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Baghdad was not the intellectual center of Islam at the time of the Mongol invasion, that was Central Asia. Neither was the Mongol invasion dispositive, though it is significant that the Mongols razed cities whose irrigation systems were one of the ingredients for the high degree of technical and theoretical knowledge supporting the enlightenment.

As I commented elsewhere in the thread, there's a terrific recent history of all of this: https://press.princeton.edu/books/paperback/9780691165851/lo...