In ZFC, everything is a pure set, and because the necessary amount of arithmetic for the Gödel's incompleteness theorems to go through is interpretable within ZFC, there are undecidable statements about sets as well.
This really blows my mind, because there are not only number-theoretic facts beyond our reach, but also relations between sets that are true but unprovable.
These may not be interesting questions about sets, but still.
My question: are there interesting relations between mathematical objects other than sets that are true but unprovable because of Gödel's incompleteness theorems?