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What are you referring to?

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

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.

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

Yup, and that’s a direct side effect of Gödel’s incompleteness theorems.

Just one: does daddy love me?