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This is a nationalist orgy. A good article could be written on this subject; it might even use the list of boasts in the middle section as a framework - but to ascribe the invention of trigonometry to someone who lived two centuries after Claudius Ptolemy is nonsense. Septentrionalis 19:49, 7 September 2005 (UTC)

Ok so if it is shown that the sheet anchor for Indian history, so that it could be matched with the western one was maliciously moved by 1200 years, would it make the stuff in here more palatable?? http://www.geocities.com/sistlas/history-reconst.htm?200627 Mpan

Many of the claims on this page are patently false. I will do what I can, but this page desperately needs an expert in this field.

Nau

Who is this Nau, that is quoted? I could find anything about him, the quote would be much more of value if there was a link to who this person is. --62.216.23.119 15:58, 19 September 2006 (UTC)

Pythagorean Theorem

I don't think there is anyone who thinks the Pythagorus was the first to state the Pythagorean theorem. Indeed it was likely used well before even 800 BC (look at the article). The fact that the Indians were the first to use a "proof with specific numbers" is nonsense. Using specific numbers is not a proof at all, it merely shows one special case. The first real proof we have is due to Euclid. A "proof with specific numbers" does not imply any deeper understanding of geometry, or an understanding of what constitutes a proof. Thus, the pythagorean theorem was used well before Indian mathematicians, and it was first proved by Greek mathematicians. Grokmoo 16:13, 15 December 2005 (UTC)

Could some one please refer me to the original sources of these proofs by Euclid etc. I have come to know from various sources that the original greek works were lost and survived only in the Arabic translation. Arabs are supposed to have recieved much of their mathematical knowledge from India as well. Considering how even after knowing the source of the mordern numerals ("On the Use of the Indian Numerals" (Ketab fi Isti'mal al-'Adad al-Hindi) 830AD), the Britsh chose to call them Arabic numerals for a long time until they were discovered on some stones in India, it casts suspicions on many of these thing attributed to the early Greek mathematicians.charudutt 06:24, 31 July 2006

First of all, calm down. This discussion - what consitutes real proof and what is just silly amatuers dabbling with numbers and have no deep understanding of geometry is not for this page. After reading through the Pythagorean theorem page, I am understanding that Indians were the first to state the theorum and first to give a numerical proof (one that uses specific numbers but in such a way that it can be generalized - not one case as you mentioned). I will change this page to reflect that. If you disagree with wording or timeline please discuss on the Pythagorean theorem page. If I have understood it incorrectly - Indians first to stating theorum and numerical proof - please discuss on this page. --Pranathi 01:14, 16 December 2005 (UTC)

I'm not so sure that there is any consensus that Indians were the first to state the theorem. There is strong evidence that it was used as far back as 2000 BC, by the monolith builders in ancient Britain and elsewhere. Indeed, there is a specific example of a solution of a problem involving the pythagorean theorem on a Bablyonian tablet which I believe is circa 1200 BC. Furthermore, "numerical proof" is nonsensical. "Proving" the pythagorean with specific numbers, but in such a way that you could also use other specific numbers and prove it for them, as well, is no proof at all.

I did not at any point imply that the Indian mathematicians were "silly amatuers" or anything of the like. They certainly had many important contributions to mathematics and science.

I have changed the wording to what I hope is an agreeable compromise. As I do not dispute the accuracy of anything written on the pythagorean theorem page, only on this page, I do believe that this is the appropriate place for this discussion. - Grokmoo

The page says Circa 2500 BCE, Megalithic monuments on the British Isles incorporate right triangles with integer sides. B.L. van der Waerden conjectures that these Pythagorean triples were discovered algebraically. I am reading that not as strong evidence but as conjecture by one person. Pythogorean triples were known by many civilizations but not their algebraic nature. To tell you the truth, I am becoming very weary of modern interpretations of mathematical history. If the same monuments were found anywhere other than Europe, there is not much chance anyone would have cared to attribute more knowledge than is directly visible - knowledge of Pythogorean triples.

In any case, the current wording is agreeable. --Pranathi 16:27, 17 December 2005 (UTC)

What does it mean by integer sides? What units are those? How is it known that the units correspond to the presents ones? Even in this age when we have SI system of units we need to deal with the fps system in scientific education in the US. Even if it is some how shown that the lengths are integers, what shows the use of Pythagorean triples there? kindly enlighten. raksasha 9:30, 1 August… 2006

It is very interesting to see Westerners not accept the fact that in the ancient world, Eastern civilizations were more advanced than the European civilization. Nobody questions the Eurocentrism in science and technology in the modern times, but it is high time to accept the contribtuions in the ancient world from not just India (which undoubtedly has the maximum contribution to the foundations of mathematics as we know it today), but from other parts of the world, specifically Asian countries, as well, besides Greece and Egypt (which, surprisingly enough, has been given credit despite not being in Europe, perhaps due to its proximity to Europe and the fact that a lot of 'European' ideas were adopted directly from there). While earliest records of trigonometry as a studied discipline exist perhaps from Greece, no doubt exists about the fact that there are much older allusions to geometry and trigonometry in the Vedas and Hindu scriptures dating earlier than 1000 BCE. Moreover, what is found in Greece is only the elements of trigonometry. Trigonometry developed as a well-explored science in India later on, and this is exactly what the text on Indian mathematics implies. Apalaria 19:31, 2 January 2006 (UTC)apalaria

If you can, you should try to get a copy of some of Ptolemy's work. If you read the Almagest, you will find a quite complete and comprehensive development of trigonometry. It is certain that many of these ideas were well known to the Greeks well before Ptolemy, but his work is sufficient to place the development of trigonometry at least as early as about 150 CE. Vague references in scripture are not development of mathematics. If you know of even a relatively complete treatment that was written before this time, I would love to see it, but I do not think any such treatise exists. Unless you can prove otherwise, the statement that the Indians developed trigonometry is patently false. Grokmoo 15:02, 5 January 2006 (UTC)

I removed the reference to trigonometry. However, I do think this Aryabhata should probably be mentioned on this page, but I am not sure where and how, so I'll let someone else decide. Grokmoo 15:06, 5 January 2006 (UTC)

The problem is that most (a lot, rather) of the works of Indian mathematicians/astronomers/etc. were destroyed in the course of the several invasions that happened. Hence, today there is not enough paper (or whatever) evidence of the original works simply because they no longer exist. It is indeed unfortunate that the works have been destroyed. As for westerners, a very few of them actually even know that science and mathematics ever existed in ancient India. And telling them so usually evokes skepticism. Rohitbd 14:36, 1 March 2006 (UTC)

If the evidence is destroyed, why are you sure the groundbreaking works ever existed? — Preceding unsigned comment added by 212.199.22.40 (talk • contribs) 02:53, July 2, 2006

On the remains of Nalanda University it is mentioned how a robber named Ikhtiyaruddin from Afganistan came with his small band of 600 dacoits and burnt the university, killed thousands of scholars. The huge collection of precious books kept in the library were destroyed and those treasures of mankind remained burning continuously for six months.[[User:mpan|mp}} 21:31, July 31, 2006

Burned for six continuous months???

Vedic mathematics

Propose a name change for the article from Vedic mathematics - to something like Vedic mathematics system by Shri Bharati Krishna Tirtha or Mental calculation system of Vedic mathematics.

- OR -

Change the section title of this article to "Mathematics of/from Vedas" or something like that. --ΜιĿːtalk 08:15, 17 January 2006 (UTC)

I've written a note in the Vedic Mathematics section of this article to inform the reader that the article Vedic mathematics is based on a system developed by Shri Bharati Krishna Tirtha. - Jagged 85, 18/01/2006

Thanks Jagged. Though I think it doesn't help much in absence of some stronger disambig or unless the other article is renamed more descriptively. Because, a user querying for Vedic + Mathematics would always land up on that page - where there are 3 disambig notices already! --ΜιĿːtalk 11:41, 19 January 2006 (UTC)

Article structure

Shouldn't this article talk about Indian Mathematics rather than Indian Mathematicians? There should be a List of Indian Mathematicians article covering this material, and Indian mathematics should be about Indian mathematics in general. In short, there are probably too much lists. There's a lot of great material in here that should be written in prose. Borisblue 13:04, 18 April 2006 (UTC)

You are right. The article is more of a list of mathematicians in its present state. Needs to be significantly improved. -- thunderboltz04:04, 3 July 2006 (UTC)

Hic Rhodus, hic salta

Anybody claiming Indian priority in inventing calculus please quote the ancient sources. Don't tell me the dog ate them or the invading Turks burnt them. I want to see your proof!

You want to see the proof? Go to Oxford or Cambridge.Your comment seems to be ridiculing the indian science and tradition. Almost all the original high value indian mathematics books were stolen from India and made available at Oxford and Cambridge around 18th centuary. Even before this Indian science and reached Europe. Sanskrit and many other Indian languages were taught in these universities, simply to stole ideas from the Indian books. It is a fact that Indian mathematics and science except Ayurveda, were never formulated as a solid systematic study like what the Europeans did. It was never co-ordinated. Instead the foolish Indian kings promoted poetry and arts. Even the science were explained through some ridiculous stories. Indians were even well aware of the theory of the origin of the universe (the Big Bang Singularity). Their concept also suggested the 'Singularity' in form of "Omkara". Also the 'Theory of Evolution' was first evident in the 'Garuda Purana' as Lord Vishnu's 'Dasavataras'. The idea is exactly similar what Darwin said some 3000years later! But the only problem lies in the addition of some irrelevant stories into this great scientific theory. Westerners cleary differentiated Science and Arts, but the Indians didn't. Here lies the problem. And it doesn't mean that Indian Science is underdeveloped. Surely, the Indian technology was underdeveloped, but not Indian science. The Indians calculated with precision, the 'Time Periods' and Inter-stellar distances of astronomical bodies and stars even 500AD. Does it mean that Newton and Kepler travelled to India in 500AD to teach Indian mathematicians how to calculate this? —The preceding unsigned comment was added by 87.192.94.150 (talk) 03:36, 5 January 2007 (UTC).

PS When I say sources I do not mean Hindutva booklets. Surely if some Indian mathematician 'long before Newton' used the notions of say derivative and integral in his work, he can be quoted directly. 212.199.22.126 00:56, 3 July 2006 (UTC)

A lot of work and ideas by Indian scientists were disregarded due to Eurocentric views of Western scientists. Yuktibhasa is the ancient text by Jyeshtadeva of Kerala School describing Calculus. -- thunderboltz03:42, 3 July 2006 (UTC)

So quote him. You seem to be genuinely convinced that Jyeshtadeva is the author of the first calculus text in the world. You surely have read this book. So please just quote some meaningful calculus passage from his book. 212.199.22.219 22:37, 6 July 2006 (UTC)

Disscussion continues on Talk:Calculus-- thunderboltz05:12, 1 August 2006 (UTC)

this article is shit

how was the quintic solved? or does my angloeuroamerciocentric racism stop me from being able to see it?

my dear Indian friends, please PLEASE PLEASE speak competently AND correctly about the contributions Indian mathematics have made and continue to make. where's Ramanujan or AKS? stop with this crap about squaring the circle and circling the square. --69.243.218.234 02:33, 26 December 2006 (UTC)

Changes made by India rising

User India rising has made a number of recent changes which need to be clarifies. First, s/he has removed the criticism of "Vedic Mathematics," moved the "Vedic Mathematics" section itself to the end of the article, and replaced the criticism by Amartya Sen and Michael Witzel by a link to an article by S. G. Dani.

The problem is that user India rising has the two "Vedic Mathematics" confused. The "Vedic Mathematics" that Sen and Witzel are criticizing is the broad program revisionist history involving Vedic Science and Vedic Mathematics (i.e. all kinds of claims for mathematics—for example, diophantine equations and the decimal place value system—originating in the Vedas) that was given a lot of publicity in the late 1990s, especially after the BJP government was formed in India, and even introduced in textbooks for children. The "Vedic Mathematics" that S. G. Dani is writing about is specifically about a book of that title, by Swamiji etc. etc. That book has been around since the mid-60s and Dani's criticism is not the first. Other critics have noted that the methods in that book are similar to the so called Tractenberg system.

I am surprised that user India rising got the two confused, especially since the section on Vedic Mathematics made a note of this fact. As for user India risings contention that Sen and Witzel are not qualified, I am not sure what is entailed in being "qualified?" Witzel is one of the world's foremost scholars on Rig Vedic sanskrit (and is Wales Professor of Sanskrit at Harvard); Sen, while primarily an economist and philosopher, is also a cultural critic, and his last book, The Argumentative Indian: Essays on Indian Culture and History is specifically about such topics. The quote from Witzel and Farmer was not included in order to be polemical, but rather to point out a number of authors (for example, S. Kak) who are involved in creating this revisionist literature.

As for the section "Vedic Mathematics" (and the Dani link) created by user India rising, it is really irrelevant, since it addresses one particular book, not the broad program of finding mathematics—created much later—in the Vedas.

I am therefore removing the new section on Vedic Mathematics created by user India rising and reinstating some of the text from the previous version of the article. Fowler&fowler«Talk» 10:02, 10 February 2007 (UTC)

India Rising has been indef-blocked for being a sock account of the banned user Hkelkar. - Aksi_great (talk) 11:15, 10 February 2007 (UTC)

Does Amartya Sen or even Witzel qualify WP:RS? Amey Aryan DaBrood 18:04, 10 February 2007 (UTC)

Yes, they do. We are not talking about "Harmonic Analysis of Semi-Simple Lie Groups" or some other 20th century topic in mathematics. This is basic, like whether the decimal place value system was stated in the Vedas, or whether Diophantine equations were solved in the Vedas. As for India rising's edit, as I explained above, he has confused "Vedic Mathematics" (i.e. the broad revisionist and political program of claiming all kinds of mathematical credit for the Vedas) with a hackneyed book Vedic Mathematics that has been around since the mid-60s, whose author use to travel around India giving demonstrations. S. G. Dani's well-written criticism applies to that book, but that is not what is being discussed here. Basically, there are two options: either do away with the section on "Vedic Mathematics" (which doesn't have any citations anyway) or admit the critical appraisal. Fowler&fowler«Talk» 18:20, 10 February 2007 (UTC)

The last 2 ip edits were made by Hkelkar. Both IPs have been blocked. Please feel free to revert their edits. - Aksi_great (talk) 09:42, 11 February 2007 (UTC)

Reverts by user:Freedom skies

First it was banned user Hkelkar, now it is user:Freedom skies, who has reverted (or rather simply blanked content in) the article. The issue on hand is the section on criticism of "Vedic mathematics," which has been described in the above section. Freedom skies refuses to join the discussion here, being content instead with enigmatic edit summaries:

and

What exactly is an "odd note?" The reason why that section is included, as I have explained above, is that "Vedic mathematics" is part of a broad revisionist political program—there being very little mathematics, other than some ritual geometry, in the Vedas. The section explains the politics behind the notion of "Vedic mathematics." As for "wikiquote" material, the quotes are specific to the section on hand, not meant for inclusion at a general site for quotations. Please explain why you are doing what you are doing. Fowler&fowler«Talk» 16:11, 11 February 2007 (UTC)

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as I have explained above, is that "Vedic mathematics" is part of a broad revisionist political program

Misplaced Pages is not a place for furthering agendas based on personal opinion. Inserting odd sections and needlessly adding flamebait material based on fears of "a broad revisionist political program" does not amount to fair rationale. "there being very little mathematics, other than some ritual geometry" is open to interpretation, your edits being based on very personal ones. I will, vigilantly remove content which is inappropriate for this article. The other related articles do not feature content of similar nature and inappropriate additions will similarily not be allowed in this one.

Regards.

_{Freedom skies| talk}  22:38, 11 February 2007 (UTC)

The agenda that is being furthered (to use your words) is the myth of "Vedic mathematics." There was no mathematics in the Vedas other than some ritual geometry. I am happy to remove the criticism if all text on anything other than ritual geometry are removed. Fowler&fowler«Talk» 02:18, 12 February 2007 (UTC)

Quoting amartya sen is out of context. What does a random guy writing a book (I got more respect for Mohammed Yunus) know about math or Hindu scriptures? Unless there is actual criticism from other eminent Hindu figures or mathematics experts it doesnt belong in this article.Bakaman 21:48, 12 February 2007 (UTC)

"A random guy writing a book!" Well, as I mentioned in the section above, we are not talking about some contemporary topic in mathematics like "Ricci flows in three-dimensional manifolds." We are talking about whether the decimal place value system was stated in the Vedas, or whether Diophantine equations were solved in the Vedas. You may know Amartya Sen as the author of works on poverty and famine or as a philosopher, but Sen has had a long and prolific career and he was a mathematical economist for the first half of his career. See for example: Wiebke Kuklys's, Amartya Sen's Capability Approach: Theoretical Insights and Empirical Applications and search on page 41, or indeed look at Sen's own Collective choice and social welfare (Mathematical economics texts). He certainly knows enough mathematics to hold forth on this topic. Mohammad Yunis got the Nobel Prize for Peace and not Economics and is not a mathematical economist (by a long shot). Fowler&fowler«Talk» 22:41, 12 February 2007 (UTC)

There was no mathematics in the Vedas other than some ritual geometry.

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GEOMETRY, is that branch of Mathematics which treats of the magnitude and relation of figures, in the most general acceptation of the word - Elements of the Geometry of Planes and Solids: With Four Plates - by Ferdinand Rudolph Hassler

There is no branch of Mathematics which occupies so large a place in the school curriculum as Geometry - The Teaching of Mathematics in the United Kingdom - by Great Britain Board of Education, Edward Doyle

Mathematics became so vast a subject that mathematicians were forced to confine their efforts to one major branch: algebra, geometry, ... - Encyclopedia of Library and Information Science - edited by Miriam A. Drake

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Geometry is a field of Mathematics, Fowler&fowler.

I am happy to remove the criticism if all text on anything other than ritual geometry are removed.

Good to know. I'll do the honors.

_{Freedom skies| talk}  11:45, 13 February 2007 (UTC)

Freedom skies: Please stop pasting a puerile sequence of quotes. No one is saying that Geometry is not a branch of mathematics; what I and the people quoted are saying is that it is incorrect to claim that topics like the decimal place value system, Diophantine equations or even Quadratic equations, which are not a part of geometry, were treated in the Vedas. The geometry Vedas was of a numerical nature involving ropes and altar constructions. Fowler&fowler«Talk» 14:16, 13 February 2007 (UTC)

No one is saying that Geometry is not a branch of mathematics

Yes you are, fowler. For everyone's benefit:-

There was no mathematics in the Vedas other than some ritual geometry.

Such inconsistencies are best demonstrated for everyone's benefit by "a puerile sequence of quotes" as you like to call them, fowler. You'll understand that I'll disregard your request of not quoting you.

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The geometry Vedas was of a numerical nature involving ropes and altar constructions.

Let's hold that little line to a challenge then; If Vedic mathematics is held to be more than altars and ropes then will you refrain from incessant, irritable reverts?

Did'nt think so.

_{Freedom skies| talk}  15:59, 13 February 2007 (UTC)

Well, here is S. G. Dani, Professor of Mathematics at Tata Institute, Bombay:

Here Dani describes a procedure using ropes, which he calls "cords." (Note that a "cord" is different from "chord" which is a straight line joining two points on the circumference of a circle.):

Here is Dani again on Pythagorean triples, which were known in Babylon many centuries earlier than in India:

I will provide more references in the coming days. Fowler&fowler«Talk» 19:05, 13 February 2007 (UTC)

The sources Fowler&fowler brings explicitely state that:-

The performance of the fire rituals (yajna) practised by the Vedic people involved construction of altars (vedi) and fireplaces (agni) in specific geometrical shapes. The constructions and the geometric principles involved in them have been elaborately described in the Sulvasutras.

The performance of the fire rituals (yajna) practised by the Vedic people involved construction of altars (vedi) and fireplaces (agni) in specific geometrical shapes. The constructions and the geometric principles involved in them have been elaborately described in the Sulvasutras.

The elaborate practical use of the Shabla Sutras then? Excellent for adding to the Shabla Sutra section.

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It is well-known that the Babylonian cuneiform tablet Plimpton 322 contains fifteen Pythagorean triples with quite large entries, including (13500, 12709, 18541) which is a primitive triple, indicating in particular that there was sophisticated understanding on the topic (see however Note 6 in the Appendix). Since these tablets predate the Sulvasutras period by several centuries, taking into account the contextual appearance of some of the triples, it is reasonable to expect that similar understanding would have been there in India.

Speculation?

You seem to have missed the following, Fowler. Must have slipped your mind:-

If we follow the suggestion of some historians that the writers of the Sulbasutras were merely copying an approximation already known to the Babylonians then we might come to the conclusion that Indian mathematics of this period was far less advanced than if we follow Datta's suggestion.

Quoting selectively/misrepresnting, fowler?

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I will provide more references in the coming days.

Of what, fowler? The fact that Vedic mathematics contained geometry? or that it was applied for practical use as your sources imply?

Sections based on flawed rationale like "There was no mathematics in the Vedas other than some ritual geometry" and "The section explains the politics behind the notion of Vedic mathematics" will be removed and editors will have to work vigilanty to remove sections like these. I, for one, will.

_{Freedom skies| talk}  21:42, 13 February 2007 (UTC)

Your callow sarcasm will not help your ignorance of what is being discussed. For the third time: No one is saying that there is no geometry in the Sulvasutras, or that geometry is not mathematics, but simply that (a) the geometry is "experimental" geometry focused around the task of rituals (b) the geometry is all without any proofs or theory (unlike Greek geometry) (c) the ritual geometry uses the language of "ropes" and "alters" (d) topics like Diophantine equations or the decimal place value system are not geometry and were certainly not solved in the Vedas. Fowler&fowler«Talk» 22:20, 13 February 2007 (UTC)

Your callow sarcasm will not help your ignorance of what is being discussed.

I have asked you to refrain from edits based on flawed rationale. Now I'll ask you to refrain from insults. Observe WP:Civility rules, Fowler.

No one is saying that there is no geometry in the Sulvasutras

No one said that anyone was saying that "there is no geometry in the Sulvasutras."

or that geometry is not mathematics

So you're claiming that you did not say "There was no mathematics in the Vedas other than some ritual geometry" now?

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the geometry is "experimental" geometry focused around the task of rituals

Your sources contradict your personal claims. Here:-

The performance of the fire rituals (yajna) practised by the Vedic people involved construction of altars (vedi) and fireplaces (agni) in specific geometrical shapes. The constructions and the geometric principles involved in them have been elaborately described in the Sulvasutras.

This was a source bought in by you, Fowler.

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the geometry is all without any proofs or theory (unlike Greek geometry)

Again, the articles in this encyclopedia are not based on personal opinion. Since you claim that "the geometry is all without any proofs or theory" are you willing to refrain if any theory or proof is provided. I can ask Subhash Kak to produce specific verses since I have had e mail contact with him.

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the ritual geometry uses the language of "ropes" and "alters"

topics like Diophantine equations or the decimal place value system are not geometry

The rationale of these statements and the context is beyond my comprehension. I'll refrain from commenting in response to them.

the decimal place value system were certainly not solved in the Vedas

Does the article say that the Rigveda solved the Diophantine equations or the decimal place value system?

I find your edits and responses extraordinary, Fowler. Not only are they based on flawed rationale but I sense the furthering of an agenda. You will understand that pollution of this encyclopedia with such material is an act that vigilant editors will not allow.

Regards,

_{Freedom skies| talk}  02:00, 14 February 2007 (UTC)

Email contact with S. Kak (or any other engineer masquerading as a historian of science) is not going to help. Here is Michael Witzel on immigrant Hindutva activists:

When was the last time that any internationally recognized journal of history of mathematics published anything by Kak? Fowler&fowler«Talk» 03:00, 14 February 2007 (UTC)

BTW, the statement, "There is no mathematics in the Vedas other than ritual geometry," means that (a) There is ritual geometry in the Vedas and (b) there is no other kind of mathematics in the Vedas (i.e. algebra, arithmetic, or geometry with proofs). As for your asking where are there references to algebra or arithmetic, well, here is the list:

In the subsection Vedas it says:

• Base 10 decimal numeral system (recognizably the ancestor of Hindu-Arabic numerals)

In the subsection Sulbasutra geometry, it says:

• The first use of irrational numbers.
• The first use of quadratic equations of the form ax = c and ax + bx = c.
• Indeterminate equations.
• Diophantine equations
• The earliest use of sine.
• The sine of π/4 (45°) correctly computed as 1/√2 in a procedure for circling the square. Template:Inote

For example, the last claim that they computed the ${\displaystyle \sin(\pi /4)}$ seems a little ludicrous, since they had no developed theory of trigonometry. They may have computed the ratio of the side of a square to its diagonal by measurement, but that is not the same thing as knowing about trigonometric functions. That's like saying that if they computed half the area of a square of side 1, they also computed the integral: ${\displaystyle \int _{0}^{1}xdx}$ and therefore they knew about integration. A bit far fetched, don't you think? India had a lot of great mathematics, but all that happened in the first millennium CE and not in the Vedas. I think it is an insult to the Indian mathematicians of the first millennium CE, like Aryabhatta or Brahmagupta, to claim that their hard-won results were all anticipated in the Vedas. Fowler&fowler«Talk» 03:33, 14 February 2007 (UTC)

PS Notice also, that I didn't say anything about Panini since the work attributed to him is both genuinely his and also profound. Fowler&fowler«Talk» 03:33, 14 February 2007 (UTC)

Email contact with S. Kak (or any other engineer masquerading as a historian of science) is not going to help.

What did I tell you about civility, Fowler?

When was the last time that any internationally recognized journal of history of mathematics published anything by Kak?

Subhash Kak contributed to the Stanley Wolpert - edited Encyc. of India (Scribner's, 2006); Edited by Stanley Wolpert himself.

Now your reasoning and agenda have become too clear too bear reasoning with you fowler. The zeal that you display is commendable, but I rarely have seen worse arguments or rationale. The amount of effort you're willing to devote to the sabotage of this article amazes me.

there is no other kind of mathematics in the Vedas

So if I display mathematics other than "ritual" geometry then would you stop? I'm willing to wonder if your extraordinary edits are based on any reasoning at all. I see a strong anti Hindu bias motivating the exertions.

India had a lot of great mathematics, but all that happened in the first millennium CE and not in the Vedas

Would that depend on personal interpretation of "great mathematics", or are you implying that we actually need to editorialize on the fact that Modern mathematics outweighs ancient ones.

With all due respect, such zealous monstrosities are not found in other similar articles and you'll understand that I'll not going to allow them here as well.

_{Freedom skies| talk}  10:33, 14 February 2007 (UTC)

An Encyclopedia of India is not the same thing as an "internationally recognized journal on the history of mathematics." An encyclopedia (as we all know) is a tertiary source and can only produce what is already out there. It is not clear what Kak wrote in that encyclopedia (in other words, if he claimed that the Hindu-Arabic numerals were developed in the Vedas etc.).

If I had an "anti-Hindu" bias, I would go after Aryabhatta or Brahmagupta or Panini, but I don't. If you think I have anti-Hindu bias, please read the first half of the History section (Ancient Indian astronomy) that I wrote in Indian Standard Time (an FA that was featured on the WP main page on Jan 21/22) or for that matter the lead I rewrote in Arabic Numerals, where I added that they arose in India etc.

My problem is with vague writing: compare for example my ancient Indian astronomy section in Indian Standard Time (which is very precise and careful in what it says) with the Vedic mathematics section on this page. I am happy to clean up the Vedic mathematics section, but then most of its vague unsubstantiated claims will have to go. Fowler&fowler«Talk» 12:26, 14 February 2007 (UTC)

The Encyclopedia is similar to Amartya Sen's book and books published by fringe theorists like Farmer in that regard then. None are recognized as authorities on mathematics.Bakaman 02:12, 15 February 2007 (UTC)

The references to both Sen and Farmer are no longer there in the text. The only people included in the criticism are J. F. Staal, J. J. O'Connor and E. F. Robertson, and S. G. Dani, all recognized experts in History of Mathematics. Also the title of the sub-section has been changed from "Criticism of Vedic Mathematics" to "Assessment of Mathematics of the Vedic Period." Fowler&fowler«Talk» 21:49, 15 February 2007 (UTC)

An Encyclopedia of India is not the same thing as an "internationally recognized journal on the history of mathematics."

You're right, it contans topics in addition to mathematics. I requested a few journals as well and procured them; they seem to disagree with your personal claims.

An encyclopedia (as we all know) is a tertiary source and can only produce what is already out there.

So that would mean that you are aware of the WP:OR? you still continue to violate that when you discover that mathematics and geometry are independent, Fowler.

The only people included in the criticism are J. F. Staal, J. J. O'Connor and E. F. Robertson, and S. G. Dani, all recognized experts in History of Mathematics.

I do agree that these men have been elaborately misrepresented by you, fowler.

"Of course the method used by these mathematicians is very important to understanding the depth of mathematics being produced in India in the middle of the first millennium BC. If we follow the suggestion of some historians that the writers of the Sulbasutras were merely copying an approximation already known to the Babylonians then we might come to the conclusion that Indian mathematics of this period was far less advanced than if we follow Datta's suggestion."

It is well-known that the Babylonian cuneiform tablet Plimpton 322 contains fifteen Pythagorean triples with quite large entries, including (13500, 12709, 18541) which is a primitive triple, indicating in particular that there was sophisticated understanding on the topic (see however Note 6 in the Appendix). Since These tablets predate the Sulbasutras period by several centuries, taking into account the contextual appearance of some of the triples, it is reasonable to expect that similar understanding would

have been there in India.- Dani

Severe OR issues here. Severe misinterpretation issues. These are in addition to the original issues which can be found earlier in the section. _{Freedom skies| talk}  01:54, 18 February 2007 (UTC)

Freedom skies, you are obviously trolling a topic with which you are not familiar. I suggest you sit back and watch F&f's work on the article, and maybe learn something. Any reasonable discussion of ancient Indian mathematics will rely centrally on the work of Staal. We are not here to fool around, hence I hope you will leave Kak and his ilk out of this from now on. This "revisionist" movement is just that, revisionism, not scholarship. It is completely unsurprising and indeed boring that all the bad faith editing, sockpuppetry, insane hype and broken grammar is only ever used unilaterally, on the part of the revisionists. Per WP:ENC we should not even honour this sort of thing with discussion, but just clean it out as a matter of course. dab (𒁳) 10:10, 19 February 2007 (UTC)

I suggest you sit back and watch F&f's work on the article, and maybe learn something.

Learn? Like, "There was no mathematics in the Vedas other than some ritual geometry." You'll understand that I'll pass such learning.

This "revisionist" movement is just that, revisionism, not scholarship.

Unless you convince Stanley Wolpert to have Kak's works removed from the his works you'll understand that I will disregard your personal opinions.

Per WP:ENC we should not even honour this sort of thing with discussion, but just clean it out as a matter of course.

I'll see to it that it's done. Edits based on distortion of sources and personal opinions belong, after all, in an underground discussion forum, not in an encyclopedia.

_{Freedom skies| talk}  10:28, 19 February 2007 (UTC)

"some ritual geometry", precisely. As it happens, comparatively advanced, or indeed very advanced for its age, but not the magical wisdom of the ancient astronauts from the north pole people would like you to believe. If you keep bringing up Kak, all you'll do is convince us that you don't know the first thing about the topic. Now cut the edit-warring, and cut the belligerent trolling. dab (𒁳) 10:46, 19 February 2007 (UTC)

The Sulba Sutras

I am removing two unsourced claims about the Sulba Sutras containing trigonometric functions. There is no evdidence of this. Since these claims were made in the WP page on trigonometric functions as well, I decided to probe it more and realized that the source provided was G. G. Joseph's book The Crest of the Peacock: The Non-European Roots of Mathematics (p. 232). However what is provided in Joseph's book is a modern-day proof of some results stated in the Sulba sutras, and that proof uses ${\displaystyle \sin \theta }$, (and that too a little redundantly since the angle is 45 degrees and he is really talking about the diagonal of a square). However, there is no indication in Joseph's book anywhere that sine, cosine, or anything resembling trigonometric functions is mentioned in the Sulbasutras. What is mentioned in the Sulbasutras is: "Divide the diameter of a circle into 15 equal part and take 13 of them to be the side of the square," (for "squaring the circle"). The Sulbasutras say that and nothing else (and no indication is given of how the result was discovered.) That is not evidence for knowledge of trigonometric functions. Fowler&fowler«Talk» 14:04, 22 February 2007 (UTC)

However what is provided in Joseph's book is a modern-day proof of some results stated in the Sulba sutras, and that proof uses ${\displaystyle \sin \theta }$, (and that too a little redundantly since the angle is 45 degrees and he is really talking about the diagonal of a square).

I was about to suggest OR violation as are apparent by constant vandalism you have caused in Indian mathematics related articles but then "The whole of Indian geometry and trignometry is dominated by the theorum of the suqare and the diagonal." (Geometry in Ancient and Mediaeval India By T.A. Sarasvati Amma page 58). _{Freedom skies| talk}  03:17, 23 February 2007 (UTC)

Request for comment:Indian Mathematics

Statement by Fowler&fowler

Indian mathematics is both poorly sourced and poorly written. For the last two weeks I have been trying to improve the article, by adding some real mathematics to the article as well as adding reliable sources (i.e. internationally recognized journals and books in mathematics or the history of mathematics). I have worked on three sections: Kerala Mathematics (only the introduction though), Charges of Eurocentrism, and Vedic Mathematics.

• To give you some idea of changes I made, here is what the section on Kerala Mathematics (intro) looked like before I began to work on the article: Kerala Mathematics intro-Before and this is what it looked like after my edits: Kerala Mathematics intro-After. All the changes you see are mine, no one else has added to them.
• Next, this is what the section Charges of Eurocentrism looked like before my edits: Charges of Eurocentrism-Before and this is the section after my edits: Charges of Eurocentrism-After.
• I tried to be careful about adding only internationally recognized journals (like those published by the Mathematical Association of America) or well-known text books. Here are the Notes before my edits: Well, actually, there weren't any! and here are the notes after my edits: Notes-After All notes between 7 and 22 (except for the website 9) were added by me.
• Finally, I've tried to edit the section on Vedic mathematics. I say tried, because the section was (and still is) so full of tall claims that it reads more like a bad fantasy than a history of mathematics. At first I simply added a number of "citation needed" tags, but subsequently added a section which was first titled "Criticism of Vedic Mathematics," and was later changed to "Assessment of Mathematics of the Vedic Period." The idea of this section was to get independent assessment of these claims by experts in the fields. The last version of this section (that I edited) looked like this: Assessment of Mathematics of the Vedic Period. Finally I added some explanation (using Taylor's Theorem) for a formula in the Vedic Mathematics section here as well as to the Misplaced Pages page Sulba Sutras it was a summary of.

• This is where user: Freedom skies comes in. I'm not sure what his goal or motivation is. Apparently he thinks I am anti-Indian or anti-Hindu. He began to revert my edits, accusing me—on the talk page—of distorting the views of the mathematicians I was quoting. In response, I began to post the exact quotes (in case you wondered why the "Assessment" section had so many quotes.) He then decided that the sources themselves were biased and began to remove the quotes one by one. See here and his next three edits. At that time, he left two paragraphs in (the section), but today, he removed the section altogether and, in addition, removed the "Charges of Eurocentrism" section (that someone else had created), and finally removed most of the "citations needed" tags in the Vedic Mathematics section and replaced them with references that not only inadequate, but, frankly, also are embarrassing. Here are his additions: Notes added by Freedom skies #3 through 16 and 19 through 22! Number 21 for example is a "homework help web site" and Numbers 11 and 20 are references to an undergraduate report by Ian G. Pearce, which I am sure is written by a very capable undergraduate, but nonetheless is not the best WP reliable source. (The only reason why Note 6 is a complete reference is that I completed it.) Most of his other references don't have a publisher (for example: "Know the Vedas By Raj Kumar (page 68)") ...

I am trying to be patient, but clearly this is not good for Misplaced Pages. I need some advice on how to deal with this. 05:26, 23 February 2007 (UTC)

PS. Since one of the comments below alluded to my inclusion of remarks by Amartya Sen, I thought I should add that the initial version of my section "Criticism of Vedic Mathematics" had "sociological" comments by Sen and others on the politics behind the resurgence of "Vedic mathematics." Here are the quotes from Sen and Staal, which I later removed and replaced with assessments of mathematics of the Vedic period. Fowler&fowler«Talk» 09:06, 24 February 2007 (UTC)

Statement by user:Freedom skies

My statements will come shortly. I have been working through my examinations. I'll present my point of view in a few hours. It would be best if editors heard both sides of the story before resorting to judgement. _{Freedom skies| talk}  16:36, 23 February 2007 (UTC)

I'll be as brief and concise about this as is possible:-

• The Changes I've made

1. I tried to replace the "citations needed" tag with actual citations. Compare my version to this one.
2. I removed the "Charges of Eurocentrism" section; this is wikipedia not some soapbox. Indian laymen accuse everything to be Eurocentric but how that finds it's way into an encyclopedia is beyong my realm of understanding. If "EU as a potential superperpower" can be deleted then why shy away from flamebait sections such as these?

Instead of adding material to that section as most people seem to think of my edits I have been removing the section which violates the WP:ENC code of ethics.

• My proficiency in the field

1. Someone called my providing citations and removing undue sections as being a "drawback" of the "anyone can edit" policy. I'm a third year engineering student and I probably see more maths than most people; suddenly I'm summed up in the very ad hominem "zealous angry young man with an agenda."

• My "agenda"

1. I will continue to provide citations for every "citations needed" tag not only in this article but others as well. In my case I have provided the name of the book and the page number, which is a perfectly justifiable under Misplaced Pages rules.
2. If anyone feels that some sources need correction then I will provide additional ones. I will not shy away from my duties as an editor for this encyclopedia. I am working through my examinations and I know that I'm going to be unduly harrasesed but then I'm doing this in any event.

• My personal feelings about this

1. Being a Hindu on Misplaced Pages is demoralizing at times. I asked for sources here and all I recieved were insults and people just kept reverting. I, of course operating alone, could not even as much as attach a tag and these people did not even care about providing explainations.

1. Before my side of the story was heard, judements were passed on my being zealous and everything. I know most people probably find this amazing but I tried to talk to Fowler on this very page before editing. He, no doubt confident that he could recruit people to make me insignificant (notice the "why cannot they just leave good enough alone" response he gets), just left the discusion and initiated edit warring.

1. I do see people disagreeing with part of my edits but indiscriminate reversion based on confidence in case of an edit war is not fair rationale. Reverting the entire, whole thing completely has been done in case of my edits, often cited as "rv vandalism". I did provide citations from the University of Michigan, British sources and the Stanford University; I'm sure mentioning them here must have slipped Fowler's mind.

• Solution

1. Point out the sources which violate the WP:RS and point out why do they violate WP:RS instead of reverting the whole thing indiscriminately. I'll bring additional sources. Being revert happy is not the solution. This solution should endure as I intend to stay longterm with this article and provide citations wherever needed.

Regards,

_{Freedom skies| talk}  10:53, 24 February 2007 (UTC)

Comments by other editors

Comments by: Dbachmann (talk · contribs)

Fowler&fowler is a mature and academic editor proficient in the field, and Freedomskies is a zealous angry young man with an agenda. Just another instance of the well-known drawback of "anyone can edit" (vice-versa its many admitted boons). Enough said, really, the case couldn't be much more clear-cut. dab (𒁳) 09:47, 23 February 2007 (UTC)

Please refrain from making comments of a personal nature. =Nichalp «Talk»= 18:20, 23 February 2007 (UTC)

I agree with Nichalp. There is no doubt that Fowler & Fowler is mature/resposible.(I have also supported his viewpoints on many cases). It does not mean we have to support him on all cases blindly. There are many people who support him blindly on all issues without going through merit of actual incidents. We have to support issues based on contents and not based on the qualities of person who raised issues. I suggest Dab and DavidCbryant to address issue directly instead of eulogising F & F or withdraw their comments. (I am not commenting on this issue since I don't have knowledge on this subject.). If you want to appreciate contributions of individual then award Barnstar instead of supporting that person on all cases. --Indianstar 06:58, 24 February 2007 (UTC)

Comments by: DavidCBryant (talk · contribs)

I have reviewed the edit history on this article, and I have looked at a sample of both Fowler&fowler's and Freedom_skies' contributions to Misplaced Pages. In my opinion, Fowler&fowler is a responsible, kind, decent, and hardworking contributor. Freedom_skies consistently pushes his own POV, does not respect guidelines, loses his temper frequently, and vandalizes Misplaced Pages with some regularity. DavidCBryant 14:12, 23 February 2007 (UTC)

Please refrain from making comments of a personal nature. =Nichalp «Talk»= 18:20, 23 February 2007 (UTC)

Comments by: Grokmoo (talk · contribs)

I have noticed the very many incredible claims made here and on other pages with regards to Indian contributions to mathematics. I have also noticed in multiple cases edits where the author clearly does not even understand what it is he/she is actually claiming. Fowler&fowler is braver than I to try to make such sweeping changes to these articles, since even the smallest factual correction is often met with great resistance (in my personal experience). I have looked over Fowler&fowler's contributions, and the quality of his edits and the great number of reputable citations have greatly impressed me. I think his edits are a large step forward in the right direction of cleaning up this page. Grokmoo 21:50, 23 February 2007 (UTC)

Comment by: Sbandrews (talk · contribs)

Fowler&fowler, I was impressed by your section Assessment of Mathematics of the Vedic Period and feel that it deserves a place either in this article or perhaps the main article on vedic mathematics. However I also feel that in placing fact tags *all over* the vedic's section you have stirred up the current controversy more than was needful. If you place the new Assessment section in this article you are amply stating your position and can leave it up to the reader which side of the story to accept. Vedic mathematics may not be rigorous mathamatics - but it is mathematics due to its name - an uncomfortable truth perhaps. If the other party has exams I will comment more when he has put his case, Kind regards sbandrews 23:51, 23 February 2007 (UTC)

Freedom_skies, well, I had an open mind, and I am still inclined to keep one, but your last edit to this page, reverting all of Fowler&fowler's edits without discussion, counts against you IMO. Why do you feel it is innapropriate to edit now? Surely this is the *best* time to edit, while many impartial observers are here to help you work with Fowler&fowler to provide working consensus approach to this page. I see three options for you two -

1. agree on areas of the article which are the sole preserve of the other - one take the vedic section, the other the critique of vedic - this has the advantage that the two of you need not communicate.
2. start to communicate, stop deleting (Freedom_skies) and stop smothering with fact tags (Fowler&fowler) and perhaps, both of you, try to understand the others position.
3. open warfare :), kind regards, sbandrews

Comment by: Bakasuprman (talk · contribs)

I have noticed that Fowler quotes Amartya Sen as if Sen is some sort of Keith Devlin or Stephen Wolfram. Freedom skies seems to have produced refs which allude to and back up many of the assertions made on the page. The first two comments (by outsiders) only serve to prove that some users do show a rabid disdain for "Indian achievement" whether real or imagined. DavidCBryant, a user who obviously has little knowledge of the situation is quick to label freedom as an vandal (I was unaware adding references was vandalism, though on planet Glingxon I'm sure they think that way). Also Dbachmann's characterization of freedom skies as an "angry young man" indicates that he is stuck (or wholeheartedly believes) in a paternalistic mindset similar to White man's burden, where those providing a well-sourced antithesis to entrenched views in the Western World are branded with terms such as "communalist", "angry young man" and in India Hindutvavadi.Bakaman 01:32, 24 February 2007 (UTC)

Please refrain from making comments of a personal nature. CiteCop 02:41, 24 February 2007 (UTC)

Comments by: CiteCop (talk · contribs)

In my experience, Freedom skies cites sources that do not meet WP:RS and, more egregiously, completely misrepresents them, citing them in support of statements they do not actually support. No matter what article he edits, Freedom skies' edits maximize the role of India whether or not reliable sources support his edits; I leave it to the reader to decide for himself whether this means Freedom skies has an agenda. Like Grokmoo, I have noticed the many incredible claims with regards to Indian contributions, not only in mathematics, but in a number of fields, as well as the great resistance that correcting these claims meets. I would also like to remind readers that implying that someone is a racist is no substitute for providing sources that meet the standards laid out in WP:RS. CiteCop 03:41, 24 February 2007 (UTC)

Comments by: Jitse Niesen (talk · contribs)

Fowler&fowler says that Freedin skies added "references that not only inadequate, but, frankly, also are embarrassing". Well, I looked at the references added by Freedom skies in this edit, which seemed representative from a reading of the article history. The first references added are (quotes from Freedom skies' version, followed by my comments)

• "The Modern Review edited by Ramananda Chatterjee. Original from the University of Michigan. Page 634" - This probably refers to the monthly magazine Modern Review, published in Calcutta. It doesn't seem to be peer-reviewed. It's unclear what Michigan has to do with it. The reference does not include a volume number, so it is impossible to find what is being referred to.
• Replacing "Mathematical Expeditions: Chronicles by the Explorers by David Pengelley, Reinhard C. Laubenbacher" with "Toward a Global Science: Mining Civilizational Knowledge By Susantha Goonatilake (page 119)" - I don't really know which source is preferable, but I have my doubts about Goonatilake's book given that it seems to be written in order to argue that Indian's contributions to science are being ignored (anonymous (?) review) and that it got a rather negative review by Kavita Philip in Isis, Vol. 92, No. 1, pp. 247-248 (quote from the review: "The chapters on medicine and mathematics cannot therefore deal substantially with the provocative claims he puts forward.")
• "Science in Ancient India By Narendra Kumar (page 9)" - I can find very little about this book, suggesting that it is not used often. It's unclear whether it can be considered reliable.
• "Vedic Mathematics By Vasudeva Sharana Agrawala, Swami Bharati Krishna Tirtha" - don't know
• "Vedic Mathematics for Schools Bk.1 By James Glover" - this is published by Motilal Banarsidass. It doesn't seem a scientific text, according from the description at Google Books

None of the references have full bibliographic information, as normal in references. Based on all this, it seems correct to consider the references inadequate.

Freedom skies says that he/she (sorry, I don't know) "removed the "Charges of Eurocentrism" section; this is wikipedia not some soapbox. Indian laymen accuse everything to be Eurocentric" However, the section had references to articles in journals as Historia Scientiarum (Japanese, peer-reviewed) and Mathematics Magazine (published by the Mathematics Association of America), so it's unclear what issues Freedom skies has and why the section is soapboxing. Freedom skies' solution ("Point out the sources which violate the WP:RS and point out why do they violate WP:RS instead of reverting the whole thing indiscriminately. I'll bring additional sources. ...") is a bit odd as it supposes that reliable sources exist, while that seems to be the whole problem.

On the wider issue, I agree with several people above that the Indian contributions in the history of mathematics are bigger on Misplaced Pages than in the other books I read. -- Jitse Niesen (talk) 14:30, 24 February 2007 (UTC)

Comments by:

Comments by:

1. Dani, S. G. 2003. On the Pythogorean Triples in the Sulvasutras Current Science, 85(2) 25 JULY 2003.

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