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?
I always thought of maths as a language, and physics as using that language to describe everything in the world. I often describe my physics degree as a degree in problem solving, so a maths degree would be similar but more abstract problem solving. So for jobs just about anything that is technical or requires abstract thought.