Programs Programs for getting both a PhD in physics and mathematics?

[GoldPheonix]

Hello, I'm an undergrad in my third year with a major in mathematics and physics.

Needless to say, since I'm in my third year, I'm looking into going into graduate school and at graduate programs. But I have a large problem:

I really like the fact that I'm doing both math and physics. I really do not wish to pick between the two (I couldn't when I started my undergrad, and now that I'm going to be heading into graduate school, I still don't wish to choose between the two). My own personal goal is, after PhD and post-doc, to join a university where I can become a professor in both physics and mathematics, where I could teach both mathematics and physics courses as well as do mathematics (in the area of geometry) and theoretical physics (cosmology, particularly in gravity) research.Are there any schools which offer graduate programs to get both physics and mathematics PhDs?

 

[Vanadium 50]

People struggle to make an impact on one field, even given a lifetime to do it. Doing this in two fields simultaneously, working half-time on each is even more difficult. People have had success in interdisciplinary work, but what you want to do has a very, very small rate of success.

Many schools will not grant two PhDs or a second PhD to someone who has one.

 

[ChemHopeful]

theoretical physics and applied math arent exactly like french and russian. there are plenty of physicists who do math problems and vice versa

when it comes time to choose exactly what department youre applying to for grad school, you will probably be able to find one that allows you to straddle the line as you see fit

 

[twofish-quant]

You probably want one Ph.D. in mathematical physics.

Also physicists and mathematicians think in *VERY* different ways. There are physicists that use math, and mathematicians that use physics, but the thought processes for the two fields are very, very different.

(And also standard disclaimer: Don't go to grad school expecting to be a professor. You probably won't be.)

 

[Vanadium 50]

You probably want one Ph.D. in mathematical physics.

I don't think he does.

Note that he wants to be a cosmologist and a geometer. Do you know of any mathematical physicists doing anything like that?

 

[mikeph]

I would think it would be hard to find a research program in theoretical physics/cosmology which doesn't require significant understanding of geometry. The other way round is certainly not true though. Based on this I'd lean towards applying to physics schools.

For me the solution is all in your choice of supervisor... if you have someone who regards maths as a tool that is sometimes a pain, it will not be what you're searching for. On the other hand, you may have a supervisor who enjoys maths and does not care about the most recently published results in some astrophysical journal. You need to find someone who will appreciate your aims, ie. to develop your mathematical ability if it's a physics department, and vice versa.

 

[GoldPheonix]

People struggle to make an impact on one field, even given a lifetime to do it. Doing this in two fields simultaneously, working half-time on each is even more difficult. People have had success in interdisciplinary work, but what you want to do has a very, very small rate of success.

Many schools will not grant two PhDs or a second PhD to someone who has one.

Really, they won't? That's curious and irritating.

It seems that the resounding answer, to the academics that I've talked to and from people on this forum, is that this is not a possibility.

I recognize that this probably will have had a very small success rate, but I still don't wish to drop both. I may consider moving over to mathematical physics, and then over time pick up a masters in mathematics, and maybe join the math community that way.

Thanks.

theoretical physics and applied math arent exactly like french and russian. there are plenty of physicists who do math problems and vice versa

when it comes time to choose exactly what department youre applying to for grad school, you will probably be able to find one that allows you to straddle the line as you see fit

This is true, I am getting the idea that I'm going to have to find a department that straddles the line very closely.

Thanks.

You probably want one Ph.D. in mathematical physics.

Also physicists and mathematicians think in *VERY* different ways. There are physicists that use math, and mathematicians that use physics, but the thought processes for the two fields are very, very different.

(And also standard disclaimer: Don't go to grad school expecting to be a professor. You probably won't be.)

1. I am very aware of the difference in how mathematicians and physicists approach problems and what their interests are in particular problems.

2. I very strongly doubt that I will never become a professor.

I don't think he does.

Note that he wants to be a cosmologist and a geometer. Do you know of any mathematical physicists doing anything like that?

Actually, I suppose that I could find subsection of cosmology which is interested in the geometry/topology of the universe (actually, my current university is interested in this).

I would think it would be hard to find a research program in theoretical physics/cosmology which doesn't require significant understanding of geometry. The other way round is certainly not true though. Based on this I'd lean towards applying to physics schools.

For me the solution is all in your choice of supervisor... if you have someone who regards maths as a tool that is sometimes a pain, it will not be what you're searching for. On the other hand, you may have a supervisor who enjoys maths and does not care about the most recently published results in some astrophysical journal. You need to find someone who will appreciate your aims, ie. to develop your mathematical ability if it's a physics department, and vice versa.

This seems to be the general solution to my problem --find a department which is interested in both.

 

[twofish-quant]

I recognize that this probably will have had a very small success rate, but I still don't wish to drop both. I may consider moving over to mathematical physics, and then over time pick up a masters in mathematics, and maybe join the math community that way.

You really don't need another degree to be part of the math community. Just be the physicist that likes going to math talks, or the mathematician that likes to go to physics talks. There's nothing keeping you from learning more math as a physicist or learning more physics as a mathematician, and it's a really good thing if you do.

The thing about a Ph.D. is that you will not merely be asked to learn new stuff, but to create something totally original. For a physics Ph.D. is going to be to do original physics with math that someone has taught you. For a math Ph.D. is going to be to do original math without worrying if it is useful or not for physics.

The trouble with doing both is that physicists want to make the math as simple as possible. If you try to use any sort of complicated math if you don't have to, you are likely making the problem harder than it is. By contrast, mathematicians don't want to limit their "creativity" by worrying if what they are inventing actually describes something physical.

Actually, I suppose that I could find subsection of cosmology which is interested in the geometry/topology of the universe (actually, my current university is interested in this).

Which you will likely find if you do this is that you'll be doing original physics, but no real original mathematics. Most of the math that is used in cosmology (differential topology and geometry) is stuff that was worked out in the 19th century. For the most part if you go down this route is that you will be *using* and *learning* a lot of math, but it's somewhat unlikely that you will be *inventing* new math.

 

[MathematicalPhysicist]

I am not sure how much two-fish quant is knowledgeable about contemporary theoretical cosmology, but there's plenty of new maths going on there.

I think, if you want to work in the borderline of maths and physics (as I am), then pick two advisors one from physics and the other from the maths, ofcourse you should pick your advisors in such a way that they will be open minded for your desire to pursue the borderline of these topics.

 

[twofish-quant]

I am not sure how much two-fish quant is knowledgeable about contemporary theoretical cosmology, but there's plenty of new maths going on there.

Most of the cosmologists that I know work in the post-inflationary era, and the math used is statistics, quantum field theory, and gas dynamics. There are people that work in quantum cosmology are inventing some new math, but very little of it seems connected with physics, and in order to get anything connected with solid observations, people are moving toward anthropic arguments, which really don't have that much new math.

The problem that I'm seeing is that the parts of cosmology that have a lot of physics content (i.e. things that you can falsify with observations) don't have that much new math, and all of the new math work seems to be in areas which aren't easily falsifiable, and hence don't have much physics content.