> Since Gödel, science even proved itself as incomplete. The best doctors will always say that if something makes you feel better, by all means do it, even if it is not backed by science.
Gödel proved mathematics to be inconsistent. This has much greater implications than just proving scientific inquiry to be insufficient. Science relies on the senses for its reliability and is grounded in the physical world. Mathematics has no such bounds.
Given a "complete" formal (scientific!) understanding of the physical world, we still wouldn't know everything, there will always be systems that intersect with it that inform our world, but can't be understood using our rules. No matter how many formal systems we define to wrap our collective brain around the world, there will always be more things to understand.
That's the significance of Gödel.
