This is kind of an off-topic question because any answer will be a matter of opinion, but I guess I will take a stab at it.
First of all, Indian mathematics was very advanced in some regards and we ended up borrowing elements of it (via the Arabs), such as the use of "Arabic" numerals, which are actually of Indian origin. Indian computation of planetary orbits was far, far ahead of Ptolemaic computations. All of this was obliterated during the Mongol invasions in the 14th century, however, so it is hard to say how they would have done if uninterrupted.
Following on this, primitive civilizations are capable of advanced technology. For example, the Mayan calendar is very sophisticated and is arguably much more flexible and accurate than our own Gregorian calendar. Also, it was invented many hundreds of years before the Gregorian calendar.
So, what we are really after is net civilization--the totality of advancement, because in any one field anyone can be dominant if they apply themselves.
If we examine successful civilizations, we notice three key things:
(1) they rise and fall, the power centers move around over time
(2) they tend to occur where useful resources are located
(3) military dedication, attitude and approach is often innovative and superior
Based on this it would seem environment is very important. For example, early on the river valley civilizations (Nile, Euphrates) were paramount, but later on civilizations in more mineralized areas were stronger. There seems to be a symbiosis betweeen local resources and current needs. For example, countries that now have a lot of oil tend to be growing faster, ceteris paribus, than those that do not. For example, Sierra Leone, Turkmenistan and South Sudan have high growth rates now due to recently-discovered oil.
Then there is a military factor. Often large civilizations are created by a small, highly-motivated nucleus of warriors. For example, the Latins, the Macedonians and the Seljuk Turks. All three started in sheltered locations adjacent to rich old civilizations they could grow at the expense of. For example, the Latins sheltered in a large swamp (Latium was originally a big swamp), and over time pillaged and fed off of the Etruscans.
The success of Europe, a relatively small area of the world, would seem to be a combination of these elements: proximity to resources of the type needed by current technology, nearness to existing rich civilizations, and a terrain that favors creation of nuclear warrior groups.
One indication that supports these ideas is that China had difficulty in communication of civilization. For example, many regions of China, such as Sichuan, were in a primitive, almost neolithic state at the same time that other parts were in the bronze age and progressing rapidly. This shows that there was difficulty in communicating and spreading civilization there.