Calculus theft

How and why Europeans stole calculus from India in the 16th c.

and why we insist on teaching it today in the inferior European way

C. K. Raju

c.k.raju@ganita.guru

Introduction

West has long boasted of its "superiority"

in the MOST evil, stupid and superstitious way.
Classic example is the racist claim of White superiority.

Why superstitious?

Boast of White superiority a MUTATION of earlier boast of Christian superiority
(to morally justify continuation of slavery after Black slaves converted to Christianity)
using gross superstitions such as "the Bible curse of Ham/Kam".

How relevant to us? (Not just Blacks and Browns!)

During colonialism boast of White superiority MUTATED to boast of Western superiority
as explained in my article "Euclid" must fall, part 1
(Why? Mutation because colonialism more profitable than slavery.

AND because of the politically useful Aryan race conjecture
that much of India had been populated by earlier White conquerors.
so claim of White superiority lacked credibility.)

Our encounter: Macaulay in his 1835 Minute USED the Dogma of Western superiority in science saying
in hard sciences "the superiority of the Europeans becomes absolutely immeasurable"
as justification for colonial education.
But this superstition NOT specific to Macaulay, used by colonizers across the world.
We accepted it without ever checking it until today. That's OUR fault.

How relevant to today's topic?

Trick of using systematic lies about history an old Western tradition, erected since 5th c.
To provide secular JUSTIFICATION for boast of Christian/White/Western supremacy.
Crusading and Inquisitional history glorified "Christians and Greek friends",
as the source of all knowledge stolen from Muslims during Crusades.

On this fanatic "history" Christians "discovered" everything first
not only calculus but also India (Vasco) and Americas (Columbus) itself. 🤣🤣🤣
(Note: Vasco came from Africa to India with an Indian navigator.
He did NOT discover sea route from Africa to India, known for 5000 years.)

This tradition of systematically false history as a political tool for domination

was carried forward by racist historians who glorified Whites as inventors of everything
Then colonial historians who glorified the West with a mere change of labels
(e.g. real or imagined Greeks labeled as Whites and then as West)
No use blaming Macaulay while continuing to teach that false history (e.g. "Euclid") in our school texts.
We promote the false history the colonizer used to dominate us.

TRICK of injecting philosophy into history

Though much Christianized/racist/colonial history is utterly fanatical and farcical
it has some subtler aspects.
Trick: it injects a claim of a superior PHILOSOPHY into history
which TRICK Indians NEVER understood.

Not a single book on history of Indian math (except mine) discusses its philosophy.
When I was on the editorial board of JICPR, I tried to introduce it
but MM Joshi sacked me: he thought only Sanskrit pandits must do Indian philosophy.
but gaṇita ≠ math and Sanskrit pundits could not translate even one word correctly in centuries.

First assertion of THEFT of calculus was in my Jan 2000 Hawai'i talk

at the 8th East West conference in Hawai'i
published 2001 in a PHILOSOPHY journal: Philosophy East and West from Hawai'i.

We think history ONLY about chronology: "we did it first!"
But if you continue to teach calculus on Western principles you implicitly admit
you are inferior because philosophy of ganita inferior.
The exact grounds on which West asserts(and you accept) its superiority unimportant.

E.g. Africans were first enslaved on the grounds that they were inferior since non-Christians
then on the grounds that the Christian god had cursed them to be Black.
Net result same: they were enslaved.
Same applies to you: whether you accept western superiority in math on grounds of history or on grounds of philosophy.

And the fact is that we do accept the superiority of the Western philosophy of math,
for that is how we teach calculus in all universities in the country.
Anyway, since most people understand neither the Western philosophy of calculus (real numbers, limits, etc.)
Nor the Indian philosophy of calculus.
Let me give a simpler example from school geometry.

"Did it first" vs "did it better"

"We did Pythagorean theorem first" — Harsh Vardhan, Minister, S&T

at Science Congress in Mumbai 4 Jan 2015
Some news reports: The Hindu, The Times of India
On Indian tradition, Harsh Vardhan should have FIRST addressed the पूर्व पक्ष.

पूर्व पक्ष: Greeks did it BETTER (NOT first)

E.g. Indian (NCERT) class IX school text
ADMITS many others did it earlier
but says "Greeks did it BETTER".

Saying "we did it first" NOT a proper response

to someone who says they did it BETTER.

Instead, we should ask:

West has made so many stupid and superstitious claims of superiority down the centuries
Is this claim of a "superior" philosophy of math another such stupid and superstitious claim?
YES!

Note clearly: "better" does NOT mean "better PRACTICAL value".

The statements of the "Pythagorean proposition"
in Baudhayana शुल्ब सूत्र 2.12 and "Euclid" Elements, 1.47 are effectively identical.
The class IX school text ADMITS it, saying Indians, Egyptians etc. did geometry for its practical value,
It says Greeks did it better bcoz they arrived at the same result in a better way using proof based on deductive "reason".

In 75 years after freedom we never questioned it, because
we internalized that belief in Western superiority
which is at the core of colonial education.

This school-text boast of Western superiority in math is based on brazen LIES

"Only Greek mathematics had proof"
Obviously false!
Indian gaṇita used the methods of proof as explicitly stated in the Nyaya sutra 2.
Explicit examples here.

"Only Greeks used reasoning in math".

Obviously false!
Indian gaṇita DID use deductive reasoning (anumāna) as also stated in Nyaya sutra 2.
A concrete example is provided by Aryabhaṭa's deduction that the earth is round
from the observation that far-off trees cannot be seen.

What is never explained is the truth

Deductive reason used in BOTH ganita and math
Starting point of deduction in Indian ganita was facts or observations as in science.
In Western (formal) mathematics the empirical is prohibited exactly as in church theology of reason:

starting point of deduction must be an axiom
axiom ≠ "self-evident truth"!!
axiom = postulate = assumption as class IX text admits.

Axioms are usually metaphysics (=fantasy) since they canNOT be empirically tested.
Specifically they are a metaphysical fantasy of infinity closely related to church dogmas of eternity.
All axioms of mathematics laid down by Westerners.
So, axioms are "superior" as the starting point of deduction
since that enables West to political control the CONTENT of math through its axioms.

Interim summary

Purported superiority of Western (formal) math does NOT mean superior PRACTICAL value (prohibits facts)
but it means superior POLITICAL value (for the West)
since it allows the West to control the CONTENT of math.
Anti-value for us to submit to such mind control.

Contrary to assertions of Western superiority

fact: in known history Europeans were historically backward and inferior in math.
learnt basic math from India which they repeatedly imported but found difficult to understand

E.g. Arithmetic

Europeans themselves abandoned their native Roman arithmetic
and adopted efficient Indian arithmetic "Arabic numerals" or Algorismus the Latin name of 9th c. al Khwarizmi
who wrote Hisab al Hind ("Indian arithmetic")
lack of understanding clear from the very term zero from cipher (from Arabic sifr),
cipher means mysterious code.

Why mysterious?

Roman numerals additive: xxii = 10+10+1+1
but in place value system 10 ≠ 1+0=1.
Efficiency of Indian arithmetic from place value.

Evil negative numbers

Zero relates to negative numbers: e.g. 9-9=0
Roman arithmetic had no negative numbers
Hence Europeans confused about negative numbers.
from Fibonacci (Liber Abaci early 13th c.) to Augustus de Morgan (19th c.)

De Morgan's folly

E.g. De Morgan a very influential professor from University College London
foolishly declared negative numbers impossible. (Morgan, Augustus de. Elements of Algebra: Preliminary to the Differential Calculus, 2nd ed. London: Taylor and Walton, 1837, p. xi.
and went on to say (1898) belief in witches 10000 times more possible than \(- 9 < 0\). 🤣🤣🤣

"Algebra" from "al Jabr waal muqabala" of al Khwarizmi

who partly translated 7th c. Brahmagupta's unexpressed arithmetic of polynomials (and linear and quadratic equations).
Primitive Greek/Roman arithmetic lacked √.
Term for √2 is SURD from Latin surdus = DEAF from Arabic asumu
- Why is √2 DEAF?

Deaf roots

In Indian शुल्ब सूत्र √2 = DIAGONAL (कर्ण) of unit square.
But word कर्ण also means ear,
hence bad कर्ण mistranslated as bad ear = deaf! 😊

Pocket trigonometry

Word "Sine" from sinus=fold from Arabic jaib (जेब) = pocket (OED).
What has trigonometry to do with POCKETS?
From Sanskrit term for it ardh-jyā - (half-chord) or जीवा
rendered in Arabic as jībā (no v sound in Arabic).

Toledo translations ca. 1125

Written as consonantal skeleton "jb" (without nukta-s) like "pls" in SMS.
Misread by Mozharab/Jew 12th c. Toledo mass translators as common word "jaib" = जेब = pocket.😊
Word "trigonometry" involves a conceptual error: it is about circles not triangles.
Hence my pre-test question what is \(\sin 92^∘\)? (In a right-angled triangle there cannot be any angle of \(92^∘\).)
West was historically inferior in math,not superior.

This arithmetical backwardness of Europeans persisted until 16th c.

The 1582 Gregorian calendar reform still used primitive leap years instead of precise fractions.
Hence, Gregorian calendar still inferior: equinox does NOT come on the same day each year.

Surprise: from ignorance of fractions in 1582 West claimed to have discovered calculus in 17th c.

In India development of calculus from Aryabhata to Madhava and Nilakanth took 1000 years
several thousand years after fractions were known.
Many startling similarities, Madhava's sine series claimed by Newton,
Likewise Leibniz series earlier found e.g. Yuktidipika.

So did Europeans steal calculus from India?

Q1. Was it calculus?
Q2. Did Europeans steal?

Q1. Where are the integrals and derivatives, their signs?

Today most people learn calculus by doing integrals and derivative
(ONLY of elementary functions: see pre-test question paper Q7d)
Hence, many people identify symbolic computation of derivative and integrals with calculus.
Especially the foolish colonised mind taught to ape the "superior" West.

But no integrals or derivatives in Indian tradition.
So, how was it calculus?

A. K. Bag's opinion (2003) while

REJECTING my paper on transmission of calculus from India to Europe for IJHS

"I personally feel that…the question of the transmission [of calculus] from India to Europe is basically a hypothetical issue…"

(Why? Since what was in India was not calculus, since no integrals, derivatives.)

Aryabhaṭa vs Madhava

Today, Indian origin of calculus widely attributed to Madhava and "Kerala school"
This was also the WRONG belief with which I started my research in 1997,
my project was titled "Madhava and the origin of calculus"
but I corrected it after I started teaching calculus without limits in 2009.

Calculus due to Aryabhata

Madhava gives table of 24 sine values precise to 3rd sexagesimal minute (tatpara)
Aryabhata's sine value 1000 years earlier precise only to first sexagesimal minute (kalā)
Key point: Madhava gives sine values, Aryabhaṭa's "sine table" has only sine DIFFERENCES
That resolves the first issue: Indians used finite differences NOT derivatives.
(Do NOT assume derivatives "better" or "superior").

How are Aryabhata's sine differences derived?

By means of a recurrence relation, NOT an algebraic equation
This equivalent to what is today wrongly called "Euler" method
of numerically solving ordinary differential equations (Nīlakaṇṭha corrects it)
(Euler familiar with Indian math texts,hence solved Fermat's challenge problem)

That is, Aryabhata effectively numerically solved a differential equation

to derive his sine values.
Solving differential equations is the heart of calculus
and the essence of ALL problems of Newtonian physics.
Corollary: NO NEED FOR ∫ sign since solution of \(y' = f(x)\) is the indefinite integral \(∫ˣf(t)dt\)

This way of doing calculus vastly superior
for real-life practical applications
since no need to restrict \(f(x)\) to be an elementary function
E.g. first serious science experiment in school, the simple pendulum,
involves non-elementary Jacobian elliptic functions

Usual wrong formula \(T= 2π \sqrt{\frac{l}{g}}\) not compatible with observations
see my son's school project.
Therefore, this is the right way to teach calculus.
Hence, this is key aspect of how I teach calculus without limits.

Brahmagupta's critique: quadratic interpolation

Brahmagupta critiqued Aryabhata for increasing the number of sine values/differences to 24
His argument: earlier 7 values 15° apart adequate for the same precision with quadratic interpolation.
Carried forward by Vateshwar who used quadratic interpolation ("Sterling's formula") + a table of 96 values.
Achieved precision to the 2nd sexagesimal minute (vikala).

Further, carried forward by Madhava and the later Aryabahta school in Kerala
who used 11th/12th order interpolation to achieve
precision to the third sexagesimal minute(tatpara)

Interim summary

Aryabhata (and Brahmagupta) invented calculus, the Aryabhata school in Kerala refined it.

PS

There is a further issue that Aryabhata was a Dalit from Bihar,
while people like Nilakantha were the highest caste Namboodiri Brahmins.
To my mind this is splendid testimony of regional integration and that caste was not oppressive prior to colonialism.
But won't go into it further.

But no one in India today interested in teaching calculus differently

on Indian method
No one interested in doing math to ensure scientific theory agrees with observation
We only want to say we are proud we did it first
but we are inferior so we will continue to ape the West
regardless of whether it results in good or bad science.

We will still do symbolic calculation of derivatives and integrals as required for IIT: entrance
bcoz education about jobs, not knowledge or its practical applications.
And for better-paying jobs you still need to ape the West.
Since we are NOT concerned about doing calculus in a better and easy way,
So let me move to the next part: was calculus stolen

Theft of calculus

Arithmetic, algebra, trigonometry were all cases of transmission of math from India to Europe
via Muslims who honestly acknowledged their Indian sources
But the cases of calculus, and probability and statistics were a matter of theft
because they went directly to Christian Europe from India.

Europeans claimed "discovery" based on the UTTERLY EVIL 15th c. church dogma of discovery
that any land OR knowledge "belongs" to the first Christian to sight it!
This dogma recently repealed by the pope since its purpose of justifying land and knowledge-theft ACCOMPLISHED
(but still part of British and US law based on it).

Since we ape, we TEACH it in our school texts (NCERT, class XI) that "Newton discovered calculus"
since our education APES THE WEST and we go by Western books and REFUSE to examine facts.

Proof beyond reasonable doubt as in criminal law

Since theft is a criminal offense,
I proposed to use the standard of evidence used in criminal law
Namely, proof beyond reasonable doubt.

(Instead of the usual standard of proof in history, of using "balance of probabilities")

Therefore, as in a murder case, in my 2001 Hawai'i paper I looked at

opportunity : (Jesuits in Cochin in 16th c. gathered and translated local knowledge on Toledo mode)
motivation: (navigational problem, needed correct calendar, precise trigonometric values)
circumstantial evidence (identical infinite series, Fermat's challenge problem, Pascal's triangle, "Euler" method, Tychonic model, Clavius' trigonometric values, Stirling's formula, etc)
documentary evidence (e.g. Ricci letter)
(though no law that a murderer/thief can be convicted only on a signed confession of murder/theft) 😀

Opportunity

Let's understand "Toledo model"
The first Western universities (Paris, Oxford, Cambridge) were set up by the church during Crusades (since Christian Europe backward, needed knowledge)
The texts were Latin mass translations of Arabic texts in a library captured at Toledo.

The church earlier burnt "heretical" texts
but needed knowledge to fight Crusades,
hence claimed all these texts from the religious enemy had a "theologically correct" origin in early Greeks"
regarded as the "sole friends of Christians" by Eusebius.

Later copied this same Toledo model in India: steal knowledge, lie about its history.
Church trusts that most people are gullible fools and will never check, as we never did.
Jesuits in Cochin systematically collected and translated Indian texts
with the help of local Syrian Christians whom they taught in their Cochin college since 16th c.
Later attributed it all to Christians(Fermat, Newton, Leibniz etc.) like "Vasco discovered India".

Motivation: Navigational problem

Europe was very poor, all dreams of wealth (whether piracy or conquest) were overseas.
Accurate navigation was needed to bring that wealth home.
Europeans had 3 key navigational problems.
Latitude, loxodromes, longitude at sea.

Latitude

Vasco did not know how to determine latitude at sea,
carried back Indian navigational instrument, kamāl
to have it "graduated in inches" &# 128513;
(Can't be done: not a linear scale it uses a harmonic scale.)

Kamāl tells latitude by the pole star.
Since pole star=kau (Arabic-Malayalam) =teeth, and the string of the instrument is held between the teeth
Vasco pompously and foolishly recorded "the pilot was telling the distance by his teeth".

Despite stealing kamal, there still remained a problem of telling latitude in daytime:
by measuring angular elevation of sun.
That requires an accurate calendar which correctly determines the date of equinox,
as explained in my Rajju Ganita geometry text for class 9.

Hence, Christian priests interested to steal calendrical knowledge
for Gregorian calendar reform of Christian calendar in 1582.

Loxodromes

Europeans navigated by plane charts
They expected that travelling in a fixed direction
will result in straight line motion
but on the curved surface of the earth it results in a logarithmic spiral called a loxodrome = curved line.

Mercator projection

The projection maps the sphere to a plane chart in such a way that straight line course
results in a straight line on the chart (loxodromes are straight lines).
This projection was known in Chinese star maps as Needham points out.

But constructing this projection requires accurate trigonometric values (table of secants).
16th century navigational manuals were full of such tables.
Simon Stevin's tables 1590, derived from Aryabhata via Arabs.

A few years later (1607) Clavius published tables with precision of nine decimal places.
Clavius as the Jesuits general in charge of the Gregorian reform
was the natural recipient of texts stolen by Jesuits.

Longitude

Longitude calculation in Indian tradition requires, as Brahmagupta says, knowledge of the radius of the earth \(R_E\)
easily calculated from elementary trigonometry
by measuring the height of a hill h and the angle of dip from it θ.
But mathematically backward Europeans could not do it.

Therefore, the European navigational problem of determining longitude at sea persisted until 18th c.
Many European nations offered large prizes for its solution,
the last being the British longitude prize of 1711-12, half of it given away in 1762
because the Board of Longitude was only half sure that the prize had been won.
The chronometer for which the prize was given became a reliable instrument only by the mid-19th century.

Why did the Europeans have such a big problem?
because Columbus to get funds for his project of traveling West to go East underestimated the size of the earth by 40%
And the fact is that though Europeans stole trigonometric values they did not know how to use them to measure the radius of the earth.

Today Internet is full of bunkum stories of Eratosthenes. Nobody gives an actual primary source? Why not? (Bcoz source from 19th c.)
Picard's 17th c. measurement was preceded by al Mamun's 9th c. measurement by 800 years as usual.
However, important point is that this is retrospect:
in prospect no navigators were willing to trust Picard
therefore European problem of determining longitude at sea persisted.

Circumstantial evidence

Long list discussed in Cultural foundations of Math
identical infinite series
- "Newton's" sine series (Newton claimed sine series, and only rigor in calculus)
- "Leibniz" series for π,
Fermat's challenge problem,
Pascal's triangle (khanda meru).

Aryabhata's recursive method = "Euler" method,
Nilkantha's astronomical model= Tychonic model,
Madhava's values = Clavius' trigonometric values an interpolated version
ahargana= Julian day-number,
Vateshvar="Stirling's" formula

Documentary evidence

primary sources Ricci's letter. (Ricci was Clavius' student.)

Epistemic test

Despite all the above evidence
West has not admitted theft of calculus.
Dishonest historians like David Pingree and Kim Plofker keeping alive the myth of "independent rediscovery".
Won't even discuss it. Any papers would be routinely censored
(Indians fully cooperate with that: IIT Gandhinagar had a conference invited Plofker, but not me: clearly they want to sideline me.)

Hence in my book I applied my epistemic test

People steal knowledge because they have an INFERIOR knowledge of the subject
like students who cheat in an exam.
(But if not caught in the act, they ALWAYS deny cheating and claim similarity of answers due to "independent rediscovery".)
As a university teacher, I developed a way to catch such cheats AFTER the act

Epistemic test: Even after stealing, knowledge thieves fail to fully UNDERSTAND what they steal

and are unable to explain what they have written in their answer sheets.
I used to ask searching question to suspected cheats about their answers while returning their answer sheets.
Lack of understanding (of their own answers) proves theft or "dependent re-discovery".

Applying epistemic test to history

Much later, I applied this epistemic test to history of calculus.
Cannot interrogate the past, but
under suspicious circumstances (my evidence from criminal law)
failure to understand is clinching proof of theft.
Fact is that Europeans failed to fully understand calculus,

What aspects of calculus did the West fail to understand?

1. How to do an infinite sum
2. Exact definition of derivative

Why needed?

Questions about 1 arose since precise trigonometric values needed for navigation)
were derived in India (14th c.) using infinite series for sin and cosine and arctangent functions.

Summing infinite series

Indians had summed infinite geometric series by 15th c.
(finite geometric series known since ancient time, e.g. Egyptian "Eye of Horus" fraction).

West got the formula but failed to understand the method by which it was derived.
Descartes realized that summing an infinite series term by term is physically impossible
it is a supertask or an infinite series of tasks which cannot be done in finite time.
Referring to the infinite ("Leibniz") series for π he said it was "beyond the human mind".

Galileo (who had access to Jesuit texts from Collegio Romano) concurred and left calculus to his student Cavalieri.
Newton defined derivative using his silly fluxions, now abandoned.

West acknowledged its difficulties with understanding calculus (especially "fluxions")

The West (e.g. Berkeley, Karl Marx) acknowledged fluxions were incomprehensible.
Berkeley: on lack of understanding of calculus.
Here is James Jurin's incomprehensible defence of fluxions.
HENCE, mathematician Dedekind proposed "real" numbers at end of 19th c. as a supposedly better way to understand calculus.

Real numbers and limits

Today all calculus texts, including Indian class XI school texts, teach that limits are essential for calculus.
Indeed, infinite sums, derivatives, integrals, and even functions all understood as "limits".
But limits need "real" numbers: e.g. sequence of partial sums of \[ \sqrt 2 = 1.414... = 1+\frac{4}{10} + \frac{1}{100} + ... \]
has NO limit in rational numbers, since \(\sqrt 2\) NOT a rational number.

So Newton, Leibniz etc. could not have understood calculus
since "real" numbers came long after them.
and Newton's absurd fluxions stand abandoned
except as proof of theft.

Why is exactitude needed?

derivative as finite difference good enough for all practical purposes
just as finite sums \(π = 3.14159\) etc are ALL that we have in real life.
But Newton linked calculus to physics
and physics to religious belief:
"eternal and universal laws of nature made by the Christian god."

Note: Hinduism has ṛta, Buddhism has conditioned coorigination
LAWS of god unique to post-Crusade Christian theology
to mark a difference from Islam (Allah has habits and regularities but continuous creation hence no rigid laws)
Newton abusively anti-church but fanatic Christian: believed laws of god had been revealed to him
superstitiously flagged Egyptian chronology as "vain" since contrary to Biblical story of creation.

History repeats itself

"Those who cannot remember the past are condemned to repeat it." — George Santayana
CKR: Those who don't learn from past mistakes repeat them, hence we study history.
"Hegel said…[history repeats] twice. He forgot to add: the first time as tragedy, the second time as farce." — Karl Marx
Correction: History repeats THRICE: first as tragedy, then as farce, then as pure humbug.😄

1st time: tragedy

calculus stolen from India in 16th c. by Jesuits
with the help of Syrian Christians from Kerala.

2nd time: farce

The thesis that the calculus was stolen from India was itself stolen
by a combination of Roman Catholics (Jesuits) and Syrian Christians
in a preplanned way.

Madhava ad

I advertised a post-doc position for my INSA project
in an international email list Historia Matematica.
Employed a Syrian Christian Jolly K. John as research associate
whom I knew from Pune U, and who was struggling without a job and used to visit my house to eat.

But my ad interested George Gheverghese Joseph (author of Crest of the Peacock)

who was a member of Historia Matematica list, and saw the ad. Wanted more info.
Contacted me very indirectly through his friend Dennis Almeida from Exeter Univ.
who contacted me through someone ELSE in NISTADS.
(So that I don't get suspicious of being targeted.)

Almeida, a complete traitor, posed as a fake patriot: said he wanted to do something for India.
Would work on this for a PhD
I fell for it.

Joseph starts serially plagiarising

George Joseph had organized a conference in Trivandrum
As conference organizer Joseph had privileged access to my papers; he grossly misused that privilege.
At a meeting in Dec 2000 Joseph SHAMELESSLY plagiarised my paper in front of me
without acknowledging or referring to my work.

Later he said I will lie "I don't know you" (Of course he does; see his email.)
Joseph said, I will say "I got the paper from Almeida."
And in the proceedings of the Trivandrum conference he erased my name
That is copyright violation. Never took copyright permission from me to publish the paper.

No Indian scholar has publicly condemned Joseph even once.
On the contrary many lauded him.
If the theft of the thesis that calculus was stolen is acceptable,
why is the theft of the calculus unacceptable??

Kak wrote an article in Sulekha saying

3 British authors had written about the Indian calculus
he sent copies of this to numerous people
and one of these was forwarded to me.

None of the authors was British, all three were Christian

one of the authors J. K. John was my postdoctoral fellow
who had passed on the material collected for my project on the promise of a higher salary
the other was Dennis Almeida, and the third was an inconsequential Russian translator

On my complaint of plagiarism

Exeter University set up an ethics committee
into which George Joseph penetrated lying that he was in neutral party
though he was himself a plagiarist
and misguided the committee thoroughly
lying that Bag and Katz had talked of the possibility of transmission of calculus.

But my case was so strong the committee was obliged to rule in my favor
as in this news item

Apart from that

I collected two letters of apology
from John and Almeida
But these rogues go right back after apologising.
Kak too never withdrew his article or corrected it

Epistemic test proves theft beyond all reasonable doubt

My latitude thesis above was that a good calendar was needed for navigation
to determine declination hence latitude from solar altitude and
These jokers Almeida and John wrote declination can be measured at sea. ]
Just as calculus was damaged by thieves, the thesis of stolen calculus is damaged by thieves.

Another example from Almeida and Joseph

In my Hawaii paper I made philosophical point that real numbers are not needed for calculus
because for all practical applications on computers, floating point numbers are used.
The joker plagiarists Almeida and George Joseph grossly misunderstood
If you trust thieves this are the utter absurdities you get.

Third time: humbug

Encouraged by successful serial plagiarism
and worried by publication of my 2007 book
in 2007 Joseph VERBATIM plagiarized those two papers
now claiming to be an author.

Some parts were published earlier in my name (e.g. Hawaii paper)
Here are some examples cut-paste copying.
This was followed by a media blitz.

Because news release was from Manchester Indian press refused to believe me
or read my book.
Only Hindustan Times actually checked facts and published a retraction.

A complaint was made to Manchester University
The University said it was a media office mistake
[[https://www.manchester.ac.uk/discover/news/indians-predated-newton-discovery-by-250-years/][And just put in an acknowledgment to my work (without admitting it was a verbatim copying)
That is its British ethical and legal standard: verbatim copying only requires a belated acknowledgment!

The Manchester University is committed to lack of ethics. This is clear from the fact that
the "paper" mentioned in its FAKE NEWS press release was NEVER published in 16 years.
(Could not be Because it is a verbatim copy) but the press release has not been retracted)
But Manchester university shamelessly maintains that fake press release.
The story is the same for many great Brit figures like Newton (or his successor Michael Atiyah!)

Interim summary

Joseph Almeida et. al have stolen most brazenly and repeatedly, deliberately
since they know that many colonised support them, few oppose.
If you can't correct THIS theft concerning calculus in the present tense
you have no hope of correcting the theft of calculus 500 years ago, or its resulting teaching.

The Orosian/colonial dog

Orosius who wrote the first false history for the church ("History against the Pagans" in 5th c.
starts by saying how easy it is to make dogs obedient.
Remember? The colonial notices: "Indians and dogs not allowed"
The colonised do behave like dogs unable to stand up against the master.
The colonizer KNOWS the indoctrinated colonial dog can only wag tail before master.

Conclusions

Europeans were backward in all departments of math
developed an inferior understanding of calculus.

Claims of discovery settled by what you TEACH not by church dogmas or regional chauvinism.
So if you accept real numbers and limits, while teaching calculus, credit goes to West.
Āryabhaṭa and Brahmagupta discovered calculus (taught as how to solve differential equations)
NOT Madhava or "Kerala school" which refined it using infinite series.

But correcting lies of history is a PROCESS, NOT a 1-time job after 500 years.
The only process the colonised know is "trust the West" Manchester etc.
Hence, the West CONTINUES to concoct brazen new lies of "discovery" in the present tense – even about the theft of the calculus.
Because they KNOW you have no way to correct it.