Applied Math or Theoretical Physics?

[Intraverno]

Hello everyone, as those of you who have helped with my other threads know I'm currently a high school student and an aspiring physicist. I'd like to start out my post by saying that I completely understand that I am very early to be thinking this far ahead, especially when I haven't experienced any real high level physics or math yet. I know there's every chance that I'll change my mind and might not even be involved in physics or math, only time can tell. That said I'm curious about the intricacies of physics and math careers and I'd just like to find out how they work, just to satisfy myself, even if those plans might not come to fruition.

So far in my education I have not come across much physics, but the physics I do see is usually classical mechanics and electromagnetism. Now, as far as physics goes, I'll admit much of my knowledge of physics comes from popular science books (which I know is not an accurate representation of what physics is really like to specialize in), but I have also read Newton's Principia and and although I'm sure I don't understand everything about it, the majority of things I understand and I do enjoy. However, the physics that I really like (as far as liking it more than math) is more along the lines of quantum mechanics, relativity, and astronomical applications to classical mechanics, which of course I have not really been exposed to.

This is where the difficulty in my mind comes from. I have also always loved math, ever since I got to basic algebra, and it's my favorite subject to this day (I'm not currently in a physics class). Part of the reason I have thought that I want to be a theoretical physicist is it would combine my love of math and physics and I would use math to solve physics problems. However, as I'm getting into higher and higher math I'm finding I like it more and more, and at this point from my reading online I'm unsure if I'd really want to be a physicist more than investigate theoretical math as a mathematician. But I still love physics, so I don't know what to do. I know people like Ed Witten that are involved in string theory, quantum field theory, and quantum gravity research use highly sophisticated abstract math, but I know the chances of me making it into one of those fields is very small.

At this point I'm leaning towards studying math instead of physics, but I don't want to lose physics completely, so ideally I would want to be a mathematician that researches into pure math, but then also applies that math to physics problems where applicable. I don't know if that kind of job really exists or is a reasonable goal to go for, but I'd like to hear the input of the people here that are actually in these fields. What kind of job do you think I would be most interested in? What do you think I would study in college to prepare for that job? Any and all input is appreciated.

 

[ShayanJ]

There is just one thing that I think should be brought to your attention. The math you learn at this level is usually not rigorous, at least not rigorous enough to satisfy a mathematician. Such courses are only designed to balance rigor and simplicity. So in fact its more likely that you don't have a accurate enough picture about math to decide going into that direction or not than about physics. You need to, at least, glance through a rigorous math book to really see what mathematicians do.
And yes, there are pure mathematicians that work on physics problems.

EDIT: And you're not even in college. You surely haven't encountered enough stuff, whether physics or math, to decide between them! You really should wait more to make such decisions. You can ask professors to guide you about different courses and take the ones that interest you in college. You can take physics courses and math courses that can be applied to physics. But don't limit your options to math and physics because you may find out that none of them are actually what interest you.

 

[micromass]

There's a very easy way to see whether you like math or not. Get the book "A book of abstract algebra" by Pinter and work through it carefully. This is a book that a high school student could read, but it will be about math that you will encounter in university. It is a rigorous book and it could in principle be used in university. It does not have a lot of prerequisites.

As for physics, you could try the same. But that's more difficult since most interesting physics requires calculus up to differential equations. I'd say to study Kleppner and Kolenkow, but you might not meet the prerequisites or not.

Anyway, if you need help or more information, send me a private message.

 

[Intraverno]

There is just one thing that I think should be brought to your attention. The math you learn at this level is usually not rigorous, at least not rigorous enough to satisfy a mathematician. Such courses are only designed to balance rigor and simplicity. So in fact its more likely that you don't have a accurate enough picture about math to decide going into that direction or not than about physics. You need to, at least, glance through a rigorous math book to really see what mathematicians do.
And yes, there are pure mathematicians that work on physics problems.

EDIT: And you're not even in college. You surely haven't encountered enough stuff, whether physics or math, to decide between them! You really should wait more to make such decisions. You can ask professors to guide you about different courses and take the ones that interest you in college. You can take physics courses and math courses that can be applied to physics. But don't limit your options to math and physics because you may find out that none of them are actually what interest you.

Thanks for the advice! As I said, I am trying to keep my options open, and I'm actually in a high school program that specializes in math and science, so I will be encountering more of these subjects and I realize that my goals and interests can very quickly change as I'm exposed to more material. You are right though, and I'll be sure I keep an open mind and still explore some other options. I mostly only asked this question out of curiosity for what I would want to do assuming my interests don't change. Thanks again for your advice, I'll be sure to follow it.