What the heck, it’s Friday, I might as well put up a little fun thing here. Over on the Maths In A Minute blog is a quartet of mathematics problems which anyone can understand on their first reading of them, but which are unsolved and which have been sitting there unsolved for generations.
There’s, realistically, no chance that you personally are going to solve them. While probably everyone has some mathematical talent, and anyone with the ability to reason is at least in principle endowed with the relevant tools, it’s not likely that you’ll find a path to solving them that hasn’t been tried and that’s failed before. But that doesn’t mean they’re not worth looking at and thinking about because you can nevertheless discover things you didn’t know before, and notice stuff about mathematics that you hadn’t realized. Even if your discovery only delights yourself, it’s still a delight to you.
(I didn’t run across this page myself, though could have; the Algebra Fact of the Day brought me to it.)