What are some fields for people(myself) that excel in Math?

As the previous commenter noted, almost all forms of engineering require mathematics at some level; mechanical, civil, and aeronautical engineering, for example, deal with stresses and strains on materials, sheer forces, aerodynamic and/or hydrodynamic forces (drag, flutter, etc.), oscillations, resonances, noise (both audible and electronic), failure probabilities, etc. Electrical engineering and materials engineering get into the quantum (physics) arena, 3D structure, lattices, and so forth. Even "squishy" fields like bioengineering involve things like statistical analysis of experimental results, topological models (e.g., protein-folding), chaos theory (population histories in unstable regimes, i.e., population explosions and crashes), combinatorics (genetics), etc. Software engineering has any number of open, extremely difficult questions involving computability (NP and siblings), formal correctness proofs of parallel, distributed systems, etc., but there's also plenty of "day to day" mathematics (and engineering) in areas like computer graphics, computer vision, AI, and robotics.

Many of the sciences are also math-heavy, most obviously physics and astrophysics, but also (perhaps surprisingly given its "dismal" label) economics and many others. And then there are mathematical fields themselves, e.g., statistics and category theory (the latter with surprising industrial applications being worked out right now--John Baez regularly posts about this: https://plus.google.com/u/0/117663015413546257905), not to mention the traditional "academic" ones, many of which have surprising and extremely subtle connections to each other (e.g., group theory, topology, complex analysis, number theory)--and many of those connections were originally hinted at by physics theories before being formalized by mathematicians.

And finally, there's (big) data analysis, data visualization, and predictive modeling, all of which are frequently relevant to all of the above. Many data sets have more than just three dimensions, so figuring out how to display them sensibly, how to make them easily navigable, how to identify "hot spots" or local minima/maxima or trends or whatever, is currently and will probably remain a busy area for some time to come. (Upcoming science missions like the Dark Energy Survey [https://www.darkenergysurvey.org/] will generate terabytes of data every day, as will personal genetic analyses, remote/satellite sensing, gravitational-wave experiments, etc.; in a few years it will be petabytes or exabytes.) Simulating/modeling complex systems has been a key component of most forms of engineering and the physical sciences for half a century; the NAS facility at NASA Ames highlights some of them: https://www.nas.nasa.gov/ . (I was fortunate enough to do some of my research there in the 1990s.)

In short, there are many potential jobs open to you, and you'll likely have time to explore a number of options in your future coursework, which will help you to define what you're most interested in. Both mathematics and physics are excellent "foundation" majors for a whole variety of careers; I studied physics/astrophysics but started my career in corporate research (graphics, compression, virtual worlds, UIs, etc.) before pivoting to web search, then cluster computing, and now distributed data infrastructure at a social-networking company. (I did embedded Linux in there somewhere, too. :-) ) Perhaps the most important thing is not to limit yourself too much, too early; flexibility and a willingness to keep learning new things throughout your career (and to take chances when new, "weird" opportunities arise) will serve you well.

If you are interested in applied mathematics, you might want to check out the website BeAnActuary (http://beanactuary.org) beanactuary. An actuary is a business professional who evaluates risk, often in an insurance company. There are also more nontraditional opportunities for actuaries because risk is so much a part of modern life.

If you like what you see on the website you should know that you need to be a self starter as an actuary, so you can pass the exams required to get the credentials while you are also working in a business environment. But you don't have to go to school beyond an undergraduate degree to get these credentials.

Hi Seth,

Excelling in math is a great starting point! My son, a high school senior, was in a similar situation when looking for colleges and he investigated careers in Engineering and Finance. Yes, you can major in finance and math, what opens the doors e.g. for investment banking. These are very much on the opposite spectrum of the scale but provided him a good contrast. Most colleges have both schools, business and engineering, and many provide a path with a major and minor across both fields. In the end, he decided to apply for a Computer Science Engineering major because he felt this field provides him more opportunities for an entrepreneurial career. He still plans to do internships in large corporations to see both worlds.

A good way to look at it is to do where you are your best. Being your best in your career has a lot to do with doing what you love.

Good luck,

Andrea