You can be useful and sentient to others in any position. If you really want to be a teacher route, do so. Teachers have more impact on their students than most other professions do, but that doesn't mean that you won't ever benefit others from a profession as a mathemetician. Trust me. Besides, I can see you (whatever you do) writing a book in your spare time and making millions off of your views on life and interesting thoughts you come across (kinda like these journals). But whatever you decide to do, you can be useful. And I can't really see you as anything OTHER than a math-related career anyway.
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