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

• 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".

• 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.

• 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.)

• 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.

• 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.

• 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.

• 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.

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

• to someone who says they did it BETTER.

• 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!

• 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.

• "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.

• 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.

• 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.

• 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.

• 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

• 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.

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

• 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.)

• 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 \(- 9 < 0\). 🤣🤣🤣

• 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?

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

• 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).

• 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.

• 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.

• 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.

• 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.)

• 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.

• 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").

• 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)

• 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 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)

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

• 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.

• 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

• 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")

• 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) 😀

• 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".

• 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.

• 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.

• 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.

• 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 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.

• 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

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

• 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

• 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".

• 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,

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

• 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.

• 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.

• 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.

• 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.

• 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.

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

• 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.

• 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.

• 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??

• 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

• 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

• 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

• 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.

• 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.

• 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!)

• 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.

• 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.