Personally, I don't think anything ever went particularly "wrong" with India.
They only fell behind the civilizations of Western Europe, not the rest of the world.
So the proper question to ask here is what suddenly went right with heretofore backward Europe.
To my mind the answer to this question is clear: The printing press.
Nearly overnight Europeans had access to several orders of magnitude more knowledge than they had before (and than anyone still relying on slow, error prone, and expensive hand-copying could possibly have).
The discourse this allowed would have had a self-multiplying effect.
The difference would be like somebody from the 1800's (or even the 1970's) trying to compete for knowledge with today's internet society.
There's just no hope for them, no matter how smart they may be.
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Every culture and civilization goes through ups and downs.
To assume that: There was a homogenous Indian civilization
It was for any length of time constantly on the up or even "better" than others
Certain expressions of advancement from certain locales mean "Indian" technology was universally more advanced would be a very narrow view.
This denies Grecian, Mesopotamian, Persian and European achievements, Industrial Revolution, and just so much more.
So what slice of time are we talking about when we discuss decline?
That keeps happening everywhere.
Greece isn't what it used to be, neither is Mesopotamia.
Rise and fall are natural cycles.
Only In the short run we can attribute causes.
As in "what were the factors that led to the fall of the Magadhan(/Roman) Empire?"
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Hmmm, in my point of view, Our ancestors never taught those technologies in written form.
The people who learned some technology don't want to teach that outside their family.
From British period we just started to read Europe's history as our indian history.
For example "Vasco da gama discovered india".
We people started to thought US and Euro only has the technologies.
:( Thats it...:)
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As late as the 18th century, India had a cotton industry that was at least as advanced as the European textile industry.
But when England conquered most of the country, she felt that it was too competitive with her woolens industry.
So England taxed India's cotton industry and otherwise prevented it from developing.
Same with a number of other industries in the country.
Instead, under "mercantilism," India was made to produce raw, not finished goods.
So colonization appears to be the culprit.
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I think the main reasons are demolition of Takshashila and Nalanda universities.
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Indians were never good at scientific method to begin with.
Scientific method aka challenging/testing/
advancing existing knowledge by peers and verification using experiments was never popular.
Most of the glory lies in individual brilliance/theories/work that was passed down as facts and absolute truths, which does not help in advancing knowledge.
Most of the Indian scientific works survive intact unchanged today because of the lack of challenges/advancing of these works by others.
This is due to the Indian psyche of not challenging ideas/elders and the inherent need to maintain status quo.
While the threats of invasion, colonization, destruction of centers of learning like nalanda/taxilla etc are true, the greatest culprit is that Indians rest on past accomplishments instead of moving to the next thing and advancing what is already known.
Indians sucked at scientific method of any kind, so development of science never happened beyond the initial work of some savant in their respective fields.
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This would certainly be linked to the Turkish and Mughal conquest of the subcontinent.
In pre-medieval India, the academia was heavily dependent on royal patronage, as the Brahmin and Buddhist scholars were attached by occupation to the court.
In this period, there had been various mathematical and philosophical advances though there seems to have been a dearth of equipment and tools required for experiment that are fundamentally important to the development of the scientific method.
Also, as the accepted answer points out, the printing press which enormously fueled the scientific revolution in the West, was absent in the present case.
With the arrival of the Muslims 1 however, royal patronage to the indigenous academia ceased; and later (to a minimal extent) replaced by scholars of Central Asian origin.
If an active interest in indigenous intellectual institutions were taken by these rulers, I think the scenario would have been markedly different.
Therefore, the reason for the lack of scientific development in the subcontinent may have not been that it "lagged-behind" as much as that there was discontinuity and in fact a total cessation of the thousand year old tradition of Indian scientific 2 thought.
1
A loose term used here to denote the succession of Central Asian empires that entered the subcontinent. 2 Denoting here the various fields of study that might have led to the development of a scientific method.
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The advancement of the 'scientific progress' of a society is largely contingent upon the society's ability to create new inventions and integrate them into their society.
India's rigid caste system and the adoption of dharma, or 'duty,' into Indian society fit new members of society into specific roles without regards to their innate talents or interests and discouraged scientific progress.
The highest ranking members of the caste, the 'brahmin' (priests) and 'ksatriyah' (warriors) had virtually no need for scientific inventions or research except for potentially firearms and so had no incentive to encourage scientific study among the other castes.
The caste system, I would argue, was India's greatest limitation with respect to scientific innovation and research throughout its history.
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India had been among the "leaders" in scientific research spanning Mathematics, Medicine, Chemistry and others.  http://en.wikipedia.org/wiki/History_of_science_and_technology_in_the_Indian_subcontinent  Controversial theories of nuclear technology in 1000 BC aside, India's leadership role is true when we talk about the "BC" era and maybe up to 1000 AD.  What went wrong after that? Is the colonization the only reason for India's seeming downfall in scientific advancements?
What went wrong with India's scientific development as a society?
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India never excelled at scientific development. The caste system was a limitation to innovation and there was a lack of teaching. The demolition of Takshashila and Nalanda universities were also reasons. The answer to this question is likely to be subjective and include multiple factors. Some people would argue that Indian scientific endeavour was never particularly strong and others would argue that it didn't ever get worse but that other regions outpaced it. Other possible reasons for stunted scientific advancement incude invasion by other cultures, the demolition of Takshashila and Nelanda universities, the caste system or even the lack of literacy. In any case, it would be fair to say that every culture and civilization has been through positive and negative periods throughout history.
Some people might argue that Indian science was never particularly advanced and that Indian civilisation was not good at advancing beyond what had been discovered. One possible reason could have been the fact that knowledge was not shared effectively throughout Indian society. Some would argue that India didn't do anything wrong. It's merely that other regions had more success scientifically. The demolition of Takshashila and Nalanda universities may have contributed to India's scientific downfall. The caste system may have limited India's ability to produce great thinkers who made new discoveries. Invasions by other cultures could have thwarted some of India's scientific progress. Every civilization goes through periods of ascent and decline.