I know multiple instances of math majors switching to non-math fields and easily getting good positions. I myself was doing fairly good research (improving on the current best technique for solving a problem that people care about) within 8 months of switching from math to robotics (although I also spent a year doing computational cognitive science in the time between math and robotics).
It sounds like the real issue is figuring out what field to go into. Personally I just tried a few different fields until I started to get a better idea of what was going on, and finally was able to narrow down to a shortlist of problems that I consider really important (probably similar to paulfchristiano’s, it looks something like synthetic biology, brain scanning / simulation, machine learning, environmental engineering, clean energy, and materials science).
If you ask yourself what you would like the world to look like, it is usually easy to at least differentiate between things that do a lot to move you towards that goal, and things that do very little; maybe at the top it is hard to figure out which research programs will be the most effective, but it is probably not difficult to find something that is more effective than what you are currently doing, which should be good enough from the perspective of deciding to switch.
Find a professor at your university that works in a non-math field but is still mathematically sophisticated enough not to bore you. Then take their class (assuming that it focuses on their research rather than being some sort of introductory-level class). Possibly you are unable to figure out if someone satisfies these criteria. If you’re willing to reveal what university you are at, and link to its course catalog, I can throw out suggestions.
I know multiple instances of math majors switching to non-math fields and easily getting good positions. I myself was doing fairly good research (improving on the current best technique for solving a problem that people care about) within 8 months of switching from math to robotics (although I also spent a year doing computational cognitive science in the time between math and robotics).
It sounds like the real issue is figuring out what field to go into. Personally I just tried a few different fields until I started to get a better idea of what was going on, and finally was able to narrow down to a shortlist of problems that I consider really important (probably similar to paulfchristiano’s, it looks something like synthetic biology, brain scanning / simulation, machine learning, environmental engineering, clean energy, and materials science).
If you ask yourself what you would like the world to look like, it is usually easy to at least differentiate between things that do a lot to move you towards that goal, and things that do very little; maybe at the top it is hard to figure out which research programs will be the most effective, but it is probably not difficult to find something that is more effective than what you are currently doing, which should be good enough from the perspective of deciding to switch.
You are right in that the real issue is figuring out what field to go into.
The thing about it is that I don’t really know how to taskify “trying a few different fields;” this is perhaps the soul of my question.
Find a professor at your university that works in a non-math field but is still mathematically sophisticated enough not to bore you. Then take their class (assuming that it focuses on their research rather than being some sort of introductory-level class). Possibly you are unable to figure out if someone satisfies these criteria. If you’re willing to reveal what university you are at, and link to its course catalog, I can throw out suggestions.