Never forget the power of marginal contribution. Instead of becoming a doctor you can help several people at the edge of becoming a doctor. Even if this happens only once you are already more successful than by becoming a doctor yourself.
Of course, if a lot of people are already doing this. you need to find something else to do.
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?