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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.