Math-Phys Double Major: Advice for Joe

[jmnance]

Hey guys. My name is Joe. I love love love mathematics. I finished calc 1, 2, 3 and diff. eq before I graduated high school. Calc 2 was done as an independent study in the summer semester after my junior year. I attended a community college just last year after graduation. I finished my 2 year degree in 1 year due to my coursework in high school. I am attending the University of Illinois- Urbana in the fall of this year.

I originally wanted to go into mathematics, mainly pure math such as algebraic topology. I have just recently after taking the 3 "university" calculus based physics courses, decided to double major in Pure Mathematics and Physics. My career goal is to go to grad school (hopefully at either University of Chicago or Northwestern) for math and possibly even physics. I want to teach at the university level and conduct research in pure mathematics and General Relativity/Theoretical Physics/Quantum Field Theory. When I have free time, I like to read about/do mathematics and physics. I especially enjoy "coming up with my own stuff" in calculus and just little mathematical things in general.

My question is, is it usual for someone in pure math to study an applied science at the same time? How frequent do people earn Ph.D.'s in both pure math and physics? If I study one, I want to go all the way.

Also... Any advice for a math-phys double major?

Thank you. I am looking foward to becoming part of the Physics Forums community.

 

[tmc]

While it is very common for someone to study both math and physics, and to double-major in them as undergraduate, you never really see anyone getting a PhD in both disciplines; it's way too broad and pointless. What is often done, however, is getting a PhD in, say, a branch of mathematical physics, or a PhD in pure math while working on stuff that is related to physics, or a PhD in pure theoretical physics. You wouldn't study physics and math separately, but rather study the part where they intersect.

As for advice: since you have such a head start in your coursework, try and fit in as much research experience as you can. Work with a prof during the year (well, maybe not in first or second year, but whenever you have time in your schedule and can find a prof), and try to find an REU during the summer.

 

[cmos]

I agree with everything tmc said. Don't worry too much right now of whether to go to grad school in math or physics. But, if you're up to it, definitely do the double major in math and physics as an undergrad. As time progresses you will come to find your peak interests and in when you are ready to apply to grad school you will better know whether to should do your PhD in math or physics.

Just to spew out some random knowledge: Many theoretical physicists (sometimes called mathematical physicists) end up with professorships in math departments. This is due to their research using advanced mathematical concepts more akin to a mathematician. Renowned theoretical physicist Stephen Hawking actually holds the Lucasian Chair of Mathematics at Cambridge University (the same post held several years ago by Isaac Newton). With all this said however, don't be surprised to see the majority of theoretical physicists to be in the physics departments (strange, huh?).

 

[jmnance]

Thanks for your replies
two questions: What is an REU ?
Where can Algebraic topology be applied to physics (namely general relativity and QFT)

 

[tmc]

An REU is research experience for undergraduates; they're highly-competitive internships given by a large number of universities every summer.

I'll let someone else answer the topology question.

 

[ehrenfest]

Hey guys. My name is Joe. I love love love mathematics. I finished calc 1, 2, 3 and diff. eq before I graduated high school. Calc 2 was done as an independent study in the summer semester after my junior year. I attended a community college just last year after graduation. I finished my 2 year degree in 1 year due to my coursework in high school. I am attending the University of Illinois- Urbana in the fall of this year.

I originally wanted to go into mathematics, mainly pure math such as algebraic topology. I have just recently after taking the 3 "university" calculus based physics courses, decided to double major in Pure Mathematics and Physics. My career goal is to go to grad school (hopefully at either University of Chicago or Northwestern) for math and possibly even physics. I want to teach at the university level and conduct research in pure mathematics and General Relativity/Theoretical Physics/Quantum Field Theory. When I have free time, I like to read about/do mathematics and physics. I especially enjoy "coming up with my own stuff" in calculus and just little mathematical things in general.

My question is, is it usual for someone in pure math to study an applied science at the same time? How frequent do people earn Ph.D.'s in both pure math and physics? If I study one, I want to go all the way.

Also... Any advice for a math-phys double major?

Thank you. I am looking foward to becoming part of the Physics Forums community.

Hello, I have almost exactly the same interests as you and I was in almost exactly your place a year ago. I was very interested in string theory and the other very mathematical areas of physics and I wanted to go to grad school in theoretical physics. Here are some things I learned in the last year.

First, as I got deeper and deeper into advanced physics, I found that the VAST majority of physicists are working in areas far removed from QFT/GR/string theory. At my school, there are 2 out of about 30 faculty members who have a working knowledge of general relativity. Everyone else is working in condensed matter physics, high energy physics, etc. Doing research in these areas is nothing like what you did in introductory physics basically because they are so so messy compared to the cleanness and self-consistency of introductory E and M and classical mechanics.

Second, even the physicists who work in theory do something that is very different than mathematics. If you pick up a book like Zwiebach's "A First Course In String Theory" and you analyze it as a mathematician, it is rather awful. It is completely unaxiomatic and relies a lot on intuition and it is only rigorous when it wants to be.

Third, people tell me that most physicists today just dismiss the highly mathematical work done in physics like string theory. They say there is no experimental evidence of string theory so they ignore it. Finding a position in a physics department that allows you to do lots of math is very rare.

Of course, you said you were interested in GR and QFT which are experimentally verified and which physicists DO NOT ignore, so maybe this doesn't really apply to you. But anyone, that is why I eventually decided to go to grad school in math not physics. So, my main advice here is to think about whether you like physics because of the science involved in it or because of the math involved it and if it is the math than getting a terminal degree in physics is probably not for you.

 

[Asphodel]

A second major in math won't do anything for most physicists. The extra math courses might, depending on what you want to work on.

 

[jmnance]

Thanks ehrenfest. I dunno. I guess I will have to just take the courses and see. I have had my mind set on being a mathematician for years. I enjoy math and I feel that I understand it. To me, MAthematics has a lot of human qualities. (sounds weird, I know.) but I feel that mathematics understands me, and I understand mathematics. I have a real intution when it comes to the structure of different mathematics.