The Barmakids were like The Medici’s in Florence who financed translation of alexandrian Esoteric books into Latin in the 1400s The Barmakids created a vector of intellectual ferment in Baghdad. Which lasted through the scientific revolution of the 800s. Baghdad soaked up the Alchemy and Occult tradition from the Greek Neo-Platonists who had taken refuge in the persian Academy of Gundishapur, which itself was the Plato’s Athens Academy in exile. TheEgyptian Occult and Alchemy traditions were also introduced into Islam through this vector.

The Indian Decimal system revolutionized Mathematics, giving Baghdad both Algebra and Bookkeeping. 

The following excerpt reprinted from http://en.wikipedia.org/wiki/Barmakids#

[The family came from an influential buddhist family in Bactria] They converted during the invasion of the Buddhist and Zoroastrian city of Balkh. They were highly educated and respected intelligentsia in Central Asia and the Levant. In Baghdad the court of Barmaks became a Centre of patronage for the Ulema, poets, scholars alike. (…)

Many Barmakids were patrons of the sciences, which greatly helped the propagation of Indian science and scholarship from the neighbouring Academy of Gundishapur into the Arabic world. (…) They are also credited with the establishment of the first paper mill in Baghdad.