C. K. Raju’s Blog

As pointed out in the previous post, calculus started not with the Kerala school but with the dalit Aryabhata, of Patna, in the 5^th c. The Aryabhata school in Kerala acknowledged him as their master, and Nilakantha somasutvan wrote a commentary (bhashya) on the Aryabhatiya. To repeat, the Indian calculus was a pan-India development, and NOT a product of the Kerala school alone.

In particular, though infinite series are an easily recognized aspect of calculus, the emphasis on them is misleading, especially for the purpose of teaching Indian calculus in universities today. The above quote in the earlier blog post continues:

“Further, if we teach the Indian calculus today in universities (as I do) the focus will be only on what Aryabhata did. So, the plagiarists’ false understanding of history also prevents us from reforming calculus teaching today. Neither of the plagiarists understands the calculus well enough to teach it.”

Another quote, in the earlier blog post, closely related to this is the following.

“Like all plagiarists, Joseph and Almeida made horrible blunders while restating my thesis (stated in the Hawai’i paper,¹ that the calculus developed in India with a different epistemology). For example, in one of their papers in Race and Class they asserted “the Kerala mathematicians used the floating point numbers”, used in modern-day computers. Ha! Ha! Ha! What a joke! Only complete ignoramuses like the two plagiarists could have thus misunderstood my thesis about floating point numbers stated in my Hawai’i paper, which was part of a course on C-programming that I was then teaching as Professor of computer science.”

No doubt this was a blunder, but why was this a horrible blunder? Because a different number system was at the heart of the Indian method of summing infinite series, but Europeans did not understand it (and did not understand how to sum infinite series), and Western historians like Plofker do not understand it till today.

This lack of understanding of Indian calculus by Europeans had serious consequences: it led to the failure of Newtonian physics. I have analysed Newton’s error in understanding the Indian calculus, the consequent conceptual error in the notion of time in his physics, responsible for the failure of his physics, and proposed a corrected theory of gravitation.² (An expository account of the new theory of gravitation is also available.³) The point about floating point numbers used to do calculus on computers is further explained in the course of this analysis, as is the point about avyakt ganit. Floats are a finite set, smaller than formal reals, with no recognizable algebraic structure, because the associative law fails even for addition; avyakt ganit results in a “non-Archimedean” ordered field larger than formal reals. Calculus can be done with number systems smaller or larger than formal reals, university calculus as taught today is not the only way to do calculus as some foolish historians assume.

The matter is simple, the Indian use of avyakt numbers very naturally led to avyakt fractions which are today called rational functions and correspond to the use of so-called non-Archimedean arithmetic. (more…)

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:

“They 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 5^th 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.”

The reference to Aryabhata as a lower-caste person is explained in this article first presented at a seminar on “Dalit Narratives in Philosophy”, 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 π claimed by Leibniz. These claims of “discovery” 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 “discovered” America or Vasco da Gama “discovered” 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 “second discoverer” of the misnamed “Leibniz” series or the equally misnamed “Gregory” series, chauvinistic nomenclature, a Western mumpsimus which must be abolished.

Because colonial pride and power were both based on false history (of early Greeks, “the friends of Christians” as Eusebius called them, followed by such Christian “discoveries”), 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 “Kerala school”.

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^th c. Not in the last two centuries since Whish. The only answer is the one I have provided. (more…)

1-The fraud-news blitz

Ten years ago, on 14/15 Aug 2007, on the 60^th anniversary of India’s independence, PTI London released a piece of fraud news. All major newspapers in India prominently carried it, Hindustan Times on the front page, The Hindu on the back page etc. According to the news, two British researchers from Manchester and Exeter universities had established that the calculus developed in India before Newton. But they added that this left Newton’s greatness unaffected.

The news was based on a press release posted on the Manchester university website (now removed from its site, since it was a fraud, but archived here).

The news was also carried internationally, for example, by the London Telegraph. I phoned them, and pointed out that I had recently published a whole book dealing with the transmission of the calculus. Cultural Foundations of Mathematics (Pearson Longman. 2007). The subtitle of the book itself said this: it was “The nature of mathematical proof, and the transmission of the calculus from India to Europe in the 16^th c. CE”. The book emphasized the development of calculus in India with a different philosophy of mathematics, and its theft by Cochin-based Jesuits. This theft of knowledge was carried out to solve the major scientific challenge then facing Europe: navigation. But, after stealing it, the same churchmen wrote utterly false histories glorifying the West by claiming that Newton and Leibniz invented the calculus. Colonialism was built on this false history, not any technological superiority, as I have explained elsewhere.

My calculus book was the culmination of a ten year effort since 1997, partly funded by two agencies: the Indian National Science Academy since 1998 (Project on Madhava and the Origin of the Calculus), and the Project of History of Indian Science, Philosophy and Culture, with which I was associated since its inception in the early 90’s, but accepted an Editorial Fellowship only in 1999. The 500-page book (an authored volume, not an edited volume) was the 50^th volume in the PHISPC series.

When I brought this to the notice of the London Telegraph they said they had not checked the news, and removed the fraud news item from their website.

In Hindustan Times the front page news carried the signature of Vijay Dutt their London correspondent.

I contacted the HT office, and further pointed out that one of the purported authors of the Manchester paper had been earlier involved in plagiarising my work and warned in 2004 by Exeter University. The HT had given prominent coverage to that news in 2004.

(If the above is difficult to read, download the pdf file posted here.) (more…)

My article on “Mathematics and censorship” appeared in Kafila on 25 June 2017.

The original censored article “To decolonise math stand up to its false history and bad philosophy” was first published in the Conversation (global edition), in October 2016. It went viral and was removed by the South Africa editor on the lame ground that “You sited [sic] yourself”. Meaning, you brown man, what right do you have to talk of a new philosophy of mathematics? What right do you have to demand evidence for Greeks like Euclid? What right do you have to say that mathematics may have had a black mother not a white father? Don’t you know Conversation boasts of academic rigor, and that means you can only cite the work of others approved by White/Western reviewers. That is our (unstated) editorial standard.

In India the censored article was re-published by Wire and Scroll. Both took it down when the Conversation did. But Wire put it back with an apology. The article currently survives here on this blog, on Wire, and on Science 2.0. The article was recently reproduced in full as part of a peer-reviewed scholarly article published in Journal of Black Studies, a draft of which is available online.

To reiterate the Conversation failed to find anything wrong with the article. It was unable to refute a single point or a single sentence in the censored article. So, the real reason to censor the article was to protect vested interests. What are those vested interests?

One such vested interest obviously relates to White domination, which persists not only in post-apartheid South Africa but elsewhere. On a myth that is still taught to Indian school children “Euclid” is declared the father of mathematics and our school texts carry an image of him as white-skinned.

However, as my censored article pointed out, there is nil evidence for the very existence of Euclid leave alone for the color of this skin. I objected to it, but the NCERT did nothing; Narlikar, Sinclair and Co,  wanted to propagate false stories. To drive the point home, I then offered a prize of Rs 2 lakhs for the slightest serious evidence about Euclid. No one claimed the prize.

Obviously there is ample counter evidence that the book Elements attributed to Euclid, was written long after his purported time, by someone else, a woman who was in all probability black as portrayed on the cover of my book Euclid and Jesus.

This “black mother of mathematics” was raped and killed on the altar of a church (though the censored article did not mention this last fact because it was tightly edited in collaboration with the Conversation editor and limited to 1000 words,). Myths are a source of power, so this attack on their myths enraged the racist Whites in South Africa. They first tried the usual technique of “proof by abuse”. When that failed, censorship was applied.

However, the actual vested interests are deeper than one imagines. (more…)