This question is on mathematics, career, and personal life.
i.) Suppose that I am a Junior in college majoring in mathematics at a top research institution in the U.S. I have "mostly" good grades in mathematics (say, around 2/3 of my grades are A's or A-'s), but I have some B's and B+'s. I've taken a good number of graduate level courses with at least half of them A or A-'s.
ii.) Earlier in my college career, there was a noticeable dip in my grades (A's becoming B's and B+'s) due to personal issues.
iii.) My goals:
(Short term:) enroll in a top pure math graduate program in the U.S. (ideally a top 6 institution) where there is a strong research community in my field as well as other fields in mathematics which may be helpful to my own research or broadening my perspective.
(Long term:) become a professor in pure mathematics at a top 30 institution (or equivalent) studying geometric topology or some related field.
II.) My Questions:
a.) Is it appropriate to talk about personal matters in one's personal statements or rec letters, if it has negatively impacted one's academic performance?
b.) What are grad school admission committee's views in regards to personal hardships? I know the short answer to this is "it depends," so I would appreciate getting the various viewpoints available on the MathOverflow community. I am sure it also depends on the school; school-specific viewpoints would be much appreciated.