## George Gheverghese Joseph serial plagiarist and mathematical ignoramus, invited for conference on math education by Hyderabad University. Part II: the ill effects of cheater-teachers on mathematics education

Please read part 1 of this blog post first.

Plagiarism, or the theft of knowledge, whether of the calculus, or of the calculus transmission thesis, has ill effects on mathematics education. This is not just about cheating in exams. When cheaters turn teachers it will naturally create a problem for the students.

As explained in part 1 of this blog post, in my Hawai’i paper of 2000 I had proposed a tough new standard of evidence for the history of transmission of calculus, as “proof beyond reasonable doubt” as in criminal law. This paper involved the very thesis that Joseph and Almeida have serially plagiarised over the last 18 years in the most shameless way imaginable.

However, later on, in my book *Cultural Foundations of Mathematics: the nature of mathematical proof and the transmission of calculus from India to Europe in the 16*^{th}* c. CE* (Pearson Longman 2007) I introduced a further test for transmission: the epistemic test. Those who cheat and copy, like students in an exam, do not fully understand what they copy. Hence, lack of understanding is positive proof of copying in a suspicious context. (I used to apply this test to my students,) Therefore, imitating the plagiarists spreads a wrong understanding of mathematics. Let us first take the case of calculus.

Though Europeans stole the Indian calculus (for their navigational needs) and understood some of its practical value, they did not fully understand it, exactly in the way they had earlier failed to fully understand imported Indian arithmetic for centuries.

Two simple examples are as follows. Precise trigonometric values were a key motive for the theft of the calculus. The Indian calculus was used to calculate the most precise trigonometric values then known (accurate to 9 decimal places). Arithmetically challenged Europeans desperately needed those values for a solution of their navigational problems (to determine loxodromes, latitude, and longitude at sea), as acknowledged in the huge prizes instituted by various European governments from the 16^{th} to the 18^{th} c.

The Jesuit general Clavius published exactly those Indian trigonometric values (to exactly the same precision) in his own name in 1607. Clavius cheated, but though he claimed to have calculated trigonometric values to such high precision, he did not understand how to apply elementary trigonometry to calculate the radius of the earth, a critical parameter for navigation. Ha! Indians accurately calculated the size of the earth, from at least a thousand years before Clavius (as confirmed by al Biruni who cross-checked also Khalifa Mamun’s physical measurement of one degree of the arc).

Likewise Clavius authored the Gregorian reform of 1582 based on Indian calendrical texts (as his favourite student Matteo Ricci confessed; see Ricci’s handwritten letter in my MIT video or presentation “Calculus the real story”.) But arithmetically backward Europeans even then did not know the correct duration of the tropical year, hence Protestant Europe did not accept the Gregorian reform for the next 170 years, until 1752, long after Newton’s death, leading to many more European deaths at sea.

Likewise, George Joseph and his accomplice Dennis Almeida reveal their utter lack of understanding of basic concepts (taught in 9^{th} standard math texts) and have made terrible mathematical blunders, on the record, which show that they are complete mathematical ignoramuses. Some of these have been discussed in my book, in the section on the transmission of the transmission thesis: for example, they foolishly and repeatedly say that solar declination can be measured at sea (how?), thereby also completely failing to understand my point that the Gregorian reform was needed to be able to measure latitude at sea in daytime.

Again in their *Race and Class*** 45**(4) 2004 article, written even as the Exeter ethics committee was going on, Joseph and Almedia copied from my Hawai’i paper of 2000, shamelessly failing to acknowledge it, though they had access to it since 1999, which they themselves acknowledged only in 2007 (but not in 2003, or 2004 when they copied from the Hawai’i paper). While some of my points about Indian pramana vs deductive proof are copied with only a few inaccuracies (but copied without acknowledgement, even while an ethics committee was on in which both participated)Joseph and Almeida some interesting statements which expose their mathematical illiteracy. Thus, my Hawai’i paper mentioned floating point numbers, and used a computer program which I then used to teach as part of my C programming course, to make a philosophical point about the failure of the associative law with floating point numbers. I pointed out that present-day practical computations with calculus are all done on a computer which uses floating point numbers.

Not understanding this mathematical subtlety, Joseph and Almeida blundered that (p. 46) “the use of irrationals…**was accepted in Indian mathematics by the use of floating point number approximations**“. How foolish! This was no typo, for they repeat , even more amazingly (p. 51), “**the Kerala mathematicians employed…floating point numbers to understand the notion of the infinitesimal and derive infinite series**.” My foot! Floating point numbers are a recent IEEE technical standard (No. 754 of 1985) specifically adapted to digital computation. Nothing to do with the Kerala school. And there is absolutely no way in which floating point numbers can be used to derive infinite series. Utter balderdash. Possibly neither Gopal Guru nor Rochelle Gutierrez understands the huge mathematical blunder involved here. But they are all ready to address a conference on math education!

As a matter of fact (see e.g. IIT-BHU presentation for the reference and sloka) Nilakantha states the EXACT sum of an INFINITE geometric series. (Finite geometric series were known from several thousand years earlier since the Eye of Horus fractions, and the Yajurveda.) So Joseph also proved he is a historical ignoramus. He lacks knowledge of the original sources or even the related language (but is ever ready to bluff and cover up one crude lie with another, as he did about rajju ganit in my presence in Berlin in the year 1999). Rajju Ganit, by the way, is a major alternative decolonised course on mathematics that I am proposing at school, as preparation for my decolonised course on calculus without limits, as clear from the linked articles in the IIT-BHU workshop. Obviously, these ignoramuses don’t understand any of its concepts. That damages mathematics education.

Why because a valid history is important to arrive at the correct philosophy with which the calculus originated, and the way it ought to be taught today.

Indeed, Europeans particularly failed to understand the epistemic issue of the Indian method of summing the infinite series from which precise trigonometric values were derived. Descartes blundered saying the circumference-diameter ratio was “beyond the human mind”, alluding to the related Indian infinite series today fraudulently called Leibniz series. Leibniz himself did not understand it, and sought help, as pointed out by Newton who called him the “second discoverer”. But Newton’s own absurdly confused doctrine of fluxions, had to be abandoned despite the foolish responses of Jurin to defend it against Berkeley’s objections to Newton and Leibniz. (Detailed references in my book *Cultural Foundations of Mathematics.*)

The fact is that Newton’s physics failed just because he made time metaphysical (as explained in my book *Time: Towards a Consistent Theory*, Kluwer, 1994), and Newton made time metaphysical (“fluxions”, “absolute, true, and mathematical time flows equably without regard to anything external”) just because he failed to understand the Indian calculus.

But, of course, Joseph, an economist, knows nothing of physics either. He only understands chauvinistic politics and lies of a low variety. Since Joseph is constantly trying to balance his claims of Kerala origins with his British citizenship, in his handcrafted fake-news release for the Manchester university website, he tried to balance both. He said the Indian discovery of the calculus did not affect Newton’s greatness!

<”The brilliance of Newton’s work at the end of the seventeenth century stands undiminished - especially when it came to the algorithms of calculus.”

Ha! What algorithms of calculus?

Eventually, because the purported originators of the calculus (“Newton and Leibniz”) failed to understand it, in the 19^{th} c., the West developed a different metaphysics of infinity (formal real numbers), aligned to church dogmas of eternity, and in the 20^{th} c., the West developed the metaphysics of infinity called formal set theory to make sense of formal real numbers, while avoiding the multiple paradoxes of Cantor’s naive set theory. And that is how we teach calculus today (using real numbers; I regret to say I too taught calculus and real analysis that way for several years); because colonial education means blind imitation of the West and denouncing every Indian critique of the West as Hindu chauvinist, is an easy way to preserve bad philosophy related to church dogma and contrary to elementary common sense (e.g. see my IIT-BHU presentation).

But this Western misunderstanding is an INFERIOR way to teach calculus, it is better to teach calculus the way it originally developed, as in my course on calculus without limits. But how can serial plagiarists and mathematical ignoramuses like Joseph ever understand that?

The problem is there is no way to actually teach a calculus course if one starts believing in wild remarks like those of Joseph and Almeida that floating point numbers can be used to derive infinite series. Nor can one understand how the calculus developed in India if one keeps wrongly imagining like Joseph and Almeida that it was purely the work of the Kerala school.

But Hyderabad university has invited such mathematical ignoramuses to speak on mathematics education at its conference which aims to influence our math education. How shameful, and how damaging to the interests of millions of students.

This is already enough social injustice, for the purported champions of social justice to commit. But the next part of the blog will have more.