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!

Share this post :

This entry was posted in culture, India, marketing, Science, society. Bookmark the permalink.
  • 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!