Do you know one thing that Most of the early scientists and mathematician were Muslims i.e., religious!
Actually many of the polymaths, scientists, and thinkers from the so-called Islamic Golden Age were agnostic, possibly atheists even and many of the ones who were Muslims would be viewed as apostates today because they believed in Sufi concepts like Kalam which the the "mainstream" muslim imams like Hanifa rejected, and some of them were even executed for heresy.
Some of the names that come to mind are....Ibn Rushd (Averroes), Ibn Sina (Avicenna), al Rundi, al-Kindi, ibn Bajjah (Avemspace), al-Razi, Abu Nuwas, al-Jahiz, al-Hallaj, al-Khwarizmi, al-Farabi, Jabr Ibn Hayyan, and there are many others.
Even if they were Muslims nominally, they were not afraid of doubt and actually sought to improve on science based on the scientific method rather than the BS that Muslims today believe in like "scientific miracles of the quran" or when they call it a miracles when they find an animal saying "allah", and creationism.
Even if we assume they are Muslims, can we assume that this implies that Islam is a the true religion. Newton and Galileo were Christians, but their achievement rarely, if ever have been recorded as "Christian Science". Same thing goes for Einstein and Judaism.
watch this after 4:30
I suppose you could say that the wuzu created the incentive for the water wheel for inventors like al jazari, and how three of the five pillars of Islam combined with the affinity for imperialism and conquest helped improve navigation and time keeping . But these are little more than coincidences, and the same thing can be said of the religions of the ancient greeks and ancient Egyptians.
In any case, the Islamic Golden Age is a thing of the past, and the reason why it succeeded was because during this times Muslims were considered progressive compared to the rest of the world, whereas today some of them, many of them, are brainwashed into believing that a backwards, barbaric,
1000 year old philosophical and legal system will bring them glory.