I have a goal: It is to be a mathematical physicist. I dream to work in field related to the Amplituhedron.
This goal is non-negotiable.
From what I've read, it is difficult for a theorist to get a job, and this field is apparently very competitive. As it stands now, my student paper-trail is bad. My physics GRE score is bad but my GPA is solid. I think I would be able to get good recommendation letters, including a very strong one from the professor under whom I currently work.
I do not doubt that, if I tried, I would be able to get into some graduate school, but I have been toying with another option. Here are the two primary possibilities:
Get letters of recommendation and apply to grad. school. Then, go to whichever grad. school will accept me. In order for this to be viable, I'd have to go to a school which would, at least, allow research in something heavily mathematical. In order to get to the position I'd like to be later in life, I'd have to excel. This is not a problem, but is unfortunately more difficult at a less reputable school.
Graduate and work for a couple of years—mostly to pay off my exorbitant student debts, get a [much, much] better GRE score, and study (I am not as good at things as I'd like to be, and this studying would serve to drastically improve my ability). With a somewhat improved paper-trail, dampened by my taking a couple of years off, I would apply to graduate schools. I think my chances of getting into a better school are higher, but getting into a good school is not necessarily my goal.
My problem is that I don't know which one would maximize my chances of being a mathematical physicist. I do not know the dynamics of graduate research, or how large the differences are in excelling at a good school and excelling at a mediocre school. I'm, basically, totally ignorant in regards to what would be the better decision—and I'm hoping someone with more knowledge could help me make a decision.
Which career plan is best for me to enroll in a cooperative mathematical physicist PhD program?