I am a highschool freshman, and I really like to have goals for my life, one of the big ones is my career of choice. Previously, I have always wanted to be a programmer, and I have written a lot of code. But it seems to me that programming can get slightly bland, whereas math never disappoints me. So my question is asking whether or not it would be a economically-feasible idea to me a mathematician. Note that I don't really care about being rich, I just want to do something I love, and keep learning for the rest of my life. What careers exist today that make mathematics a money-making (however little) job?
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To get a nice start in exploring potential careers in math, see the Mathematical Association of America's MAA careers-in-math webpage.
See also the American Mathematical Society's AMS-careers webpage., which a number links; if you scroll down the page a bit, you'll find a link Career information for High School Students which seems quite expansive.
Also of interest might be the following link: fastest-growing-careers-in-math.
Given your young age, I think you need only feel assured that you can make a living out of math. Less important at this point in time is knowing a specific career path to follow.
Why don't you elaborate a bit more on what it is you like about math? You're very young, so given what you've encountered in your math classes thus far, can you clarify what it is that "never fails" to fascinate you?
You've got the opportunity, in your studies, to explore the vast domain that is mathematics, to learn better whether you are drawn to its usefulness and/or its beauty, among other things.
You've got many years in which to do so! What specific career you ultimately choose to pursue will "fall into play" and materialize along the way.
So for now, explore and follow your passions!
There's a lot of options and it depends on what specifically in math you want to be doing. If you truly want to, as you said above, be sitting next to a whiteboard doing math all day it sounds like you would like to become a professor. I believe professors tend to be content and fulfilled people, though their salaries are mediocre, so if you see yourself spending most of your time researching that's the way to go. You need to keep in mind, however, that you will need to go through grad school along the way which can in some cases be expensive and life consuming (there are certainly lots of people who have started a family in grad school, but it usually takes even longer to complete in that case). In many cases grad students aren't able to get a job and start a family until their late twenties.
Alternatively, if you don't want to go to grad school and would like a more fiscally sound job, lots of math majors can easily find work in finance.
Another fiscally sound career choice is to major in Computer Science instead of math. You would still take a lot of math courses along the way (though a lot of it will probably be more focused on subjects like discrete mathematics than pure mathematics) and once you graduate you could make a good deal of money as a software engineer (or if you wanted to stay with math work on something like physics simulations).
Don't fret it now, anyhow, you won't be able to accurately answer these questions until you're a few years into college, at the very least.
I'm a recent college grad, so I was in a very similar situation not too long ago. In high school, I realized that I liked math, I was good at math, and I was especially good at teaching/explaining/tutoring math, so I decided I was going to be a high school math teacher. When I was applying to college, I became concerned that teaching math would become too redundant and boring, since teachers have to teach the same lessons every year. So, with no previous experience in design or programming but an interest in both art and computers, I decided to go for dual majors in Graphic Design and Computer Science. I now work as a web developer and love it, although I miss math so I tutor calculus when I can.
Fortunately, math and programming go very well together and there are many lucrative fields that you may be interested in. Many mathematical careers actually require a lot of programming work, as most of the work is not done by hand anymore. My mother has been an actuary for the past 40 years and now has to write a lot of code to pull important information from large amounts of data so she can properly analyze it. Your strong experience with coding will make you a very desirable applicant for most mathematical positions. My best advice would be continuing to persue both, and when you get to college, get a minor (or potentionally dual major) in the other. Also keep in mind that if you exclusively choose one, you could always freelance in programming or tutor in math.
Some good options are teacher, professor, actuary, accountant, financial analyst, information analyst, broker, trader, etc. The links that amWhy provided would be a great reference. Unless you are interested in a specific mathematical career path now (such as teaching), I would recommend just continuing to explore as many options as you can during high school and college as you may find something you are more interested in.