Actually... they weren’t exactly “leading”, either. What they had was a lot of knowledge that was lost with the collapse of the Western Roman Empire and that they’d begged, borrowed, or stolen from cultures further to the East. Almost none of their vaunted cultural, artistic or scientific knowledge was actually developed by their culture. Algebra was stolen from the Hindus; mosaics were stolen from the Greeks, their medical science was stolen from the Chinese and Hindus... And so on.
The Arabic/Islamics took all this stuff, filed the numbers off, and passed it out as “their inventions”. They also wrote great works about their supposed developments that turned out not to be true (much like the bragging on Egyptian carvings, come to think of it).
Later medieval European chroniclers took what the Islamic/Arabic scholars told them as the honest truth, and that’s how it’s recorded in Western history.
*Eastern* history tells a *very* different tale.
In case you’re wondering why Islam seems stuck in the 13th or 14th Centuries, it’s because it is. They annoyed their neighbors by decapitating their ambassador and then sending the head back home in a bag with a “whatcha gonna do about it” note.
Ghengis Khan was greatly displeased and showed them what he was going to do about it. In the process, thanks to both Mongol thoroughness and the true stupidity of classical Arabic combat traditions, all the leading lights, smartest and brightest of the culture went out and got themselves killed off.
Ah, Hulegu Khan was a good egg...