Archive for the ‘Uncategorized’ Category

The Kerala school vs calculus teaching today

Wednesday, August 16th, 2017

As pointed out in the previous post, calculus started not with the Kerala school but with the dalit Aryabhata, of Patna, in the 5th 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…)

Kerala school vs Bihar university

Wednesday, August 16th, 2017

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 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.”

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 16th c. Not in the last two centuries since Whish. The only answer is the one I have provided. (more…)

George Joseph: serial plagiarist

Tuesday, August 15th, 2017

1-The fraud-news blitz

Ten years ago, on 14/15 Aug 2007, on the 60th 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 16th 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 50th 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.

HT front page news
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.HT plagiarism report 8 Nov 2004

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

Myth, math, and censorship

Thursday, August 3rd, 2017

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.

Black mother of math?

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…)

Decolonising math and science: Amsterdam

Saturday, July 8th, 2017

My talk to the Critical Collective co-organized by the New Urban Collective and the University of Color at the University of Amsterdam on Decolonising mathematics and science.

This was followed by an interview with Grapevine TV.

Western superstitions in science

Wednesday, February 1st, 2017

The Black House Kollective initiated a welcome conversation in Soweto on decolonisation in relation to Western superstitions in science.

Soweto poster

For example, the first lesson in science is typically about Newton’s “laws”. But how do we know there are any eternal laws of nature? That was just a church dogma enunciated by Aquinas in Summa Theologica.  (Recall how a priest given a PhD in philosophy of science by Cambridge tried to turn the classroom into a pulpit, at Universiti Sains Malaysia, but could not state a single eternal law of nature when repeatedly challenged to do so.) Of course, a non-mechanistic physics is possible, as I have shown.

More subtle is the creep of superstitions into science through the metaphysics in formal mathematics, falsely declared to be universal (or superior) with the help of false myths like those of Pythagoras and Euclid PLUS false myths of the deductive proofs in the Elements PLUS false myths about the infallibility or superiority of deductive proof.

However, colonised minds, who believe in and propagate these superstitious beliefs, are terrified when asked to publicly explain why 1+1=2 in formal math. So far, no formal mathematician, anywhere in the world, has shown the guts to try to defend formal math in public. That itself tells everyone that the truth is with normal math.

Here is the initial part of the very interesting conversation in Soweto (3.5 MB mp3 file) and a photo of the participants.

Trailer of conversation in Soweto

Participants in Soweto meet

Protest against racist censorship

Friday, November 4th, 2016

False history of the kind that “Much, though certainly not all, mathematics was the creation of dead white men” has been traditionally used to defend racism. My Euclid challenge prize for Rs 2 lakhs is offered to demonstrate that this racist history is based on faith not any facts. Therefore, the only way to save that rotten history is to prevent its articulation. Hence the Conversation took down my article “To decolonise math, stand up to its false history and bad philosophy.” Here are two protest letters and an article.

1.Protest letter to Conversation from Decolonial International Network

2. Protest letter from Mr S. M. Mohamed Idris, Chairman, Citizens International, to International Association of Universities.

3. Note on censorship of decolonised math.

As a mark of protest against this censorship do reproduce the  original article re-posted at Or link to it. Feel free to reproduce the protest letters, (more…)

To decolonise math stand up to its false history and bad philosophy

Wednesday, October 26th, 2016

[This article was first published in the Conversation (Global edition) on 24 October 2016. It quickly reached a readership of 16737, before being taken down, obviously because it represents a dangerous piece of dissent against racism and colonialism. For more details see the next blog post. ]

A false history of science was used to initiate colonial education, in support of colonialism. This false history persists. In a recent article about decolonising mathematics, for instance, Professor Karen Brodie asserts that “Much, though certainly not all, of mathematics was created by dead white men.”

This is not true.

A false history

Consider the most elementary mathematics of fractions. Did the white man invent it? No. The Rhind papyrus shows that black Egyptians knew about fractions from at least 3700 years ago. Moreover, Greeks and Romans did not: there is no systematic way to represent fractions in traditional Greek and Roman arithmetic. Europe imported the arithmetic of fractions, and it came into the Jesuit syllabus only around 1572, and the white man finally started learning what Ahmose the scribe was teaching black children 3000 years earlier.

What mathematics could “dead white men” have created without even a knowledge of fractions?

Of course, Western historians have long claimed that “real” math was invented by Greeks: Pythagoras, Euclid and so on. However, Pythagoras is myth and there is no historical evidence for Euclid, as I’ve explained in my book Euclid and Jesus.

The “evidence” for Euclid is so thin, that I’ve instituted a challenge prize of around R40,000 for serious evidence about Euclid. This stands unclaimed and has done for several years.

Further, though the text Elements (which Euclid supposedly wrote) comes from Alexandria in Africa, its author is commonly visualised as a white man. But it is rather more likely that the anonymous “author of the Elements” was a black woman.

When this is pointed out, some people try to save the myth: they say they don’t care about the author, only the book. However, it is another false Western myth that the book Elements is about deductive proofs. The actual book contains no pure deductive proofs. Its very first proposition is proved empirically, as is its fourth proposition (the side angle side theorem), needed for the proof of its penultimate proposition (“Pythagorean proposition”).

Deductive proof doesn’t lead to valid knowledge

Stripping off the false history exposes the central philosophical claim: that “real” math is about deductive proofs which are infallible and lead to “superior” knowledge. However, that claim too is false: deductive proofs are fallible. So an invalid deductive proof can be easily mistaken for a valid one. For centuries, the most authoritative Western scholars collectively made this mistake, when they wrongly praised “Euclid’s” Elements as a model of deductive proof.

Worse, even a validly proved mathematical theorem is only an inferior sort of knowledge, since we never know whether it is valid knowledge. For example, the “Pythagorean theorem” is not valid knowledge for triangles drawn on the curved surface of the earth. However, Europeans kept applying the “Pythagorean theorem” to such triangles to determine latitude and longitude on their navigational technique of “dead reckoning”. This led to centuries of navigational disasters and made navigation – and determination of longitude – the key scientific challenge for Europeans from the 16th to the 18th centuries.

In fact, a mathematical theorem need have no relation at all to valid knowledge. For example, we can easily prove as a mathematical theorem that a rabbit has two horns: 1. All animals have two horns. 2. A rabbit is an animal. 3. Therefore, a rabbit has two horns. This is a valid deductive proof, but is the conclusion valid?

Mere deductive proof does not lead to valid knowledge. We must check whether the assumptions are true. In this case the assumptions are false: simply point to an animal which has no horns. However, formal math forbids such commonsense, empirical proofs, based on its central dogma that deductive proofs are “superior”.

Anyway, the postulates of formal mathematics, say set theory, cannot be empirically checked. So formal mathematics is pure metaphysics. The only way to check its assumptions is to rely on authority – and in practice we teach only those postulates approved by Western authority. For example, calculus is done with formal real numbers (and not Indian non-Archimedean arithmetic, or floating point numbers used in computer arithmetic). School geometry is taught using Hilbert’s far-fetched synthetic postulates, not Indo-Egyptian cord geometry.

A slave mentality

Thus, formal mathematics creates a slave mentality. It creates a person who blindly relies on Western authority and conflates it with infallible truth. So finding better ways of inculcating that slave mentality – teaching the same maths but differently, as Brodie proposes in her article – is absolutely the last thing we should do.

False claims of “superiority” are a trick to impose Western authority, exactly as in apartheid. Everyone understands 1+1=2 in a commonsense way. But Whitehead and Russell took 378 pages in their Principia to prove 1+1=2. Declaring such mountains of metaphysics as “superior” knowledge has political value. People who cannot understand those 378 pages “needed” for 1+1=2 are forced to trust an “expert”.

The entire colonial tradition of education teaches us to trust only Western-approved experts, and distrust everyone else. This creates epistemic dependence for even the simplest things like 1+1=2, making epistemic dissent impossible.

But epistemic dissent is central to decolonisation. And much work has already been done to decolonise mathematics.

A successful alternative

There is an alternative philosophy of mathematics, consolidated in my book Cultural Foundations of Mathematics and now renamed zeroism.

It rejects the Western metaphysics of formal mathematics as religiously biased since the days of Plato, who related mathematics to the soul. Actual teaching experiments have been performed with eight groups in five universities in three countries – Malaysia, Iran and India.

This decolonised math is so easy that the calculus can be taught in five days. Work on this approach to decolonising mathematics and science has been reported in various meetings on decolonisation organised by the Multiversity. It was publicly discussed in newspapers, and blogs, and prominently reported in newspapers, magazine articles, interviews and videos.

Decolonised math rejects the redundant metaphysics of formal math as inferior knowledge. It reverts to a commonsense practical philosophy of mathematics as a technique of approximate calculation for practical purposes. By making math easy, it enables students to solve harder problems that are usually left out of existing courses. It also leads to a better science, the simplest example being a better theory of gravitation arising from correcting Newton’s wrong metaphysical presumptions about calculus.

(CK Raju explains how decolonised maths leads to better science. [Click image to go to video of MIT talk])

In short, math can be decolonised. The simple way to do it is to have the courage to stand up to its false Western history and bad Western philosophy, and focus solely on its practical value.

Author’s note: Publication details for cited references are available here.

Conversation with the Dalai Lama

Wednesday, October 26th, 2016

The video of my conversation with the Dalai Lama is now on You Tube.


It is also still available on the official site .

Reports of this appeared in Tibet Post,

Tibet Post

and in the Sunday Guardian

and sundry news agency reports.

Gravitational waves and Einstein

Tuesday, February 16th, 2016

What did Einstein really say about gravitational waves?

First, the background. In almost twenty five years, no one has answered the objections I raised about Einstein. Namely that he did not fully understand the special theory of relativity invented by Poincare. Special relativity requires functional differential equations, as Poincare realised. But Einstein never understood that till the end of his life, and kept trying to approximate functional differential equations by ordinary differential equations which is manifestly a mistake. See my book Time: Towards a Consistent Theory (Kluwer Academic, 1994).

In the more recent series of articles on FDEs in Physics Education, the first article explains the mistake.

Sadly, though special relativity is a first year undergraduate subject, it continues to be taught incorrectly. Even at that elementary level, scientists go by the force of social authority, and just ignore the force of a scientific argument.

Further, even in the case of general relativity, it is known that Einstein had the wrong equations before Hilbert sent the right equations to him. Withing 5 days he then claimed he had suddenly and coincidentally arrived at the same equations independently of Hilbert, just as he claimed he suddenly and coincidentally arrived at the special theory of relativity shortly after Poincare’s article on it was published!

Now, the popular image of Einstein is as a great mathematician, but knowledgeable people understood that Einstein was ignorant of mathematics: as Hilbert said, “every boy in the streets of Goettingen knows more about 4-dimensional geometry than Einstein”. (more…)