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Mathematician here (algebraic topology). Pure maths is pretty much an internship in academia. Applied math is anything between basically physics to actuary and finance. Since pure math is highly academic, though, there is no predefined job path following a degree, which is why the question is as interesting as it is hard to answer.
In academia, we do weird and wonderful things that only a few peers in the world probably will see and understand, due to the highly specialized fields of study. In industry, anecdotally, we do surprisingly little math and are mostly sought for analytical skills and proficiency in problem solving.
Sadly, most people that hire us outside of academia do not know much math themselves. I believe there are lots of real problems that could benefit from having a mathematician working on them, but there is just too little understanding of mathematics to identify the need.
Honestly I would love to hire a statistician to do the analysis on any clinical research I do. I just wanna collect the broset scores every shift and request and assign staff to best balance them then let somebody else count how many (hopefully less) people got punched by patients vs not doing that. No way even the research hospital would've paid for that though.