Length of statement of objectives [mathematics / MIT] While most other schools seem to have some recommended length (e.g. 1000 words) for the statement of purpose, MIT (maths) simply states


  Please explain why you are a good candidate for graduate school. You should describe why you wish to attend graduate school, what you would like to study, and any research experience you have. Describe one or more accomplishments you are particularly proud of that suggest that you will succeed in your chosen area of research.


As a mathematician I would like to keep it short because if I was in their position the last thing I would want is another long essay. However, since there is no possibility to upload a CV (and I am afraid they won't take a very close look at my website) I am inclined to describe my research experience as well as experiences with researchers (showing that I do take initiative, am not easily discouraged, etc.) there. This rather detailed description turned out to have 995 words.

Should I try to keep it shorter at the expense of, say, descriptions how I got interested in a particular field?
Most statements of purpose written by applicants to math PhD programs in the US are 1-2 pages (single spaced).  So 1000 words sounds just fine to me...as does 995, of course.  

If you write a statement of purpose that is any longer than two full pages, the likely outcome is that it will be read rapidly or skimmed.  Much the same will happen if your statement is shorter, by the way.  In short: what you propose is a very reasonable length for me. (It may help you to know that I am the Graduate Coordinator of the math PhD program at UGA.)  I don't see any problem here.  If you wanted to make it a little shorter or a little longer, you can, but don't worry so much about it.  This statement of purpose is probably not the most important part of the application anyway. 



By the way, I interpret the more specific instructions given by MIT (as opposed to many other programs) more as helpful advice for writing an effective statement of purpose than as asking for something much different from other statements of purpose.  It is actually quite difficult to write a statement of purpose that really grabs an admissions committee.  Most commonly students seem to want to declare their ardor for mathematics and tell the narrative of how that romance began.  That is more than understandable (probably I wrote something like that myself, many years ago) but when you start to read these by the hundreds they run together pretty quickly, and I expect that most faculty essentially mod out by that part of the statement of purpose.