The Islamic world used to be a beacon of knowledge, culture and tolerance. They invented a lot of stuff still used today and AFAIK are partly responsible for illuminism. What happened to them? How did they become so impoverished and violent?
Quite a complicated question...
The history of the Middle East can be messy and complicated, so I will do my best to answer your question.
The Ottoman Empire started to dissolve in the 1800s, falling behind Europe in terms of military and economic power. After WWI, it collapsed and was divided among allied European powers, such as France and the UK. In these newly occupied states (Syria and Iraq for example), they established parliaments and constitutional governments. After the events of WWII, the European powers abandoned these Middle Eastern states allowing them to become independent, also leaving their parliament and constitutional governments behind and still intact. However, those left in charge were so inept it lead to them being overthrown and dictators being installed in their place. These dictators only cared for themselves and did very little, if anything, to improve the lives and conditions in the Middle East. Anti-Western sentiments and wars with Israel did not help.
So, in short, the Middle East is no longer the cultural center of the world due to European Imperialism and incompetent rulers after states such as Iraq, Syria, Lebanon, Egypt, and Jordan became independent.