[Keysh]

No, Baghdad was located in the heart of the former Persian (Sassanian) Empire, a mere 35 km from the site of the Sassanian capital (Ctesiphon). Although the whole area gradually became Arabized, at the time it was still significantly Persian.

(Frankly, I doubt we know where Al-Khwarizmi was educated. We know he was originally from what's now Uzbekistan, and that he ended up in Baghdad, but not much more than that.)

[notinpersia]

He wrote his treatise on Algebra in Arabic because he was educated in Arabic and the language of science was Arabic in that area and at that time. AlNassirya in Baghdad was the most advanced educational institution in the world at the time. I don’t know if he was a student or teacher there but it also has an Arabic name and was built by an Islamic caliph. The same with mathematicians from India traveling all the way to Baghdad to tell the caliph about their invention of zero. Persians has many amazing contributions to science and math but Persia itself has none. Like the Romans, they were war mongers and Their culture was toxic to science.

[csomar]

> No, Baghdad was located in the heart of the former Persian (Sassanian) Empire, a mere 35 km from the site of the Sassanian capital (Ctesiphon).

Mesopotamia was conquered by Arabs in 633. Al-Khwarizmi was born in 780. Most the Arabic lands were gained by conquest. Even modern day Yemen and Oman were not under Arabic influence if you go back far enough. The "original" arabs spread from Hijaz and Najd.

edit: from wikipedia

> The Abbasid Caliphate first centred its government in Kufa, modern-day Iraq, but in 762 the caliph Al-Mansur founded the city of Baghdad, near the ancient Sasanian capital city of Ctesiphon.

My guess is that families from the Sassanid have immigrated to the new city and as a result Al-Khwarizmi was born there.