Causal inference! (I am half joking.)
As someone who gave up a career in medicine in order get a doctoral degree in Causal Inference, I am half-upvoting this, because I really want it to be true :-)
I originally trained as a medical doctor, but came to the conclusion that what I was doing had almost no value on utilitarian grounds. Sure, once in a while you feel good about helping a patient, but really, if you weren't working that day, somebody else would have done the same thing. I decided I would rather have my one-in-a-thousand chance of coming up with an original idea with real impact,...
A high school student with an interest in math asks whether he's obligated on utilitarian grounds to become a doctor.
The commenters pretty much say that he isn't, but now I'm wondering-- if you go into reasonably pure math, what areas or specific problems would be most likely to contribute the most towards saving lives?