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Mathematics in India

Last year Communist ideologue P Govindapillai wrote an article in the Malayalam newspaper Mathrubumi about Eurocentrism and lamented that Europeans did not give sufficient credit to Muslim scientists. In the article Govindapillai conveniently left out mathematicians from his own state — the Kerala School of Mathematics — and their discoveries. This lead to an Op-Ed in Mail Today.

In his review of Kim Plofker’s Mathematics in India, David Mumford, Professor of Applied Mathematics at Brown University, writes that the prosperity and success of India has created support for new Western scholars who are looking at India without the old biases. I have not read the book yet, but the review is positive.

Chapter 7 of Plofker’s book is devoted to the crown jewel of Indian mathematics, the work of the Kerala school. Kerala is a narrow fertile strip between the mountains and the Arabian Sea along the southwest coast of India. Here, in a number of small villages, supported by the Maharaja of Calicut, an amazing dynasty17 of mathematicians and astronomers lived and thrived. A large proportion of their results were attributed by later writers to the founder of this school, Madhava of Sangamagramma, who lived from approximately 1350 to 1425. It seems fair to me to compare him with Newton and Leibniz. The high points of their mathematical work were the discoveries of the power series expansions of arctangent, sine, and cosine. By a marvelous and unique happenstance, there survives an informal exposition of these results with full derivations, written in Malayalam, the vernacular of Kerala, by Jyes.t.hedeva perhaps about 1540. This book, the Gan.ita-Yukti-Bhasa, has only very recently been translated into English with an extensive commentary.18 As a result, this book gives a unique insight into Indian methods. Simply put, these are recursion, induction, and careful passage to the limit.[Mathematics in India via IndiaArchaeology]

10 Responses to Mathematics in India

  1. froginthewell February 18, 2010 at 6:30 am #

    JK, this is particularly exciting, because, while it is true that Mumford is a professor at Brown university, he is much, much more than that. He is a really big mathematician for the work he did in algebraic geometry (which he later quit for some reason I don’t know). He received a fields medal in 1974 (only 48 mathematicians have received the fields medal in history).


  2. raj February 18, 2010 at 6:53 am #

    I had seen an entry onthe MAdhava school in the Brittanica blog, but the link is not working. An extract can be seen in my post http://chennaikaran.blogspot.com/2007/03/we-taught-them-mathematics.html

  3. Nilesh D February 18, 2010 at 9:29 pm #


  4. Sabarish Sasidharan February 18, 2010 at 10:14 pm #

    Not surprising… I would be surprised if such facts made it to Indian mainstream education (schools) though. It would bolster maths education in schools by a huge margin. The very fact that these concepts were ours will push the students to understand them better.

  5. svat February 18, 2010 at 10:53 pm #

    (Apologies if I’m saying things already well-known.)

    Indeed, Mumford is one of the biggest mathematicians, as the first commenter pointed out. (The Fields Medal, is in a way more prestigious than the Nobel Prize, being awarded only once every four years to a mathematician under 40. (I’ve heard (possibly misinformed speculation) that Mumford’s Fields Medal was for work he did with C. S. Seshadri, but the latter was just over 40.))

    Mumford seems to have taken an interest in Indian mathematics lately, as he says on his website under “Current Research”, B) The History of Mathematics is usually taught from a very Western-centric point of view. […] I have been studying Indian math in particular, which is astonishing in both its similarities and differences from the West…. He’s teaching this semester a course at Berkeley (with Hartshorne, another name familiar to everyone in algebraic geometry) on A Cross-Cultural History of Mathematics, which is good.

    Thanks for the link to the review! (Just in case you want to fix the diacritics in the post: Gaṇita-yukti-bhāṣā, Jyeṣṭhadeva.)
    [BTW: have you read George Gheverghese’s The Crest of the Peacock: Non-European Roots of Mathematics?]

    Because Indian mathematics was more algorithmic and algebraic (rather than geometric) and not as proof-focussed as the Greek, historians of mathematics have tended to treat it as if it wasn’t mathematics at all. (In addition to all the usual Eurocentrism; “the Bakshali manuscript cannot possibly be that old” simply because it is too advanced wrt their prejudices about India at the time, etc.) It’s good that there are some people waking up here and there, but a lot needs to be done.

    • jk February 18, 2010 at 11:44 pm #

      When I wrote the post, I did not know the greatness of Prof. Mumford. It is indeed great that Indian math is getting this level of promotion.

      I owned a copy of The Crest of a Peacock, but that was too much math for me.

  6. amit February 19, 2010 at 9:22 pm #

    Actually , we have a rich tradition not just in mathematics but also in Engineering and medicine . The Mayamatam , Samarangana Sutradhara are fantastic examples of secular writings in Engineering !!

  7. vakibs February 20, 2010 at 10:07 am #

    Systematically underplaying the contributions of Indian, Chinese and Arab mathematicians and glorifying those of ancient Greeks had been important for the European colonialist enterprise. Texts which were written centuries ago are continuing to persist in western school books.

    Nobody knows about Indian contributions to geometry, linguistics and algebra. It is simply impossible to teach early mathematics in schools without using Indian discoveries. But nobody knows of them as having been discovered in India. India is thought of as a country which invented “zero”, but it is MUCH more than that.

    Similar is the case with the history of democracy in the world. India had very established republic systems from very ancient past. This has been ascertained by all sorts of visitors, including Alexander’s Greek army. But this Indian contributions to democracy were always downplayed, and it is brandied upon as a western invention.

    And think about it.. Greeks were not even heartland Europeans. They were much closer to Persians and Indians than to the rest of the ethnicities in European continent. They hardly ventured beyond the Balkan mountains. There is a LOT of evidence that Greeks borrowed a lot of knowledge from India and Egypt. This could be especially true of medicine (where Indian Ayurveda system was much more advanced), mathematics (Pythagoras resembles an Indian ascetic saint for all purposes) and astronomy.

  8. Ashok February 23, 2010 at 12:31 am #

    Readers might be interested in George Ghevarghese Joseph’s latest book — ‘A Passage to Infinity: Medieval Indian Mathematics from Kerala’ (SAGE Publications, 2009).


  9. प्रवीण February 24, 2010 at 12:47 pm #

    Very informative post.
    With the same thread I want to share english translation of book “Aryabhatiya from Great Mathematician Aryabatta”. This book was translated from Sanskrit in 1930 and published by University of Chicago Press.
    If someone is interested to experience astuteness of Indian Mathematics can downloand and read book from following link:-

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