First off, I have no interest in being a mathematician. Math was always and continues to be quite difficult for me.
So, as an outsider to advanced math, it blows my mind that there are people who’s entire job title is mathematician. How does that work? What does a mathematician do?


From my, admittedly limited, interaction with mathematicians in my life and a bit of extrapolation:
There’s a lot of overlap between all three but I roughly split them up based on where I’d expect the majority of jobs like that would be (e.g. I’m sure NASA employs a good deal of mathematicians, but so does Lockheed Martin and friends). Also a lot of people get a degree in mathematics and then specialize further with a masters and/or doctorate in computer science or physics, since both of those can be quite math-heavy and are better-funded fields.
does DSP count as maths, because there’s plenty of that in radar design. or any other sensor with some double-use potential for that matter
I wouldn’t count it as just math. Probably more science or engineering. I did some DSP stuff during my computer engineering degree. But then again, science is applied math and engineering is applied science.
CS and advanced statistics is what lots of applied math is anyway