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I am debating whether I should go to grad school in physics or applied math and it is tearing me apart.

Let me first say that I have absolutely no interest in performing any sort of experiment. What I am interested in is mathematical model-building. However, I am interested mainly in building mathematical models in

I really want to do something like to what Ed Witten is doing that is on the borderline between math and physics. That is, I want to focus my work essentially on physics but I want to be able to publish in mathematical journals and go to math conferences from time to time. Wikipedia says that Witten went to grad school in applied math but then transferred to physics. Why do you think he did that?

There are two things that I absolutely hate about physics:

1) being "good" at some physics subjects (e.g condensed matter) consists of memorizing massive amounts of information. I want problem-solving to be the test of "goodness" of the field that I go into. Can I just forget about all of the non-theoretical parts of physics that relate to chemistry/engineering/materials science if I go to grad school in physics and specialize in theoretical physics?

2) The math grad students and professors even are just so much more motivated and sharper and even nicer than the physics grad students. They clearly have command over what they study, while on the other hand, the physics grad students just go to the blackboard and start blankly sometimes. But maybe that is just my school...

Is it harder to get into the best math programs than it is to get into the best physics programs? It seems to me like it is based on 2) above.

I don't know what do to. :(

EDIT: I am also considering applying to both physics and math graduate programs, but that seems like it would reduce my chances of success for both since I would have to prepare for both the math and physics GREs, but that is probably what I will do right now since I just can't decide.

Let me first say that I have absolutely no interest in performing any sort of experiment. What I am interested in is mathematical model-building. However, I am interested mainly in building mathematical models in

*physics*, not in engineering or economics or anything else. I want to do work in quantum field theory, general relativity, string theory, quantum computing algorithms, and similar things. I am NOT interested in actually constructing the problems that I solve like professionals pure mathematicians do. That is, I don't wan't to just prove tons of theorems because they are interesting and clever. I think nature provides enough interesting problems.I really want to do something like to what Ed Witten is doing that is on the borderline between math and physics. That is, I want to focus my work essentially on physics but I want to be able to publish in mathematical journals and go to math conferences from time to time. Wikipedia says that Witten went to grad school in applied math but then transferred to physics. Why do you think he did that?

There are two things that I absolutely hate about physics:

1) being "good" at some physics subjects (e.g condensed matter) consists of memorizing massive amounts of information. I want problem-solving to be the test of "goodness" of the field that I go into. Can I just forget about all of the non-theoretical parts of physics that relate to chemistry/engineering/materials science if I go to grad school in physics and specialize in theoretical physics?

2) The math grad students and professors even are just so much more motivated and sharper and even nicer than the physics grad students. They clearly have command over what they study, while on the other hand, the physics grad students just go to the blackboard and start blankly sometimes. But maybe that is just my school...

Is it harder to get into the best math programs than it is to get into the best physics programs? It seems to me like it is based on 2) above.

I don't know what do to. :(

EDIT: I am also considering applying to both physics and math graduate programs, but that seems like it would reduce my chances of success for both since I would have to prepare for both the math and physics GREs, but that is probably what I will do right now since I just can't decide.

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