In the context of classes, it is very often that discussion on the history of mathematics arises, whether it'd be on who should a lemma be attributed to or a certain event that occurred during the discovery of the proof (the elementary proof of the prime number theorem is one such example).
My question is:
What does a math historian do? Is he simply a mathematician who dabbles in search for the history behind his research or does he commit his time fully investigating past mathematical facts? Also, is it closer in nature to mathematics or is it closer in nature to history (i.e. is the context behind the discovery of the proof emphasized or is the insight that led to the proof emphasized)?
EDIT: Due to the nature of some of the answers, I am now curious to as to whether math historians are mathematicians or historians (ie do they work in math departments or history departments). Does anyone have an answer to this?