I'm currently working on a Ph.D. in Mathematics right now, and I am also hoping that I can steer my research activities towards things that will do good. Still not sure exactly how to do this, though.

Hi Adele. Given what you write in your introduction, it's likely that you have already heard of this organization, but if this is not the case: you may want to check out 80,000 Hours. They provide evidence-based career advice for people that want to make a difference.