Zayn al-Abedin's son, al-Bakir, and al-Bakir's son, Jafar al-Sadiq taught at a university (in Medina and elsewhere) believed to be 25000 students strong at its peak.
Indeed a majority of Islamic theological offshoots, including the largest one in Hanafi Islam, take root in this university.
Jabir (latin: Geber) is perhaps amongst al-Sadiq's famous students. He invented modern Chemistry. al-Sadiq's students believed to have written cryptic books on al-Kimia (Alchemy), and in a way, writing such esoteric books in a cryptic manner gave rise to cryptography as a medium of securing text and thought.
The Ummayids, who ruled from al-Shaam (Syria), disliked these Alids and their universities and everything they stood for (especially in terms of religious authority) and heavily persecuted them. The Abbasids, who pretty much came to power after a bloody rebellion in support of the Alids turned out to be worser in their treatment of Alids than the Ummayids.
In the face of Abbasid cruelty, the Alids retreated to al-Misr (Egypt) and ruled from there for around 300 years over the Magbreb (Northern Africa), parts of Italy, the Levant, Hejaz (Western Saudi Arabia), and Yemen whilst the Abbasids ruled the rest of the Middle-Eastern Islamic world from Iraq.
al-Rashid's House of Wisdom (Dar al-Hikma) was allegedly setup as a counter to the one run by the Alids of Egypt (who were now known as the Fatimids). It was alleged the Fatimids amassed a lot of wealth due to their knowledge of Alchemy.
A rebellious offshoot of the Fatimids under Hasan al-Sabah, a student of the Fatimid House of Wisdom (Dar al-Ilm), would later fight in the Crusades and come to be notoriously known as the Hash-Hashins (or the Assassins).
With the rise of the Turks and the Mongols sealing the decline of Abbasids of Iraq, Safavids of Iran, and Fatimids of Egypt; the Islamic Golden Age would rather come to a swift end.
A physical embodiment of Baghdad's Dar al-Hikma hasn't survived but that of Cairo's Dar al-Ilm lives on in al-Azhar, which is considered to be one of the most (if not the most) important Islamic universities even today.