I know that getting into graduate programs, in any field, without first having an undergraduate degree is extremely rare. But it's not unheard of. I dropped out of school well over a year ago and going back is absolutely not an option. I don't have the money but even if I did, there aren't any schools with good math programs in my city and state. Moreover, I was not a math major in college so I would have to take a bunch of classes on topics that I have already learned on my own. What is the most important factor in being admitted to a Phd program? I can conduct research on my own, but how important is that relative to grades, test scores and letters of recommendation (none of which I have, obviously)? Nor am I talking about the very top schools. I mean, maybe one of the schools ranked below the top 25 in U.S. News and World Report. Do you think such a feat is possible by producing an original, albeit not spectacular, result?