The concept of zero, along with our current numbering system, is definitely an important one.

Although it wasn't invented by Muslims, it was certainly brought to Europe by them, hence the term "Arabic numerals". The first European writings on them date from Spain in the 10th century. They began to be used in European mathematics in the 12th century, largely thanks to Fibonacci, and entered common usage a few centuries later (of course, "common usage" is a bit misleading here. They were the commonly used numeral system, but most people weren't literate and wouldn't have been using them)

It allowed for many advancements in mathematics, both because the concept of zero is necessary for some advancements and also more simply because the Hindu-Arabic decimal numbering system is far more convenient for calculations - Roman numerals are far more unwieldly.

Before the European Renaissance there was a Renaissance in Islam. Harun al Rashid has ordered the translation of Aristotle and Plato transmitted through Aramaic christians, along with Persian literature like the tales of 1001 night and Sanskrit philosophy. The latter is what we today regard as responsible for much of our modern day mathematics and for our «Arabic» numerals. This load of new knowledge also lead to own inventions. Footing on Aristotle Avicenna worded out the scientific method for medicine. Alfarabi was a very fruitful writer in the fields of mathematics and musicology. For his Tabula Rasa John Lock was footing on a philosophical 12th century novel by Ibn Tufail. Hegel got his Zeitgeist talk from Maimonides describing radical determinist philosophers in his Guide for the Perplexed. The Renaissance in the Islamic world is usually regarded to have ended with the sacking of Baghdad by the Mongols in 1258 but it did not come to standstill in the very West, in Spain, and in the very East, in India. There is a fine and very detailed description of the entire intellectual development inside of the Arabic speaking world over at www.historyofphilosophy.net.