• Bhata (भट) is dalit, bhatta (भट्ट) is Brahmin (जनसत्ता, 30 Sep 2018.
• Wrong spelling breaks the story of ancient India's integration
• across regions and caste.
• (Aryabhata, a dalit from Patna, had disciples who were the highest caste Namboodiri Brahmins from Kerala).
• Raju, C. K. 'Aryabhata Dalit: His Philosophy of Ganita and Its Contemporary Applications'. In Theory and Praxis: Reflections on the Colonization of Knowledge, ed, Murzban Jal and Jyoti Bawane, 139–52. Routledge, London, 2020.

• The approach paper for this meeting mentioned "Vedic math".
• However, there is nothing Vedic in "Vedic math" (Hindu 3 Sep 2014).
• वैदिक गणित में वैदिक कुछ नहीं (जनसत्ता, 10 Aug 2014).

• (a) NO connection whatsoever to the Veda-s
• Bharti Krishna Tirtha gave no source when challenged.
• The book Vedic Math itself says (p. v, p. xxxv)

obviously these formulas are not to be found in the present recensions of the Atharvaveda

• Jagadguru Swami Sri Bharati Krsna Tirthaji Maharaja, Vedic Mathematics, Motilal Banarsidass, New Delhi, Rev. ed. 1992, reprint 1997.

• M. D. Pandit, Mathematics as Known to the Vedic S amhitâs , Sri Satguru Publications, New Delhi, 1993.
• Hence, title of the "Vedic math" book is grossly misleading.
• The Veda-s are sacred, wrong to use them for misleading marketing.

• Some promoters of "Vedic math" quibble: "Vedic" not about actual "Veda-s".
• (This should be put on the cover.)
• They say "all ancient knowledge is Vedic".
• Q1. How do you know this is ancient knowledge?

• Source hidden, probably modern since source not in Veda-s but also
• these sutras NOT mentioned by any traditional Indian mathematician across over 3000 years.
• from Vedanga Jyotisa (\(-1500\) CE), to Nilakantha (+1500 CE).
• Later-day katapayadi system IS mentioned in the "Vedic math" book.

• Many people in ancient India were ANTI-Vedic

"The agnihotra, &c., are only useful as means of livelihood, for the Veda is tainted by the three faults of untruth, self-contradiction (व्याघात), and tautology (पुनरुक्ति);

…the three Vedas themselves are only the incoherent rhapsodies (प्रलाप) of knaves (धूर्त) …"

• Sarva-Darshan-Samgraha, trans. E. B. Cowell and A. E. Gough (London: Trubner, 1882), p. 4.

• Since marketing label "Vedic" is misleading and invalid
• we should discard it. But what is left?
• Merely some tricks of elementary mental arithmetic
• of nil value to science and technology today in these days of computers.

• Genuine Indian arithmetic algorithms, which went to Europe
• and returned to India during colonialism.
• Why abandon the real Vedic for the fake "Vedic"?

• "Vedic math" has nothing to do with Veda-s.
• Not even ancient (and everything ancient in India not Vedic).
• Only some simple tricks of mental arithmetic, of no relevance to S&T.
• Seeks to replace genuine Indian math, with key contributions from dalits, such as Aryabhata,
• and makes us a laughing stock.

• Word "algorithm" from 9th c. al Khwarizmi's Latinized name "Algorismus" or "Algorithmus".
• He wrote Hisab al Hind from which Europe learnt arithmetic.
• This arithmetic returned to India during colonialism.
• Arithmetic we teach in schools today is of Indian origin.

• Indian arithmetic went to Europe in three phases.
• Phase 1: Gerbert of Aurillac (10th c.), later Pope Sylvester II, imported it from Cordoba, Muslim Spain.
• Phase 2: Fibonacci (12th c.) Florence, Liber Abaci, imported it from Africa (trans. of Hisab al Hind)
• Phase 3: Christoph Clavius (16th c.), Practical Arithmetic, Rome, imported it direct from Kochi.

• Why? Were they stupid?
• Basically because their native arithmetic ("Roman numerals") used the abacus
• a system quite different from the Indian arithmetic of algorithms (after al Khwarizmi)

• Gerbert of Aurillac (later pope Sylvester II) imported it from Cordoba (Muslim Spain).
• He had authored a learned tome on the abacus,
• hence wrongly thought that the abacus was the only way to do arithmetic.
• Consequently, he got a special abacus (apices) constructed for "Arabic numerals" in 976.

• But NOT the the efficiency of algorithms over the abacus.
• The very act of constructing an abacus (for "Arabic numerals")
• which does arithmetic on the primitive coin-counter system
• destroyed this efficiency of Indian arithmetic.

• E.g. 1788 written as MDCCLXXXVIII in Roman numerals
• requires 12 symbols instead of the 4 used in 1788.
• Large numbers such as \(10^{12}\) (found in Yajurveda 17.2)
• or तल्लक्षण (\(10^{53}\), ललित विस्तर सुत्त chp. 12) cannot be written at all in Roman numerals.
• Myriad (=10,000) was the largest Roman number (regarded as almost infinitely large).

• 89 + 89 = 178 (trivial using algorithm for addition)
• But let us do it in "Roman numerals" (abacus method)
• 89 = LXXXIX in Roman numerals
• Step 1: Write in full as LXXXVIIII.

• Think of L, X, V, I as coins or counters of 50, 10, 5, and 1.
• Method is to pool all coins/counters and simplify. (C = count, R = replace)
• Step 2: Pool all the "counters" in the numbers to be added, namely LXXXVIIII, and LXXXVIIII.
• Step 3: Simplify, starting with the smallest.

• (8 C) We count there are 8 I's which we simplify to 1 V and 3 I's.
• (1 R) The 3 I's are left as they are, and the 1 V is "carried".
• (3 C+1 R) Next there are 3 V's (including the carried V) which simplify to 1 X (carried), and 1 V.
• (7 C and 1 R)Next there are 7 X's (including the carried X) which simplify to 1 L (carried) and 2 X's.

• (3 C and 1 R) Finally, the 3 L's simplify to 1 C and 1 L.
• Thus the final answer is CLXXVIII = 178
• but obtained in a very inefficient way
• which involves far more steps
• 21 counts and 4 replacements = 25 operations.

• The inefficiency of native European arithmetic is more marked in multiplication and division.
• Multiplication = repeated addition: to do \(89 \times 89\) add 89 to itself 89 times!
• That is, the previous 25 operations must be repeated 89 times = 2225 operations.
• (Likewise division = repeated subtraction).

• In contrast the usual (Indian) algorithm for \(89 \times 89\) involves
• 4 single digit multiplications + 6 single digit additions = 10 single digit operations

• very inefficient compared to (Indian) algorithms
• For multiplying two two-digit numbers abacus needs 2225 operations compared to 10 for algorithms.
• Efficient Indian arithmetic gave comparative advantage in commerce
• to Arab traders.

• Fibonacci was the son of a Florentine merchant.
• Realized the comparative advantage of efficient arithmetic ("algorithms") for commerce,
• while dealing with Arab traders in Africa.
• Learnt it, and enthusiastically wrote about it: Liber Abaci (ca. 1202 CE)

• Some Florentines accepted the new system.
• But many were suspicious of the "new-fangled" "Arabic numerals".

• The reason for suspicion was ZERO.
• Roman numerals are additive: XII means 10+1+1
• But, the place value system is not additive,

\(120 \neq 1+2+0 = 3\).

• Therefore, \(120 \neq 1200 \neq 12000\)

• Florentines complained that "zero has no value in itself,
• but adds any amount of value to the preceding number."
• This led to financial frauds: financial contracts could be changed by adding trailing zeros.
• 120 could be changed to 12000.

• Therefore, in 1300 Florence passed a law:
• financial contracts written in "Arabic numerals" should also be written in words.
• We still follow this law ( e.g. in writing cheques).
• Zero from sifr = cipher = secret code.

• Foreigners told us a story with a grain of truth:
• "contribution of Ancient India to mathematics was zero"
• Their aim: to HIDE the real story of their own arithmetic incompetence.
• We happily accepted this "small praise" (without investigating) and there is even a film song on it (Manoj Kumar, Purab Paschim)

• But India's contribution is not just "zero".
• And we did not teach the world to count.

• Ancient India's contribution was EFFICIENT ARITHMETIC.
• But that story shows Europeans as arithmetically challenged, as they really were.
• Hence, Western historians hide that history,
• but why do WE erase that real history by talking only of zero and "Vedic math"?

• Greek/Roman arithmetic had no way to represent general fractions.
• Romans understood only simple fractions (parts of 12 on which their coinage was based e.g. 12 pence = 1 shilling)
• Because Europeans were arithmetically challenged
• they could not even SAY the right length of the year.

• HENCE, original Greek and Roman calendar were so awfully bad.
• After Julius Caesar's conquest of Egypt,
• under Egyptian guidance
• the Roman calendar was reformed into the Julian calendar with great fanfare.

• To avoid fractions (year = \(365 \frac{1}{4}\) days) the Julian calendar used the system of leap years.
• In the first 20 years, Romans did not understand this system of leap years.
• Instead of every fourth year as a leap year, they miscounted every THIRD year as a leap year.
• (They counted the present year as 1 😜.)

• Augustus Caesar who corrected this mistake had a month named after him, for this reason.
• Because the central issue was not scientifc timekeeping
• but the vanity of the two Caesars, he increased August from 30 to 31 days like July!
• (And we swallow it all, neat.)

• The church adopted the Julian calendar as the official Christian calendar in the 4th c.
• Church/colonial education brought this calendar to India
• and it is the ONLY (unscientific) calendar most colonially educated people know.

• Fractions were first introduced in the European (Jesuit) syllabus in 1570s
• by Christoph Clavius author of the Gregorian reform of the calendar
• The Gregorian reform of 1582 corrected the duration of the (tropical) year in the Christian calendar to 365.241 (tropical) days.
• BUT it used LEAP YEARS, not a precise fraction.

• Every 4th year is a leap year, every 100th year is not, every 1000th year is
• \(365.241 = 365 + 0.25 - 0.01 + 0.001\)
• However, this conversion from fraction to leap years accurate only over a 1000 year average.
• Not from year to year—equinox still does not come on the same day each year.

• Efficient Indian arithmetic (basic algorithms for \(+,~ \times\) etc.) went to Europe,
• repeatedly from 10th to 16th c. for its use in commerce and navigation (calendar).
• The real story of zero is this:
• Europeans took over 6 centuries to understand and accept Indian arithmetic.

• "Ancient Indian science: implications for Modern Technology".
• So, how is the story (I just told) about ancient Indian math relevant to modern technology?

• Those who only buy technology think it is about machines
• but whose who BUILD technology, know it is about knowledgeable people.
• Multiple failures of technology missions in India due to lack of knowledgeable people.

• especially Silicon Valley.
• We think technology is all about MACHINES.
• But, ever since the "Sputnik crisis" of 1958, - the US has understood that winning the technology race is about knowledgeable PEOPLE.

• The cutting edge of modern technology is machine learning and data science.
• The corresponding math has been called "21st c. math".
• Properly trained people are needed.

• Therefore, the California education department has revamped its K-12 school math syllabus
• to meet the projected needs of future technology.
• The aim is to teach statistics and data science.
• But the catch is that this is an ALTERNATIVE to the calculus.

• On the grounds that the calculus is very difficult,
• and teaching it at the K-12 level serves no particular purpose and is inequitable.
• Hence, critics have bashed it as "cancelling the calculus"
• and asked for it to be revoked.

• Core notions of statistics such as probability "measure", average (= mathematical expectation)
• involve an advanced theory of the (Lebesgue) integral.
• Further, statistical inference is proverbially misleading (or misused):
• "there are lies, damned lies, and statistics"

• Without a proper understanding of statistics, it is easy to arrive at wrong conclusions.
• A wrong algorithm in artificial intelligence (or an algorithm without an understanding of its limitations)
• can spell disaster in the future
• where people will depend more on decisions made by machines.

• A simple alternative is to teach decolonised calculus
• and
• the way they originated in India as ganita.

• See Cultural Foundations of Mathematics…the Transmission of calculus from India to Europe in the 16th c. CE
• For a description of the courses see Decolonising mathematics
• or see the video of my MIT lecture, or the slides, or abstract.

• See my article: Probability in Ancient India, Handbook of Philosophy of Statistics, Elsevier, 2012, 1175–96.
• Or see video of my JNU talk on Statistics…should we teach it using formal math or normal math?
• or see the slides.

• Or see this popular-level account.
• Part 2 to appear on 18 Dec.
• (See under "Education" section at Boloji.com)

• Because the thesis is that
• the calculus is difficult because Europeans (Newton and Leibniz) failed to understand it
• because they stole the calculus from India
• (and we blindly imitate their lack of understanding).

• Knowledge thieves often fail to fully understand what they steal
• Like students who cheat in an examination.
• Or the way Europeans took six centuries to understand even elementary Indian arithmetic.
• (But difficult to explain the same point aboutIndian calculus.)

• So, the solution to calculus difficulties is to reject its Western understanding, and
• to teach calculus the way it originated in India.
• That makes calculus easy while preserving (actually enhancing) all its practical value.

• But how can I talk about Aryabhata's philosophy of ganita in calculus (in 30 mins!)
• to those who don't even know calculus and unsure of the correct spelling of Aryabhata?
• Read my books and articles, particularly the article appearing today.

• Our understanding of calculus is worse than that of West
• for colonial education only teaches the colonised to imitate the West,
• and copy its mistakes including its miserable calendar.
• So, no point in talking about calculus when you don't know why 1+1=2 in real numbers (and think 30 mins is enough)

• WRONG to consult a mathematician privately.
• Because ganita is so different from mathematics,
• from which the mathematician derives his livelihood
• Public debate is essential; but no mathematician in willing for it.

• If you know anyone willing to participate in such a PUBLIC debate please let me know.
• Prerequisite: First meet my "Cape Town challenge", repeated in JNU with a prize of Rs 10 lakhs:
• "Axiomatically prove 1+1=2 in REAL numbers from first principles (without assuming any result from axiomatic set theory)"
• like Bertrand Russell's 378 page proof of 1+1=2 in cardinals.
• Don't judge someone as a "math expert" just by his foreign degrees, judge him by the above 1+1=2 test.

• NCERT refuses to discuss the matter (e.g. see this critique)though they promised to.
• Have talked about the advantages of ganita even to the chair of the parliamentary committee on education.
• That is the most I can do in India, it is NOT my personal agenda.
• If you can do better, do it!

• That requires respect for our own knowledge, which the Indian society has lost,
• because colonial/church education taught us that we are inferior
• and must hence blindly imitate and trust only the West.