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Transfer of mathematical knowledge from India to Europe (such as a positional number system with zero) allowed Europeans to develop arithmetic. But was there also a reverse direction (probably via Arab mathematicians) in which knowledge was transferred from Europe to India?

Especially I'm curious when Euclid's Elements (probably the most known ancient mathematical book) was introduced to India.

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    $\begingroup$ "Transfer of knowledge from India to Europe (positional number system with zero) allowed Europeans to develop arithmetic". This is highly doubtful and it has been discussed at length in this forum. Chinese had their own counting system, and so did the Arabs. This idea sounds like a part of recent wave of scam. BBC made a serious report on this topic bbc.com/news/world-asia-india-46778879, where statements such as "The head of a southern Indian university cited an old text as proof that stem cell research was discovered in India thousands of years ago." $\endgroup$
    – AChem
    Apr 28, 2019 at 15:24
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    $\begingroup$ @M.Farooq I have read, for example, " Hindu astronomers and mathematicians Aryabhata, born in 476, and Brahmagupta, born in 598, are both popularly believed to have been the first to formally describe the modern decimal place value system and present rules governing the use of the zero symbol." bbc.com/travel/story/20180807-how-india-gave-us-the-zero, but maybe there are some other concepts. However the question was about Euclid's Elements in India. $\endgroup$
    – Widawensen
    Apr 28, 2019 at 15:47
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    $\begingroup$ This is a rather recent wave of nationalistic view of mathematical history. Such views when taken up by any culture (and then exaggerated) distort truth and history. Not all algebra was invented by Arab mathematicians, although the name al-jabr lingers today. Algorithm is an named after an Arab mathematician. Can Arabs claim they invented modern algorithms? Problem is with very old stuff, there is no primary information. I would ask where are books by Aryabhata? Where are the translations for Europeans? Even with the Euclid original work, was there a culture of learning Greek in ancient India? $\endgroup$
    – AChem
    Apr 28, 2019 at 16:16
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    $\begingroup$ @M.Farooq Yes, there are many connections between different ( also scientific) cultures and to identify all links it is not a simple task. $\endgroup$
    – Widawensen
    Apr 28, 2019 at 16:24
  • $\begingroup$ @Widawensen What is this site hrdjfy.blogspot.com/2019/04/… ? $\endgroup$
    – user5402
    May 13, 2019 at 19:52

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According to The Hindu Business Line, quoting the scholar TA Sarasvati Amma:

It was only in the 18th century, nearly 2,000 years after active contact of Indians with the Greeks, that Euclid’s Elements were translated into Sanskrit and even then perhaps the example of the Arabs provided the inspiration.

TL/DR;

Concerning Indian mathematics at about the time Euclid, according to Frits Staal, professor of Philosophy and South/Southeast Asian Studies at UC Berkley:

The ancient Greeks developed logic and a notion of rationality as deduction best exhibited by Euclid’s geometry. These discoveries contributed substantially to the development of Western science. Ancient Indian civilisation was an oral tradition and the oral transmission of the tradition became the first object of scientific inquiry.

Thus arose two human sciences, closely related to each other in their formal structure: the sciences of ritual and language.To begin with, while a number of key contributions were made by Indian mathematicians, they somehow remained in complete darkness about conic sections. These are simply the various dissections of an hourglass (or, a double cone) which are the ellipse, the parabola and the hyperbola. The importance of these curves in the history of science up to the time of Isaac Newton is unparalleled in geometry. Planets were found to move in elliptical orbits, cannonballs and projectiles fell in a parabolic arch under the influence of gravity, and shadows on sundials moved in a hyperbolic path.

The other omissions concern solid geometry, and the existence of only five Platonic solids, namely — tetrahedron, cube, octahedron, icosahedron and the dodecahedron. These five elemental solids were used since the time of Plato in pondering the structure of atoms, crystals and matter in general.

Thus, according to Staal, ancient Indian mathematicians were primarily concerned with a scientific exploration of ritual and mysticism, applying their geometry to things like the construction of elaborate altars.

Further reading: History of Geometry - wikipedia

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    $\begingroup$ Alexander the Great, did visit (or rather conquer) areas which are now in Pakistan. One can find remnants of Greek culture in the Northern part and even very ancient graveyards. The views of Staal and Amma seem to be close to reality rather than web-based myths. $\endgroup$
    – AChem
    Apr 28, 2019 at 16:42
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    $\begingroup$ @M.Farooq Indeed. The Silk Road established shortly after the time of Alexander, would have, for over a millenium, introduced Greek culture far beyond what is today called Pakistan. $\endgroup$
    – nwr
    Apr 28, 2019 at 17:14

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