Why the ‘West’ has dominated the last couple of centuries is an interesting question with many aspects. It is especially so considering how many important technologies and ideas were either first or concurrently invented elsewhere.
The Western civilizations, for example, failed to come up with it even after thousands of years of mathematical inquiry. Indeed the scale of the conceptual leap achieved by India is illustrated by the fact that the classical world was staring zero in the face and still saw right through it. The abacus contained the concept of zero because it relied on place value. When a Roman wanted to express one hundred and one, he would push a bead in the first column to signify one hundred, move no beads in the second column indicating no tens, and push a bead in the third column to signify a single unit. The second, untouched column was expressing nothing. In calculations, the abacist knew he had to respect untouched columns just as he had to respect ones in which the beads were moved. But he never gave the value expressed by the untouched column a numerical name or symbol.
This is a passage from Here’s Looking and Euclid, which further proposes the failure to see zero was in part due to the West being down its own particular philosophical tangent. Whereas India was a place with a rich history that embraced nothingness:
Indian philosophy embraced the concept of nothingness just as Indian math embraced the concept of zero. The conceptual leap that led to the invention of zero happened in a culture that accepted the void as the essence of the universe.
Author Alex Bellos goes on to assert that it is partly the transmission of these Indian concepts that spurred the scientific revolution.
With the adoption of Arabic numbers, arithmetic joined geometry to become part of Western mathematics in earnest, having previously been more of a tool used by shopkeepers, and the new system helped open the door to the scientific revolution.
Of course the story is much more complicated.
Not only did the use of Arabic numerals and arithmetic require a rich intellectual and practical tradition upon which to glom on to. But the right combination of openness, education, wealth (etc.), and technologies like paper to kick off the revolution.
What is really clear is how important the interplay between civilisations has been for progress. Culture, philosophy, ideas and even biology all crossed borders. Some many times over.
The real question then is, why was the West the main beneficiary?
As always my emphasis.