I imagine that there are three kinds of "unsolved" problems in mathematics: problems that are unsolved because people have tried and failed to solve them, problems that people haven't yet tried to solve but aren't particularly difficult to solve once attempted, and problems that both haven't been tried but would likely result in failure anyway.
How much math does one have to study before one has a reasonable chance of encountering a problem of the second type - one that an "average" tenured mathematics professor at an "average" university of no special prestige is likely to be able to solve once the problem is brought to their attention? Do they even exist?
I would guess that there are many problems that nobody cares about. Producing new problems in math isn't really that hard. Just add a new axiom to an existing theory and you have a bunch of new problems.
The problem is that nobody necessarily cares and so they won't cite you.
This is a thread where people can ask questions that they would ordinarily feel embarrassed for not knowing the answer to. The previous "stupid" questions thread went to over 800 comments in two and a half weeks, so I think it's time for a new one.