What is the approximate composition of a statement of purpose in Mathematics?
When I review graduate applications, the statement serves three purposes:


If you are not a native English speaker, it may tell me something about your English proficiency.  However, it cannot be relied upon too heavily since you may have gotten at least editorial help from a friend or even a professional.
More importantly, it is an opportunity to demonstrate that you know something about a research area that interests you.  This is more important for PhD applications than for MS applications, obviously.  If you have already done some research, hopefully your recommendation letters speak about that.  Your statement can sometimes be useful in showing that you keep up with some research area even though you haven't yet contributed to it.
Finally, your statement can address issues in your application, like a period of low grades related to something in your personal life, a gap in your schooling/employment, etc.


There is in my opinion no correct ratio of personal versus research components; it depends on the individual.