Intelligence is not easily demonstrated.
It is not demonstrated by sterile memorization and recitation of dry facts and figures.
It is not learning the names of all the element, completing a rubix cube, knowing your multiplication tables or naming every state.
Intelligence is ADAPTIVE. It is the ability to find understanding and pursue exigence in the face of minimal information or compounding and confounding inputs that are muddy, unclear, inexact elements and data points.
Intelligence is solving a novel problem, in a novel way.
When intelligence is unavailable people often fall into patternicity, a term invented by Michael Shermer. This term describes what often occurs in the minds of simpler people, where they struggle to produce understanding from sources they cannot derive understanding from and that causes them to SEE patterns where there are none. In a desperate attempt to MAKE SENSE out of what may indeed be senseless they CREATE truth out of gibberish, signal out of noise, and this is all done in service to ego.
The human ego DEMANDS this make sense, DAMNIT. and if it doesn't, then i will MAKE SENSE OUT OF IT. If i cannot, that must mean i'm stupid, and i can't live with that truth.
No one wants to be stupid. No parent wants their child to be stupid. At one point in social being stupid really was that proverbial scarlet S that no person could bear the shame of.
That time is gone.
You see, patternicity is common in conspiracy theorists. That makes it useful to despotes and propagandists. That makes the simple minded effective tools for spreading misinformation, nonsense and imagined signs and signals from the sea of random noise.
Intelligence is suspecting your source could be wrong or compromised. Knowing that that data could change as new information is discovered.
Intelligence is knowing that you cannot, do not, will not, EVER know everything.
and having the lack of ego and the wealth of understanding to be confident enough to live with that.