Yeah, and it's hard to get exposure to areas that might be fertile for inquiry if you aren't spending time with other people who are working on mathematics. It'

Yeah, and it's hard to get exposure to areas that might be fertile for inquiry if you aren't spending time with other people who are working on mathematics. It's a social networking effect, in the same way that you pick up programming tricks and get exposure to new frameworks/languages/techniques by spending time with other developers. I'm sure there is a sizable number of "amateur" mathematicians who work on problems in their free time, but it is hard to know what to work on and where to look.