> I think you can be wise without being clever (having a high IQ).

I think it depends on how you define "clever". Does knowledge of things like how to sort a list correlate with cleverness?

I know wise people who don't have formal education, but I'd still consider them exceedingly clever.

I built a wood shed many years ago. I looked up the recommended roof slope and used trigonometry to calculate the angles of my cuts. The next time I made one, someone with more wisdom showed me that you could simply assemble a flat roof with joists sticking out both sides, raise one side until it seems right, and then run a circular saw vertically along the side to create a neat edge.