Posted on: 4 February 2015

An important and well-researched essay that unravels the myth of 'Greek origins behind Hindu mathematics' and how this was perpetuated down the ages...

The Reception of Ancient Indian Mathematics by Western Historians
By Albrecht Heeffer
Center for Logic and Philosophy of Science, Ghent University, Belgium

While there was an awareness of ancient Indian mathematics in the West since the sixteenth century, historians discuss the Indian mathematical tradi- tion only after the publication of the first translations by Colebrooke in 1817. Its reception cannot be comprehended without accounting for the way new European mathematics was shaped by Renaissance humanist writings. We show by means of a case study on the algebraic solutions to a linear problem how the understanding and appreciation of Indian mathematics was deeply influenced by humanist prej- udice that all higher intellectual culture, in particular all science, had risen from Greek soil.

During the fifteenth century Italian humanists eagerly started collecting editions of Greek mathematics. One of the most industrious was Cardinal Bessarion who lived in Venice. By his death in 1472 he had accumulated over five hundred Greek manuscripts (Rose, 1975, 44-46 and 90-109). Regiomon- tanus, who had befriended Bessarion, began to study these Greek texts around 1463, including Diophantus’ Arithmetica. He reported his find of the six books of the Arithmetica in a letter to Giovanni Bianchini (Curtze, 1902, 256-7). By then he was well-acquainted with the Arabic algebra. He owned a copy of the manuscript on algebra by al-Khw ̄arizm ̄i, possibly from his own pen (MS. Plimpton 188). Highly receptive to influences between traditions, he immedi- ately conjectured a relation. In his Oratio, a series of lectures at the University of Padua in 1464, he introduced the idea that Arabic algebra descended from Diophantus’ Arithmetica (Regiomontanus, 1537). This heralded the initiation of a myth cultivated by humanists for centuries. Diophantus, first considered to be the source of inspiration for Arabic algebra, became the alleged origin of European algebra. Several humanist writers such as Ramus, chose to neglect or reject the Arabic roots of Renaissance algebra altogether (Høyrup, 1998). As a matter of fact, Diophantus had almost no impact on European mathemati- cal practice before the late sixteenth century. Diophantus inspired authors on algebra such as Stevin, Bombelli and Vi`ete because by then symbolic algebra was well established. By overrating the importance of Diophantus and down- grading the achievements of Arabic algebra, humanist writers created a new mythical identity of European mathematics. Suddenly Greek mathematics be- came European mathematics. However, most Greek sources were unavailable before the sixteenth century. In fact, Greek mathematics was more foreign to the European mathematical practice than Arabic mathematics was; the lat- ter was slowly but surely appropriated with the abacus tradition. Ironically, the medieval qualitative arithmetic, which was a genuine European tradition, became completely forgotten.

Only later, European historians learned about ancient Indian mathematics and what they learned was strongly influenced by the humanist mathematical tradition. We will now give a brief overview of the first assessments of Indian algebra in the West.

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Bramhagupta (598–c.670 CE)

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About time for some home truths....our history has been totally distorted

Oh yeah...our history has been distorted by all those evil 18th/19th century indologists. Let's get back to reading Puranas for history.

On a more serious note, I don't understand why we have this straw man construction of "Greek origins" of Hindu mathematics. No respectable historian has ever denied the achievements of Hindu mathematics since their discovery in the West in 18th/19th centuries. And nobody has ever ruled out independent development of Indian mathematics. At most, what scholars have hinted at is a possible hellenic influence on Indian mathematics as these cultures did interact a lot. Heck, we even had Greek satraps ruling over much of North west India just prior to the Christian era. So I don't see how one can totally rule out an influence. Its remarkable how just about everything in our history is viewed through revisionist lenses lately with an attempt to establish India as the "fount" of all knowledge. Ridiculous at best.

Shrikanth Krishnamachary: I think that was a melodramatic over reaction at best. Rediscovering the achievements of ancient Indians/Hindus is by no means claiming them to have monopoly over knowledge of all mankind.

These are not rediscoveries. Men like Brahmagupta, Aryabhata have been discussed for centuries. They have been acknowledged the world over. Revisionism of this kind deserves strong reactions

Are you referring to the essay that has been posted above?

Not so much the essay. But the comment above that talked about "history" being distorted. Also with all due respect Sir, I don't agree with your comment on top of the article about the "myth of the Greek origins of hindu mathematics" Indologists have never denied independent development of mathematical thought in India as is often supposed. One needn't look at everything through an "us versus them" prism.

Also the general historical consensus has acknowledged the Indian (and later Arabic) genius for notations and algebra. While Greeks have been noted for their pioneering work in Geometry. Greeks have never been lionised for their "algebra" as one gets the impression from this paper.

Also I think Indology has evolved a great deal from its days of inception in early 18th century. I think it reached a very tall peak in the 1950s what with AL Basham's "The Wonder that was India". But it took 200+ years to reach that summit. It is rather pointless to now discuss what the very very early Indologists in 18th century thought. Because those opinions have long been superseded and dismissed by other great Indologists in the 19th/20th centuries. My point is that there is a world of a difference between the Indology of HT Colebrooke and the Indology of a Basham. We all stand on the shoulders of giants. And yes, it is pointless to dig up the false conclusions/hypotheses made by some very ancient Indologists of 18th century as the profession has moved on since.

Good article and here is a must read for those interested in non-European roots of Mathematics...Crest of the Peacock by Joseph George Gheverghese, University of Manchester

Your views have generally been balanced and fair Shrikanth Krishnamachary. And they have earned my respect and admiration. You might have a point in your observation, but the reason for me provide the above preamble was due my recent education from the many books on the history of mathematics that I have posted recently. Where I have seen that many/most of the respected historians have glossed over the contribution by ancient Indian mathematicians and have clearly given credit to those of Hellenic origin. GR Kaye is one such example. And also the recent deplorable slugfest between the pro-Hindu and anti-Hindu political parties (both of whom might be ignorant of the layers of ancient scientific history) - that has made it necessary to educate oneself from the rare books published earlier. You might be well educated about Brahmagupta, Aryabhatta or even Mahaviracharya, but almost all of modern India is not. Their only source of information are the silly claims and counter claims between each other in the newspapers. And that is not only sad but also dangerous in my opinion. Hence we are posting a series of books on the achievements of ancient India - not to breed chauvinism but pride with factual knowledge of the past.

Fair enough Sir. I admire your great efforts on this site. However what I fear is your well intentioned work providing unintended succour to rabid revisionists with no sense of history. Already we have had one comment on "history distortion". Being a devout Hindu I fear the way revisionism is hurting the reputation of my civilisation the world over.

Silly and rabid comments are routinely deleted from this site. The more clever, couched and nuanced ones sometimes escape our attention. The rabid comments are posted by people who do not read or have no ability to understand the layers of history. But there are probably many more who will take the effort to 'rediscover' these histories once again. Blind hatred is dangerous, just as its natural reaction - that is chauvinism, which is equally dangerous and embarrassing. Both can be countered and tempered only by factual knowledge. In our own little way, that is what RBSI is attempting to do.

Indian nationalism is still very dominant in Indian intellectual discourse and to admit ancient connections with the West is still not popular (how many Indians do you hear talking about the ancient Greek kingdoms in India?). Unfortunately, this hinders the progress of Indian academia to become more objective and produce accurate research in many fields, and also creates obstacles to legitimizing itself in the eyes of the world, because the dominant rhetoric about anything historical in India is largely nationalistic and influenced by post-colonial narrative. That's not to say that this article isn't true, either, but certainly many people have noticed the trend, and if they haven't they should, and adjust accordingly.

Revisionism is only a natural process since 'written history' has been the handmaiden of the victors. How much ever we lament over it, one just cannot stop it. We in fact should only hope that any revision is based on research, facts and fairness devoid of a propagandist tilt. But then, that is the responsibility of scholars and cannot be expected from the political parties.

Well put!

You are right. One but has to expect such a reaction after 150 years of the colonial narrative and 60 years of the marxist narrative! We should wait for the water to find its own level. Give it some time.

Well, these are just my impressions. I'm glad they seem to be confirmed. I just think it's unfortunate that people feel the need to be so biased, especially in India, a country with one of the most fascinating histories in the world, but alas such is usually the case the world over also.

I agree that on a 'popular' level the water needs to find its own level because it's largely an 'historical imperative' as you allude to.

To elaborate further on your observation - Yavaneswara might just be the ancient mathematician you are looking for. A greek (Yavana) who translated the greek astrology to sanskrit in the 1st century AD. Of course there are many legitimate doubts about the genuineness of his work. But that apart, history has always been a syncretic process and no achievement would have happened in isolation.

Well I certainly think that India probably influenced Greece just as much as the other way around. Both influences should be acknowledged and researched as objectively as possible. By the same token, Greece has mostly forgotten its debt to India too. That's really interesting about Yavanaswara, I need to tell my friend who's doing a Phd on Indo-Asian Buddhist astrology and its connections to Western astrology about this. Jeffrey Kotyk

Shrikanth Krishnamachary, it looks you don't study but pass ill-informed opinionated comments, read below, your eyes shall be opened up in light of facts - History of Modern Decimal Counting System Do we know how we count numbers in English in multiple of Tens, what is the history behind it, that we got to know in context, Pls have a look - Twenty = Twen(Ty) Thirty = Thir(Ty) Forty = For(Ty) ------- ------- Ninety Did you notice, we follow a "Ty" system, Where it does come from, Let me tell you, it comes from Rigveda and followed by all in entire world, Pls look at Vedic Numbers in the Rigvedic System of counting - विंशति (Vimsha-Ti ) त्रिंशति (Trimsha-Ti ) चतुर्विंशति ( Chatvarimsha-Ti ) -------- ------- नवति ( Nava-Ti ) This is the Rigvedic "Ti" system that has become "Ty" system in English. True history of mankind is fascinating, India has been the origin of many things that has made the world modern

Discovery of India NO-2 should be written..

Mr Mishra - I thought one of the ground rules of this forum is that we mustn't get personal. I don't see how you can ascribe the syllabic similarity in the pronunciation to "Rigvedic" system of counting. These are lingual similarities arising from the fact that Latin, Greek, English and Sanskrit all spring from the same family of Indo-European languages. Also could you tell me more about this "Rig Vedic" counting system? Does this feature in the "Samhita"? Or the Brahmanas? or the Upanisads? Which part of the Rigveda?

RBSI : "written history" may have been the handmaiden of "victors" in the old days of Imperial court writing. (as epitomised by say Mughal historians). But not in the modern age (last 300 years) when history has emerged as an academic discipline pursued by lay men of scholarship (starting with the likes of David Hume and Edward Gibbon). I am still old fashioned enough to believe that all history is not simply "political narratives". That it is possible to write fact-based histories over which there can be consensus regardless of one's race, creed or political orientation.

Aren't you a bit too idealistic, Shrikanth Krishnamachary? We in India are bombarded with daily articles on Marxist and Hindtuva narratives in the school textbooks and thereby influencing millions of students. Marxist historians replaced by nationalist historians in bodies like ICHR. One trying to right the others wrong. In the meanwhile the general populace is kept suitably ignorant of history so that any version that is dished out is unquestioningly lapped up for political gains. This is how it has always been and will continue to be. In India, we can trace it back to the colonial narrative beginning with Macauley, that was countered by the Indian nationalists during the freedom movement, that was again altered by the Marxist narrative after Nehru and Congress which is now being challenged by the present BJP government. This will always go on. All the narratives have some truth in them, but it is the intent and conclusion that makes it political. Hence the people themselves have to understand this and discover the many layers that exist in history and gain perspective.

Please go thru, "India in Greece" by Edward Pococke, published by Griffins n Co., London, 1852.

RBSI : So are you saying there was none of this business of "narrative construction" pre Macaulay? Do you think Puranas represent "Objective" academic historical writing? Or do you regard imperial court writing of the Muslim period as academic history? Objective study of the past with attention to dating and social milieu begins with European humanistic studies (Post 15th-16th century). And let's always separate "interpretations" / "value judgments" from "plain facts / reportage". It is perfectly okay for interpretations of historical events to be influenced by political world views. I am good with either marxist or conservative interpretations. Nothing evil about that. What is worrying is when facts end up getting distorted in the process. Eg: Let's take the varna system. A Marxist may condemn it and say it was "evil". While a conservative Hindu (like myself) may regard it as a product of its time (not to be passed judgment over with 21st century lenses). Both views are perfectly valid. The problem arises when these biases start influencing your ideas of how the varna system came about, its timelines, its development etc. These are "facts" over which we should attempt to build a consensus (though it is hard given the lack of historical evidence).

And I am sorry to say that this tendency to distort facts is becoming very rampant in the Hindutva camp lately. (Perhaps even more so than it ever was in the past even in the heyday of Marxist history). The Marxists at least had some scruples when it came to fact-distortion (which is lacking in these hindutva types).

I disagree that one political narrative is better than the other. And yes, they have always existed and many centuries before Macauley. I mentioned that to give the topic a more recent recall. I entirely agree with your angst as a proud Hindu when cringeworthy claims are being made quite tactlessly. I understand that we would not want to be represented by narrow views and history-illiterate representatives. But the Marxist were even more devious where they distorted and misinterpreted the roots so much that one had to feel ashamed of ones past. Hence, one has to find a balance and discover on ones own. That has been the stated agenda of RBSI from the beginning - that there are many truths in history and one has to unlearn the political narrative in order to learn afresh again.

"Marxist narrative even more devious" You are contradicting yourself here as you earlier mentioned all political narratives are "equal" in a sense. I am no Marxist as you know. Guess you remember our debates early last year with a few others on economic history where I took strong stances against Marxist history. Having said that I don't think Marxist interpretation "shames" my past. I may disagree with it. But I stop there. Whether one gets shamed or not depends on one's sensitivity. For e.g. : If a historian says that its likely that the origins of Vedic culture is not native to India. That's a hypothesis informed by some historical facts. Nothing to feel pleased or ashamed about. One has to learn to face facts instead of cringing at every little inconvenient truth as Hindutva types often do.

We have to accept that there are many ways of seeing the past and the lens by which you see it will alter what you perceive. If one sees the past of a land through the Christian eyes it would be very different from that of a Hindu eyes. The same for any ideology based views. The American Indian for example believed that the 'he belonged to the land' and he couldn't understand when the White man said that the 'land belonged to him'. Slightly unrelated but the perception is based on the religion and cultural roots, is what I am trying to say. The Hindu timeframes, it's mythologies, its continuing and living civilisational connection all makes it very different from the others.

Supremist evangelism is bad ...however ideologically driven suppression of Indian scientific achievement under garb of strawman and adhomein attacks by caricaturing needs exposure .....dissemination ...good work Sir/ Ms

Search in YouTube about evolution of mathematics in india, the program by inspiring India

Not just this ..we need more serious purvpaksh ...

Rare Book Society of India I think we must stop belabouring our opposition to the Eurocentric view of history by proposing an "Indocentric" (worse, Hindu-centric) view of history. The scholarly paper you have posted does not have a single modern Indian source quoted in its main proposition about the Greek influence (or the lack of it) on Indian mathematics. I do not see any escape from the fact that the language of modern algebra with its statements containing unknowns in the form of equations and arithmetic operations thereon is the contribution of European mathematicians of the 17th, 18th and 19th century. Knowledge is never absolute nor is it free of influence from predecessors and peers. Neither is influence a one-way street. It will be in interest of science if we stop eulogizing scientific achievements of our (Indian) ancestors. We will benefit only if we adopt the modern scientific way of enquiry conducted with rigour and resourcefulness. Else, we become the laughing stock of the world in our own eyes. Your contention that there are many ways of looking at history appears to be false though your comment about the lens is bang on. Since prejudice cannot be wished away. May I invoke the phrase "scientific temper" that has been maligned in recent times?

Shekhar Sathe: Of course we need a scientific temper! But why should it be at the cost denying culture, tradition, belief, religion and all those those things truly makes India what it has been and what it is. A Eurocentric view just cannot understand the complexity of India...its far too complex and confusing for it. We need to understand the reality, context and bring in the rigours of a scientific temper alonngwith it. Pride in the past should only propel us to become better - strangely not many seem to see it this way.

I would like to draw attention of all discussants above to a recent national seminar organised by indian institute of sciences in Bangalore . It had many interesting scientific papers on Indian science achievements of the past not glorifying but exploring the facts . need of enriching world history by exploring the histories of all regions of world came out very clearly

As a person endowed with scientific temper, one should (learn to) look at culture, tradition, belief and religion करतलाम्लकवत् (like a gooseberry held in one's palm, with detached attachment). Humility is a value preferred over pride just as integrity is preferred over loyalty.

A person who truly understands the magnitude of achievements of his predecessors would only be overwhelmed by humility.

Yes, I agree if the emphasis is on "truly". Newton compared his own knowledge with a speck of sand on the seashore.

Some space has opened for alternative narrative....explorations .... other than what is championed as scientific or systematic "mainstream" historical studies ... constantly labeling the alternate perspective or the perspective that challenges seated dogma as revisionist ...nationalist ...communal .has been as damaging as silly and rabid comments which really damage genuine ...there is place for many alternate narratives .... parallel ...contradictory .....however a more level playing field for open and rigorous peer review is a welcome development ....even if still a long way off ...

We must know what ritten in

puran first

There are points in both Shrikanth Krishnamachary and you, but Your elaboration on the need to publish the series to make people aware of the golden past of Indian Mathematical / scientific achievements needs no further support. But what Shrikanth rightly observed and logically afraid of being a tool in the hand of ignorant or devilish politicians who want to create false pride in things to generate hysteria among the public for their benefit. By doing this they actually underrate the great achievements of our culture

this is the fear of all true citizens of this country and as a matter of fact for all civilized people. thank you to express the agonies so eloquently


Please do not pass comment only because you need to oppose.

Weel replied

Sir, Yo are partly correct ... or should I say that you're mostly correct, however, the Academic historical writing is also presently getting better of sectarian publicity or tilted interpretations of the same fact. in fact the present generation readers are now very intelligent, they read both or all the versions before making their own decision. However, this practice is not so common among the general people, who tend to buy the journalistic history ( I mean the news published in the various media).

This is entirely a funny argument by those who oppose corrections in ancient indian history, When historians like Romila Thapar, Michael Witzel etc have been engaged in FACTUAL FALSE history writing when we validate their writing against Vedic content, we dont get amused with bizzare ignorance and mediocrity and then we come across their daring attitude to hide the nonsense they have been writing by making another propaganda that their false writing should not be corrected. I am sure such advocacy of false writing doesnt work in developed countries, and those who turn to adovcate these mediocres dont know of Indian history. Its shameful for Indians who have better knowledge and resources with ability to think through.

I am sure Romila thapar has not read even 10 hymns of Rigveda otherwise she could not have done such open false writing, She could triumph because she knew that the crowd, she is surrounded with doesnt have even elementary exposure to what is written in source books i.e Vedas, it was like a fool heading other fools, these gentlemen who appear to give sermon, i am sure have not read first hundred pages of Rigveda, had they done so, they wd have run another campaign to throw out Romila like historians who write trash, absolute nonsense. Professional honesty is something that cant be compromised but her false writing shows, she never cared it and under the threat that if people starts cross verifying, validating her essays, writings etc, she will get exppsed, she is engaged into more dangerius game of making propaganda. This is disgusting.

dont be distracted by self humiliating tendencies,write what you wanna write.There are Indian stories that need to be told on large platform like fb .when others are proud of their culture and knowledge,why cant we?

With apologies sir its absurd to broad brush or blame all politicians it not absurd what has been happening for 67 years in University's , ...and institutions of higher learning ? A system that created an Illuminati and Gulags ...any descent ...brand communal ...communal ...

Srhikantth Krishnamahary's another blind belief is the false idea of "Proto Indo European" or "PIE" language which brings in European language of later age such as "English", "French", "Italian", "Greek", all at par with Sanskrit in terms of antiquity and the irrational idea that all of these languages have their origin in one common imaginary language that is called "PIE". Obviously, Srhikantth Krishnamahary' doesn't have basic idea of history of languages and fundamentals of linguistics. Pls, don't ever try to give sermons, have some stuff to present in argument then only come to debate.

For the knowledge of Srhikantth Krishnamahary and many like him, I intend to share that the "Father of Proto Indo European Thesis", LORD COLIN RENFREW of CAMNRIDGE UNIVERSITY confessed just three weeks ago in a one on one communication with me that he doesn't know, doesn't understand Sanskrit therefore he is not in a position to defend his thesis wherein I cited UNFATHOMABLE HOLES but our Indian academicians are embracing his thesis mindlessly, a thesis in which LORD COLIN RENFREW himself is no confident.

Yes yes. I am the one who is ignorant. I don't need you to prosecute me. By the way I never said English or French or Italian are as old as Sanskrit. Never said any such thing. All I said is that Sanskrit and most European languages belong to a common language family.

Brother, you know very well that what you intended to do with following and extending, the latest round of blind belief that Sanskrit and Most European Languages are from same language family, your attempt was to show English, Greek or Italian, etc have not received decimal numeral terms from Vedic Sanskrit, in other words they knew Sanskrit decimal numbers on their own. You had been in so hurry that you didn't apply even your common sense and couldn't see that reception by European Languages is "With Sasnkrit Grammar Rules" it's not mere "reception of Sound Vowels", do you get me, see, let me tell you the first fundamental, the broken Sanskrit words found in European Languages is a "Full Package " borrowing, words go with Vedic Grammar and it means, the mother Language, the Sanskrit has gifted these words who already had perfectly evolved grammar by the time European's started borrowing, this shows Vedic People spread from India to Europe, Are you getting it. Your beloved lady historian doesn't have mind to grasp it. Pls note that It's the Sanskrit that gives meaning, rules of pronunciation, and as already said the grammar, put together, other languages are derived from Sanskrit. Lord Renfrew could not counter this finding and chose to not to defend his PIE theory that you have embraced and feel you are becoming a great modern scholar since you have just heard some linguistic terms - "PIE" or "Common Language Family", however lacking insight to know what is what. So, brother, pls don't sell ignorance to us, there are no takers, study more and talk sense.

Brother, it's very good that you admitted the truth that you have no study of Vedas but how you can talk so much without knowledge and study, how it helps you, It looks very superficial to me, reading first three lines of your arguments, I could realize that you are just running a tape recorder, outdated and boring, this is all that what you teach to students, Pls stop misleading audiences with fancy English !!


Mr Mishra - I am not particularly keen on your "fraternal" mode of address. Oh By the way you haven't gotten back to me on the "Vedic" system of counting? Is it in the Samhita or the Brahmanas? Please enlighten

Shrikant Krishnamachary - I am enjoying funny questions from you, Pls take up studies from today only, OK, however, to answer you, terms "Vedic System of counting" itself shows it's there in Vedas, Right from Rigveda to Atharva Veda to Brahamans to later date classical Sanskrit to today's English, Hindi, Russian, German, Greek, Arabic who all received it from Vedic Sanskrit.

And for more knowledge of yours, let me tell you that, Shatpath Brahamna categorically records counting numbers on fingers, that is the oldest reference to counting on fingers, Your lady historian has not known even this and written in her good for nothing books that Aryans were not literate., Don't you find it a joke. Indians Aryans who invent mathematics, are called illiterate, loudly projected as not knowing writing even

What a discussion and knowledge ...beautifully mentioned all the great beings my India ....what a collection you have Mr mishra ...very nice ....always show your Abhutpurv collection with details ..

What more lie and fallacies can be taught to students of Indian History, Romila like historians should have been asked to put in papers, decades ago, they have misled and spoilt many generation of students. What was her agenda, is that money or politics ?

Now she is running pillar to post to save her disgraced face, that she only did

'वादे वादे जायते तत्वबोधः' continue..............!!!

Every individual is entitled to his or her opinion - and it is not necessary to make personal references if we would like to participate in a debate. I know this is a tall order when an 'old wound' is being discussed, but all the same... these are the guidelines.

Mr Mishra - I am not sure which "lady historian" you keep referring to. I made no reference to any lady historian. Regarding Aryans being "literate" or "illiterate" : In reality they were both literate and illiterate. One needs to develop a more nuanced understanding of history. What do you mean by "Aryans"? Are you referring to the Aryans of 1500 BC? Or the assimilated Aryans of 500 BC? Are you referring to Aryan society as a whole? Or specific tribes like the Bharata clan? Or are you referring to Vedic priestly clans in particular? Your literate / illiterate conundrum depends on these qualifications. No society over 3000 years old anywhere on earth was completely literate. Heck. Literacy rates in India were around 5-10% even 100 years ago. They were very low (< 20%) even in Europe some 500 years ago. Historians make statements based on available evidence. Not based on hunches. The reality is that while we have a wealth of literary evidence from the Vedic age, there is no evidence available to prove that this literature was written down (as opposed to being orally transmitted). It is very likely that parts of Vedic society were literate. But it may also be true that oral tradition was preferred over writing stuff down for cultural reasons. Also we need to stop talking in terms of abstractions like "Aryan" or "Non Aryan". The reality is more complex. Among the people who migrated to the Indus plain circa 2000-1500 BC, we have diverse cultures. Not everyone adhered to Vedic brahminism (or its proto version). It was a complex situation with multiple tribes and diverse cultures co-existing. The Vedic culture we like to talk about evolved to become the mainstream "Indo-Aryan" culture much later (circa 1000-500 BC). PS : Pardon me for correcting your north indian islamised pronunciation. But it is not "Shathpath Brahmana". It is "Shata patha Brahmana" :)

Romila like historians are the enemy of our country..they misguided our generations..reconstruct our history is earnestly needed...

well said.

Arijit Karmakar


You have done a great job Sir Ravi Sankhi & Bhola nath jee with Rare Book Society of India!! Thank you!!

Yes the slugfest is the politics of ignorance at best. World has recognized the prowess of Indian civilization yet Indians have a some kind of chest thumping attitude. I agree that you need to publish a series of books on this matter as people need to know. I would also like to see books on chinese maths too

Very Poor Shrikant Krishnamachari, why you continue to talk without knowledge, it's only you or probably that lady Romila etc, who don't have evidences available to prove Vedic Literature was also "Written Down", however, the irony is, she herself never shown honesty to put a single evidence that can prove "Writing Down" of Vedic Literature is ever denied, just goto her, ask and then put that evidence here, this is open challenge to you, Show us how much history you know ? If you ask us, We have more than a dozen evidences to show Vedic people were not only reciting hymns and listening to but writing as well , since, we have thorough studies and we are all ready to erase the nonsense that Vedic people didn't know writing, Since, you don't do studies but spend time in superficial arguments, you may not know truth. Who told you that satpath is a Islamized pronounciation can you give me that linguist's name ? :) , what I see is typos and spelling mistakes are the the last straw for you to argue, never it is data, facts, evidence etc .. Indeed even British linguists don't say that English has phonetic capabilities but your mind triggers you to think English spellings has phonetic standards which is the worst unscientific language of the world, and since, you don't know that what is written in shatpath brahman, you are stuck with it's English spelling We see how you omit here to make a cover up false history written by likes of lady historian ( Romila Thapar ) and ignorant of her school.

Please do not use such rough language. No need to do so. Everyone is entitled to their opinions in a polite manner

We need to educate ourselves with historical truth not from who said what to whom. There in lies the the truth. I would love to see RBSI publish more ancient texts to ensure that we know this truth. No one yet has been able to correctly identify the source of sanskrit. It is currently considered as having links to ancient Bruhi language of central asia. We dont yet. Many manuscripts were lost during major fires and earthquakes. As technology advances more even carbon dating is becoming accurate. Yes some Indians need to feel that they are superpower so the politics. They look silly. But majority of the west knows that India has a very rich heritage of maths and science.

Shrikant Krishnamachary, seen you were sighting some headcounts, can you tell pls what was the total Vedic population in 1500 BCE, 500 BCE etc and what is your source of information, really, this is an interesting infatuation to build up further.

Mr Mishra - I plead ignorance of demographic details of Vedic age. I cannot pretend knowledge of something, that can be at best a guesstimate. Oh by the way, in an earlier comment you talked about the "Rig Vedic system of counting". In a later comment you claimed that the earliest reference to counting is in Shata pata Brahmana. That's interesting because the Shata Pata Brahmana is an appendix to the Shukla Yajur Veda (not Rigveda). This is baffling. Because if you believe that Vedic math owes its origin to Shata Pata Brahmana then you can't possibly talk of "Rig Vedic system of counting" as you did in an earlier comment because the Rig Veda precedes the Yajur Veda in its composition. Interesting :D

well said Bhaktiprasad Adhikari Ji

My God Shrikanth Krishnamachary Ji, Now you have started deliberately mis-reading the content, that is written on the wall, where you are leading to ? Pls read once more, hope you can make distinction in both - 1) Vedic Decimal System of counting is available from "Rigveda to Atharva Veda to Brahamanas .... etc " 2) Shatapath Brahaman provides oldest "record of counting on fingers"

Mr Mishra - Even the caveman could count on his fingers. Shatha patha Brahmana is a very important text for a number of reasons - especially as a source of some very important mythological narratives. But for the first time I am seeing someone lionising this text for its mathematics. Oh and yeah. Please do elaborate a bit more on the "Decimal system of counting" that you claim is in the Rig Veda. I have always regarded it as an achievement of classical India (and not the Vedic period). But I do not mind being corrected. Please be precise in your pointers. Let me know which Mandala you are referring to.

why can't people be respectful - what is the point is talking down - sorry, admin :(

Mr Raste - Mr Mishra has some interesting claims. And we are attempting to enlighten ourselves with his wisdom. One ought to listen to one's betters.

Shrikanth Krishnamachary, your's is a dull case from historicity perspective, any body can count on fingers but do you have a record as well, in history a record is important, right and it's we who present that record to world, never Greek or Germans, who you vouched for in the beginning of thread.

Mr Mishra - My objective is to understand the past. Not to vouch for or talk against any specific group or culture. Regarding Indian mathematics : This is just my understanding. And ladies and gentlemen who know better can correct me - The only part of the Veda that discusses mathematical concepts is the Sulba Sutra - which dates roughly to the late Brahmana period and can be regarded as Vedic. The Sulba sutras are essential for the performance of the Shrauta rituals and discuss geometric ideas (including pythagorean triplets). However the notational innovation in Indian math (including the 10 symbol-based decimal system that spread across the world) dates to the classical era (roughly 1st to 5th century AD). It is not an accomplishment of the Vedic period as is being claimed over here. Also the more advanced mathematical achievements of Indian civilisation (especially the works of Bhaskara I and II or Brahmagupta) belong to late Gupta/Early medieval times. And are at least a millennia after the dusk of the Vedic era. This is my understanding of my country's past from the point of view of mathematical accomplishments. However I understand there are members here who have a very different understanding. In which case please substantiate your views with references.

The sulba sutra is nothing more than a practical guide for altar construction, a sort of a DIY manual. It is child's play to construct right triangles for any given perimeter. Empirically, it is relatively easy to find only the early primitive Pyathagoran triplets. It will be a folly to attribute great mathematical insight (in the modern sense) to those sutras. In itself, the sulba sutra, at best represents a pinnacle of achievement for the nomadic vedic society as it must have existed then, an amazing feat for a few learned men of pastoral community. Numerical representation of numbers in the decimal form was certainly not known n vedic times. Else, we would have seen examples of that. What we have is just number names (for large numbers) from the later literature.

That's correct Mr Sathe. Unfortunately when we discuss these matters in an objective light, we get labelled as "anti-hindu" or even anti-India by some. That's just a very childish reaction. I have nothing except the very highest regard for these remarkable Vedic seers. For their absolutely astounding feats of memory, their passion for classification, and their drive to understand the world (even if that drive was motivated by superstition). They represent a primitive yet beautiful flowering of intellect at the dawn of civilisation. Hats off to those rishis, whose names are still amongst us thanks to the Hindu gotra system! To ascribe impossible sophistication to these primitive intellectuals is very very unfair. Please appreciate them for whatever they were. Don't turn them into comic supermen.

And yes, thanks for your comment. You just spoke my mind on the Sulba sutras :)

Shrikanth Krishnamachary: "To ascribe impossible sophistication to these primitive intellectuals is very very unfair."... I would have easily agreed with you earlier and even today I don't disagree entirely with your above comment. But I suspect our anglicised and eurocentric view of the world has made us almost arrogant in our belief that our way of seeing is the best and only way. And that our intellect and understanding is far superior to the other etc. etc. But today, I would like to view these things with a sense of wonder without too much certainty as there are many dimensions, layers and perspectives which I might not yet be aware of.

RBSI : Well as I just said, I have nothing but sheer wonder for these rishis. Especially for their out-of-the-world feats of memorisation. Their philosophical inquisitiveness, their storytelling prowess, their ability to combine speculation (Upanishads) with practical action (Brahmanas-based sacrificial ritual). These guys were terrific. And I am very very glad that we still remember at least some of them thanks to our Gotra system. But my pride in these great men doesn't prompt me to ascribe to them insights which i know for a fact they didn't possess. (or at least have no evidence handy to prove they possessed it).

And I feel this debate between Shrikanth Krishnamachary and Lalit Mishra is going on in an uneven and unfair tangent. Both are knowledgeable gentlemen from different cultural backgrounds debating in essentially a foreign language to either of them with different levels of mastery. There can never be a reconciliation here nor a reasonable conclusion as what each of them are saying is from totally different perspectives. One wants proof, the other needs none. And their convictions speaks for itself. This is how different people are. I respect both of their views. No point in browbeating the other.

RBSI : I have no problems with belief. Though I somehow lack belief myself partly because of my background. I have always admired religious people from a distance. I honestly wish I was religious. Which I am not, despite hailing from a very traditional brahmin family. Faith is a great great thing. But it should be restricted to the God room. It should not impact one's assessment of entire cultures and ideas of history as well as politics. Thats my only request.

I completely agree with you here and can also relate to what you are saying. For many of us, being religious can be exasperating and exhausting. That is why Hinduism gives you the options of Jnana yoga, Bhakthi yoga and Raja yoga - to suit each one's temperament. Each person is different and the way they see the world is different.

RBS : It's never about culture, religion, tradition etc, It's about DATA, FACTS and HISTORICITY that are falsely put in by likes of Romila Thapar etc and Shrikanth Krishnamachary here is trying to advocate that such a false history writing should not be reviewed, revised, corrected, rather, this falsity should be allowed to continued which is not acceptable to us. You need to take a stand here, whether you are one who too support to false history writing or you are for corrections

Shekhar Sathe : You presented a circular logic, You need to change your twisted view on Shulba Sutras, Do you know that Shulba Sutras are not books of mathematics but preparatory books for making Vedic Altars wherein they used and applied mathematical knowledge available to them those days ( Before 700/ 800 BCE, A rough estimate ), You need to find out in rest of world in whatsoever civilization you are in infatuation with, the similar books wherein same level of knowledge of Mathematics is found You can not compare Shulba Sutras with complex mathematics used in programming SPACE SHUTTLES to ridicule mathematics of Shulba Sutras. I don't know how much Mathematics is known to you but a student of mathematics doesn't ridicule his basic studies, the fundamentals when he does his masters or doctoral researches. You presented a circular logic

Mr Mishra - Nobody is ridiculing the Shulba Sutras here. In fact I delivered a eulogy to the seers who wrote it (was it Baudhayana and Apastambha?). And I am sure Mr Sathe brooks them no ill will either. We all stand on the shoulders of anonymous giants. And I agree with you that these men were special people. Mr Sathe was attempting to offer a context and present the achievements of texts like the Shulba Sutras in proper perspective by reminding ourselves of the milieu inhabited by these sages.

I being an engineer can understand that Mr Sathe was not putting Shulb Sutras in "Right Perspective" but entirely in "Wrong Perspective"

Review and revision, as I have mentioned earlier is a natural process and will go on whether one likes it or not. Our discussions on RBSI have revealed time and again that many of the fundamental presumptions regarding the dating, geographical locations and the ensuing history might have been wrong either due to an error in judgement, misreading of facts, unavailablity of sufficient archaeological evidence, lack of cultural understanding, political motivation or plain prejudice. Much as we should admire and be grateful to early Indologists who set up the foundation, format and structure for India's history as we know today, we also need to keep in mind that their probable erroneous conclusions might be perpetuated as holy grail to this day.

Nobody wants anything to be regarded as "Gospel". Nevertheless you don't revise something for the sake of revising! But yes, you do revise it as new facts come to light. This is an objective process. You just nicely summarised some 6-7 reasons why some fundamental assumptions on dates among other things could be wrong. One of them being plain prejudice/bias. Now that's one thing which is found aplenty in many of our "new vintage" pro-Hindu historians (including perhaps some of us because of our Hindu background though we may not acknowledge it). How does one ensure that this bias doesn't result in a so-called "revised" history that is even more inaccurate than whatever existed in the past? For eg : Scholars 100 years ago had a consensus period of 1500-1000 BC for Rig Veda. Maybe they didn't have all the information. Maybe they had cultural misunderstandings. Because of which they probably got the date wrong by say 500-1000 years. I don't rule out Rig Veda being perhaps a little older than that. Let's say 2000 BC or even 2500 BC. But that's not the position of several revisionists. They want to ascribe extremely impossible dates of 7000 BC - which defies all conventional common sense. Is this objectivity?

And very often this dating business is a political thing. Because as Mr Mishra himself has asserted many times - India was the fount of civilisation. So that kind of a grandiose claim becomes hard to sustain with dates of say 1500 BC (as is the case now). Because we had highly evolved Sumerian, Mesopotamian and Egyptian civilisations that are much older than that (circa 3000 BC). A date of 1500-1000 BC makes Vedic culture contemporaneous with even the Hebrew jewish culture of middle east or the Mycenean culture of Greece. So for India to trump those cultures, one needs to come up with a much much older date :)

I am a conservative by temperament. And a gradualist. I believe in skepticism. And suspended judgment. I am not the sort who likes revising every date in the book and claiming that historians 100 years ago were wrong about the timeframe of Vedic culture by some 5000 years and change the dates from 1500 BC to 7000 BC in the text books, just because some ruins were discovered in Dwarka. That's not the kind of a person I am. When you want to change anything in the history books, you first need to build a scholarly consensus. If you cannot build it, it doesn't deserve to be in the books.

RSB : Much appreciations to your right efforts in right directions, we are with you, let these corrupts make lobby against review of fraudulent writing of mischievous historians, who cares these fellows.

Mr Shrikanth Krishnamachary, Tell me, when Vedic God Indra is respected and mentioned in Mesopotamian Tablets, dated before 2100 BCE, How Romila Thapar and others, including you date Vedic Civilization to have been started in 1500 BCE ? Why you don't study history properly, I w'd request to not to believe what trash is dumped in the name of history by mischievous writers of Marxist mound and Euro funded schools. . This is another show of not knowing the history and posing as knower, a sincere scholar, isn't it ? where from this no 1500 BCE is coming to discussion of Indian History, Do you mean Vedic Civilization came into existence in 1500 BCE, You are utterly wrong.