Spectrum of careers for Pure Mathematics?

[SetTheory]

Hello,

I've just been accepted and will begin as an undergraduate in physics this fall. I'm planning on taking classes, in addition to the required courses, concentrated in particle physics, QM, field theory, etc. Also, I took courses on Set Theory and Topology, and fell in love with what I could garner from the experience.

So my questions are the following: If I were to look into a career in Abstract Math, what sort of options would I have? Academia, education?

Furthermore, I've been told there is a lot of abstract math ideas in many areas of physics. In what ways and areas do abstract math and physics overlap?

What sort of careers could I hope to have that would require knowledge of math and physics in these (theoretical/abstract)ways?


Thank you,

 

[homeomorphic]

Also, I took courses on Set Theory and Topology, and fell in love with what I could garner from the experience.

You shouldn't judge math based on the first courses. I made that mistake, too. I thought that just because I took real analysis and topology and was good at it and liked it that being a mathematician was a good idea, but that turned out to be a disaster for me. I thought I was hot stuff because I was "doing real math" and my professors even seemed to agree with that, but it was a bunch of baloney. Now, of course, you may have a different opinion of the research-level stuff than I did if you get there, but I'm just saying it's really nothing like your first topology class. There's just as big of a difference between calculus and your first topology class and topology research, if not more. Also, if you are not a super-star in research, you should have a strong interest in teaching because the way the job market is, I don't think it's THAT bad, but if you study pure math, you may very easily find yourself teaching at a community college or maybe a 4-year college. So, my advice to people wanting to do pure math is to set aside some time to do some tutoring and practice public-speaking skills, unless they have a good plan to become more marketable to industry in grad school (for example, a lot of people doing numerical methods will get a lot of programming experience and maybe they could get an internship towards the end and then they would be probably be okay leaving academia). One of the big reasons it was a bit of a disaster for me was that my teaching was not well-received, and I don't enjoy it, so given that I'm not a research super-star, it's either career change or teaching-oriented stuff (I'm opting for the former). Some might say that I gave up too quickly on research and that it takes time to get good at it and not be overwhelmed by the amount of information, but they would be misconstruing my reasons for giving up on it. It's true that I now consider myself to be pretty bad at it, but even if that were just the initial hurdles of getting started, I decided that it was just too abstract and too complicated and too removed from reality, so I don't really even think it's worth being good at it anymore.

Furthermore, I've been told there is a lot of abstract math ideas in many areas of physics. In what ways and areas do abstract math and physics overlap?

Well, I think about classical mechanics in terms of manifolds and symplectic geometry and that sort of thing. So, you can view a lot of stuff through a more mathematical lens. I found it enlightening. You could try reading V I Arnold's book, Mathematical Methods of Classical Mechanics to find out more about this. Also, there's stuff like the use of fiber-bundles and Lie Groups in particle physics (but physicists have a tendency to just take what they need from these theories). Roger Penrose used some topology/geometry techniques to prove the existence of singularities in black holes.

http://en.wikipedia.org/wiki/Penrose–Hawking_singularity_theorems

He also wrote a book called Techniques of Differential Topology in Relativity.

Beyond that, stuff like string theory or loop quantum gravity is very mathematical, but it's also kind of pie-in-the-sky stuff, that's a bit out there in some ways.

What sort of careers could I hope to have that would require knowledge of math and physics in these (theoretical/abstract)ways?

Mainly just being a professor of math, physics, or engineering or something like that. In industry, the places to do that sort of thing are few and far between and very competitive. There are a few spots for it, like maybe some quant jobs, but I wouldn't count on getting one of them. The more likely route is to have to pull a massive career change maneuver and not use much of what you learned if you leave academia.

 

[SetTheory]

Yes, I am too young and inexperienced to truly know where I can see myself in terms of career yet. I was hoping just for some personal experience and insight, thank you :)

In agreement with you, I feel as if abstract math is a bit too disjoint from reality (for me)as well. That's one of the reasons I chose to major in physics. Honestly, I am not sure how talented I really am in pure math. I just loved the way it twisted my mind and I want to continue to take classes in it, to put it simply. I thought before anything I needed to be realistic with what exploring that type of work would really mean for a career.

Thanks for the examples of mathematical perspectives in physics, I am definitely going to go look those up!

So academia is my best bet if I do end up seeing myself in the abstract areas, is what I am concluding. I was very much looking into research in particle physics at some of the government run labs(Fermilab, Lawrence Berkeley, Los Alamos).

Is this at all a feasible career goal to shoot for? I imagine the path to get a career at those places requires knowing some of the staff or having connections. Is that one of the reasons it is so difficult to get a job at those places?

Would you happen to know what sorts of mathematics a physicist might do at these big name laboratories?

I know this sounds premature to think about as just an undergraduate, but I always thought it was better to know my options earlier than later.

Thanks,

 

[homeomorphic]

In agreement with you, I feel as if abstract math is a bit too disjoint from reality (for me)as well. That's one of the reasons I chose to major in physics. Honestly, I am not sure how talented I really am in pure math. I just loved the way it twisted my mind and I want to continue to take classes in it, to put it simply. I thought before anything I needed to be realistic with what exploring that type of work would really mean for a career.

Well, I think that's partly a matter of personal preference. Some people even do PhDs with no intention of going any further with it. As long they have a great exit plan, that's fine, if that's what they want to do. I don't share their perspective, but I can definitely see where they might be coming from, since I realized I just like learning about math and physics, as opposed to doing research in it. You do have to do some research in grad school, but it's hard to get a good opportunity to really delve into the material in depth without it. Unfortunately, in terms of jobs--particularly those actually involving physics, physics is probably even worse than math, even if it is more in tune with reality.

So academia is my best bet if I do end up seeing myself in the abstract areas, is what I am concluding. I was very much looking into research in particle physics at some of the government run labs(Fermilab, Lawrence Berkeley, Los Alamos).

Is this at all a feasible career goal to shoot for? I imagine the path to get a career at those places requires knowing some of the staff or having connections. Is that one of the reasons it is so difficult to get a job at those places?

My sense is that those are pretty competitive, but not impossible. I think it's all about having an exit plan if you want to take a shot at it. Having connections always helps in getting any job. Sometimes, you get lucky and don't need a connection, but more often than not, you do, for most of the worthwhile jobs. Which is probably why I'm still struggling to get one, even though I don't care if it's particularly competitive. In truth, I'd probably take anything that paid me over 15k at this point, if I could use it as a stepping stone to anything else, but I'm just afraid that people will think I'm desperate, so I, instead, put on the show of asking for like 50-60k (which is about what should be expected for the types of things I am applying for). I'm starting to think about doing something like working for Starbucks or Walmart, just to buy myself more time to retrain myself. So far, I've just been tutoring a bit. I'm also considering going back and getting a masters in a different subject, but after being in school for so long, the idea of going back for more is a bit hard for me to swallow.

Would you happen to know what sorts of mathematics a physicist might do at these big name laboratories?

I'm thinking the basic physics curriculum math--calculus, linear algebra, differential equations, numerical methods, prob/stat, Fourier transforms/series. Maybe some complex analysis. I'm pretty far from the experimental side of things, though, as a math guy.

I know this sounds premature to think about as just an undergraduate, but I always thought it was better to know my options earlier than later.

It's not premature. It's always good to go into it with a plan. Otherwise, you end up like me, having to come up with a plan from scratch, after the fact.

 

[SetTheory]

Okay, got it. So a few practical exit plans encase things don't turn out how I plan, especially with the competitive careers.

A few of my study partners in the math classes I took told me the value of a math degree in getting computer or programming jobs. I'm not sure if that's what interests you, but it might be worth looking into. I bet that experience would be more valuable than a service sector job (:

Anyways, thank you for lending me your experience,

and best of luck finding a job!

 

[homeomorphic]

A few of my study partners in the math classes I took told me the value of a math degree in getting computer or programming jobs. I'm not sure if that's what interests you, but it might be worth looking into. I bet that experience would be more valuable than a service sector job (:

Yeah, I have been looking into that, along with actuarial work. I have a minor in computer science, and I recently started programming games as a hobby (potentially, I might sell them and make money, but presumably not very much). The issue is whether I can actually get one of those jobs. No luck, so far, but I guess I haven't tried very hard on the pure programming front. I've applied to actuarial and financial stuff, and a couple programming jobs. Closest call was a programming job, actually. Got a phone interview for that last week, but no more.

It's pretty rough looking for a job right now if you're not good at networking (which I'm not). So, you might want to start thinking about that, now. That's part of a good exit strategy.

and best of luck finding a job!

Thanks.