I am always amazed at how some of the most vexing, curious and fascinating puzzles in mathematics can be stated so simply, even as they evade solution or even complete understanding for centuries. It is one of the more alluring aspects of this trade.
Here's one: Just how big can the gaps between consecutive pairs of prime numbers get as one traverses the natural numbers out toward infinity?
One would expect the gaps to get larger and larger and also tend toward infinity in the long run, no? But showing this, and providing some sort of measure of the growth of the size of the gaps as one goes "out there" has been remarkably elusive.
I'll let you read this nice article by Erica Klarreich in Quanta Magazine, to "see" that progress has recently been made, and there is promise of more progress coming.