People like to say that arabics were more developed than europeans in middle ages. That's true until 13 century.
In other words, you have a problem with people noting that the Arab world was more advanced than the Christian world in the Middle Ages because you don't think it applies after the thirteenth century . . . which is basically the end of the Middle Ages. Yeah, Europe started to catch up with the Islamic world at the start of the Renaissance, thanks to the inflow of texts from the Islamic world. The intellectual flowering of Europe thanks to contributions from the Islamic world began in the twelfth century.
Arabs conquer most of Byzantines and found texts of greek philosophers. That allowed them to be as developed as byzantines.
The Byzantine Empire managed to hold on for quite a while. It lasted into the fifteenth century, when it was finally conquered by the Ottomans. Centuries of warfare and cultural exchange cannot simply be reduced to the Arabs conquering the Byzantines and stealing their knowledge.
That happened later? Nothing, they learned to repeat those texts. )
Not only did scientific innovation occur in the Islamic world, but it played a key role in the development of the Western world. The European Renaissance was build off both classical texts preserved by the Arabs and the scientific discoveries and inventions of the Islamic world.
Why do you think that the word "chemistry" has an Arabic origins? Have you never heard of Avicenna or the influence he had on the development of medical science? Have you ever looked at the night sky? Assuming that you come from the Northern Hemisphere, you might notice something odd about the names of many of the stars that you see. Rigel, Altair, Betelgeuse, Vega, etc. Have you ever wondered why so many of the stars have names derived from Arabic?