No blame to you, it's a widely-circulated misconception.
Our Arabic numerals are actually Hindu. I don't have the link, but you can Google it, and prepare to be as surprised as I was! ;)
Their advances in astronomy? Hogwash. They were blessed with clear skies. They simply named the visible dots. They did NOT invent the telescope.
Medicine? They reaped the benefit of some surviving Greek manuscripts when they overran formerly Roman lands.
They deserve little credit; they merely acted as an agent of knowledge propogation, but not invention. To date, they've done very, very little.
If I were a Muslim, I'd personally be very ashamed of the lack of advancement of my people. But that's just me. ;)
These Roman lands were densly populated with highly developed culture and learning. (It was Byzantium - the remaining part of Christian Rome).
Muslims at first were the small groups of barbarians ruling over the educated people. They did not need to search for the "some surviving Greek manuscripts" - they just hired the local teachers.