What were the reasons modern science and mathematics emerged in the West

Aristotle did observe the natural world, which was a start to biology. But they did not do much experimental science.

I don’t think that’s true. On the contrary, Pre-Socratic philosophers attempted to describe the real world by moving away from tradition and myths and embracing logic, proof and arguments. Nowadays, most of their theories seem silly but the fact remains that this is the foundation of the scientific method.

Regarding the OP, Fernand Braudel is his Grammaire des Civilisations argued, in addition to other factors mentioned above, that China’s huge population stunted its technological advances. When they encountered a logistical problem, the Chinese could just throw thousands of people at it until they brute-forced a solution. That was impossible in more sparsely-populated Europe, so Europeans were forced to be creative and develop machines.

I didn’t expect mathematicians to look down on geeking out.

I remember another theory talking about how Europe developed more quickly after a plague.

Could that be the reason for India, too?

Would we not expect Japan to have been more technologically developed than it was?

Well, it was only one of the reasons he listed.

I’m pretty sure he also mentioned the fragmented, and thus, highly competitive nature of European states. Lots of rival entities on a relatively small strip of land with limited resources. They were driven to be innovative in order to have an edge over the others.

What royal couple? Fernando of Aragon thought he was nuts; Isabel of Castille financed him all on her own and with her personal funds.

Absolutely not.

Japan was ruled by the bakufu, the Tokugawa shogunate from 1600 and only ended after it fell to internal pressure after Japan was forced to open its doors to increased trading with Western powers starting in the mid 1800s.

In addition to the extremely rigid society which made changes difficult, the shogunate powers had every reason to stifle technological development. Their rule depended on none of the rival powers become more powerful. There were no large scale wars during this 250-year period and the samurai had no incentive to allow the development of firearms which would weaken their position.

I’m not sure this explanation withstands scrutiny in light of China’s history of technological innovation - up until relatively recently (say, the 16th century AD), China was generally more technologically advanced than anywhere else … many things associated with Western technology in fact developed first in China. See Science and Civilisation in China - Wikipedia

China has since ancient times been densely populated; if dense population was making China backwards, why did this only happen in the last few centuries and not before?

To my mind, theories based on an argument based on some essential element of the nature of Chinese civilization (and there have been many – Confucian conservatism is also often cited) founder on this fact – that the “backwardness” of China is purely a relatively modern issue, and so requires a relatively modern explanation.

Beginning in the 16th century, a culture of (wrong) Answers changed into a culture of Questions. Copernicus, Columbus, and Martin Luther all contributed to this; they were contemporaries of each other and all lived a few decades after Gutenberg’s invention of the movable-type printing press.

It’s hard to escape the conclusion that the mass printing of books Gutenberg’s invention allowed was the key driving force for the Age of Science. China and the Islamic world were using paper long before Europe, and had mass printing before Gutenberg’s invention. Why didn’t they produce a Scientific Revolution? The plausible answer seems too trite: Neither Chinese pictographs nor cursive Arabic script were amenable to the movable type invention.

From Wikipedia:

Which is not to say that printing wasn’t a lot easier in the west, with an alphabetic script.

This explanation also founders somewhat on the facts: while it is true that the Chinese language makes movable-type printing more difficult, China nonetheless had such printing - as did Korea.

The Korean language does not suffer from the problems of Chinese; in the 15th century (before Gutenberg), the Koreans adopted a written language of only 24 symbols, well suited to printing:

Given that Korea had (a) movable-type printing before Gutenberg, and (b) an alphabet just as well suited to printing as those of Europe, it must be other factors that prevented a ‘printing revolution’ from happening in East Asia, and not merely the difficulty of printing east Asian languages.

The article above suggests it was government/elite monopolization of printing that did it, plus certain technical advantages that the Gutenberg process possessed.

Korea developed a very printable script, Hangul, in the 15th century. It consists of only 24 symbols. Though admittedly these are grouped in syllabic blocks.

There is no strictly technical reason Korea could not have experienced a movable-type printing revolution like in Europe … suggesting other factors were at work.

To me, I’m amazed it didn’t happen a lot sooner.

The Classical Greeks were well on their way to going full modern. But they didn’t.

The Romans were less interested in “basic research” and focused on more practical matters. Their tech could have really taken off, but without the foundations it didn’t.

Etc.

So here and there were civilizations in Europe, Egypt, Persia, India, China, etc. that could have been The One.

In short eventually some people just plain got lucky and broke thru and the feedback loop took off.

Why them? Someone had to be first. Sometimes it just comes down to a bunch of small, sometimes random, events that don’t seem to be really all that important on their own.

Paul Kennedy in his book The Rise and Fall of the Great Powers hypothesized that it was the political plurality of Europe that made the spread of the printing press- and the ideas it could promote- possible. There wasn’t a single central government that could suppress either individual books or the whole technology from the entire continent. There was always somewhere else an author or printer could move to to escape persecution and continue publishing.

This makes a lot of sense, and fits with the note that Korea did not experience a “printing boom” because of government control.

According to Neil DeGrasse Tyson, the Mesopotamian area (Iraq, Iran, etc.) was the center of learning and innovation in science, mathematics, and astronomy just prior to the Dark Ages in Europe. Most of our stars were named by Arabic scholars. The very name of “algebra” is an Arabic invention. We use Arabic numerals.

Then along came a Muslim fanatic, Al Ghazali, who declared all science evil, and it was suppressed by the Islamic clergy. They have not recovered since and were eclipsed by other regions less bound by religious edicts.

Not just the name, the concept itself. But I understand the numerals are actually from Northern Africa.

India.

The word comes from the first real text on algebra by Muhammad ibn Musa al-Khwarizmi whose name also gave us the term “algorithm”. That’s a pretty good two-fer.

Another thing which set back the Arabs was the sacking of Baghdad by the Mongols in 1258.

Which was another advantage the West had: they were (mostly) out of reach of the Mongols. OTOH, they were in reach of Goths, Vandals, Huns, etc. which caused a little tiny setback earlier.

Not just the Mongols, but a continual interference from the steppe - Mongols, Turks, etc. - and rulers heavily influenced by steppe modes of war and ruling - Tamerlane, Nader Shah and the like.

These caused trouble not just for Arab/Persian civilization, but for Indian and Chinese civilization as well, and goes a long way towards explaining why Western Europe in particular had a relative advantage.

Christianity might have had something to do with it. In two ways, the first is that Christianity is a more physicalist religion than many others. There’s a strong philosophical bend within Christianity that equates God with His creation and an idea that God (via Christ) is not unapproachable or unknowable, but rather personal and wanting to be discovered. If we look at the early underpinnings of the Scientific Revolution, they had a strong religious bend. They were attempting to deduce attributes of God by studying his creation.

The second major impact was due to the Reformation. You suddenly had competing truth claims within Christianity that had equal (or reasonably so) scriptural and theological backing. This forced people to turn to other sources to judge these claims and the sciences helped fill that gap.