Indian mathematics miscellany

Sreenivas Paruchuri, organizer of racchabanda and other sites (and one of the most learned people I know on Indology topics) informs of the arrival of Mathematics in India: 500 BCE-1800 CE by Kim Plofker . Kim Plofter did her Ph.D. in 1995 with
David Pingree and wrote several scholarly articles about Indian mathematics . Many wondered why India has not been able to keep up with these wonderful achievements(see, in particular Kerala school of astronomy and mathematicsand the work of Madhava ). Frits Staal reviews some of this work and comes up with his own speculations in Artificial Languages Across Sciences and Civilizations and the briefer reports The Generosity of Artificial Languages and The Generosity of Artificial Languages in an Asian Perspective . Some excerpts from the later report:
"An illustration of our topics of discussion is the discovery by Madhava of Kerala, Southwest India, who lived around 1400 CE, of infinite power series that are expansions of pi and the trigonometric functions sine, etc. This took place almost three centuries before these same series were re-discovered in Europe by Newton and Leibniz. In Europe, that event led to the infinitesimal calculus, which could not have been expressed without the help of an artificial mathematical language. In India, that revolution in language did not take place: Madhava and his followers continued to write in Sanskrit or Malayalam, the Dravidian language of Kerala. The accompanying illustration depicts, on top, the infinite power series that expresses the circumference of a circle with diameter D (i.e., two times the radius R) in Sanskrit, followed by a translation into English by A. K. Bag. At the bottom is the series in its modern form which is basically the same as what was written by Newton.
...
Newton's laws were not always written in an artificial form. He formulated in cumbrous Latin, later disambiguated and clarified by Euler, the law of motion that is now taught to children as f = ma.

Absence of artificial notations and especially of the calculus go far towards explaining why modern science did not originate in India or China. Earlier forms of Asian mathematics inspired the algebra of the Arabs but to what extent was that an artificial language? India did develop a formal or artificial language but that was in linguistics and two millennia earlier."
From the longer paper (page 130):

"In Indian mathematics, infinite power series were discovered almost three centuries before it happened in Europe. Indian mathematics is, in this respect, as good as Newton's, but Samskrit was not artificial enough, it was not replaced by equations and the Indian development ground to a halt.
My next conclusion is more tentative. It is elicited by several questions. Indian grocers have combined the use of place value (already to known to the Babylonians) with Indian numerals including the zero that have been called the essential part of the development of civilization. But why did Indian mathematicians use cumbersome expressions derived from linguistics? Was it to add the prestige of the science of language to the humdrum activity of mathematical calculations? Was it because they thought of mathematics itself as a language, good for composing verse and telling stories and useful for doing sums? Was it for excluding outsiders? Was it for several or all of these reasons? I tend to think that India's lingustic skill may have been not merely irrelevant or superfluous, but detrimental to the development of her mathematics- brilliant as it was."
Perhaps the stupendous achievements of Panini have cast a long shadow. Similar questions about science in China (sometimes both China and India) are discussed under
titles like Needham question .