Therein lies the best career advice I could possibly dispense: just DO things. Chase after the things that interest you and make you happy. Stop acting like you have a set path, because you don't. No one does. You shouldn't be trying to check off the boxes of life; they aren't real and they were created by other people, not you. There is no explicit path I'm following, and I'm not walking in anyone else's footsteps.…
Hamming would be against that.
Maybe for him these two were the same. There is something cold about his recommendation, though. I'm not sure what motivated him. Impressing himself with important discoveries? I never in all his talking about missile trajectories and weapons-related work came across any evidence of ethical considerations. Godement's Algebra with its inspiring political and ethical conscience - its author was man as well as mathematician - made me vividly aware of how a work of mathematics/physics can either be ethical, or it can pretend that ethics are not its concern. Or rather, like a heartless child, act without ever even considering consequences. Maybe Hamming was just working on the important problems in his field, and disregarding all else, and thought that was enough.