Vienna ideas didn't shape anything in particular. They were just standing on the shoulders of the giants. The west was shaped by the thousands years of European's history and wars.
One of the key contributions that in my opinion influenced the Renaissance greatly was the work by numerous Muslim translators on the translation of Greek works to Arabic. In the process, many of the works of the great Greek thinkers and philosophers were preserved for future scholars. Also, Muslim scholars were responsible for bringing works from the East (China, India, etc.) back to Baghdad, making them more accessible to the West.
Arabic was so widely used that it was the lingua franca for most of science for a period of time (~12th century). European scholars who wanted to learn more about the latest discoveries and inventions had to learn Arabic at one of the large learning centers (Baghdad, Damascus, Granada, among others). Sicily[6] was another place where East and West combined for the sake of learning.
[1]: https://en.wikipedia.org/wiki/List_of_Muslim_philosophers
[2]: https://en.wikipedia.org/wiki/List_of_Muslim_astronomers
[3]: https://en.wikipedia.org/wiki/List_of_Muslim_doctors?wprov=s...
[4]: https://en.wikipedia.org/wiki/Mathematics_in_medieval_Islam?...
[5]: https://en.wikipedia.org/wiki/Alchemy_and_chemistry_in_medie...
[6]: http://archive.aramcoworld.com/issue/197806/muslim.sicily.ht...
The Islamic world peaked in the 15th century, then began to slowly decline. The current lack of output from Muslim scientists is in my opinion primarily due to petty internal religious conflict, poor unity due to conflicting interests, the colonisation of most of the larger Muslim countries which led to them skipping the more critical periods of scientific development and education, the lack of interest in innovation, and the lack of freedom to innovate because of perceived religious contradictions.