Mathematics PhD route to theoretical research?

In summary, the conversation is about a senior physics/math major who is interested in pure mathematics and the abstract side of physics. They are considering pursuing mathematics as a graduate instead of physics and are wondering how this may affect their ability to enter research areas such as string/particle, QFT, and unification theory. They are also interested in exploring the overlap between physical theories and pure mathematics. Some advice is given on schools that offer interdisciplinary PhD programs in mathematical-theoretical physics and the possibility of earning a PhD in Physics and a MS in Mathematics. The conversation also touches on the challenges of balancing both physics and pure mathematics, and the rarity of finding mathematical physicists. The conversation ends with a summary of the opportunities for physics in the mathematics department at Indiana University
  • #1
ran13
19
0
Hi PFers,

I'm a senior physics/math major and very interested in pure mathematics (esp. algebra and number theory) but I'm also interested in the very abstract side of physics like string/particle, some QFT and unification theory.

If I pursue mathematics as a graduate as opposed to physics, how disadvantaged will I be in entering these research areas? I'd still love to be able to contribute to pure math, but what I am keen on is learning how physical theories and pure math overlap, and being active in that area too.

I find my upper div physics classes awesome (quantum, EM and electrodynamics, nuclear, etc.) but I find the 'artistic' methods (don't mean to sound pretentious...) of problem solving in math to be really exciting and rewarding, especially as a break from the strictly applied stuff.

Any advice? Application cycle for 2012-2013 has started and I'm about to decide which programs to apply to and how to craft my SOP.

Thank you :)
 
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  • #2
Granted, I'm at about the same stage of career whatnot as you (about to start graduate school), and even though I'm going into applied mathematical neuroscience / biophysics ... I'm pretty sure there programs in mathematical physics that are specifically designed to spit out PhDs who work with the mathematics of theoretical physics?

I could swear I have seen PhD programs that are more or less the classes you'd take to earn a masters in pure math plus the classes you'd take for a masters in mathematical / quantum physics ... then after qualifiers you do your dissertation in the theoretical physics area.

Umm, I don't recall where all I've seen them but I know for a fact I have seen them so at least one of the schools my fiancee and I are applying to have the programs I'm talking about:

U Pittsburgh, Northwestern, Penn State, Harvard, Iowa State, U Maryland, Renssellaer, U Washington, and probably a bunch more have stuff like this ... maybe look at any of those school's math / physics departments and see what degree programs they offer ... I swear that there are a few who do interdisciplinary PhDs in mathematical-theoretical physics.

p.s. after you find whatever school(s) I saw those programs at, just look at where the profs of theoretical / mathematical physics got their degrees, and you'll start to generate a much bigger tree-list of programs that are exactly in that area.
 
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  • #3
I'm trying to do something similar. I ended up getting sucked more into pure math because I got into a school that didn't have too much mathematical physics and it's just hard to do both. The stuff I am doing is very close to loop quantum gravity, and fractional quantum hall systems, but I only know enough physics to see the connection, not enough to understand the physics papers. It's possible to work in my area without knowing much physics.

I didn't get a double major. I only took a couple extra physics classes in undergrad.

You can probably resist the pull towards pure math if you go to the right place, but it's just hard to do both. It's hard enough to do one of them. That's why real mathematical physicists are pretty rare these days. There are physicists who dabble in math and vice versa, but only a few who really know both.
 
  • #4
I'll look into those mathematical physics programs then. Shame that they're rare... It seems like a fascinating field. I could only register for one subject GRE (math) so hopefully that will not be an issue?

Any other tips on this topic? Anyone who's made this transition or achieved something similar? Thanks again.
 
  • #5
Bump! Any advice at this point in time would be appreciated. I don't want to end up enrolling into the wrong program... PhDs don't really allow room for double dipping :(
 
  • #6
http://www.math.indiana.edu/graduate/mathphysics.phtml [Broken]

I found one of the programs I remembered seeing ... it's from a school Debra and I crossed off our list (due to the program she was looking into not the strength of their math department).

If you haven't found more programs like this yet, I'd start by looking at where all the profs that are listed as chairs/profs/advisers got their degrees.

*on an additional note, a friend from undergrad did (from what I understood of the program) grad school at the University of Miami where you go into their physics department and then take all of the graduate level "mathematical physics" classes they offer along with whatever else you need to learn in order to pass your physics qualifiers, then you take 7-8 graduate level pure math courses, take the math PhD qualifiers, then switch back to do the rest of your physics PhD (most likely in theoretical / QFT / particle physics or whatever ... sorry I'm not really a physicist), and technically I think they award you a PhD in Physics and a M.S. in Mathematics.

So yeah, not sure if that's something of interest, but if nothing else, there are two programs you might not have heard of that sound like what you're into.
 
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  • #7
Funny you should mention Indiana--that is where I am. It's pretty pure-math oriented here, despite the presence of the mathematical physics program. We have an algebra/number theory guy who has dabbled in some quantum computing stuff, an algebraic geometry guy with links to string theory, a couple topology profs with ties to quantum stuff (more like gauge theory for topology's sake, and then, there's my adviser, Turaev, who has had a big impact on the TQFT world, though, really, my impression is that he's pretty pure math, despite doing things that have somewhat physical flavor), some guys in PDE who do Ginzburg-Landau theory, fluid mechanics, Navier-Stokes. So, there's some stuff. But, there aren't a whole lot of options as far as classes to take or seminar talks. If you want physics, it's mostly in the physics department. I guess you can be in either department with the math physics degree. On that side, I'm not very familiar with the physics department, aside from knowing a few grad students and having taken two classes. However, my impression is they might be a little on the non-mathematical side, with maybe a couple exceptions.

There's a condensed matter theorist who is cross-listed in physics and math. I know a student of his who is very mathematical, but he's in the physics department.

Maybe, UC Riverside? Perhaps, not the highest ranked, but I guess Baez is going back there (he quit quantum gravity, but maybe he'll still take students doing it?), and they have other people there, too, doing quantum mathematics.
 

1. What is a mathematics PhD?

A mathematics PhD is a doctoral degree in mathematics that typically requires 4-6 years of study beyond a bachelor's degree. It involves advanced coursework, original research, and a dissertation that contributes to the field of mathematics.

2. What is the purpose of pursuing a mathematics PhD?

The purpose of pursuing a mathematics PhD is to become a highly skilled and knowledgeable mathematician who can contribute to the advancement of mathematical research and knowledge. It also opens up opportunities for careers in academia, industry, and government.

3. What is the difference between a PhD in mathematics and a PhD in applied mathematics?

A PhD in mathematics focuses on pure mathematics, including abstract topics such as algebra, geometry, and analysis. A PhD in applied mathematics, on the other hand, applies mathematical principles to solve real-world problems in science, engineering, and other fields.

4. What is the typical timeline for completing a mathematics PhD?

The timeline for completing a mathematics PhD can vary, but it typically takes 4-6 years. This includes 2-3 years of coursework, followed by 2-3 years of research and dissertation writing. The exact timeline may also depend on the individual's research progress and the requirements of their specific program.

5. What are the potential career options for someone with a mathematics PhD?

There are many career options for someone with a mathematics PhD, including research and teaching positions in academia, as well as careers in government agencies, research institutes, and private companies. Some specific job titles may include mathematician, data scientist, operations researcher, or actuary.

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