On The Origins of Homo Mathematician and Professor Calculus

On the occasion of India’s 60th Independence Day, the news world and blogosphere is abuzz with the news story that Calculus was created in India, 250 years before Newton.

The official news source says:

A little known school of scholars in southwest India discovered one of the founding principles of modern mathematics hundreds of years before Newton according to new research. Dr George Gheverghese Joseph from The University of Manchester says the ‘Kerala School’ identified the ‘infinite series’- one of the basic components of calculus – in about 1350.

And 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.

While admitting factors such as the obscure medieval Malayalam language of the source, Dr. Joseph further adds the European imperialist angle:

There were many reasons why the contribution of the Kerala school has not been acknowledged – a prime reason is neglect of scientific ideas  emanating from the Non-European world – a legacy of  European colonialism and beyond.

For some unfathomable reasons, the standard of evidence required to claim transmission of knowledge from East to West is greater than the standard of evidence required to knowledge from West to East.

There are several cynical responses to this current news item. From ‘What’s new? We knew this all along!’, to ‘So what? Of what use was the Indian invention if it remained in obscurity in a remote Indian region?’.

To be fair, the press journalists obviously not trained in mathematics, did exaggerate. The Taylor Series of trigonometric functions and representation of Pi are building blocks of Calculus. They do not, in themselves, form the entire branch of mathematics that is Calculus. Not surprisingly, Dr. Joseph’s origins are from Kerala!

There is nothing new in this discovery as Wikipedia shows. But I’m inclined against dismissing and ignoring this news altogether, for three reasons:

1. Imperialism certainly plays a factor in how knowledge spreads. While these medieval Indians used mathematics to create almanacs and calendars, the Europeans used it for navigating to conquer other lands. It is because of imperialist adventurous travelers that knowledge spread during most of mankind’s history. Imperialism and its derivatives are still very much in action. For instance, check the history of Wikipedia’s article on the Kerala School, after this story broke out in major news circles.

2. The truth about this was known before, but it was known only to a select few. Forget calculus, how many knew the truth about Pi? Shashi Tharoor wrote about it, but we couldn’t make him the UN Secretary General. The excellent project and site, History of Indian Science and Technology provides fascinating insights into the scientific achievements of Indians in fields such as township planning, water management, healthcare, surgery, metallurgy, etc. It even has a paper on exactly how and why the Taylor series and building blocks of Calculus were imported to Europe from India (PDF).

But how many of us know all this? Indians need to learn the art of marketing from the Westerners. We excel in science and technology, arts and philosophy. But we cannot sell well. We cannot put the right ‘spin’, such that the world takes notice. Once the exaggerated headlines hit the world press, the blogosphere pounces on them, tearing them to shreds in analysis and comments and trackbacks. That’s how information is disseminated. True, it’s not always correct. But at least more people will think of India the next time they encounter Calculus!

3. This story highlights how we must cherish and safeguard our knowledge assets. Most scientific texts of the ancient times are in a dilapidated condition, neglected in universities and shrines. There are projects by the Government and Google to digitize them, as I’d written earlier. Just like corporations prize knowledge management, countries should too!

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  • We cannot sell ourselves – yes. But isn’t it an Eastern cultural thing? After I came here, all I noticed is that people keep talking and exaggerating about themselves. Time and again they train us to repackage our humble achievements and present them as if we did something to save the world.

    I feel so proud that Indian civilization made unbelievable advances in science and philosophy while the kiddie civilizations were learning to crawl. But, what did we do after that? The knowledge renaissance sortof started to stagnate with the imposition of caste system, then the Moughals arrived and we started losing most of what we had.

    You raise an important point about making Indians aware of the awesome things their ancestors did. BUT, I’m sure the pseudo-secular parties (read Congress, Left and rest of the crap) will tag it as saffronization of education (without bothering to know what this term means).

    Nevertheless, this revelation is a reason to cheer.

  • Priyank, yes, it is an Eastern cultural thing, and I think we need to change it in the more and more globalized world. Countries who sell themselves better will attract more tourism, more investment, and thus have more economic opportunities. Our recent campaigns during the World Economic Forums are manifestations of how we can attract investment if only we learn to sell.

    You are right. We have lost what we had in the ancient times. It is indeed shameful. But rather than lamenting on the past, I’m trying to focus on what we can do today.

    //…will tag it as saffronization of education//
    You are so right. That’s why, the HIST project I referenced is very important. Their home page introduction is itself encouraging: “Others who are deeply brainwashed in India phobia might find it convenient to dismiss this book series as “Hindutva”, “right-wing fundamentalist”, and so forth. This is completely baseless since Indian science is not about any particular religion. It is the heritage of every Indian, regardless of faith or lack thereof. Just as Newtonian laws are not Christian and Einstein’s relativity theory is not a Jewish science, so also the scientific discoveries of Indians are independent of their faiths.”

    I really hope they succeed in their venture!

  • Of course this confirms something that I have known all along: There are only two kinds of mathematicians in the world. Indians, and those who know math only because of Indians.

    PS: aikaterine would probably relate to this 😉

  • 🙂 It reminds me of a russel peters’ joke about India’s greatest contribution to mathematics being “zero” and he remarks – “You see. We Indians have always been so cheap ass and miserly that even our biggest contribution is a zero”
    Perhaps now we can lay some claim to the other end of zero, namely infinity 🙂

  • Sorry, Mahendra, I have no useful contributions to your post, but Russell Peters rocks, bloody!

  • This is a very interesting post, Mahendra! I have known for sometime that India was a powerhouse of mathematics in the ancient world, but this gives me new insights. Thank you!

    Not too long ago, Faisal left a comment on my blog that a Hindu professor of his recently told him an advantage the West had over many other cultures came down to this: In the East, knowledge typically was passed on secretly to an insiders group, while in the West knowledge was typically passed along publicly to everyone. So, it was easier to loose knowledge in the East than in the West. Do you know anything about that?

  • Paul,
    He is partially right. Knowledge (at least certain kinds – scripture, philosophy, mathematics etc ) was, for a long time, “owned” by one community/caste – the Brahmins. Even among other communities, because of the profession based delineation of the castes, all knowledge of a particular kind (say agriculture or tanning or weaving) was closely held within that caste.
    The second big reason is the oral tradition. Very few things were ever written down for a long time. The habit of keeping knowledge within one’s caste’s insider group contributed to this. It was safer for father to pass knowledge orally than write it down and run into the risk of the knowledge becoming public.

  • Paul: thanks! I’m glad!

    Ashok: thanks for responding on my behalf! 🙂

  • Mahendrap,

    Thanks for linking to this post on my site. It’ll take me a while to read through all the links you have provided.

    But the first thought that came to my mind upon reading your post–and the news article–was that what does this say about the controversy surrounding Leibniz’ claim to the invention of the Calculus? If the Keralite Dr. Joseph wishes to have the “Kerala School” lay claim to some fundamental ideas of calculus, then what about the historical accounts that talk about how Leibniz and Newton both independently arrived at the mathematical invention, with the only question to be resolved being–who came up with it first? And therefore, who should be credited with the invention?

    On another point: Krishahok and Paul are not right in differentiating the transmission of knowledge between the East and the West as being mostly esoteric and guarded in the former while being free and open in the latter. Historical accounts also relate how the Greeks were very secretive about their domains of knowledge–often regarding that specific domain of knowledge as mystical avenues to the realm of Gods and higher beings–for which reason, greeks have known to have several secret societies and “brotherhoods”, a tradition which carried on even throughout the better part of the Enlightenment. Indeed, I wonder if the present institutional phenomena of “Greek societies” both in and out of academic insititutions is a throwback to this era of secret societies in the west.

  • Ergo:

    This news does not indulge in the Newton/Leibniz controversy because both of them started work on this only after the 1660s, whereas this invention of the infinite series is from the fourteenth century. My take on this is that there is no single “it” that needs an inventor to be credited. Infinite series should be credited to the Kerala school (if their evidence is substantiated), while integral and differential calculus were independently discovered by both Newton and Leibniz independently, as is the consensus today.

    Thanks for the insight regarding the Greeks. I wasn’t aware of this Greek culture, and am shocked to learn about “Greek societies” in today’s institutions!