I do self-identify as a mathematician. I've worked abroad as well, and the amount of math I was able to do while working full-time abroad was a very small fraction of what I've been able to do while employed as a graduate student. Maybe I didn't have enough discipline, but I was usually exhausted at the end of a day and needed the weekends to recharge.

I think this applies more generally to any intellectual output. There are people who can be intellectually productive even when they have a near full time day job. I'm not one of those people. Academia or a research position it is for me.