I was in exactly your position nine months ago (applied math rather than pure math). I was geographically limited by where I looked for faculty positions, and while I got interviews, they never led to offers.
As mathematicians we have an advantage compared to other sciences: our research is often not limited by a lack of funding. Not sure what side of pure math you do, but my guess is that to get work done all you need is pencil, paper and laptop. Get yourself a day job, and treat math as a hobby. Work on hard problems that you were too afraid to work on before, perhaps for lack of progress or a perception that "this problem is for people with job security". Publish as unaffiliated or, if you don't want to list your home address as your institution, incorporate and register a non-profit research centre that only exists on paper (I'm looking to do this right now, if only because it's an adventure in its own right). Or, as others have suggested here, try to get a job where publication is expected.
If a professor position is your dream, that's fine. But don't let the dream tie you down. You might find, like I did, that there are plenty of interesting careers outside of academia, many of which pay more (either initially, or have a longer runway of earnings potential), allow great work-life balance and provide superior benefits. And besides, there's no rule saying that you can't go back later. Industry experience is valuable, and depending on the industry you enter and the role you get, you might find that what you do is transferable if you decide to throw your hat in the ring for a tenure track job along the line.