Arraya: As far the scientific, medical and mathematic advances under Islam: There is a lot of credit claimed here, but I would also point out that, from a historical vantage, quite a few of these advances were the product of non-Islamic talents (including Jews and Christians) operating within Islam’s confines. Not saying this to take anything from Islam during that period, just making a point.
Also, I’d be curious as to your thoughts about the Mongol Empire(s). Often overlooked by historians, there were tremendous innovations that occurred under the various Khans and Khanates and many people forgot that the Mongol Empire existed until the early 20th century.