Caliph in Constantinople: Hellenized Islamic World ATL
The Arab conquests of the 7th century, brought the Islamic world into contact with Hellenistic culture. As Islamic armies swept into Egypt and Syria, the Byzantines left behind strong elements of Greek math, science, and most importantly philosophy. The Muslim reaction to these Greek influences was mixed. Arab philosophers such as Averroes and the Mu'tazilites embraced Greek reason. By contrast the followers of Al- Ghazali and the Ash'arites began a campaign of deHellenization. During the 8th century the Mu'tazlites achieved supremacy under the patronage of Abbasid Caliph Al-Ma'mun and his immediate successors. This however did not last long and the Ash'arites gained power and would remain in full control to this day.
This then brings us to the question of what if the Islamic World embraced Hellenism? How would this have been accomplished?
Averroes being more popular then Al-Ghazali?
A stronger Abbasid Dynasty that fully embraces the Mu'tazilites?
Byzantine Victory at Battle of Manzikert in 1071? Byzantine resurgence might help the spread of Hellenism. Seljuk Turk leaders Alp Arslan and Nizam al-Mulk were also big supporters of the Ash'ari.
Neo-Mu'tazilite movement?
Ok, let me point out some things.
As I annoyed my students to no end about, things far more complicated than that.
1) Hellenic culture was mediated by (partly) Persianate and Aramaic milieus historically - it passed more through Iraq than Syria, precisely because in Syria it was more deeply rooted and, therefore, politically suspicious to the conquerors (again, this is oversimplication, but still Iraq was the center of Islamic Hellenizing).
2) Hellenic culture was emphatically viewed as completely detached from present Byzantines. Islamic sources clearly state that "Ionians" (the Ancient Greeks" and "Romans" (the Byzantines) were different peoples. "Ionian" is very frequently referred to as a completely dead language. Indeed, the Abbasids made a point (revamping a late Sassanid tradition, as Dimitri Gutas demonstrated) about THEM being the true inheritors of the old philosophical wisdom, as opposed to those narrow-minded endarkened Christians in Constaninople. There is even argument (although that's controversial) that the Arabic interest in older Greek cultures was the main cause of the renaissance of philology in the Byzantine Empire itself around the time of Photius (I am agnostic on the matter).
3) With a POD under the Early Abbasids at latest, you obviously won't see either al-Ghazali or Averroes.
4) The Abbasid-Mu'tazilite connection never stood a chance. The Mu'tazilites valued rational reasoning over communal consensus (oversimplistic here again). This was politically dangerous and conducive to discord within the community, and was opposed on that basis. Unless the Mu'tazilites were willing to reconsider a LOT of their epistemology, they were bound to remain an intellectual movement without mass following.
5) The Early Abbasid caliphs' views on religion, community, and their own role are a fascinating mess. Crone's reconstruction in
God's Rule has the big merit of making sense, but I am not sure I buy it. Short summary: each major caliph had his own view, different from the others and, in a couple of cases at least, evolving dramatically during the reign. This is particularly true of al-Ma'mun. None of these views, as reconstructed by Crone, fit easily in what would become the Islamic consensus (stabilizing at that time or shortly thereafter). No Abbasid was a committed Mu'tazilite either, including al-Ma'mun (who, if anything, appears to have been a very odd sort of Shiite).