India’s national Republic Day motto is “Satyameva Jayate“, Truth alone triumphs! In my quest for truth, I discovered this…
by Jonathan J. Crabtree

Jagadguru Shankaracharya Swami Bharati Krishna Tirtha’s view was that Vedic maths is NOT to be approached from a factual standpoint. If it is accepted that the Vedas are the source of all knowledge, then the 16 Sutras of Vedic Maths should have been contained in them.

Dr. V.S. Agrawala, friend of Bharati Krishna Tirtha and Editor of the book titled ‘Vedic Maths’.

Are the 16 Sutras of Vedic Maths from India’s Ancient Vedas? What do Indian scholars say?

VEDIC SCHOLAR PROF. DR. SUBHASH KAK

“First question: What is Vedic mathematics? It is not mathematics from the Vedic period. Rather it consists of many clever mathematical sutras and algorithms that were devised by Swami Bharati Krishna Tirtha (1884–1960) who for a long time was the Shankaracharya of Govardhan Matha in Puri.

The teaching of Vedic Mathematics cannot be justified on the grounds that it tells the students something about India’s ancient mathematical heritage. This heritage without even counting the invention of zero was brilliant and unique but Swami Bharati Krishna Tirtha’s Vedic mathematics has nothing to do with it.” Source

BIOGRAPHY: Subhash Kak is Regents professor of electrical and computer engineering at Oklahoma State University and a Vedic scholar.

MATHEMATICIAN PROF. DR. C. K. RAJU

“Advocating ‘Vedic mathematics’ as a replacement for traditional Indian arithmetic is hardly an act of nationalism; it only shows ignorance of the history of mathematics.

But where in the Vedas is “Vedic mathematics” to be found? Nowhere. Vedic mathematics has no relation whatsoever to the Vedas. It actually originates from a book misleadingly titled Vedic Mathematics by Bharati Krishna Tirtha. The book admits on its first page that its title is misleading and that the (elementary arithmetic) algorithms expounded in the book have nothing to do with the Vedas. This is repeated on p. xxxv: “Obviously these formulas are not to be found in the present recensions of Atharvaveda.”

Regrettably, the advocates of “Vedic mathematics,” though they claim to champion Indian tradition, are ignorant of the actual tradition in the Vedas.

We should also be honest and refrain from using the misleading label “Vedic” which is the main selling point of Bharti Krishna Tirtha’s system, and which attracts gullible people who infer value just from the wrapper.

Promoting the wrongly labelled “Vedic mathematics” suppresses the mathematics that really does exist in the Vedas. For example, Yajurveda 17.2 elaborates on the decimal place value system…

We need to change the Western and colonial education system, especially with regard to mathematics. Traditional Indian ganita has much to offer in this process, but “Vedic mathematics” is definitely not the right way.” Source

Eminent Mathematics Historian Prof. C. K. Raju who advocates for decolonising Indian maths education

“The claim that Maths “is ancient, hence Vedic” holds no water. How do we know it is ancient? Our actual source is a modern one: Bharati Krishna Tirtha.

Tirtha never produced the relevant parishishta, even when challenged. How strange that not a single mathematician commented on these aphorisms for over 2,000 years. Such faith-based history — based solely on the word of one person — should be clearly separated from history based on evidence.” Source

BIOGRAPHY: Prof. C.K. Raju is the author of Cultural Foundations of Mathematics. He was a professor of mathematics, and an Editorial Fellow of the Project of History of Indian Science, Philosophy and Culture.

In the Times of India article Vedic Maths: Not quite adding up we read,

The so-called 16 sutras which form the foundation of Vedic Math are nowhere to be found in the known corpus of Vedic texts,” says Madhav Deshpande, Sanskrit expert and professor at University of Michigan, Ann Arbor.

In all probability, Tirthaji authored the sutras himself, says Avinash Sathaye, professor of math and a Sanskrit expert at Kentucky University. “As he himself reported, he spent eight years thinking about mathematical topics and I would not be surprised if he made these up. He was indeed asked numerous times to give a source for them while still alive and though he maintained their existence in old manuscripts, he never revealed the source,” says Sathaye.

Nowhere in the book is there any reference to the actual Atharva Veda text that inspired Tirathji’s sutras, points out Amba Kulkarni, head of the Sanskrit department in Hyderabad University. Kulkarni, who is working on the use of Sanskrit in modern computational systems, says the work neglects the other contributions made by ancient Indian mathematicians.

But do Tirathji’s sutras actually work?

Shrikrishna Dani, professor of math at the Tata Institute of Fundamental Research (TIFR), Mumbai, is not convinced of their usefulness. “The so-called Vedic Maths consists of a few arithmetic and algebraic tricks which can lead to quicker answers in special cases. It does not facilitate the learning of more complex things,” he asserts.

https://timesofindia.indiatimes.com/home/education/news/Vedic-maths-Not-quite-adding-up/articleshowprint/45839520.cms

So What Is Vedic Math? Is It Derived From The Vedas? Is It Useful? The Term ‘Vedic Maths’ Became Popular After A Book By That Name Was Published In 1965. It Lays Down Word Formulae (Sutras) That Are Supposed To Facilitate Quick Mental Calculations.Written By Shankaracharya Bharti Krishna Tirthaji, The Book’s Introduction States Clearly That The Work Is The Result Of The Author’s Study And Interpretation Of The Vedas. But The Book Has Been Popularized As A Vedic Text.

The proponents of Vedic Maths rarely dwell on its limitations. Sathaye, who teaches a course on ancient Indian maths, says a large part of Tirathji’s book is devoted to the basic techniques of adding, multiplying and division of integers. “It is true that the shortcuts as described will indeed give the answer in a much shorter time than the traditional technique, but the time spent on thinking of the right method or sutra to use is not mentioned.

Thus, with training, a student can get good at a limited set of problems; but may not know how to do the most general case, if it does not fit one of the standard cases,” Sathaye explains.

He points out two other, big conceptual negatives of Vedic Maths: one, that it may lead to the false notion that “maths means fast resolution of selected textbook problems”; and two, that it might generate blind faith in these techniques leading to spurious `proofs’ and a focus on computation rather than proving.

India has a rich heritage of mathematics, which has become part of global knowledge. This whole heritage is absent from the Vedic Maths currently being publicized. Proper research should be done in unstudied works, says Dani. Some knowledge systems such as the language sciences that originated in India as early as in the 5th century BCE with Panini, have their relevance even today. “However looking for clues to our present problems in past works may not quite be fruitful,” Dani said.

LECTURER PROF. DR. AVINASH SATHAYE

QUOTE: To most of us, Vedic refers to the entities related to the four Vedas, the Vedangas as well as the various philosophical treatises known as the Upanishads. Usually, this does not even include the Smriti Granthas though they are well respected and does not include the Puranas. Swamiji proposes a much wider meaning. He wishes to include later treatises like Dhanurveda, Gandharva Veda etc. and puts forth the opinion that true Vedas must include all knowledge needed by mankind for spiritual as well as “secular” or “worldly” matters, essential for the achievement of all-round, complete and perfect success in all conceivable directions… In effect, his contention is, that any such useful knowledge must be found somewhere in the Vedas as we know them. He reports that he had a strong personal desire to prove this in relation to Mathematics and sciences and that it was further fired up by the contemptuous or, at least patronizing attitude adopted by the Orientalists, Indologists…

Thus proving that the view of Mathematics developed by him after many years of hard work was rooted in a Vedic source was a very clear priority, nay, perhaps even an axiom for him! This is more or less like the philosophy of Gita which declares that the best among each worldly species is the part corresponding to the Lord Krishna. He reports being agreeably astonished and intensely gratified to find … ultra-easy Vedic Sutras contained in the Parisista of the Atharvaveda. It is unfortunate that these are nowhere to be found by the rest of us and the general Editor V.S. Agrawala has to concede (in his note in the book Vedic Mathematics by Swamiji) that this Parisista should simply be regarded as a new one attributed to Swamiji himself, despite Swamiji’s own assertion and conviction to the contrary. He proposes that whatever is contained here stands on its own merits and is presented as such to the Mathematical world. Source.

MATHEMATICIAN & HISTORIAN PROF. K. S. SHUKLA

“The title of the book, Vedic Mathematics or Sixteen Simple Mathematical Formulae from the Vedas, written by Jagadguru Svāmī Śrī Bhāratī Kṛṣṇa Tīrthajī Mahārāja, Śaṅkarācārya of Govardhana Matha, Puri, bears the impression that it deals with the mathematics contained in the Vedas — Ṛgveda, Sāmaveda, Yajurveda and Atharvaveda. This indeed is not the case, as the book deals not with Vedic Mathematics but with modern elementary mathematics up to the Intermediate standard.

… From what has been said above it is evident that the sixteen sūtras of Swamiji’s Vedic Mathematics are his own compositions, and have nothing to do with the mathematics of the Vedic period. Although there is nothing Vedic in his book, Swamiji designates his Preface to the book as ‘A Descriptive Prefactory Note on the Astounding Wonders of Ancient Indian Mathematics’ and at places calls his mathematical processes as Vedic processes.

The deceptive title of Swamiji’s book and the attribution of the sixteen sūtras to the Parisistas of the Atharvaveda, etc., have confused and baffled the readers who have failed to recognise the real nature of the book, whether it is Vedic or non-Vedic. Some scholars, in their letters addressed to me, have sought to know whether the sixteen sūtras stated by Swamiji occurred anywhere in the Vedas or the Vedic literature.

Some time in 1950 when Swamiji visited Lucknow to give a black-board demonstration of the sixteen sūtras of his ‘Vedic Mathematics’ at the Lucknow University, I personally went to him at his place of stay with Bolling and Negelein’s edition of the Parisistas of the Atharvaveda and requested him to point out the places where the sixteen sūtras demonstrated by him occurred in the Parisistas. He replied off hand, without even touching the book, that the sixteen sūtras demonstrated by him were not in those Parisistas, they occurred in his own Parisista and not in any other.

Let us now examine briefly the contents of that part of Swamiji’s book which demonstrates the sixteen sūtras. These are divided into 40 chapters which run as follows:

Ch. 1 deals with the conversion of vulgar fractions into decimal or recurring decimal fractions. Here it may be remarked that nobody in the Vedic period could think of decimal or recurring decimal fractions. The decimal fractions were first introduced by the Belgian mathematician Simon Stevin in his book La Disme which was published in ad 1585. The decimal point (.) was used for the first time by Lemoch of Lemberg. The recurring decimal point (.6 for .666 . . . ) is the invention of Nicholas Pikes (ad 1788).

Chs. 2 and 3 deal with methods of multiplication and chs. 4 to 6 and 27 with methods of division. All these methods are quite different from the traditional Hindu methods.

Chs. 7 to 9 deal with factorisation of algebraic expressions, a topic which was never included in any work on Hindu algebra.

Ch. 10 deals with the H.C.F. of algebraic expressions. This topic also does not find place in Hindu works on algebra.

Chs. 11 to 14 and 16 deal with the various kinds of simple equations. These are similar to those occurring in modern works on algebra.

Chs. 1 and 20–21 deal with the various types of simultaneous algebraic equations. These are also similar to those taught to Intermediate students and do not occur in ancient Hindu works on algebra.

Ch. 17 deals with quadratic equations; ch. 18 with cubic equations; and ch. 19 with biquadratic equations.

Ch. 22 deals with successive differentiation, covering the theorems of Leibnitz, Maclaurin and Taylor, among others; ch. 23 with partial fractions; and ch. 24 with integration by partial fractions. These are all modern topics

Ch. 25 deals with the so called Kaṭapayādi system of expressing numbers by means of letters of the Sanskrit alphabet. It is called by Swamiji by the name ‘the Vedic numerical code’ although it has not been used anywhere in the Vedic literature.

Ch. 26 deals with the recurring decimals; ch. 28 with the so-called auxiliary fractions; and chs. 29 and 30 with divisibility and the so-called osculators. These topics too do not find place in the Hindu works on algebra.

Ch. 31 deals with the sum and difference of squares.

Chs. 32 to 36 deal with squaring and cubing, square-root and cube-root.

Ch. 37 deals with Pythagoras Theorem and ch. 38 with Appolonius Theorem.

Ch. 39 deals with analytical conics, and finally ch. 40 with miscellaneous
methods.

From the contents it is evident that the mathematics dealt with in the book is far removed from that of the Vedic period. Instead, it is that mathematics which is taught at present to High School and Intermediate classes. It is indeed the result of Swamiji’s own experience as a teacher of mathematics in his early life. Not a single method described is Vedic, but the Swamiji has declared all the methods and processes explained by him as Vedic and ancient.

Source Shukla, K.S. (2019). “Vedic Mathematics: The deceptive title of Swamiji’s book”. In Kolachana, Aditya; Mahesh, K.; Ramasubramanian, K. (eds.). Studies in Indian Mathematics and Astronomy: Selected Articles of Kripa Shankar Shukla. Sources and Studies in the History of Mathematics and Physical Sciences. Singapore: Springer Publishing. doi:10.1007/978–981–13–7326–8. ISBN 9789811373251

MATHEMATICIAN PROF. S. G. DANI

The so-called ” Vedic mathematics” is a case in point. A book by that name written by Jagadguru Swami Shri Bharati Krishna Tirthaji Maharaja (Tirathji, 1965) is at the centre of this pursuit, which has now acquired wide following; Tirthaji was the Shankaracharya of Govardhan Math, Puri, from 1925 until he passed away in 1960. The book was published posthumously, but he had been carrying out a campaign on the theme for a long time, apparently for several decades, by means of lectures, blackboard demonstrations, classes and so on. It has been known from the beginning that there is no evidence of the contents of the book being of Vedic origin; the Foreword to the book by the General Editor, Dr. A.S.Agrawala, and an account of the genesis of the work written by Manjula Trivedi, a disciple of the swamiji, make this clear even before one gets to the text of the book. No one has come up with any positive evidence subsequently either.

What does the swamiji’s “Vedic mathematics” seek to do and what does it achieve? In his preface of the book, grandly titled “A Descriptive Prefatory Note on the astounding Wonders of Ancient Indian Vedic Mathematics,” the swamiji tells us that he strove from his childhood to study the Vedas critically ” to prove to ourselves (and to others) the correctness (or otherwise)” of the “derivational meaning” of “Veda” that the ” Vedas should contain within themselves all the knowledge needed by the mankind relating not only to spiritual matters but also those usually described as purely ’secular’, ’temporal’ or ’worldly’; in other words, simply because of the meaning of the word ’Veda’, everything that is worth knowing is expected to be contained in the vedas and the swamiji seeks to prove it to be the case!

It is shocking to see the extent to which vested interests and persons driven by misguided notions are able to exploit the urge for cultural self-assertion felt by the Indian psyche. One would hardly have imagined that a book which is transparently not from any ancient source or of any great mathematical significance would one day be passed off as a storehouse of some ancient mathematical treasure. It is high time saner elements joined hands to educate people on the truth of this so-called Vedic mathematics and prevent the use of public money and energy on its propagation, beyond the limited extent that may be deserved, lest the intellectual and educational life in the country should get vitiated further and result in wrong attitudes to both history and mathematics, especially in the coming generation.”

Source Myths and reality : On ‘Vedic mathematics’ Prof. S.G. Dani School of Mathematics, Tata Institute of Fundamental Research. https://www.tifr.res.in/~vahia/dani-vmsm.pdf


MATHEMATICIAN PROF. S. G. DANI & OTHERS

Neither Vedic Nor Mathematics

We, the undersigned, are deeply concerned by the continuing attempts to thrust the so-called `Vedic Mathematics’ on the school curriculum by the NCERT.

As has been pointed out earlier on several occasions, the so-called ‘Vedic Mathematics’ is neither ‘Vedic’ nor can it be dignified by the name of mathematics. ‘Vedic Mathematics’, as is well-known, originated with a book of the same name by a former Sankracharya of Puri (the late Jagadguru Swami Shri Bharati Krishna Tirthaji Maharaj) published posthumously in 1965. The book assembled a set of tricks in elementary arithmetic and algebra to be applied in performing computations with numbers and polynomials. As is pointed out even in the foreword to the book by the General Editor, Dr. A.S. Agarwala, the aphorisms in Sanskrit to be found in the book have nothing to do with the Vedas. Nor are these aphorisms to be found in the genuine Vedic literature.

The term “Vedic mathematics’’ is therefore entirely misleading and factually incorrect. Further, it is clear from the notation used in the arithmetical tricks in the book that the methods used in this text have nothing to do with the arithmetical techniques of antiquity. Many of the Sanskrit aphorisms in the book are totally cryptic (ancient Indian mathematical writing was anything but cryptic) and often so generalize to be devoid of any specific mathematical meaning. There are several authoritative texts on the mathematics of Vedic times that could used in part to teach an authoritative and correct account of ancient Indian mathematics but this book clearly cannot be used for any such purpose. The teaching of mathematics involves both the teaching of the basic concepts of the subject as well as methods of mathematical computation. The so-called “Vedic mathematics’’ is entirely inadequate to this task considering that it is largely made up of tricks to do some elementary arithmetic computations. Many of these can be far more easily performed on a simple computer or even an advanced calculator.

The book “Vedic mathematics’’ essentially deals with arithmetic of the middle and high-school level. Its claims that “there is no part of mathematics, pure or applied, which is beyond their jurisdiction’’ is simply ridiculous. In an era when the content of mathematics teaching has to be carefully designed to keep pace with the general explosion of knowledge and the needs of other modern professions that use mathematical techniques, the imposition of “Vedic mathematics’’ will be nothing short of calamitous.

India today has active and excellent schools of research and teaching in mathematics that are at the forefront of modern research in their discipline with some of them recognised as being among the best in the world in their fields of research. It is noteworthy that they have cherished the legacy of distinguished Indian mathematicians like Srinivasa Ramanujam, V. K. Patodi, S. Minakshisundaram, Harish Chandra, K. G. Ramanathan, Hansraj Gupta, Syamdas Mukhopadhyay, Ganesh Prasad, and many others including several living Indian mathematicians. But not one of these schools has lent an iota of legitimacy to `Vedic mathematics’. Nowhere in the world does any school system teach “Vedic mathematics’’ or any form of ancient mathematics for that matter as an adjunct to modern mathematical teaching. The bulk of such teaching belongs properly to the teaching of history and in particular the teaching of the history of the sciences.

We consider the imposition of `Vedic mathematics’ by a Government agency, as the perpetration of a fraud on our children, condemning particularly those dependent on public education to a sub-standard mathematical education. Even if we assumed that those who sought to impose `Vedic mathematics’ did so in good faith, it would have been appropriate that the NCERT seek the assistance of renowned Indian mathematicians to evaluate so-called “Vedic mathematics” before making it part of the National Curricular framework for School Education. Appallingly they have not done so. In this context we demand that the NCERT submit the proposal for the introduction of `Vedic mathematics in the school curriculum to recognized bodies of mathematical experts in India, in particular the National Board of Higher Mathematics (under the Dept. of Atomic Energy), and the Mathematics sections of the Indian Academy of Sciences and the Indian National Science Academy, for a thorough and critical examination. In the meanwhile no attempt should be made to thrust the subject into the school curriculum either through the centrally administered school system or by trying to impose it on the school systems of various States.

We are concerned that the essential thrust behind the campaign to introduce the so-called ‘Vedic mathematics’ has more to do with promoting a particular brand of religious majoritarianism and associated obscurantist ideas rather than any serious and meaningful development of mathematics teaching in India. We note that similar concerns have been expressed about other aspects too of the National Curricular Framework for School Education. We re-iterate our firm conviction that all teaching and pedagogy, not just the teaching of mathematics, must be founded on rational, scientific and secular principles.

S.G.Dani Professor of Mathematics, Tata Institute of Fundamental Research, Mumbai
Madhav M. Deshpande Professor of Sanskrit and Linguistics Department of Asian Languages and Cultures, University of Michigan
Indranil Biswas Professor of Mathematics at TIFR.
Nirmala B. Limaye Professor of Mathematics University of Mumbai
B.V. Limaye Professor of Mathematics Indian Institute of Technology Bombay
Alladi Sitaram, Indian Statistical Institute, B’lore
S. Ramasubramanian, Indian Statistical Inst., B’ore
V. Pati, Indian Statistical Inst., B’lore
G. Misra, Indian Statistical Inst., B’lore
Jishnu Biswas, Indian Statistical Inst., B’lore
D. P. Sengupta, Indian Inst. of Science(Retd.), B’lore
Alladi Uma, Dept. of English, Univ. of Hyderabad
M. Sridhar, Dept. of English, Univ. of Hyderabad
Amitava Bhattacharya
S.Subramanian, Tata Institute of Fundamental Research Mumbai
Professor Nitin Nitsure, Tata Institute of Fundamental Research, Mumbai”
SOURCE www.sacw.net/DC/CommunalismCollection/ArticlesArchive/NoVedic.html


EDITOR OF VEDIC MATHS BOOK DR. V.S. AGRAWALA

“It is the whole essence of his assessment of Vedic tradition that it is not to be approached from a factual standpoint but from the ideal standpoint viz., as the Vedas, as traditionally accepted in India as the repository of all knowledge, should be and not what they are in human possession. That approach entirely turns the table on all critics, for the authorship of Vedic mathematics need not be labouriously searched for in the texts as preserved from antiquity. …

In the light of the above definition and approach must be understood the author’s statement that the sixteen Sutras on which the present volume is based from part of a Parisista of the Atharvaveda. We are aware that each Veda has its subsidiary apocryphal text some of which remain in manuscripts and others have been printed but that formulation has not closed. For example, some Parisista of the Atharvaveda were edited by G.M.Bolling and J. Von Negelein, Leipzig,1909–10. But this work of Sri Sankaracharyaji deserves to be regarded as a new Parisista by itself and it is not surprising that the Sutras mentioned herein do not appear in the hitherto known Parisistas.

A list of these main 16 Sutras and of their sub-sutras or corollaries is prefixed in the beginning of the text and the style of language also points to their discovery by Sri Swamiji himself. At any rate, it is needless to dwell longer on this point of origin since the vast merit of these rules should be a matter of discovery for each intelligent reader. Whatever is written here by the author stands on its own merits and is presented as such to the mathematical world.”

Source Pages 6–7 Vedic Maths by Jagadguru Shankaracharya Swami Bharati Krishna Tirtha. Image below.

Does truth matter? I offer a ₹5,00,000 INR ‘Vedic’ maths reward  … for serious primary evidence and proof the 16 mathematics sutras of Bharati Krishna Tirtha irrefutably exist in any extant written Vedas.

The only evidence possible to counter everything already known would be Jagadguru Shankaracharya Swami Bharati Krishna Tirtha’s own personal copy of the Parisistas of the Atharvaveda. If they exist, they would be greatly treasured by anyone who knew of their existence. So if such a document is found and authenticated by carbon dating I will happily pay ₹5,00,000 INR for the joy it will provide so many Sanskritists and historians of India and mathematics.


Regarding Bharati Krishna Tirtha’s claim his maths was ‘Vedic’.

There is no doubt that one of Jagadguru Shankaracharya Swami Bharati Krishna Tirtha’s motivations in writing Vedic Maths was to promote Indic knowledge in the face of cultural oppression by the British Raj. On that point perhaps we can all agree on the need to promote the mathematics of Bharat.

VEDIC MATHEMATICS – ‘VEDIC’ OR ‘MATHEMATICS

Dr. W. B. Vasantha Kandasamy Author of

VEDIC MATHEMATICS – ‘VEDIC’ OR ‘MATHEMATICS’: A FUZZY & NEUTROSOPHIC ANALYSIS

Extract from Preface
In this book the authors probe into Vedic Mathematics (a concept that gained renown in the period of the religious fanatic and revivalist Hindutva rule in India): and explore whether it is really ‘Vedic’ in origin or ‘Mathematics’ in content. The entire field of Vedic Mathematics is supposedly based on 16 one-to three-word sutras (aphorisms) in Sanskrit, which they claim can solve all modern mathematical problems. However, a careful perusal of the General Editor’s note in this book gives away the basic fact that the origin of these sutras are not ‘Vedic’ at all. The book’s General Editor, V.S. Agrawala, (M.A., PhD. D.Litt.,) writes in page VI as follows:

“It is the whole essence of his assessment of Vedic tradition that it is not to be approached from a factual standpoint but from the ideal standpoint viz., as the
Vedas, as traditionally accepted in India as the repository of all knowledge, should be and not what they are in human possession. That approach entirely turns the table on all critics, for the authorship of Vedic mathematics need not be labouriously searched for in the texts as
preserved from antiquity.

In the light of the above definition and approach must be understood the author’s statement that the sixteen sutras on which the present volume is based from
part of a Parisista of the Atharvaveda. We are aware that each Veda has its subsidiary apocryphal text some of which remain in manuscripts and others have been
printed but that formulation has not closed. For example, some Parisista of the Atharvaveda were edited by G.M.Bolling and J. Von Negelein, Leipzig,1909-10. But
this work of Sri Sankaracharyaji deserves to be regarded as a new Parisista by itself and it is not surprising that the Sutras mentioned herein do not appear in the hitherto known Parisistas.

A list of these main 16 Sutras and of their sub-sutras or corollaries is prefixed in the beginning of the text and the style of language also points to their discovery by Sri Swamiji himself. At any rate, it is needless to dwell longer on this point of origin since the vast merit of these rules should be a matter of discovery for each
intelligent reader. Whatever is written here by the author stands on its own merits and is presented as such to the mathematical world. [emphasis supplied]”

Dr. W. B. Vasantha Kandasamy

The argument that Vedas means all knowledge and hence the fallacy of claiming even 20th century inventions to belong to the Vedas clearly reveals that there is a hidden agenda in bestowing such an antiquity upon a subject of such a recent origin. There is an open admission that these sutras are the product of one man’s imagination. Now it has become clear to us that the so-called Vedic Mathematics is not even Vedic in origin.

Extract from ‘Introduction to Vedic Mathematics
In this chapter we just recall some notions given in the book on Vedic Mathematics written by Jagadguru Swami Sri Bharati Krsna Tirthaji Maharaja (Sankaracharya of Govardhana Matha, Puri, Orissa, India), General Editor, Dr. V.S. Agrawala. Before we proceed to discuss the Vedic Mathematics that he professed we give a brief sketch of his heritage.

He was born in March 1884 to highly learned and pious parents. His father Sri P Narasimha Shastri was in service as a Tahsildar at Tinnivelly (Madras Presidency) and later retired as a Deputy Collector. His uncle, Sri Chandrasekhar Shastri was the principal of the Maharajas College, Vizianagaram and his great grandfather was Justice C. Ranganath Shastri of the Madras High Court. Born Venkatraman he grew up to be a brilliant student and invariably won the first place in all the subjects in all classes throughout his educational career. During his school days, he was a student of National College Trichanapalli; Church Missionary Society College, Tinnivelli and Hindu College Tinnivelly in Tamil Nadu. He passed his matriculation examination from the Madras University in 1899 topping the list as usual. His extraordinary proficiency in Sanskrit earned him the title “Saraswati” from the Madras Sanskrit Association in July 1899. After winning the highest place in the B.A examination Sri Venkataraman appeared for the M.A. examination of the American College of Sciences, Rochester, New York from the Bombay center in 1903. His subject of examination was Sanskrit, Philosophy, English, Mathematics, History and Science. He had a superb retentive memory.

In 1911 he could not anymore resist his burning desire for spiritual knowledge, practice and attainment and therefore, tearing himself off suddenly from the work of teaching, he went back to Sri Satcidananda Sivabhinava Nrisimha Bharati Swami at Sringeri. He spent the next eight years in the profoundest study of the most advanced Vedanta Philosophy and practice of the Brahmasadhana.

After several years in 1921 he was installed on the pontifical throne of Sharada Peetha Sankaracharya and later in 1925 he became the pontifical head of Sri Govardhan Math Puri where he served the remainder of his life spreading the holy spiritual teachings of Sanatana Dharma.

In 1957, when he decided finally to undertake a tour of the USA he rewrote from his memory the present volume of Vedic Mathematics giving an introductory account of the sixteen formulae reconstructed by him. This is the only work on mathematics that has been left behind by him. Now we proceed on to give the 16 sutras (aphorisms or formulae) and their corollaries. As claimed by the editor, the list of these main 16 sutras and of their sub-sutras or corollaries is prefixed in the beginning of the text and the style of language also points to their discovery by Sri Swamiji himself. This is an open acknowledgement that they are not from the Vedas. Further the editor feels that at any rate it is needless to dwell longer on this point of origin since the vast merit of these rules should be a matter of discovery for each intelligent reader.


VERTICALLY AND CROSSWISE NOT VEDIC
Bharati Krishna Tirtha’s most famous multiplication shortcut involved the multiplication of numbers such as 9 × 8. This was the first problem he demonstrated at the California Institute of Technology in 1958.

9 – 1
8 – 2

Arranged in this way you subtract 1 from 8 or 2 from 9 to get 7 which is written down.

9 – 1
8 – 2
7

Then –1 × –2 = 2 which is then written down.

9–1
8–2
7 2

Such a trick is fun, yet hides Āryabhaṭa’s wonderful system of Base 10 positional notation. Such a trick without compensating instruction could be a bad maths lesson as it just makes maths seem like magic, which is how Vedic Maths is often sold. Too bad if you want to understand maths rather than learn special case tricks. See if you can work out 8 × 7 the ‘Vedic Maths’ way.

Such ‘tricks’ were known as the Sluggard’s Rule for people too lazy to study mathematics. For example in Robert Recorde’s Ground of Arts first published in 1543 we see the exact same procedure sold as ‘Vedic Maths’ today.

Bharati Krishna Tirtha then did 77 × 97 as follows with the same trick.

77 – 23 
97 – 3

Arranged in this way you subtract 3 from 77 to get 74 or 23 from 97 to get 74 which is written down.

77 – 23 
97 – 3
74

Then –23 × –3 = 69 which is then written down.

77–23 
97–3
7469 which again works like magic, provided the two factors being multiplied are close to a common base, which is not that common!

Far from being a method from Vedic times, this method used to be taught to children hundreds of years ago as an introduction to the multiplication table.

From a 1696 edition of Arithmetick surveighed and reviewed we see the vertically and crosswise method currently claimed to be Vedic in origin.

The most famous ‘Vedic Maths’ short-cut trick was common in Europe centuries ago.
It’s better to learn the multiplication table than the vertically and crosswise method.

It should be noted the vertically and crosswise multiplication trick was also called Regula Ignari in Latin, or the Rule of the Ignorant.

Alex Bellos the author of several maths books who twice met the current Shankaracharya promoting the Vedic maths sutras wrote: “Tirthaji’s Vedic Mathematics is, it would seem, at least in part, a rediscovery of some very common Renaissance arithmetical tricks.”

The men most familiar with Vedic mathematics were the people who studied Vedic mathematics to invent modern positional base 10 mathematics. These men, like Āryabhaṭa, Brahmagupta, Bhāskara and others never mentioned anything like the 16 so-called Vedic Sanskrit sutras. If the 16 maths sutras existed, at least one of the hundreds of mathematicians and astronomers that followed would have mentioned them. Instead, nobody in history ever mentioned the 16 sutras of Vedic maths until Bharati Krishna Tirtha. Why, when he was asked to show the Vedic source of his sutras, did Bharati Krishna Tirtha refuse?

Conclusion of Australian Mathematics Researcher, Historian and Indophile Jonathan J. Crabtree

Are the 16 sutras of Vedic Maths merely western concepts dressed up in Sanskrit clothing to falsely promote a narrative that never happened? I would like to believe such a huge ‘Vedic Maths’ education industry wasn’t built on a misunderstanding. That’s why, if a genuine carbon dated ancient Vedic Sanskrit manuscript exists with the 16 sutras, I will happily pay the person who proves it ₹500,000 INR.

Regardless of the truth regarding whether or not the 16 Sutras in the book Vedic Maths are of ancient Vedic origin or not, what is not disputed is the superiority of the 18 Sutras of Brahmagupta (built upon the mathematical foundations of Āryabhaṭa over what is taught in classrooms today.

The Vedic Era ended ≈500 BCE. Around 1000+ years later Bharatiya Maths or (Post Vedic Maths) was created by Āryabhaṭa, Bhāskara I & Brahmagupta. As Bharatiya Maths is Post-Vedic it’s built on better astronomy.

So, Bharatiya Maths is more modern & powerful than Vedic Maths. It’s a matter of historical fact that Bharatiya Maths extant manuscripts 500+ CE have: specific numerals that weren’t alphabetical letters, a zero symbol (first a solid dot then a circle) and sutras revealing symmetry of negatives and positives. The Vedic Era Maths pre 500 BCE did not. Having said that, there is geometry gold to be found in the Baudhyana Śulba Sūtras. Whatever the proven source, my goal is to make modern maths foundations better with Bharatiya Maths!

For completeness, I will conclude by providing the 18 Sutras of Symmetry as first documented by Brahmagupta in 628 CE.

Thank you for reading.

If you would like to learn more about Bharatiya Maths, I have made all my research available free at www.podometic.com

Stay safe
Jonathan J. Crabtree
Founder Podometic Simply Better Maths
www.podometic.in | www.podometic.com

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