In academia they are paid to produce papers (and get some chores done like teaching), hopefully ones that can result in bombastic press releases, or winning awards.
On a more abstract level they are paid to bring funding and prestige to the university, but that often goes through the route of papers. And papers often involve proving theorems.
Actually, no. They are hired to do research but not paid for it. They get a 9 month salary to teach, not for research.
They have to publish papers to get tenure but the university doesn't pay most math faculty for it.
If they want to get paid for research they apply for grants and get the max of a third more salary.
Most other departments make getting grant money a prerequisite for tenure. Math departments typically don't.
So in most math departments faculty members don't bother with grants. Usually only a minority of them do because they want more money.
They're not paid to do research.
I consider "get paid to do X" to be equivalent to "you get to have your paid job and career as long as you do X". In that case research and papers qualify. Whatever is technically written in the contracts is just surface level bureaucracy. Publish or perish.
> I consider "get paid to do X" to be equivalent to "you get to have your paid job and career as long as you do X". In that case research and papers qualify.
Actually, it doesn't. Both math departments I'm familiar with had faculty members who published only to get tenure, and never published again until they retired.
But if they didn't teach (or taught extremely poorly), they got fired, even though they had tenure. If you didn't show up to a scheduled class a number of times, you got in trouble.
I know you weren't saying this, but it's frustrating reading so many comments about mathematicians "getting paid to have fun and good riddance". No - the majority of what they do is teach non-math students. If people here don't like that, by all means dissolve the departments and have the engineering departments teach math.