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, instead of spending the rest of my career as a doctor, where my utilitarian impact would almost certainly be negligible.
I came to the Harvard School of Public Health intent on going into academic Global Health, but after I took an introductory course on applied causal inference with some basic DAG theory, that all changed. Partly, this was because I recognized the importance of Causal DAGs from reading Less Wrong. I ended up staying at HSPH to get a doctoral degree with some of the leading researchers in the field; this even allowed me to take a course that Ilya was a Teaching Assistant for (I ended up being a TA for the same course the following year)
Currently, my career plan is to get a faculty job at some school of public health, where I see my mission as taking part in a "reboot" of epidemiology and comparative effectiveness research, to cleanse it of the cargo cult science and magical thinking that is currently all too common, and train investigators in rigorous causal reasoning. I honestly believe that this could have a major utilitarian impact, because in the absence of randomized trials, proper causal reasoning about observational data is the only way we can learn how to make better clinical decisions that optimize patient outcomes,
( Hopefully, if I play my cards right, this career choice will also have the added benefit of giving me sufficient status in the medical community to get a real discussion started on some of the most horrific things that doctors do to patients)
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.
Unfortunately this applies to most new math results as well (perhaps not on the same day, but eventually).
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?