Who is a Math Historian? 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?
 A: First of all, as far as I know,   serious historians of mathematics are or were in their majority mathematicians: the reason is that mathematics is very difficult and you can't analyze it in depth without   a very serious technical background.
There might be exceptions for very ancient  mathematics, but even there I wouldn't trust a historian studying Diophantus who wouldn't have some knowledge of arithmetic/algebraic geometry and number theory.
What often happens is that aging mathematicians start writing about the history of the subject they have devoted their life to.
Prestigious examples are for example:
Weil on number theory,
 Dieudonné and his wonderful histories of algebraic geometry and  algebraic topology,
 Marcel Berger on differential geometry,
Dickson and his monumental history of the theory of numbers.  
Younger mathematicians may also be interested :
 Bourbaki has very nice historical surveys at the end of some of his chapters, written at the time by necessarily young members (there was an age limit for participants)
  Schappacher is an excellent research mathematician who already as a young researcher wrote about the history of number theory,
Krömer has written a great thesis on the genesis of category theory (including  the incredible  beginnings of sheaf theory  in a prisoner of war camp ) ,
and to finish on a personal note, here is the fairly recent thesis on the birth of group cohomology by Nicolas Babois, whom I taught at the  undergraduate level (but I had no rôle in his thesis). 
In conclusion, my point of view is that a historian of mathematics is essentially a mathematician, and historical science  in the usual sense is of secondary  importance.
This is certainly controversial.
 My convictions  on this subject essentially derive from  Dieudonné's and Houzel's points of view. (Houzel is an other example of a  mathematician with high technical skills attracted very early by the history of mathematics)
A: It depends on the historian. Most historians of mathematics probably have deep associations with mathematics in some way, but being a mathematician it is not required any more than a sports historian should be a professional athelete. But surely the more mathematics one knows the more one tends to appreciate its history.  
