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I think Bill Bryson writes about this much better than I can, but in short, European political fragmentation and nascent capitalism meant that educated polymaths could offer their services to different landed aristocratic or royal patrons. Brahe and Kepler fall into those categories. So does Gauss and Euler. The creation of the Royal Society in 1660 created the venue for exploring Natural Philosophy... what ultimately became "science". It was in this atmosphere that Newton was able to publish the Principia (1687)

It's hard for us to understand this today, but science as we know it did not really exist back then in either England or anywhere else.

The invention of gunpowder in China came about from searching for an elixer of immortality. The original book on Al-Jabr was written for practical purposes in the 9th century, around the time when the foremost scholars of the Islamic Age (See Al Ghazali) would argue that ascribing the origin of the universe to a chain of cause and effect rather than the direct action of God was a form of atheism and therefore apostasy.

Europe wasn't really any better in this regards even in the 17th century. Isaac Newton himself spent the vast majority of his career working on alchemy and searching for the Philosopher Stone which he believed was harbored in the Book of Revelations.

It took decades, and the generation after Isaac Newton to begin to adopt the philosophy that many natural phenomena could be ascribed to mechanical laws (like the physics of Newton), and it's from that philosophical foundation that led to the invention of "science"

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