The manifold wisdom of God is something of studied inquiry by heavenly beings. It must be that there is something about the revelation of God’s saving purposes that is an object of longing for the angels. The apostle Peter said:
“It was revealed to them that they were serving not themselves but you, in the things that have now been announced to you through those who preached the good news to you by the Holy Spirit sent from heaven, things into which angels long to look.” (1 Peter 1:12, ESV)
This is what makes the angels ache.
The church in all of its folly is still the displayer of the manifold wisdom of God towards these heavenly beings. (Ephesians 3.10).
They are not satisfied in their researches until they see the plan for the church consummated.