Mathematics in India [Hardcover]

Kim Plofker (Author)

Book Description

Publication Date: December 29, 2008 | ISBN-10: 0691120676 | ISBN-13: 978-0691120676

Based on extensive research in Sanskrit sources, Mathematics in India chronicles the development of mathematical techniques and texts in South Asia from antiquity to the early modern period. Kim Plofker reexamines the few facts about Indian mathematics that have become common knowledge--such as the Indian origin of Arabic numerals--and she sets them in a larger textual and cultural framework. The book details aspects of the subject that have been largely passed over in the past, including the relationships between Indian mathematics and astronomy, and their cross-fertilizations with Islamic scientific traditions. Plofker shows that Indian mathematics appears not as a disconnected set of discoveries, but as a lively, diverse, yet strongly unified discipline, intimately linked to other Indian forms of learning.

Far more than in other areas of the history of mathematics, the literature on Indian mathematics reveals huge discrepancies between what researchers generally agree on and what general readers pick up from popular ideas. This book explains with candor the chief controversies causing these discrepancies--both the flaws in many popular claims, and the uncertainties underlying many scholarly conclusions. Supplementing the main narrative are biographical resources for dozens of Indian mathematicians; a guide to key features of Sanskrit for the non-Indologist; and illustrations of manuscripts, inscriptions, and artifacts. Mathematics in India provides a rich and complex understanding of the Indian mathematical tradition.

**Author's note: The concept of "computational positivism" in Indian mathematical science, mentioned on p. 120, is due to Prof. Roddam Narasimha and is explored in more detail in some of his works, including "The Indian half of Needham's question: some thoughts on axioms, models, algorithms, and computational positivism" (Interdisciplinary Science Reviews 28, 2003, 1-13).

Editorial Reviews

Review

This is a much needed and splendidly executed book, a history of mathematics in the Indian subcontinent that embraces the full breadth of its rich subject. . . . For anyone acquainted with the scholarly literature on these disputes, it is refreshing to read a discussion of them that keeps to the evidence, is frank about the evidence's limitations, and eschews charges of personal incompetence or bias. (Alexander Jones Journal for the History of Astronomy)

This carefully researched chronicle of the principal contributions made by a great civilization covers the earliest days of Indian history through to the beginning of the modern period. . . . Kim Plofker's book fulfils an important need in a world where mathematical historiography has been shaped by the dominance of the Greco-Christian view and the Enlightenment period. (Pervez Hoodbhoy Nature)

[T]he author does a remarkable job presenting the mathematics of India. Anyone delving into this book, general reader or historian, will find straightforward explanations of the mathematics involved, learn of the culture that surrounded the subject, and come away with a clearer understanding of the Indian civilization and its mathematics. (Jim Tattersall MAA Reviews)

[T]his book is reliable, authentic and helps to rectify the wrong notions on either side, regarding Indian mathematics. It is a great contribution to the history of mathematics in general. (T. Thrivikraman Mathematical Reviews)

The book is well written and easy to read. There is a good balance of commentary and technical detail. . . . Plofker's book finally offers us, at least in outline, an up-to-date and coherent narrative for the history of mathematics in India. (John Hannah Aestimatio)

[M]eticulously researched and engagingly written. . . . Plofker's attempt to situate Indian mathematics in the proper context [leads] to a very detailed treatment of mathematical astronomy (at times far more detailed than mathematics itself), but that is no drawback, for the book serves as an excellent introduction to mathematical astronomy as well. (S. R. Sarma Journal of the American Oriental Society)

From the Inside Flap

"Mathematics in India presents an accessible, readable, and well-informed treatment of the history of India's mathematical traditions. It includes topics discussed little to date: the social setting of the mathematicians, the textual practices learned in Sanskrit, and the realm of observational and timekeeping practices. The survey of the Kerala school and the later life of Indian mathematics are detailed, unique, and valuable."--Christopher Minkowski, University of Oxford

"No reliable book of this kind has been available, and Plofker's work makes an underdeveloped area accessible to all who are interested."--Johannes Bronkhorst, University of Lausanne, Switzerland

See all Editorial Reviews

Product Details

• Hardcover: 384 pages
• Publisher: Princeton University Press (December 29, 2008)
• Language: English
• ISBN-10: 0691120676
• ISBN-13: 978-0691120676
• Product Dimensions: 6 x 1.3 x 9 inches
• Shipping Weight: 1.7 pounds (View shipping rates and policies)
• Average Customer Review: 3.0 out of 5 stars  See all reviews (4 customer reviews)
• Amazon Best Sellers Rank: #793,436 in Books (See Top 100 in Books)

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Most Helpful Customer Reviews

2 of 3 people found the following review helpful

5.0 out of 5 stars Very Good book and I learnt a Lot June 25, 2009

By Ruwan Rajapakse

Format:Hardcover|Amazon Verified Purchase

I think many Indians are concerned that Plofker's assertion that decimal system came from China. I think more evidence is warranted for a claim of such magnitude. But other than that the book contains lots of important information. Specially on Kerala school. Looks like all labors of Kerala school went to waste since they did not travel to the stream of math flow for the future. Very good analysis on solution of indeterminate equations (Kuttaka) and their use of it. Honestly this is the first time I have seen someone addressing this area in a book thoroughly.

I am planning to return to that chapter again when I can find some time. It seems Indian astronomy was more based on algebra while Greek astronomy was more based on geometry. That explains why Arabs liked Ptolemy more than Brahmagupta. Geometry is much easy to visualize than indeterminate analysis which was completely ignored by later Arabic astronomers.
Good analysis on Sulba sutras. There is way too much on Bhaskara II.
Bhashkara II was a great math popularizer like Al Khwarizmi. Not an originator or an inventor. Except improving the Chakrawala method of Brahmagupta he did not invent anything.

I tend to agree that Indian astronomy borrowed from Greeks. I tend to believe Romaka and Paulisa siddhantas are from Greece. Also interesting to see day light difference in winter and summer in Surya siddhanta which indicate some borrowing from a northern country.

Drawbacks I found which can easily be amended in a future edition;
1) Not much analysis was done on development of the four fundamental operations. (Doesnt matter it is called arithmetic or not, these four operations are the heart of commerce, engineering and large portion of mathematics itself....)
2) Did the decimal system came first and four fundamental operations came after? Or they developed together? If the author decides to write a second edition I would like to see more on this momentous discovery.
3) Not much is said on the development of the equation for the quadratic. This is another momentous discovery by Brahmagupta.

4) Also there are numerals with decimal system and ten based place value system in Sri Lanka. Which was noted by Florian Cajori. Read more ›

18 of 31 people found the following review helpful

1.0 out of 5 stars Plodding and unremarkable July 21, 2009

By N. Murthy

Format:Hardcover

I was about to purchase this book but was fortunately able to look at a copy before doing so. The author, with almost no professional comprehension of the intricacies of Sanskrit grammar and linquistic theory, attempts to comment rather erratically on the connection between the abstract, symbolic nature of Paniniyan grammatical nomenclature and Indian mathematical categories.

What is truly puzzling is that this is supposed to be a text wholly devoted to Indian mathematics--but she herself, in one chapter, claims there is not enough "space" to expatiate on a rather important topic.

Her arguments and assertions never really evolve--nor does she bother to back up her assertions with any relevant cross-references. I am fully prepared to accept that the decimal system of Indian place value notation originated in China--but the author herself admits there is no real evidence for such a claim, yet feels comfortable proposing it as serious enough to devote a torpid half-page to. Worse, she makes no effort to comprehend any argument as to why such a system would be indigenous to Indian mathematical development (despite evidence to the contrary).

Reading, one gets the constant feeling that she stumbled upon the idea of writing this book rather haphazardly and then decided it wasn't such a a good idea after all.

9 of 24 people found the following review helpful

1.0 out of 5 stars A falied attempt to save Indo-European linguistics April 4, 2010

By Mayuresh Kelkar

Format:Hardcover

This book is yet another western attempt to portray Vedic astronomy and mathematics as vague, ahistorical , unscientific, and borrowed. All AIT opponents are summarily dismissed as "Hindu Nationalist (p. 2)." The author's complete ignorance of archaeological facts is evidenced by the statement "...Indus cultural sites do not contain remains of characteristic Indo-European goods such as horses or chariots (p. 7.)." The reader is assured (p. 5) that Vedic Sanskrit has "unmistakably descended" from the reconstructed Proto Indo-European, never mind that reconstructed languages are not historical facts, but merely a tool of linguistic research. The author admits that "there is no known evidence, textual or otherwise, that indisputably proves any of these dates (like 3000 BCE) to be impossible for the composition of Vedic works, (p. 35, paranthesis added)," but they must be rejected as they do not fit in with the imperialist and Eurocentric reconstructions of what Vedic history should be. A very scientific approach for someone who claims to be a mathematician and claims to have written a book about it. Here is another comical argument (p. 42)--"The suggestion of a Mesopotamian origin thus furnishes a coherent and plausible explanation for at least some of the features of Indian mathematical astronomy at the close of the Vedic period. On the other hand, there is nothing in these similarities that necessarily has to be accounted for by transmission, and there are no indisputable traces such as Akkadian loan-word technical terms in Sanskrit texts." Duh?!.

6 of 20 people found the following review helpful

5.0 out of 5 stars A scholar book on the field May 27, 2009

By Manoel De Campos Almeida

Format:Hardcover

This a a scholar book on the field, by a master on the topic. Isn`t a book for naive readers, but everyone that is seriously interested in
math`s history will apreciate it.