1. They gave us the word Byzantine.
2. Arab expansionism gave them control over vast regions and their sedentary populations; they co-opted the bureaucrats and academics to help them run and build a new empire; the academics secondary pursuits included preserving their libraries and translating them for their new overlords.
3. Money and generosity attracts academics.
4. One thing the West was better at was in telling stories, whether they were true or not; that's why we have great epics to inspire us. The public relations machinery of the Byzantine Empire needed work; there might be sympathy, but no empathy for them.