It All Came from India, Ch LVIX

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So here’s another piece of ammo for your “everything came from India” uncle –

Newton’s Infinite Series: We heard it in Malayalam first

NEW DELHI: A group of Malayali scholars had predated a ground-breaking Newton ‘discovery’ by over 250 years, according a research paper published on Monday.

The team of researchers from the Universities of Manchester and Exeter reveal that the ‘Kerala School’ identified the ‘infinite series’- one of the basic components of calculus – in about 1350.

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p>And thus, by discovering one of the building blocks of calculus first, Mallu’s used the knowledge to, uh, well, uh, I’m not quite sure…. The researchers were quick to note that this discovery shouldn’t be used to reduce Newton’s stature but instead, add some brown names to the pantheon of genius –

[Dr George Gheverghese Joseph, one of the researcher and Honorary Reader, School of Education at The University of Manchester said,] “The brilliance of Newton’s work at the end of the seventeenth century stands undiminished – especially when it came to the algorithms of calculus.

“But other names from the Kerala School, notably Madhava, Valloppillil, and Nilakantha, should stand shoulder to shoulder with him as they discovered the other great component of calculus- infinite series.

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p>However, Dr. Joseph does note that perhaps, just perhaps, Newton wasn’t inspired by the proverbial apple at all –

…there is strong circumstantial evidence that the Indians passed on their discoveries to mathematically knowledgeable Jesuit missionaries who visited India during the fifteenth century.

That knowledge, they argue, may have eventually been passed on to Newton himself.

Let the attribution games begin! (Hat tip – Venkat & Sindhya)

24 thoughts on “It All Came from India, Ch LVIX”

  2. But other names from the Kerala School, notably Madhava, Valloppillil, and Nilakantha

    Hey Vinod, isn’t that, like, your middle name or something? 🙂

  4. Hey Vinod, isn’t that, like, your middle name or something? 🙂

    or last name… Well done, ancestor of Vinod! Who’s yo daddy, Newton?

  5. if a non european discovered something, it dont count. i mean…a lot of historians reffer to math and science as “western math” and “western science”.

  6. Is it just me or is it a little odd that they don’t mention what exactly these medieval mathematicians did with infinite series – aside from “discovering” them

    Puliogre, where have you seen the phrase “western math”? The word algebra, for one, comes from the name of an Arab mathematician.

  7. Puliogre, where have you seen the phrase “western math”? The word algebra, for one, comes from the name of an Arab mathematician.

    So does the word “Algorithm” — supposed to be derived from an Arab name: “Al Khowarizmi” or something

  9. But other names from the Kerala School, notably Madhava, Valloppillil, and Nilakantha

    Nice try Vinod ! Some of us actually click through to the linked article 🙂

    Mallu’s used the knowledge to, uh, well, uh, I’m not quite sure

    Knowledge for knowledge’s sake (and bragging rights, of course). Actually, if I remember correctly, it’s possible he used it to figure out the path of planets (his predecessors like Bhaskaracharya did).

    I found this BBC radio show on the topic quite interesting (via an old 3QD post) : http://www.bbc.co.uk/radio4/history/inourtime/inourtime_20061214.shtml

  11. A main use of the mathematics the School in Kerala developed was to make calendars (pancha-angam). Accurate measurement of time (before mechanical clocks) using astronomical observations is a difficult mathematical problem. Nowadays, we think of the pancha-angam and jyotisham only in association with astrological superstitions, but in those days there was a real world use for such almanacks. Kerala had the most accurate calendar in the world, until the Gregorian calendar was instituted in the sixteen century AD.

    See http://www.sgrajeev.com/the-almanack for a non-technical discussion of the Kollam calendar as it is used today.

    That uncle of yours that said everything is from India is occasionally right!

  12. My grandpa will be tickled. A handful of his favorite mathematicians are southies 🙂

  15. Dear Friends

    This news has been around for a while. But unfortunately the world takes notice only when it is announced and endorse by z white westerners.

    I don’t think the news is specifically about Kerala. IT just happens the jesuits happened to be there in large numbers during those times and they obtained it from there. Panchanga is common all over India.

    For those who wish to explore further here are some links:

    The Infitisimal Calculus: How and Why It was Imported Into Europe http://www.indianscience.org/essays/31-%20E–Infinitesimal%20Calculus.PDF

    More info http://indiancalculus.info/

    http://indiancalculus.info/book_details.htm#Part%20II

  16. Here’s a neat little write up on the Kerala School. Not surprisngly, it was a white man who first unearthed the claims of Kerala mathematics for broader consumption:

    http://www.siddha.com.my/ubb/Forum3/HTML/000053-8.html

    On recognizing the past: the Kerala School

    Ethnocentrism has been a characteristic of most great civilizations. The Greeks, the Chinese, the Hindus, the Arabs, all imagined themselves in their respective glory days to be unique in some ways, perhaps superior to others.

    So during the first few centuries of modern science many European thinkers imagined that they were the first to discover the scientific mode, and that others had done little, if any, in the field of scientific research.

    At the same time, starting with the European Enlightenment in the 18th century, scholars began to probe into humanity’s cultural legacies. From the untiring quest of such scholars much of ancient history, from Greek and Egyptian to Chinese, Hindu, and Arab science came to be uncovered from their long-forgotten relics. This was and is a slow process. But already in the early 19th century, when it was discovered that the concept of the zero had originated in India, Laplace, one of te greatest mathematicians of the age, wrote: “The ingenious method of expressing every possible number using a set of ten symbols (each symbol having a place value and an absolute value) emerged in India. The idea seems so simple nowadays that its significance and profound importance is no longer appreciated. Its simplicity lies in the way it facilitated calculation and placed arithmetic foremost amongst useful inventions. the importance of this invention is more readily appreciated when one considers that it was beyond the two greatest men of Antiquity, Archimedes and Apollonius.”

    The quest for the forgotten past has continued, not only through archeology which unearths and reconstructs lost civilizations but also by deciphering ancient scripts and translating fading manuscripts in leaves, parchments, and such. One of the results from such efforts was reported by the British scholar Charles Whish in 1835 in the Transactions of the Royal Asiatic Society of Great Britain and Ireland. Whish wrote about mathematicians in Kerala whose significant works had been all but forgotten. He also asserted that some of their ideas were essentially the fluxions of Newton: the derivatives that form the core of differential calculus which is at the core of practically all modern higher mathematics. He went on to unravel in the ancient manuscripts the equivalent of what we now call infinite series, particularly of some trigonometric functions and of pi. Whish’s discoveries were so revolutionary in their interpretation and so demanding in their claims that they was set aside and ignored.

    More than a century later, some Indian historians of mathematics referred back to this paper and pursued the matter to greater depths. More importantly, they have brought all of this to the attention of the larger international establishment.

    Unfortunately, in the meanwhile, historical scholarship had morphed into quarrels over priorities: Indian scholars, in their understandable anger at Western marginalizing of their culture and heritage, accused the European mindset as ethnocentric in interpretations of history; European scholars, in their difficult-to-erase conviction that their own civilization was the one that had developed the results of modern science and mathematics, accused others of excessive claims, fueled by chauvinism rather than facts.

    Leaving aside these controversies which are certain to be resolved in due course, it seems to be now established that the contributions between the 13th and the 16th centuries of what is called the Kerala school of mathematics were path-breaking. To that school belonged such creative mathematicians as Madhva of Sangamagramma who formulated the notion of limit to infinity (a key concept in calculus), Nilakantha who derived an infinite series for pi/4 (the so-called Gregory series), the astronomer Paramesvara who wrote extensively on planetary motions, Jyesthadeva’s 16th century text Yuktibhasa in Malayalam, rich in astronomy and mathematics. One Hindu historian has suggested that their results were transmitted to European thinkers via Portuguese missionary-scholars, and inspired the Scientific Revolution.

    It is fashionable these days to pay frequent and explicit homage to the Islamic world as the root of modern science. Beyond its factual basis, many political forces are at play in drumming up this view. The facts of history may be blown up or belittled, depending on who writes the history, and for what purpose. In this context, the time has come to publicize to the world more vociferously that some of the seeds for those roots were sown in India.

    The eloquent, persuasive and scholarly publications of some Indian historians of science have been gradually accomplishing this in recent years.

    What matters ultimately – or should matter, as I see it – is not national boost or cultural pride but setting the record straight. After all, great thinkers, be they scientists or mathematicians, poets or philosophers, have sprung over the ages from every culture and creed, and they all deserve to be acknowledged in just and fair ways for their contributions, since they all deserve humanity’s collective respect and homage.

  17. Shameless plug, but with more technical information including translation of relevant passages from the yuktibhasha:

    http://www.pas.rochester.edu/~rajeev/canisiustalks.pdf

    Beyond shallow issues of national pride, it is useful to know how important mathematical ideas were discovered; because it can help us to cope with today’s problems. Isn’t that the point of studying any kind of history? Discoveries are not made in a straightforward, deductive way. We work in a fog of ignorance with occasional flashes of insight, and many steps backwards. `Reverse-engineering’ (not actual copying) of competitor’s ideas always plays a bigger part in research than people acknowledge. It would not be shocking if the flourishing of European mathematics (just about the time that missionaries arrived in Kerala) was helped by such a process.I would need hard evidence to be convinced that the missionaries actually transmitted whole mathematical works to Europe. More likely that the European mathematicians heard of some of the results and fragments of theory and were stimulated to think in certain directions as a result.

    Methematics,astronomy, medicine and linguistics have many roots. India is just one of them. Many modern branches of science, like physics, grew out of these original fields.

    It was not the proverbial `white man’ who brought the work of Madhava and his school to light. Credit goes to K. V. Sharma (and his collagues like K. S. Shukla). Also to George Geverghese Joseph for publicizing the history. But Western scholars are indeed the ones that unearthed many other aspects of India’s forgotten intellectual history.

  18. I’m no mathematician, but I don’t think there is serious controversy about the ancient “cosmic math” of India. http://en.wikipedia.org/wiki/Hindu_cosmology, only the extent to which it influenced European discoveries. Nobody tries to hide the origin of the zero or Arabic numbers, as far as I know. Back in the 80s, Carl Sagan went to India, and was filmed there; he discussed the mathematical and astronomical attainments in one of his programs and used them as an introduction for whatever else he launched into. As far as influencing Newton, why not? Genius stands on the shoulders of other geniuses. A genius said that. However, discoveries can also made independently of one another. A little off topic, Newton had what would be today described perhaps as Aspergers syndrome. He couldn’t have explained to anyone how his mind worked. http://news.bbc.co.uk/1/hi/health/2988647.stm

  19. Just to keep the technical people happy. This is my understanding of what the desi dudes did.

    1. Calculate series expansions of sin / cos and inverse tan.
    2. From these they got equivalents of gregories series for pi.
    3. I think there were also continued fraction expansions and these are probably the algorithms used to compute stuff

    On the application, it is the same as it had been all over the ancient world: astronomy. Incidentally, even the napier log tables were actually tables of -log ( sin (x) ) and – log (cos (x) ) for the same reson.

  20. we used to snigger at our high school math teacher for maintaining that De-Morgan’s (of the law’s fame) real name was thiru-murugan, …a little bit of wiki-digging and I realise that he wasn’t that far of the map- sorry TTV, forgive us of unfaithful ingrates..

  21. Beyond shallow issues of national pride, it is useful to know how important mathematical ideas were discovered…

    Hear hear!

    And thanks for the interesting links and additional information, Prof. Rajeev .

  23. Presence of the Kerala school of mathematics is news to me. Thanks for bringing it in the open.

    But already in the early 19th century, when it was discovered that the concept of the zero had originated in India,
    Methematics,astronomy, medicine and linguistics have many roots. India is just one of them.

    In this context, is it true that native South Americans too have the concept of zero? Aztecs, perhaps. May be someone can shed some light on that.