True Versus Provable

Can something be true and yet not provable? We look at the following is a quote from "What is Gödel's proof? - Scientific American"

QUOTE
Kurt Gödel's incompleteness theorem demonstrates that mathematics contains true statements that cannot be proved. His proof achieves this by constructing paradoxical mathematical statements.

To see how the proof works, begin by considering the liar's paradox: "This statement is false." This statement is true if and only if it is false, and therefore it is neither true nor false.

Now let's consider "This statement is unprovable." If it is provable, then we are proving a falsehood, which is extremely unpleasant and is generally assumed to be impossible. The only alternative left is that this statement is unprovable. Therefore, it is in fact both true and unprovable. Our system of reasoning is incomplete, because some truths are unprovable.
UNQUOTE

I said in my haste, All men are liars. (Psalm 116:11 KJV)