I was watching Ancient Discoveries last night about the significant contributions
to Science and Engineering from the Arab world.
Most of these advances were between 900 and 1500 AD
I have read stories about European travelers in the 15the century
marveling at how refined the culture of Spain was
compared to the rest of Europe.
I wonder what changed in the Arab world that slowed or stopped their
desire to advance Science?
There are many aspects here.
1.) The "Christian" European powers were dominated by the Catholic Church and the Vatican. The leftovers of the Roman Empire were weak politically and economically. It was called the dark ages for a reason. This mean the religious dogma as dictated by various crack pop Popes and other religious "scholars" out of Rome and locally dominated politics during the the years you listed. Among the things brought to us in this marvel of ignorance was the anti-scientific aspect of the Christian faith.
2.) The Islamic world on the other hand was just starting out and growing.. both through conquest but also by peaceful means. While the Christian church went out of its way to rid it self of the knowledge of the Romans and Greeks, the Islamic world embraced it and saved much of the knowledge from destruction. One of the biggest havens of knowledge was Al-Andalus, which by many historians is seen as one of the glowing jewels of civilization in human history. Al-Andalus was for centuries the center of knowledge for the whole world (well European areas and Middle East and Africa) and scholars, both Muslim, but especially Christian and Jewish, flocked to the courts of Al-Andalus who welcomed them with open arms. All this created an atmosphere to for more inventions and knowledge to be created. Yes think about it.. Jews, Muslims and Christians lived in peace and almost equals (Jews and Christians paid more in taxes) for centuries in Al-Andalus.
3) The reformation came around and the Christian Church was split which resulted in bloody civil wars that cost millions of lives. The French Religious wars are estimated to have cost 10-30% of the population their lives. In the end the Catholic Church was split into the Orthodox Church and the Protestant Church (and a bunch of other smaller groups) and Europe was some what divided up. The Byzantium Empire to the East was the cradle of the Orthodox Church (and soon to fall), the Vatican was the cradle of the Catholic Church and dominated Portugal, Spain, what is known as Italy today and had serious influence in France, Austria and parts of what is known as Germany. The Protestants moved into most of Northern Europe, UK, and parts of France. Point is that Christianity had its civil war, and came out in a stalemate. By the time the civil war was over, the Islamic world was at its pinnacle and the Christian Kingdoms saw something they wanted and went after it.
4.) Lack of a reformation in Islam. This plagues us even to this day, and ultimately cost the Islamic world its domination. The Ottomans unified the Islamic faith under their Sultan by taking over the mantel of Caliphate in 1517. For centuries the Ottomans were the major power in Europe. But complacency and wars and the complicated tribal nature of their empire plus the added flair of religious disagreements within Islam ultimately lead to the downfall of the Ottoman Empire and hence the the Islamic world domination. And then Atturk happened. In 1924 he dismantled the Ottoman Caliphate.. the only thing that had held together the Islamic world and driven it for centuries to excel.. and we all know how it has gone since then.