I'm finishing up my BSc this year and am applying to PhD programs in math for next fall. All the applications want me to write some sort of personal statement. For example, Princeton gives the following instructions: Please write a statement of your academic and future career plans as they relate to the Princeton department to which you are applying. In doing so, please cite relevant academic, personal, and professional experiences that motivate you to apply for a graduate degree here. Your statement should not exceed 1,000 words and must be written in English. To anyone who has written one of these and been accepted, or who is responsible for looking at and evaluating incoming applications, what advice can you give me? Essentially, I enjoy studying math and plan on getting a PhD in (pure) math, and ultimately doing math as a member of an academic institution. So I'll probably end up being a professor, which I would look forward to. In the unlikely event that things don't go this way [if I don't enjoy studying math/being a professor, if I need/want more money, if I can't finish my PhD, etc.] then, after picking up an extra degree if necessary, I can pursue another career path, perhaps in finance, computers, etc. I essentially want to go to Princeton because it's got a great reputation, and every professor that I talk to and every website that I find ranks Princeton's math department as one of the best in the world. In writing my essay for Princeton, I would present some cleaned-up version of the above. But what I have is not very elaborate, detailed, impressive, etc. It's certainly nowhere close to 1000 words. On the one hand, nothing explicitly requires me to say anymore, and I appear to have fully answered the questions asked in the instructions. On the other hand, what I have so brief and lack-lustre that it seems like it can't be good. So what do the evaluators look for? Do I need to say more? If so, what kind of things do I need to say? Thanks.