Personal Statement

Unlike undergrad applications, the Statement of Purpose (SOP from here on) is meant to be more "professional" than "personal". The purpose of SOP is literally to state your purpose for joining a program: what kinds of math are you interested in? Do you have experiences (research, reading UROPs, classes) in the areas of math you are hoping to pursue? Why are you applying to this specific program, e.g. are there (tenured) professors doing active research in the things you are interested in? In other words, your goal is to convince the professors reading your SOP that the program is a good match for you in terms of your research interests, and to sneak in relevant experiences you have to prove that you can survive (and succeed in) the program.

While there is no "best" template for SOP, there are things that you definitely should avoid. For instance, it is not a good idea to try too hard to impress, especially by writing about mathematical ideas that you don't understand fully. The professors are agile at catching those. It is also generally not a good idea to state that you are only interested in working with one particular professor in the program, unless this is what you really intend to convey. That one professor might not be taking students and your interest might change, so it would make you seem a "riskier" candidate .