The Arabic empire, like the Roman empire, adopted science and mathematics far beyond their own home-grown intellectual abilities from the classical Greeks. The Arabs did fairly well with it, and even made some improvements, for a few centuries, but then fell into cultural stagnation.
Yes, they made the mistake of letting their clergy call all the shots.
A mistake I hope we never make, judging from some of the bile on this thread.
To be precise the Muslims took it from the conquered Byzantine Christians (Greeks, Arabs and others). As Christian population declined first economicaly and then numerically, the Muslim civilization did too.