> And while the importance can discussed all those cultural innovations were built upon western (white) accomplishments
Western accomplishments, which mostly happened from the Reinassance onwards, became possible when:
1) Paper was introduced in Europe. Before that, printing a book would require "parchments" made out of sheep or goat skin. It would take in average 300 goats to print a bible.
2) The Church was influenced by philosophers such as Saint Thomas Aquinas and became more tolerant of science. Before that it would be considered blasphemy, apostasy or witchcraft.
3) A vast number of volumes of philosophical and scientific literature books was translated into Latin.
4) The introduction of better numerals and algebra.
Who is specifically responsible for that?
1) The Islamic Caliphate of Cordoba, in what today would be modern Spain. Specifically the Toledo School of Translators.
2) Refugees from fallen Constantinople carrying literature with them.
So, in short, the European Reinassance, the process that started the "white achievements" you mention, could not be possible if it wasn't because of the contributions of the Islamic civilization.
The follow up reaction to this is usually: if these guys were so advanced, what happened to them? Two things: Spanish Reconquista, and a massive invasion by the Mongol empire which razed all their cities, agriculture, irrigation, infrastructure, and killed all the scholars.
Knowledge is an uninterrupted chain of teachers and students and a missing generation is enough to kill it.