What's your standard for unsolvable? I would say that a statement that's independent of ZFC but can be proven in ZFC+Con(ZFC) isn't truly unsolvable - anyone who uses ZFC should clearly accept such a statement as true. But it is impossible to prove it in ZFC, so this leaves us with two possible standards: Does the statement just have to be undecidable in ZFC alone, or does it also need to be undecidable in any system of axioms that a user of ZFC should accept, like ZFC+Con(ZFC), or ZFC+Con(ZFC)+Con(ZFC+Con(ZFC)), etc.?

Another thing to consider is whether new axioms that become accepted by the majority of mathematicians should be considered. For example, what if some new axiom, A, becomes widely accepted, so much so that ZFC+A becomes the standard system of axiomatic set theory. Should it then be required that the problem must be proven independent of ZFC+A to count as undeciable, or would it still count even if it is only shown to be independent of ZFC, because that was the standard system when this question was written?

Are any Millenium Prize problems undecidable/unprovable/unsolvable?, 8k, beautiful, illustration, trending on art station, picture of the day, epic composition