Nearly all graduate schools will ask you for a personal statement. Here are my personal opinions of dos and don'ts for writing your statement, based on my experience reading these letters.
Do describe what you have done as a student, what you like about mathematics, and what you want to do with it.
Don't evaluate yourself or compare yourself to other students. That is your letter-writers' job.
Do emphasize your strengths. For example,
Don't merely list facts that can be found elsewhere in your application (such as your grades; that's what the transcript is for).
Do be scrupulously honest about stating your qualifications and experience. In particular...
Don't write, "I am attracted to Insert Your University Here because of your world-renowned faculty, outstanding curriculum and highly unique campus." This kind of content-free flattery does not help your application, particularly if it is an obvious mail-merge. (This is really just a special case of "don't make stuff up.")
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