I did something like this to study math after a startup exit (so money wasn't an issue), around 2005, well before the recent spate of free online courses. I did a combination of self-study (reading books), informally sitting in on classes in the local university, and some small study groups I organized. That was all well and good, but it eventually became clear I'd make much faster progress in a more formal setting, so I went back to school. Formal deadlines are a powerful motivator. Also, reading math is hard and conversations with experts can often speed along understanding. Five years later, I'm in my 3rd year of grad school in a pure math program.