By coincidence, I was just looking up reviews of the excellent book Mathematics in India by Kim Plofker,
http://www.amazon.com/dp/0691120676
which I read a few years ago, just before I saw this post. There has been a lot of new scholarship about ancient India both in India and around the world since this submitted article was supposedly originally written, and here on Hacker NEWS we should be looking at more up-to-date information, I think.
http://www.amazon.com/Mathematics-India-Kim-Plofker/dp/06911...
The highly divergent Amazon reader reviews (I really ought to add my own five-star review, as I have read the whole book), and especially how divergent some of the Amazonian reviews are from the professional reviews of the book, show how controversial some of these issues are. The issue of the history of science and technology in India is tightly interwound with domestic politics in India. The whole notion of "Vedic mathematics" is based on willful misunderstandings of the sources. Plofker in footnote 7 from page 16 of Mathematics in India cites works by scholars in India who have dug into the primary sources, and disagree with the usual claims about "Vedic mathematics."
(One difference between India and either China or the near east is that the writing materials used in India, often plaited sheets of palm leaves, were much less durable than the silk sheets or bamboo slats used in China, or the fired clay tablets or papyrus sheets or parchment hides used in the near east. So many of the earliest writings from India have perished, while remarkably old writings still exist from either China or Sumer.)
[1] http://www.amazon.com/Mathematics-India-Kim-Plofker/dp/06911...