[jacobolus]

From observation, some of the people I know who were sharpest at learning new technical subjects and solving hard technical problems were way behind as undergraduates compared to folks who were not as good at problem solving but had been steeped in a technical culture from a young age, and as a result the newcomers had to work a lot harder to catch up.

“Easy to teach” comes from understanding your vocabulary and references, having seen similar material before, not being confused by severe misconceptions, coming in with similar mindset, etc., not necessarily from being the best at new research (or whatever other real work task).

Someone who is a 4th generation mathematician is going to be completely comfortable talking about mathematical topics in casual conversation, irrespective of any genetic differences.