Phd advice good idea what schools?

[epsilon>0]

Phd advice...good idea...what schools?

I'm a couple years out of grad school (M.S.) mathematics, and I am considering applying this fall for a phd program. My math UG math gpa is a 4.0 except for a b+, my grad gpa is a 3.8, and my physics gpa is a 3.7. My gpa dipped my last semester partly because of a serious medical situation and burn out. I took a practice GRE and my score was about 700 verbal and just short of 800 quanitative...with practive I think I could pull them up a little. I have a low math gre score that I took when I was sick, so I'll have to retake and I'm not sure what my range would be currently. My classes are:
UG: Real 1&2, Alg 1, Topology, Combinatorics, Complex, Number Theory, calculus sequence, linear alg 1&2
Physics-general, modern, optics, e&m 1, quantum 1, mechanics 1, astro, electronics
Grad: Measure, functional, pde, logic, alg 1&2, probability (it was a dual degree so i have less classes)

My first question is what sort of schools are my target range for mathematics or physics phd programs?
I will take the subject test, but I am unsure about what my score will be. I don't have as many physics courses, because I started physics late, my junior year. Will that hurt me, or will a high subject test cancel it out?

Secondly, I'm trying to figure if getting a phd is the right choice. Currently I'm teaching and trying to finish a novel. I'm interested in almost every field of study...provided I could get an academic position I would be happy researching philosophy, literature, and other academic subjects. Is this a hint that I should not consider a phd, because of the specialization involved?

I'm very interested in certain subfields of philosphy, quantum and particle, but I find mathematics to be profoundly beautiful. I know that if I did a phd, I would still try to write on other subjects. I've heard that you should do a phd only if it is the only thing that you can imagine doing...I can imagine doing many things, but most of them are academic. Anyway, I'm hoping you guys/gals can give me some advice on this.

 

[R.Mesri]

In terms of what schools are a good fit for your background, it really depends on the specific program and how competitive it is. Generally speaking, you should aim for well-known top tier universities with strong programs in math and physics. Some schools that might fit the bill include Stanford, MIT, Harvard, UC Berkeley, Princeton, Caltech, and many others. As for whether getting a PhD is the right choice for you, that is something only you can decide. If you have an interest in multiple fields, it may be more beneficial to pursue a degree that allows you to explore these interests. PhDs require a great deal of specialization and focus, so it is important to make sure that you are passionate about the field you are pursuing before embarking upon a PhD program. If the idea of a PhD still excites you, then go for it! It could be a great way to open new doors and opportunities for yourself.