Debating Grad School in Physics vs Applied Math

[ehrenfest]

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 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.

 

[Howers]

What is 50 - 25.75. If you can do that in your head in under 5 seconds, go math. If not, go physics. If you can't do it in your head, go commerce.

 

[ekrim]

You said it yourself that you want to pursue research somewhere between math and physics. This means that depending on the school this might be classified as applied math or physics. Go to the websites of the schools you're interested in and checkout the research of their math and physics departments. When you find something you like, apply to said department.

What is 50 - 25.75. If you can do that in your head in under 5 seconds, go math. If not, go physics. If you can't do it in your head, go commerce.

this works as well

 

[Antz002]

That 50-25.75 test seems awfully simplified. Do you really think its that simple? I'm asking as someone wondering about doing applied maths

 

[cristo]

That 50-25.75 test seems awfully simplified. Do you really think its that simple?

No, I think that's a stupid way to make a decision like that!

 

[maze]

I believe Dirac started out grad school in applied math before switching to physics.

 

[Howers]

That 50-25.75 test seems awfully simplified. Do you really think its that simple? I'm asking as someone wondering about doing applied maths

The point I am making is you have to be super good at math to even attempt grad school with it. You'd be surprised how many people can't do simple calculations in their head and contemplate a math degree. If you are not lighting quick with this kind of stuff (not just mental calculation, but math in general), don't waste your time and money. I learned this from friends who took topology.

To the poster, have you considered mathematical physics? Its physics as it is taught by the math department. Most of the work is in applied math, and they try to rigorously re-formulate physics. In fact, this field seems almost ideal for you. You're a mathematician who solves physics. The only problem may be the job prospects.

I'm only an undergrad, so I don't know how hard it is to get into either department. I would imagine math is easier, as in general most math classes get nearly empty once you hit senior years - which suggests people can't take it or lose interest. And let's not forget being a mathematician is a lot like being a musician...

As for people, don't base your career on a few tard TAs you may have seen. Math is more challenging, so maybe a larger proportion is smarter. But I've seen some really dumb math students, and some really bright physics ones.

 

[will.c]

I think whether math or physics is more challenging is largely a matter of perspective. The violin only has four strings, and the piano 22 times that many keys. Is chopsticks more challenging than Paganini?

To the OP: I think if you really feel the way you do regarding physics (i.e. being "good" at condensed matter requires rote memorization and no problem solving; physics grads are vapid and unmotivated) that this is a no-brainer. Be a mathematician.

(Also in defense of CM: quantum field theory is very popular right now amongst CM theorists to solve some very interesting natural problems. Also, who [not counting mathematicians and TCS guys] do you think works on quantum computation theory? It's not the string cosmologists.)

 

[confusio]

Hi ehrenfest. First I should say that your interests and mine are very similar. I was torn between an applied math and a physics graduate program. I chose to join a terminal master's program in math and worked with a condensed matter guy for my thesis. There are plenty of interesting math techniques put to use in condensed matter, for a few exotic examples check out Mikio Nakahara's book on geometry and topology. I encourage you to take a wider view that the methods you and I develop could be generalized to different branches of physics, for example conformal symmetry on the disc pertains to both tree-level open string amplitudes and conductance of graphene.

Anyway funding for particle theory is really limited (chalk is expensive I guess) so it is very competitive. This fall I start my phd at a physics program, but I got really lucky in terms of adviser and funding. If I had not been so lucky, probably continuing in an applied math program would have been my choice. If my coursework and qualifier don't go extremely well I will probably be nudged toward experiment or computational physics groups, in which case I would take a masters and go back to math.

I totally agree about the way students in the two disciplines interact. In my experience, math grad students are very laid back and don't leech one another academically, but the physics students all seem a little rough around the edges. Also, people love to get on the internet and badmouth other people's high energy physics theories, whereas the math community has much less drama if any.

Another part of my experience was that the physics gre is extremely competitive and does not reward a wide knowledge base in computer science or math like my own. Whatever you do, apply to places which will give you a masters if you change your mind in two years. Good luck!

 

[mordechai9]

I too have struggled with this kind of problem...

If you are in this position, I say go for the math department. Even better, try to find some department which incorporates or unifies the two disciplines. For me, my interests are rather broadly in aerospace engineering and math, but I also have a strong interest in physics and simulation. Fortunately there are some good programs (e.g. Stanford Institute for Computational and Mathematical Engineering, or UT Austin Institute for Computational Engineering and Science) which attempt to manage math, an application area, and computation/simulation instruction at the same time. So, these things aren't mutually exclusive, at least, not necessarily.

But, outside of these integrated programs, I would still recommend going for applied math, rather than physics. That is a pretty contentious argument and I know it has been debated here and many people are bound to disagree. But in my mind, if you want to be a theoretical expert, (in any field), you ought to be trained by the best theoreticians out there, and in my mind, those are mathematicians. There comes a point in high level physics and engineering theory where the difficulty in understanding is more an obstacle of mathematics, rather than intuition. Once you get a Ph.D. in applied math, I think you are best prepared to expand into other fields, but you may have a lot of work to do and you may have more to prove. But, if you've already completed a phd in one thing, you are probably capable of fleshing out those other goals. Just make sure you apply to an applied math program with applied math research, because there are math departments out there that are completely "pure" and they definitely wouldn't be the right thing for you (or me).