No, this is more about the philosophy of mathematics -- the question of "to which degree is mathematics 'real'?" Gödel did have an impact on this, with formalis

No, this is more about the philosophy of mathematics -- the question of "to which degree is mathematics 'real'?" Gödel did have an impact on this, with formalism no longer being a particularly viable viewpoint. But this is less of a strict mathematical question and more of a philosophical one.