanation for the weakest part of your application could be helpful for many students.

2. I look at the personal statement first as a writing sample, second as a very broad measure of (mathematical) cultural awareness and sophistication and third as a chance to show that the applicant received a decent supply of rope and managed not to hang him/herself. You are right that there is a lot of cluelessness and ignorance displayed in personal statements...but usually of a rather standard sort that just means that the person is not yet in a math PhD program so has quite foggy ideas of what such a thing is. However some kinds of clueness, ignorance, stubbornness or hints of anti-social behavior are less common and could be red flags.

One of my favorite stories about a personal statement was told to me in a departmental information session when I was an undergraduate applying to grad school, by the head of the CS department at the University of Chicago. (I think it was Lance Fortnow, but I am not completely confident of this.) He said that he once got a personal statement that said that the student wanted to go to grad school in CS because he thought that any other career would involve a lot more work, and he was trying to take it easy. This put the department head in a bit of a pickle. As he proceeded to explain, this was exactly what he did not want to hear in a personal statement. But how seriously does one take the personal statement? Maybe the student was trying (and failing) to be funny. Because the application was very strong in all other respects, the applicant was eventually admitted. He failed out of the program less than a year later, because he was not willing to do any work. The department head said that he had learned his lesson: the next time a student said something like this in their personal statement, they would not be admitted.

Answer 2

In addition to @PeteL.Clark's good-advice answer, I would also want to say that I have come to find the Statement of Purpose quite-often useful to "hear the voice" of the applicant. Sure, also quite-often, this voice is immature or ill-informed, but that's expected. But enthusiasm and interest and curiosity are hard to gauge from a transcript.

Yes, letters-of-recommendation give more mature appraisals of students, but, given the likely immaturity (mathematical and otherwise) of undergrad students in the U.S., it is not at all clear that they will communicate effectively-enough with faculty so that faculty will really know what goes on in their heads.

So, through the filter of acknowledged inexperience and immaturity, I do want to hear the "voice" of the applicant. Diffidence or misguidedness (or angry crackpottery) are typically visible (based on my own unfortunate observational experience... protracted anecdotal) in the statement of purpose.

It is also interesting in that applicants typically do not "know what the admissions committee wants to hear". Exactly. It's a sort of Rorschach test, on which it's hard to "cheat", and "there's no right answer".