Talk:Kerala school of astronomy and mathematics

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We need citations!

Contents 1 And then what? 2 Does any mathemetician know how to clean up? 3 Explanation of Warning 4 Gregory 5 references for claims made 6 Title 7 Other evidence section 8 Mathematics was banned from use in European accounting 9 Citations 10 Greeks and Moors 11 Docking the Hagiography and Bogus Mathematics

[edit] And then what?

There's not much discussion about the physical aspects of the school. Was it a school in the modern sense of a learning institution? When was it formed? What happened to it? It was named the "Kerala School" long before the conception of the Kerala state? I'm trying to research the history of education within Kerala, and while this is the oldest form of formulized education that I could find before the western missionary schools arrived, this information does not really provide many answers for me.

[edit] Does any mathemetician know how to clean up?

I don't want to be too critical of this article because it's a topic I know nothing about. But is there a competent mathemetician who is familiar enough with this topic to know what to make of:

• Infinite series expansions of functions.

Ok. How? By Taylor series? Fourier series?

• The power series.

Power series of what?

• The Taylor series.

Taylor series of what? There are 4 or 5 trigonmetric functions listed below.

• Trigonometric series.

...

• Rational approximations of infinite series.

...

• Taylor series of the sine and cosine functions (Madhava-Newton power series).

Ok. Wouldn't that fall above?

• Taylor series of the tangent function.

Likewise

• Taylor series of the arctangent function (Madhava-Gregory series).

Likewise?

• Second-order Taylor series approximations of the sine and cosine functions.

What's the 2nd order Taylor series? If the "1st order" is just sin(x) ~ x, then the second order would be sin(x) ~ x + x^3/3!.

• Third-order Taylor series approximation of the sine function.

So that would be sin(x) ~ x + x^3/3! + x^5/5! ?

• Power series of π (usually attributed to Leibniz).

Which one? π = 4/1 - 4/3 + 4/5 - ...

• Power series of π/4 (Euler's series).

Which one? Does this mean Leibniz above?

• Power series of the radius.

What radius?

• Power series of the diameter.

What diameter?

• Power series of the circumference.

What circumference?

• Power series of angle θ (equivalent to the Gregory series).

??? What does this mean?

• Infinite continued fractions.

Ok. As solutions to quadratics? Cubics?

• The solution of transcendental equations by iteration.

As solutions to ...

• Approximation of transcendental numbers by continued fractions.

Which transcendental number?

• Tests of convergence of infinite series.

Ok...

• Correctly computed the value of π to 11 decimal places, the most accurate value of π after almost a thousand years.

Ok...

• Sine tables to 12 decimal places of accuracy and cosine tables to 9 decimal places of accuracy, which would remain the most accurate upto the 17th century.

Ok...

• A procedure to determine the positions of the Moon every 36 minutes.

Ok...

• Methods to estimate the motions of the planets.

Ok

• Integration.

Including the fundamental theorem of calculus? Which rules? Integration of polynomials?

• Term by term integration.

Ok

• Laying the foundations for the development of calculus, which was then further developed by his successors at the Kerala School.

...

Thanks! --M a s 01:47, 12 May 2006 (UTC)

If you read Wikipedia with an open mind (may I suggest lobotomy?) you'll find out that Hindu Science is the source of all possible knowledge and the so-called western scientific discoveries are stolen from Hindu Pundits by unscrupulous plagiarizers like Newton and Einstein. There's nothing to clean up. You should memorize the list and sing it to yourself in reverent meditation. 212.199.22.107 22:50, 17 March 2007 (UTC)

[edit] Explanation of Warning

I have placed the warning message on this page, particularly because almost all of this "information " derives from George Gheverghese Joseph's The Crest of the Peacock: Non-European Roots of Mathematics. Is it any surprise that George Joseph himself was born in Kerala? Furthermore, the bibliography of this article is very misleading, because it makes it looks as though scholars have independently verified Joseph's work, yet if you dig deeper you find:

• Three of the citations refer to Ian G. Pearce, who was an undergraduate (not a professional historian) at university at the time he wrote the articles cited. Those are suitable for an informal college report but not encylopedic nor peer reviewed.
• The citation referring to D. P. Agrawal in fact refers to a non-peer reviewed opinion piece, not a scholarly work. It should be noted that D. P. Agrawala admits that historians do not agree with George Joseph's work, and Argawal labels them "Eurocentric." (Is Agrawal guilty of the same kind of bias?)
• The citation associated with Dr. Sarada Rajeev refers to the syllabus of a history class at Canisius College that he is teaching, not information; futhermore, Rajeev's course syllabus on that page indicates the course is regurgitating George Joseph's Crest of the Peacock, not providing independent corroborative archaeological evidence.

Unfortunately, many related Wikipedia pages state the "contributions" of the Kerala school as "fact". All of them need to have a warning put on them that this interpretation is fairly new and not univerally accepted. This is exactly why the Wikipedia: No original research policy was created.

4.228.213.30 04:01, 24 June 2006 (UTC)

[edit] Gregory

I've taken issue with the last bit of the following:

James Gregory, who first stated the infinite series expansion of the arctangent (the Madhava-Gregory series) in Europe, never gave any derivation of his result, or any indication as to how he derived it, suggesting that this series was imported into Europe.

Absence of evidence is not evidence of absense. There can be many reasons why Gregory never gave a derivation of his result, the an obvious one being along the lines of the gist of this whole article - that he did have one but it was lost.

If a reputable scholar makes the claim that because Gregory didn't have a derivation, then this SUGGESTS that he got it from Keravala then I would like to see the exact quote, the reputation of the scholar, etc.

Suggesting is a very strong word. First things to reach a compromise I would like to see a more neutral word, or a phrasing that's in-lines with a reputable scholar.

Thanks and regards,--M a s 17:14, 27 June 2006 (UTC)

I did not understand the words "absense" or "keravala" and I do not think "suggesting" is too strong a word.Bharatveer 18:26, 27 June 2006 (UTC)

Hey alright. I'll ignore that.

I suggest that you please answer: Who suggested? Please place this person's observations as clearly as you can int his article. --M a s 20:55, 27 June 2006 (UTC)

Quoting from the article : "Other pieces of circumstantial evidence include:

James Gregory, who first stated the infinite series expansion of the arctangent (the Madhava-Gregory series) in Europe, never gave any derivation of his result, or any indication as to how he derived it, suggesting that this series was imported into Europe."

I think this sentence is pretty clear in that the circumstantial evidences suggests that this series was imported into Europe.I think that is the answer to your question. Anyway,I have added the reference to the sentence.Bharatveer 04:21, 28 June 2006 (UTC)

Thanks for the reference Bharatveer. There's two different Gregory's though- one's a pope in the 16th c and one's a mathemetician in the 17th c. The pope made the changes to the calendar. In my eyes this evidence is pretty obstruse. But thanks for the interesting reference. --M a s 20:08, 28 June 2006 (UTC)

I wonder what information could one possibly get from that article beyond the obvious fact that nationalism doesn't need facts for self-glorification? Have you seen any Indian texts on calculus dating from pre-Newtonian era?—The preceding unsigned comment was added by [[User:{{{1}}}|{{{1}}}]] ([[User talk:{{{1}}}|talk]] • [[Special:Contributions/{{{1}}}|contribs]]).

[edit] references for claims made

This article is extremely biased - the claims are mainly ridiculous, and most either have no factual evidence to support them, or the ideas in question can be traced back to the Ancient Greeks. People should be aware that this is a favourite topic of Hindu nationalists.

all of the claims on this page need specific references to articles in the bibliography, otherwise it becomes very difficult to verify them. secondly, it is important that all of the references used for this article are peer-reviewed and the opinions of other historians on these works is described. i noted in particular that the "passage to infinite procedures" was not a new idea at the time indian mathematicians considered it (it goes at least back to the ancient Greeks), so it would be better if their specific contribution to this area was described. many of the other claims are also not specific enough... like the claims of inventing calculus, for instance. - 72.57.120.3 21:18, 29 July 2006 (UTC)

Indians are coming, my friend. Do not ask for references. Just turn away from Wikipedia. No use to fight. Let them own this increasingly smelly pile of BS. 212.199.22.122 19:57, 4 September 2006 (UTC)

[edit] Title

I think the title for the article is not very apt. Shouldnt it be something like "Kerala School of Mathematics" or some other similar name?-- ॐ Kris 18:56, 21 October 2006 (UTC)

I agree. It should be renamed. Does anyone know the original Malayalam name of the school? Else, we should go for Kerala school of astronomy and mathematics, IMO.--thunderboltz^(Deepu) 07:16, 22 October 2006 (UTC)

Melvyn Bragg's programme on BBC Radio 4 today simply used the term 'Kerala Mathematics'; St Andrews, which is usually quite reputable, [http://www-history.mcs.st-andrews.ac.uk/history/Projects/Pearce/Chapters/Ch9_1.html], uses 'Keralese Mathematics' and also refers to 'Kerala Mathematics'. Davy p 22:50, 14 December 2006 (UTC)

[edit] Other evidence section

I removed: "There was some controversy in the late 17th century between Newton and Leibniz, over how they independently 'invented' calculus almost simultaneously, which sometimes leads to the suggestion that they both may have acquired the relevant ideas indirectly from Keralese calculus."

The controversy was primarily concerned about whether Leibniz had access to Newton's work or used it in developing his calculus. The above comment suggests more of a conspiracy theory angle as if the simultaneous development of calculus was a miraculous coincidence, and the phrase "sometimes leads to the suggestion..." probably falls under the "weasel wording" category(or whatever you call it), if it has led to this suggestion then please cite a reputable source that is not oneself.

[edit] Mathematics was banned from use in European accounting

BBC Radio 4's programme by Melvyn Bragg, 'In Our Time', today was entitled 'Kerala Mathematics'. It's available, I think, as MP3 from the BBC website. I missed most or the programme, but noted that Indian numerals and, if I heard correctly some sorts of maths, were banned from use in bookkeeping in parts of Europe until the 19th century; and the concept of zero was treated with great suspicion until comparatively recently. The programme usually brings 3 experts on a subject together, so it should be accepted as reasonably authoritative. Davy p 23:03, 14 December 2006 (UTC)

what? please explain. indian numerals were banned from accounting in the 19th c? zero was treated with great suspicion until when? who says?

[edit] Citations

Let me commend St Andrews as a non-Indian source which might help to reduce claims of nationalism. Their website seems to be as unimpeachable as any other academic source. [http://www-history.mcs.st-andrews.ac.uk/history/Projects/Pearce/Chapters/Ch9_2.html] Davy p 23:19, 14 December 2006 (UTC)

See Rick Norwood's comment on Talk:Calculus page - "These are certainly interesting references, but they do not lay all the problems to rest. The history of Indian mathematics, for example, is by a grad student, Ian G Pearce, whose specialty is the study of insects. It seems to be very well researched, but to rely almost entirely on secondary sources". I wanted to add a little joke in the sense that soon somebody will say that Indians invented the radio but to my dismay I found that this claim was already made (look up Invention of radio). Not funny anymore 212.199.22.122 19:39, 18 December 2006 (UTC)

These Hindutva arguments are generally along the lines of: whoever can't understand the great significance of the Indian subcontinent to the history of mathematics are obviously racists and/or neoimperialists. Is this correct?

All of the editors who recognize this article for what it is have one point in common: This kind of bullshit does more harm than good.

I believe you are the same user with who I had a long discourse on Talk:Calculus some time back. Even if you are not, you can scroll down to Talk:Calculus#A_desperate_call_to_our_Indian_friends and see these primary sources you are asking for. The original discoveries are noted in palm leaf manuscripts, not book and paper, so they wouldn't be available to the public. Also, if you indeed are the same person, please don't waste my time again. Those comments speak loads about the person who wrote them.--thunderboltz^(Deepu) 04:12, 26 December 2006 (UTC)

Hi there, I'm the guy up above with the comment about Hindutva. I'm not the same person you had a discussion with earlier, nor to the "A desperate call to our Indian friends." My comment was directed not to anything you had said but to the comments from 87.192.94.150. There are many of us "Westerners" who recognize the many contributions and the lead taken by those on the Indian subcontinent in many areas of science. However, bloated exaggerations and claims of priority with little hard evidence does the damage to the credibility for the incredible and truely unbelievable things that Indian mathemeticians HAVE done. And to throw out accusations of racism or neoimperialism or "stealing" I think is above the cuff, and speaks loads about the persons who wrote them. --203.117.92.2 09:13, 9 January 2007 (UTC)

[edit] Greeks and Moors

Much of the mathematics and logic seems to have reached northern Europe by a rather long route, moving east to Persia when the ancient Greece crumbled and then to Spain in part via the Moors. My own knowledge of history is somewhat hazy, but this seems to be an important part of the story. Pythagorus' Theorem, for example, seems to have made its way to Kerala and thence back to Europe. Some coverage of this aspect might be useful, if anyone expert enough can be found. Davy p 23:19, 14 December 2006 (UTC)

Pythagors was ~500BC. Europe never forgot it, but most of the Greek works went to the Arab lands and then back again. --203.117.92.2 09:17, 9 January 2007 (UTC)

[edit] Docking the Hagiography and Bogus Mathematics

This article is abysmally written. Not only are the achievements of the Kerala school exaggerated beyond recognition, but what results are given, are described with a lack of precision that would make any mathematician cringe. I initially encountered text from this article in the article on Indian mathematics—which too is poorly written—and was so frustrated by the writing that I was driven to the secondary sources in mathematics journals. I emphasize "mathematics," because the descriptions in the History of Science journals or the nationalistic Indian web sites were (obviously) written by authors whose own grasp of the mathematics (and sometimes of reality) was infirm, as anyone who knows the style of writing mathematics can easily discern.

I am therefore rewriting some of the lead and early sections of this article to at least give a mathematically literate reader a general idea of the achievements of the Kerala school—which were both manifold and remarkable—but without the hype. Fowler&fowler«Talk» 19:36, 20 February 2007 (UTC)