Hi Koot. I see what you're saying, however, Baghdad is not Persia any ways. I mean mesopotamia/Iraq/babylon et al was not persian seat of rule only a vital province anywyas. Majority of the population element was mixed but non persian such as Medes (possibly ancestral to Kurds), assyrians, Chaldeans, jews, babylonians (aramaic speakers) etc..until the peninsular Arabs conquered it and Arabic became the lingua Franca. Besides the Abbasids (Caliphs of baghdad) were still sunni Arabs. And look at Khwarizmi's last name it is a good indication from whence the name came unless we want to beleive his family was one of arab traders who settled in central asia and then migrated back. Such things were not uncommon and many arab s Jilanis, Wastis etc..did venture forth mostly as traders or refugees then back. But that is speculation. But saying he was persian is as inaccurate and insensitive as saying Avicenna was Arab. I think it is not unreasonable to have the intro state that "AK was a Chorosmian muslim math. and phil." 
 omerlives