The Climbing Magnets Mystery (ft. Steve Mould)

From 1veritasium, 2veritasium, or sciencium.

When spun on a screwdriver, magnets climb up its length, but why?
This video brought to you by my friend Steve Mould:

This all started with a question on twitter, when someone wanted to know why a chain of neodymium magnets climbs up a screwdriver when the screwdriver is rotated. A search for the explanation ensued, culminating in the stick-slip conclusion presented in this video. Let us know what you think in the comments.