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?
In the very old times, you’d have to be born rich already to do maths. You then don’t concern yourself with making a living, because your slaves do it for you.
In the old times, you’d live the same as artists: find a rich dude (exceptionally rarely: dudess) to pay your bills, and in exchange name shit you discover/invent after them.
Last few decades you also have a couple new options. You can work (teach) at a university for pennies, and typically have a second job/side hustle so that you can actually survive. And/or you can write books/make a YT channel, and if you’re lucky and get popular enough, that can be your living then, but it’s probably not going to be anything too advanced. And/or, if your area of expertise has some vaguely practical application (e.g. cryptography or statistics), you can actually find a job that pays you to do theoretical research in that area in hopes of finding practical application, but you’d have to be pretty lucky to get that.