Writing a Personal Statement (Mathematics Ph.D Programs) I am beginning to plan for graduate school. I will be applying to many Ph.D programs and a few Masters programs as a backup plan (all pure mathematics).

I am starting to think about how to write my personal statement. I am seeking advice regarding the process of writing a personal statement . I am mostly curious about what people usually talk about in these things. I obviously want to convey my interest and potential in mathematics research. But my problem is: I do not have the mathematical background to have an idea what I want to specialize in. I know that this hurts my chances at being competitive. My undergraduate degree has simply not exposed me to enough mathematics. 

I appreciate any advice - relevant to my concerns or just advice in general.

Thank you.
Honestly, it seems like you are worrying more than you should about not having chosen a specialization.  I wouldn't worry about that: that's not something which is expected of students finishing a BA in the US.  Even if you think you have, changing your mind about it is something which is normal and expected.  So, it's very reasonable to worry about having less background than other students, but more in the context of general preparedness, rather than your personal statement.  

So what should you write in your personal statement?  Generally it's for things that the person considering your application would like to know, but which aren't clear from the other parts of your application. Things like: explaining about something unusual in your career path, like taking time off after finishing your degree; what your ultimate career plans are; how you became interested in mathematics; how your undergraduate research projects went and what you did in them; any work you did outside of courses (which is relevant to math! No one cares about your great success in the marching band). I have to admit, generally these personal statements contain no useful information, and a lot more attention is paid to transcripts and letters.  I generally only read them carefully if there's something I'm confused about with the application they should explain.