Searched: I've searched the history math, a timeline of math, proofs, theorems, ect. - I've been finding a lot of stuff on when things were discovered or solved, but I'm not sure how helpful that stuff is. Especially since my knowledge of math in real life only goes as far as *extremely* basic algebra, at best. So, my questions:

1.) What kind of mathematical quandries would fit the bill of "it's just sitting there" and possibly "really useful", but also "unsolved" at least in the Dark/Middle/vaguely-medieval-enough-for-a-

2.) Even if there is something that "needs to be solved", what types of mathematical proofs, equations, ect. would be considered difficult, and thus a sign of extremely high intelligence or saucery to solve? If someone wanted to show off their brains, basically, what kind of math would they be putting on the table?

3.) Any other scientific, or even pseudo-scientific, challenges that someone could put on parchment and post on a wall you can think of, i.e. I'm thinking chess strategies? Anything which, again, would be good for showing off how smart you are to those around you?

Thank you!