Thank you for the excellent response. Why does it seem that PhDs in all fields have subpar career prospects (at least to careers relevant to their degree)? Are there any disciplines where it's not like this?
Engineering and computer science come to mind. Operations research/industrial engineering.
I want to consider a major that can lead to a fine job or a stepping stone to a PhD, so I can keep my options open. I've been considering Applied Mathematics and Engineering, but I fear the latter would not fit me as well. I'll have to find out when I get to college what fields suit me best.
The thing you have to consider is what job will suit you the best in the end, more than what major. Unless you change careers a lot, the job is going to take a much bigger portion of your life.
Nonetheless, despite having not yet touched it, research fascinates me and it seems like that would be a good fit since the nature of research corresponds to my personality and interests.
Some people like it, but a lot of people think that and then find out it's not all it's cracked up to be. It's really hard to say whether you'll like it. Personally, I thought I would like it, but frankly, I find it hard to believe anyone would like it after my PhD, at least in the current academic climate, and this is coming from someone who was initially pretty hardcore about math and ready to go to great lengths to succeed. I think I might have liked research if this were about 200 years ago when things were a little less complicated. I'd rather be like Arthur Cayley, doing his linear algebra on the side as a fun hobby, as he worked as a lawyer, rather than today's overloaded professors, burdened with their high-pressure academic environment and over-grown subjects that are so hard to keep up with. Part of what inspired me to do a PhD was looking at historical figures and the math they did, but I don't think that's such a good inspiration in light of how things have changed. Also, I think it would have helped if I had done physics or engineering or something along those lines because then it's more clear that you are doing things that help you understand nature or advance technology.
But if a PhD is a research degree and if you don't end up getting a research job or some other type of relevant career in the end it seems a bit redundant for me to do it. As much as I would love a subject there's no point if I am not practicing it.
I agree. If you want to practice it, you might think about engineering. If I go back to grad school, it will most likely be computer science, but I'm also considering going back to EE--specifically communications engineering. You might have to slog through some engineering courses that are sort of ho hum, but eventually in EE, you can find a lot of good mathematical material. For example, information theory or coding theory.
Here's an interesting article about coding theory:
http://plus.maths.org/content/coding-theory-first-50-years
The astonishing thing about coding theory is that it's so mathematical, yet so useful.
And here's a nice video series about information theory:
http://www.youtube.com/watch?v=p0ASFxKS9sg&list=PLbg3ZX2pWlgKDVFNwn9B63UhYJVIerzHL
There's cool stuff in engineering.