For real though, I feel like "mystery" is the wrong word here.

Mystery requires a certain level of intrigue to me. "P=NP?" is, at its heart, a pretty straightforward yes-or-no question that would not be difficult to explain in not-fully-rigorous-but-gets-at-the-essentials level to a bright middle schooler.

It's just one where we don't know the answer. But not every unanswered question meets the criteria for a mystery!

I think a good example that gets at the essence to me is Fermat's Last Theorem.

FLT, to me, is a proper mystery. But not because of the actual theorem. (Wiles' 1993 proof is generally accepted.)

The mystery was not "is this true or not". The mystery was "what was the truly marvelous proof that Fermat's margin was too small to contain?", and like a proper mystery, we may never know. (Also, that proof - like most other attempts at it - was almost certainly wrong, but that doesn't even matter.)