In math:

Whether an algorithm run on a Turing machine will halt.

It’s also known that there are true mathematical statements, than can never be proven. As in, they are definitely true, but we will never rigorously know for sure.

https://yewtu.be/watch?v=HeQX2HjkcNo

It is proven that some mathematical questions can never be answered. This is known as Gödel’s incompleteness theorem. Veritasium made a nice video about it.

Just one: does daddy love me?

What are you referring to?

To broadly answer your question, to name a few, there are…

• paradox questions (eg - what happens when an unstoppable force hits an unmovable object)
• impossible scenarios ( eg - what would happen if Hitler rode a dinosaur as a child)
• questions we may be able to answer in the future, but cannot at the moment (eg - p vs NP)