Do graduate schools look down upon applicants who do not immediately want to pursue a career in academia? If I want to do something in between graduating with my Ph.D. and my academic career, should I leave that out of my personal statement?
Specifically, I am seeking admission to a Ph.D. program in mathematics. After getting my Ph.D. I want to enlist in the Navy and become a SEAL. After I leave operational capacity, I want to serve as a mathematics professor at the Naval Academy or the Naval Postgraduate School.
Should I include this in my personal statement, or only mention wanting to become a professor one day?