The previous blog post contains two important points which need some elaboration. The first is elaborated in this post the second in the next.<\/p>\n
To quote:<\/p>\n
\u201cThey made out the Indian calculus to be solely a product of Kerala, when in fact, as explained in my book, it originated in Patna, in the 5th<\/sup> c., with Aryabhata, a lower caste person. The Kerala school certainly developed it further (and these highest-caste Brahmins from the south, such as Nilakantha Somasutvan, had no difficulty in honestly calling themselves disciples of the low-caste Aryabhata from the north). Even the later achievement of Madhava involved essential inputs from Narayana Pandit of Benaras, as explained in my calculus book. That is, the Indian calculus was a pan-India development, and NOT a product of the Kerala school alone. But, this important story of national integration across regions and castes, in pre-colonial India, is lost in the story of regional chauvinism personally profitable to the thieves who did not understand the subtleties of what they stole.\u201d<\/p><\/blockquote>\n
The reference to Aryabhata as a lower-caste person is explained in this article<\/a> first presented at a seminar on \u201cDalit Narratives in Philosophy\u201d, at Patna, and variously published.<\/p>\n
The infinite series from Kerala are known to Western scholars since the 1832\/1835 paper of Whish. These include the sine series claimed by Newton and the series for \u03c0<\/span> claimed by Leibniz. These claims of \u201cdiscovery\u201d were based on the genocidal Doctrine of Christian Discovery<\/a>, that a piece of land (or knowledge) belongs to the first Christian to spot it. (As in the beliefs that Columbus \u201cdiscovered\u201d America or Vasco da Gama \u201cdiscovered\u201d India, so also in scientific discoveries.) As the US Supreme Court observed, though this was a papal doctrine, Protestant countries like Britain (from which US inherited its laws) fully accepted it. Newton implicitly referred to this doctrine when he called Leibniz the \u201csecond discoverer\u201d of the misnamed \u201cLeibniz\u201d series or the equally misnamed \u201cGregory\u201d series, chauvinistic nomenclature, a Western mumpsimus which must be abolished.<\/p>\n
Because colonial pride and power were both based on false history (of early Greeks, \u201cthe friends of Christians\u201d as Eusebius called them, followed by such Christian \u201cdiscoveries\u201d), the finding of infinite series in India was a shock. Since infinite series are an easily identifiable aspect of calculus, today, many people who do not properly understand the calculus, have taken up the refrain of the \u201cKerala school\u201d.<\/p>\n
However, how were the Indian infinite series summed? No one else has given an answer. Not when the calculus first went to Europe in the 16<\/strong>th<\/strong><\/sup> c. Not in the last two centuries since Whish. The only answer is the one I have provided. <\/strong> <\/p>\n
Because apologetic Western historians like Pingree and his student Plofker do not understand the answer, and anyway their mission is to run down Indians, as much as possible, they chortle that Indians did not have the metaphysics of limits. Obviously not. Indians did not think of math as malleable metaphysics in the manner of the church or formal math. Thank goodness!<\/p>\n
As I have pointed out (see, e.g. my articles for the Springer Encyclopedia on \u201cCalculus\u201d1<\/sup><\/a>, \u201cCalculus transmission\u201d2<\/sup><\/a>, and \u201cZeroism\u201d3<\/sup><\/a>) Indians used Brahmagupta’s avyakt ganit<\/em> to sum infinite series, such as the sum of the infinite<\/em> geometric series given by Nilakantha. (The finite<\/em> geometric series is very old and found in the Yajurveda and the Rhind papyrus etc.) As explained in my book, this is equivalent to limits by order counting. (See, also the following blog post.)<\/p>\n
Secondly, ignoramuses like Iain Pearce who are promoted as historians of math, on the strength of a single unpublished and un-publishable essay, praising a plagiarised paper) are decidedly ignorant even of high-school math (since he could not spot the errors in elementary math in the plagairsied paper he praised). They are also ignorant of Sanskrit, hence lack access to any Indian primary sources. Indeed, they are so ignorant of Indian culture, they cannot even tell the difference between one Narayana and another. (Narayana is a common name, as common as Smith.) At a meeting in US, in 2004, Pearce foolishly asserted that Narayana Pandit of Benaras was from the \u201cKerala school\u201d! Ha! Ha!<\/p>\n
There is even an attempt to incorporate Aryabhata of Patna into the \u201cKerala school\u201d an attempt which the late K. V. Sarma (who coined the term \u201cKerala school\u201d) vigorously refuted.<\/p>\n
To add to K. V. Sarma’s points, Bihar was obviously the key centre of knowledge in 5th<\/sup> c. India and remained so, as we learn from Hiuen Tsang. The Tabaqqat-i-Nasiri describes how Mohammad-i-Bakhtiar-i-Khalji destroyed the University of Nalanda in the 12th<\/sup> c., and killed all the \u201cBrahmins with shaven heads\u201d and there was no one left to read the books (which he burnt), for in the \u201cHindui language Bihar or Vihar means college\u201d. He left behind his insignificant legacy in the village of Bakthiarpur near Nalanda.<\/p>\n
References<\/h3>\n
\n1<\/a>\u201cCalculus\u201d<\/span>, \tEncyclopedia of Non-Western Science, Technology and Medicine<\/em>, \ted. Helaine Selin, Springer, Dordrecht,\u00a0 2014, 2016, pp. pp. \t1010-1015. \thttp:\/\/ckraju.net\/papers\/Springer\/ckr-Springer-encyclopedia-calculus-1-final.pdf<\/a>.<\/p>\n<\/div>\n
\n2<\/a>\u201cCalculus \ttransmission\u201d, Springer Encyclopedia above, pp. 1016-1022. \thttp:\/\/ckraju.net\/papers\/Springer\/ckr-Springer-encyclopedia-calculus-2-final.pdf<\/a>.<\/p>\n<\/div>\n
\n3<\/a>\u201cZeroism\u201d, \tSpringer Encyclopedia above, pp. 4604-4610. \thttp:\/\/ckraju.net\/papers\/Springer\/zeroism-springer-f.pdf<\/a>.<\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"
The previous blog post contains two important points which need some elaboration. The first is elaborated in this post the second in the next. To quote: \u201cThey made out the Indian calculus to be solely a product of Kerala, when in fact, as explained in my book, it originated in Patna, in the 5th c., with Aryabhata, a lower caste person. The Kerala school certainly developed it further (and these highest-caste Brahmins from the south, such as Nilakantha Somasutvan, had no difficulty in honestly calling themselves disciples of the low-caste Aryabhata from the north). Even the later achievement of Madhava involved essential inputs from Narayana Pandit of Benaras, as explained in my calculus book. That is, the Indian calculus was a pan-India development, and NOT a product of the Kerala school alone. But, this important story of national integration across regions and castes, in pre-colonial India, is lost in the story of regional chauvinism personally profitable to the thieves who did not understand the subtleties of what they stole.\u201d The reference to Aryabhata as a lower-caste person is explained in this article first presented at a seminar on \u201cDalit Narratives in Philosophy\u201d, at Patna, and variously published. The infinite series from Kerala are known to Western scholars since the 1832\/1835 paper of Whish. These include the sine series claimed by Newton and the series for \u03c0 claimed by Leibniz. These claims of \u201cdiscovery\u201d were based on the genocidal Doctrine of Christian Discovery, that a piece of land (or knowledge) belongs to the first Christian to spot it. (As in the beliefs that Columbus \u201cdiscovered\u201d America or Vasco da Gama \u201cdiscovered\u201d India, so also in scientific discoveries.) As the US Supreme Court observed, though this was a papal doctrine, Protestant countries like Britain (from which US inherited its laws) fully accepted it. Newton implicitly referred to this doctrine when he called Leibniz the \u201csecond discoverer\u201d of the misnamed \u201cLeibniz\u201d series or the equally misnamed \u201cGregory\u201d series, chauvinistic nomenclature, a Western mumpsimus which must be abolished. Because colonial pride and power were both based on false history (of early Greeks, \u201cthe friends of Christians\u201d as Eusebius called them, followed by such Christian \u201cdiscoveries\u201d), the finding of infinite series in India was a shock. Since infinite series are an easily identifiable aspect of calculus, today, many people who do not properly understand the calculus, have taken up the refrain of the \u201cKerala school\u201d. However, how were the Indian infinite series summed? No one else has given an answer. Not when the calculus first went to Europe in the 16th c. Not in the last two centuries since Whish. The only answer is the one I have provided.<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3,4,8,1],"tags":[],"class_list":["post-133","post","type-post","status-publish","format-standard","hentry","category-history-and-philosophy-of-mathematics","category-history-and-philosophy-of-science","category-science-and-society","category-uncategorized"],"_links":{"self":[{"href":"https:\/\/ckraju.net\/wordpress_F\/index.php?rest_route=\/wp\/v2\/posts\/133","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/ckraju.net\/wordpress_F\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/ckraju.net\/wordpress_F\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/ckraju.net\/wordpress_F\/index.php?rest_route=\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/ckraju.net\/wordpress_F\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=133"}],"version-history":[{"count":0,"href":"https:\/\/ckraju.net\/wordpress_F\/index.php?rest_route=\/wp\/v2\/posts\/133\/revisions"}],"wp:attachment":[{"href":"https:\/\/ckraju.net\/wordpress_F\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=133"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/ckraju.net\/wordpress_F\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=133"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/ckraju.net\/wordpress_F\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=133"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}