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UPDATE: I've updated the title of the question from Why did India lag behind in discovering Maths and Science? to Why did India miss the Great Revolution in Maths and Science? after some of the answers and comments provided.

NOTE: This question lies more in the "discussion" category rather than an "objective answer" category. But bear with me. I am asking this here because I want an objective answer. Or at least some reference to some research paper which answers this question.

The Question is simply this:

India had a lot of time in her hands. They, alongwith Greece, developed a mature Philosophy in the times of BC. Everything went well for a good thousand after that (i.e. till 1000 AD). India lived a peaceful Golden age during this time where no philosophy was violently suppressed.

Enter West. They went through Dark age for those good 1000 years. But as soon as they recovered from the Dark age, they started discovering a good deal of Maths and Science in just a couple of centuries.

Now, some would argue that various crucial Maths/Science was also discovered before those times, like the contributions of Pythagoras (Greece) or Brahmagupta(India). Sure, they were good contributions but what I am talking here about is that advanced Maths which revolutionized the whole scenario. Calculus would be one such revolutionary candidate, apart from others.

PS: This question is not meant to incite any debate or hurt anyone. This is a sincere academic question.

A Few Reasons Upfront

We came up with a few answers which I would like to mention upfront:

  • India was always a very rich and content country, while Europe had to suffer through a lot. So, probably while India laid back, Europe HAD to discover and invent things.
  • India always hanged on to its religion and culture. While Europe was almost completely devastated by "The Plague" which lowered the faith of people on Church, nothing as devastating for the Indian religions/culture happened in India. After the Plague, the Science of Reason and Logic (which was already present in Europe but suppressed) rose above the Church.
  • Maybe there was some small but very crucial discovery which changed everything. Had it not happened, things would have been different. After that discovery, everything escalated pretty quickly in the West while Indian laid back.
  • The Westerners are a superior race. (I am mentioning this reason purely for the sake of mentioning all the possible options. No intention to incite any debate or hurt anyone. FYI, I am an Indian.)
  • In his book "The Shape of Ancient Thought", Mcevilley says that both Greek and Indian philosophies developed together and enriched each other. And both had the same amount of rationalities and irrationalities. However, there was one crucial difference: While Indian philosophies had rationality in them, they never quite cracked the code of Logic and Deduction. So, maybe this caused major difference in thinking processes of the Indians and the Westerners.
  • The famous Nalanda university was decimated completely and with it, perhaps, all the knowledge was gone. Several other instances also happened in India where various Mulsim invaders devastated various knowledge centers.
  • The West had an expansionist outlook, approach or way of life. They wanted to conquer, expand and enforce themselves. This demanded desperately innovations in technology. While India never had any such approach.
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    $\begingroup$ Of course, if you did a little research, you would find that Indians did invent advanced mathematics without Western help... $\endgroup$ – Marius Kempe Feb 10 '15 at 22:03
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    $\begingroup$ The issue with these kinds of worded questions is that they seem to assume a single direction of progress in which one is either "ahead" or "behind" and that all cultures want to make progress in this direction, yet in spite of their best efforts, some "lag" behind others. I would encourage you to consider and question these assumptions. It is common that hindsight makes the important and successful trends of today seem to be the goals and objectives of yesterday. $\endgroup$ – usul Feb 16 '15 at 14:10
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    $\begingroup$ The Scientific Revolution happened in Europe because the societies and cultures of Western Europe were very different from India (and also the Middle East and China) during the Renaissance and Enlightenment. Instead of being ruled by a centralized government (the Mughal Empire) Europe was splintered (in part due to geography) into hundreds of kingdoms and independent cities. The influence of the Roman Catholic Church (which attempted to stifle Galileo's findings) was waning and had to compete with secular powers, unlike in India. $\endgroup$ – RobertF Mar 23 '16 at 13:57
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    $\begingroup$ Free thinkers who were abused by their monarch could find a new patron or university in the neighboring kingdom. There were many universities and researchers corresponded (often in Latin) and published findings thanks to the printing presses found in every large city. There was no caste system limiting social mobility, feudalism was in decline. Encouraged by a temperate climate, rich soil and navigable rivers, Europe was rich from trade and commerce and had large cities which could support a burgeoning middle class which was literate and sent their sons to universities to be educated. $\endgroup$ – RobertF Mar 23 '16 at 14:04
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    $\begingroup$ Westerners were not a superior race of course - it was just a curious coincidence of geography and historical accident. The Muslim, Chinese, and Indian worlds certainly made important contributions (and the Hellenistic and Roman civilizations as well). Europeans happily and shamelessly borrowed & distributed ideas from these cultures. However, I think having a stable, centralized government as well as a State religion discouraged the advance of science and mathematics. Which is the opposite of what you might expect considering the many wars between kingdoms Europe has suffered. $\endgroup$ – RobertF Mar 23 '16 at 14:19
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India did not "lag behind". It was the ancient Greece, its successor Hellenistic states, and Renaissance Western Europe where Math jumped ahead. (More precisely, one can say, one Hellenistic state:-)) India was not much different in comparison with most of the rest of the world.

The correct question would be "Why in ancient Greece and renaissance Europe mathematics suddenly developed so much". By comparison there was almost no development in Europe in the period from 2-nd AD to 17 century, like in the rest of the world. "Almost none" in comparison with those short periods of intensive development.

One has to conclude that intensive development of mathematics is not a rule but a rare exception which happened only in two cultures, and took relatively short time. The first period took essentially 300 years, and the second (modern) 400 years. These are short periods for history.

In my opinion, the same applies to science, though I understand that many people will object.

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    $\begingroup$ Completely side comment: The phrase is "In my opinion", not "on my opinion". It's idiomatic. English is not your language. Your answers here and elsewhere have been very good. $\endgroup$ – David Hammen Feb 20 '15 at 12:58
  • $\begingroup$ Regarding development of mathematics: This happened in many stages, and in many places. Our ancestors learned to count tens of thousands of years ago. Archeologists have unearthed stones, bones, and sticks with obvious tally marks on them all over the world. Our ancestors learned the basic rules of mathematics (addition, subtraction, multiplication, and division) five thousand years or so ago, once again in multiple places throughout the world. $\endgroup$ – David Hammen Feb 20 '15 at 13:01
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    $\begingroup$ The key to mathematics, however, was very elusive. That key was the concept of nothing, of zero. The Babylonians had a place-value notation (e.g., this year is 2015; note the 0) and had a marker for "nothing here" (the "0" in 2015), but they did not have a true zero. The Mayans came even closer, but they too did not have a true zero. The concept of zero as both a placeholder and a number is uniquely Indian. That is their key contribution to mathematics. $\endgroup$ – David Hammen Feb 20 '15 at 13:04
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    $\begingroup$ It is a very strange idea that notation for zero is a "key to mathematics" :-) $\endgroup$ – Alexandre Eremenko Feb 20 '15 at 13:51
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    $\begingroup$ From How was zero discovered?: Yet behind this seemingly simple answer conveying nothing lays the story of an idea that took many centuries to develop, many countries to cross, and many minds to comprehend. Understanding and working with zero is the basis of our world today; without zero we would lack calculus, financial accounting, the ability to make arithmetic computations quickly, and, especially in today's connected world, computers. The story of zero is the story of an idea that has aroused the imagination of great minds across the globe. $\endgroup$ – David Hammen Feb 20 '15 at 14:30
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At one time, India led rather than lagged. The Indo-Arabic numerals that are now used worldwide originated in India. We count 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, ... Note that I made 0 (zero) bold. The concept of representing nothing with something is uniquely Indian. The world owes a lot, a whole lot, to India and to Brahmagupta in particular.

The real question here is why India (and also China, the middle East, pre-European Americas, and even Greece and Rome) were intellectually and economically overtaken by the undereducated, unsophisticated, and brutal barbarians from northwestern Europe. This is perhaps a better question for the sister SE site, http://history.stackexchange.com.

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    $\begingroup$ ...overtaken by the undereducated, unsophisticated, and brutal barbarians from northwestern Europe... When you put it this way, it appears that the Industrial Revolution and the urge to colonize was a big motivation, albeit an indirect one. Industrial Revolution motivated invention of machines and such, which led to the development of various Mathematics and Science. $\endgroup$ – shivams Feb 25 '15 at 4:41
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    $\begingroup$ Maybe they were not "undereducated, unsophisticated, and brutal barbarians"? $\endgroup$ – Martin Berger Feb 25 '15 at 14:57
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    $\begingroup$ @MartinBerger - The word "vandalism" originates from the damage committed by the Vandals during the second of three sacks of Rome that occurred during India's Golden Age. The other two sackings of Rome were committed by the Visigoths and Ostrogoths. By the time Brahmagupta was formalizing the rules of arithmetic, western Europe was in full decline, characterized by decreasing population, literacy, and trade. $\endgroup$ – David Hammen Feb 25 '15 at 16:57
  • $\begingroup$ @DavidHammen So? Rome was a slave-holder society. The behaviour of the Vandals was perfectly normal by historical standards. The idea that the sacking of Rome was particularly bad arose, as far as I'm aware, as part of an apologia of English imperialism. Incidentally, ancient Rome's main 'contribution' to mathematics was killing Archimedes. $\endgroup$ – Martin Berger Feb 25 '15 at 17:14
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In the discussion of how different cultures developed mathematics, it is important to remember that patterns of cultural exchange influenced this development. Mathematics did not just independently pop up in Greece, then India, then Europe; rather, the legacy of mathematics was inherited, refined, and passed on to descendants and neighbors in mostly continuous fashion, and it is in this sort of context that one should view the history of Indian mathematics.

For much of ancient history India did not at all "lag behind" its western contemporaries. Besides the invention of zero, Indian mathematicians independently discovered the Pythagorean theorem, the series expansions of the trigonometric functions, the quadratic formula, several theorems in geometry, and more.

If any culture could lay claim to the title of "foremost in mathematics" before the advent of calculus per Newton and Leibniz, it would be the Muslim world. The golden age of Muslim civilization saw numerous advances in mathematics and the true rise of a symbolic calculus. All of this was aided by the fact that Muslim scholars had the works of the Greeks and Egyptians to draw from, and also were in contact with the work of the Indians.

Europe around this time was somewhat mathematically bankrupt. The legacy of the Greeks had long passed by the end of the first millenium CE, and the Romans were only ever interested in practical mathematics. Quoth C. Edwards, on Cicero's restoration of the tomb of Archimedes in Syracuse: "The Romans had so little interest in pure mathematics that this action by Cicero was probably the greatest single contribution of any Roman to the history of mathematics."

But as we approach the Rennaisance years there was an increase in communication and trade between Europe and the Muslim world, and with this Europeans catch up quickly in their mathematical knowledge. Moreover, this coincides with many other important advances in European science and technology, the printing press being one of the more notable ones. It is important to consider that the Europeans only got wide access to Euclid around this time - until this time it had remained with the Muslim scholars in its original Greek (with Ptolemy's commentary) and its Arabic translation. One should also consider the enlargement of the European economy and the Age of Discovery in this time period.

A lot of European mathematics around this time was practically motivated - Napier's invention of the logarithm, Fermat's work on optics, Pascal's work on probability, etc. The highlight, of course, is the invention of calculus by Newton and Leibniz (though preceding mathematicians, like Archimedes and Fermat, had already hinted at several notions like the derivative or integral), following which European mathematics and science exploded in sophistication. As to why "pure" mathematics exploded likewise...who knows? I haven't the foggiest why Fermat was so motivated to do number theory, though surely he found it vastly entertaining.

As to why so little of this explosion made its way back to the Muslim world, who knows? But it's not hard to imagine why India never got to see the European advances - with the Ottoman Empire standing in the way, India was in extremely infrequent contact with the Europeans, and what contact they did have was largely mercantile, not scholarly. And unfortunately, much of the later contact between the Indians and the Europeans was of an exploitative or colonial nature - hardly a breeding ground for intellectual exchange.

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You make a fair amount of valid points however you need to see the progression of what was happening at the time.

If we assume that Indian math developed independently you'd see they were at the forefront of a lot of "inventions" and "discoveries" in math. Here are a few in as close chronological order as possible from Aryabhatta to Bhaskara II and Madhava in 1500 CE:

  1. The base 10 numeric system and the creation of 0 that actually makes modern math "easy" in a sense as opposed to sexagesimal system of Babylonians or Greek/Roman numerals
  2. Creation of sines and cosines as opposed to Ptolemy's chord - literally creating the field of trigonometry
  3. Prediction of Heliocentricity w.r.t. computing the orbits of the planets (although this is still being debated since the computational models of Aryabhatta seemed to be based on epicycles. Wikipedia should provide necessary references on this and further reading)
  4. Discovery and acceptance of negative numbers as "numbers" and how to operate with them
  5. Discovery of the quadratic formula taught in schools
  6. Discovery of the various infinite series for sine, cosine and also $\pi$ - mostly by Madhava around 1500 CE, 200 years before Newton/Liebniz rediscovered them.

These are just the hallmark discoveries I've highlighted. After 1300 CE we see invasions by the Khilji Dynasty, followed by the Moghuls. Takshila University predated Nalanda but was caught up in wars around the first 300 yrs CE. A large amount of knowledge was perhaps decimated. But the Kerela school where Madhava taught was perhaps safe from all this (my conjecture).

However, this brings us to the second case with Indian Math - AFAIK Indians were not into "spreading" their discoveries/knowledge. Culturally, people "went to India" to seek knowledge. In the European world, you see a lot of peer snubbing and arrogance to "show each other" how good they were and thus you see a lot of "correspondence" going back and forth (apologies for my strong opinion on this). A side effect of this was proliferation and sharing of knowledge and how our modern "conferences" were born.

India lacked this so it took us this long to even know that discoveries we attribute to Newton, Liebniz and other prominent European mathematicians, Indians already had a good grasp on it. In fact, Newton wasn't even aware of the advances of Indian math!

Also, "if it didn't come from Europe it wasn't any good" was a common belief owing to the "math superiority" at the time. Hence there's a high chance that everything else was ignored.

At the time, India was really struggling with too many invasions and would continue to do so until 1947 (India's freedom from the British rule). Some folks like Ramanujan were fortunate to be recognized but not many were that fortunate.

Change of schooling system: The British rule put forth a new system of education as per the needs of the industrial revolution - it involved "understanding the current state of affairs/knowledge" without much regard to innovation/thinking (as well as not accepting Indian education as a "good enough").

Given all this, you can see that circumstances just weren't in India' favor and hence the feeling of "lagging behind". It "missed out" because India was busy trying to just survive and focus on freeing itself from the various empires.

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    $\begingroup$ Your perspective on "spreading" attitude was interesting. And thanks for some highlighting some interesting contributions of India. However, please add some references for all those facts. It's important. Otherwise, false knowledge may prevail. $\endgroup$ – shivams Mar 2 '18 at 22:32

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