I know of no research to back up the statements which follow - they are based soley on observation and experience. The most scholarly of you may skip this or read on in amused skepticism.
In music it is a well-known and commonly observed fact that being a great player has absolutely no bearing on ones ability to teach. Conversely, many of the best teachers are only mediocre players. A student musician showing exceptional talent and ability will generally undertake a quest to find the teacher that is both a great player and a great teacher, but until such a person is found this student becomes adept at teaching themself.
Why would one expect mathematics to be any different ?
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