I've been having a nagging thought. I've just recently switched from CompSci to Math and while research is important for a CompSci student, research is pretty much *the goal* for a Math student. So getting into a research program would probably be my main goal from now until graduation. But I'm not going in without a backup plan. I'd like to know: what could I do with myself if I can't get into undergrad research? Is it possible to do math research on your own? Ignore the naiviety of that question for a moment. What prevents individuals from submitting academic papers without a college backing them? Okay, you do need some experts reviewing your work. And yes, I know it would be time consuming, but I'm betting that grad schools will be competitve. And I'm not a charismatic genius that can sway faculty to take me on. I just want to have some papers in my name when it comes time to apply for grad school, and I'm willing to put in the extra work to make it happen. How crazy would it be if I started tackling problems undergrad research problems and at least blogging about my attempts, if not just submitting something to arxiv when I'm ready for it to be reviewed?