Talk:Kerala school of astronomy and mathematics

message: 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)
replies: text: 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)

text: India also had many inventions which Islamic Golden Age did not do and has influence on modern times, like Islamic scholars did not make advances in Metallurgy like India did, gave world crucible steel, pure zinc, rust free iron and so much more Narayana venkateshwara iyengar (talk) 06:01, 13 September 2023 (UTC)
replies: text: Note that Wikipedia talk pages are not a general-purpose forum (see WP:NOTFORUM). The purpose of this talk page is discussion of how to improve this article about the Kerala school of astronomy. Trash talking about whether medieval Arabic-sphere scientists or medieval South Asian scientists made more important contributions is completely pointless and off topic here. –jacobolus (t) 06:34, 13 September 2023 (UTC)
thread_title:  Does any mathemetician know how to clean up? 

message: 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)
replies: text: Do you know who got the abel prize for year 2007? Nope. Do you Ramanujan's reputation, what Hardy said about him? Forget all this, do you know that most of the western technology actually got invented by Germany and that too in the time of hitler? Nope, you don't. Western technology developed because of war and because of the wealth that they generated from their loots of a few hundred years. When you have millions of slave and billions of dollars at your disposal you can get a lot done. Now the same question will be asked of westerners 100 years from now, that if they were so advanced in technolgy in 2007 why they look to China and India for it now:-)
Ramanajunan read mathematical works of western authors. And his mentors all were western. No Indian origin nobel laureate currently works in India. ChandlerMinh (talk) 21:03, 10 January 2020 (UTC)
thread_title:  Explanation of Warning 

message: 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)
replies: text: 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)
thread_title: references for claims made

message: 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)
replies: text: 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)
replies: text:  Melvyn Bragg's programme on BBC Radio 4 today simply used the term 'Kerala Mathematics'; St Andrews, which is usually quite reputable, , uses 'Keralese Mathematics' and also refers to 'Kerala Mathematics'. Davy p 22:50, 14 December 2006 (UTC)
thread_title:  Title 

message: 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.
Discover Magazine and  ? Joshua Issac (talk) 11:48, 21 March 2008 (UTC)
thread_title:  Other evidence section 

message: 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)
replies: text: BBC Radio 4 Joshua Issac (talk) 17:53, 17 February 2008 (UTC)
thread_title:  Mathematics was banned from use in European accounting 

message: 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)
replies: text: 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)
thread_title:  Greeks and Moors 

message: 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)
thread_title: Docking the Hagiography and Bogus Mathematics

message: I don't know what exactly the original verse said, but the series given here as an expansion for sin x has an undefined r term in it. It appears to be the series for r * sin(x/r). -Chinju 23:17, 31 March 2007 (UTC)
replies: text: Have corrected it.  You are right.  Thanks.  Fowler&fowler«Talk» 09:44, 1 April 2007 (UTC)
thread_title:  Sine series 

message: I've moved the complete disputed section Possible transmission of Kerala mathematics to Europe here. Apart from mentioning an unspecified paper in the first paper, it is completely without sources.
:There are a number of publications, including a recent paper of interest written by D. Almeida, J. John and A. Zadorozhnyy, which suggest Keralan mathematics may have been transmitted to Europe. Kerala was in continuous contact with China, Arabia, and from around 1500, Europe as well, thus transmission would have been possible. There is no direct evidence by way of relevant manuscripts but the evidence of methodological similarities, communication routes and a suitable chronology for transmission is hard to dismiss.
:A key development of pre-calculus Europe, that of generalisation on the basis of induction, has deep methodological similarities with the corresponding Kerala development (200 years before). There is further evidence that John Wallis (1665) gave a recurrence relation and proof of the Pythagorean theorem exactly as Bhaskara II did. The only way European scholars at this time could have been aware of the work of Bhaskara would have been through Islamic scholars (see Bhaskara: Influence) or through Kerala 'routes'.
:Although it was believed that Kerala calculus remained localised until its discovery by Charles Whish in 1832, Kerala had in fact been in contact with Europe ever since Vasco da Gama first arrived there in 1499 and trade routes were established between Kerala and Europe. Along with European traders, Jesuit missionaries from Europe were also present in Kerala during the 16th century. Many of them were mathematicians and astronomers, and were able to speak local languages such as Malayalam, and were thus able to comprehend Kerala mathematics. Indian mathematical manuscripts may have been brought to Europe by the Jesuit priests and scholars that were present in Kerala.
:In particular, it is well-known that Matteo Ricci, the Jesuit mathematician and astronomer who is generally credited with bringing European science and mathematics to China, spent two years in Kochi, Kerala after being ordained in Goa in 1580. During that time he was in correspondence with the Rector of the Collegio Romano, the primary institution for the education of those who wished to become Jesuits. Matteo Ricci wrote back to Petri Maffei stating that he was seeking to learn the methods of timekeeping from "an intelligent Brahman or an honest Moor". The Jesuits at the time were very knowledgeable in science and mathematics, and many were trained as mathematicians at the Jesuit seminaries. For a number of Jesuits who followed Ricci, Kochi was a staging point on the way to China. Kochi was only 70km away from the largest repository of Kerala's mathematical and astronomical documents in Thrissur (Trichur). This was where, 200 years later, the European mathematicians Charles Whish and Heyne obtained their copies of manuscripts written by the Kerala mathematicians.
:The Jesuits were expected to regularly submit reports to their headquarters in Rome, and it is possible that some of the reports may have contained appendices of a technical nature which would then be passed on by Rome to those who understood them, including notable mathematicians. Material gathered by the Jesuits was scattered all over Europe: at Pisa, where Galileo Galilei, Bonaventura Cavalieri and John Wallis spent time; at Padua, where James Gregory studied; at Paris, where Marin Mersenne, through his correspondence with Pierre de Fermat, Blaise Pascal, Galileo and Wallis, acted as an agent for the transmission of mathematical ideas. It is quite possible that these mathematical ideas transmitted by the Jesuits included mathematics from Kerala.
: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. (See Infinitesimal Calculus - How and why it was imported to Europe.)
:*Kerala's established trade links with the British East India Company, which began trading with India sometime between 1600 and 1608, not too long before Europe's scientific revolution began.
We are not allowed to speculate ourselves. And in reporting the speculations of others, we have to select carefully, give specific references, and attribute opinions.
Pjacobi 13:42, 3 May 2007 (UTC)
replies: text: Thanks for removing the text.  I had been meaning to do that myself since I had written a sourced section on the same topic for the Indian mathematics page.  I have now added that section here.  Fowler&fowler«Talk» 14:16, 3 May 2007 (UTC)
thread_title:  Reliable sources needed 

message: It would be a great asset for this article if we can add some historical context. At present the article seems to be an account of the mathematicians and their works. I searched a bit and am still puzzled by these historical details such as
* When exactly it came into existence ?
* What was the school called in local tongue ?
* What happened to the school and if there are there any physical remains of it today ? Sibi_antony (talk) 16:02, 14 September 2010 (UTC)
thread_title:  Historical account 

message: This article has been edited by a user who is known to have misused sources to unduly promote certain views (see WP:Jagged 85 cleanup). Examination of the sources used by this editor often reveals that the sources have been selectively interpreted or blatantly misrepresented, going beyond any reasonable interpretation of the authors' intent.
As an example of the problem, the text in Reliable sources needed (above) was added by Jagged 85.
Jagged 85 made 116 edits to Kerala school of astronomy and mathematics. Diffs for each edit are listed at cleanup2, however it is easier to view the full history of the article. Following is a summary of all the edits. Each item is a diff showing the result of several consecutive edits to Kerala school of astronomy and mathematics by Jagged 85, in chronological order.
*
It might be useful to discuss which references can be regarded as valid. I recommend heavy pruning of all material with poor sourcing because that is desirable in general, and is essential in cases related to Jagged 85 because we have numerous examples of that editor completing misrepresenting sources. Johnuniq (talk) 00:14, 15 September 2010 (UTC)
replies: text: If unreliable sources are being systematically used, we should revert to the version of the article prior to the changes by this editor.  Tkuvho (talk) 01:41, 15 September 2010 (UTC)
replies: text: I also think strong action is required, with severe pruning. However, Jagged has been active for several years (the first link in the summary diffs above is from 2005), so it is not really feasible to rollback to a prior date. Johnuniq (talk) 08:27, 17 September 2010 (UTC)
replies: text: Can you please elaborate why Kak does not look reliable? Is it because he is Non-European? Please explain why he is not reliable. I do not want to hear your downright conclusion of "Kak is does not look reliable" and agree with you without any reason.71.191.248.251 (talk) 07:39, 7 May 2011 (UTC)

text: I would suggest the following procedure: (1) identify the problematic editors who are adding this junk, and (2) revert to the version (probably a few years ago) before they got a chance to scribble here.  Tkuvho (talk) 12:25, 5 May 2011 (UTC)
replies: text: I had cleaned up much of the older text, but left section 2 in, for example in this edit of 2008.  The best thing would be roll back to that edit and remove section 2 there (and also sections 1.2, 1.3 and 1.4).  Section 1.1 there is well-sourced (not to Peirce), but to Kim Plofker and to various History of Mathematics papers.  Fowler&fowler«Talk» 04:07, 10 May 2011 (UTC)
replies: text: I have now rolled the page back to that version and removed the problem sections there.  Fowler&fowler«Talk» 04:40, 10 May 2011 (UTC)
replies: text: PS the footnotes there (of Plofker, Pingree, Bressoud and others) lay to rest all revivalist fantasies of the Wiki India/Kerala nationalists who have meddled with the page during the last two or three years.  Fowler&fowler«Talk» 04:45, 10 May 2011 (UTC)
replies: text: The section Kerala_school_of_astronomy_and_mathematics#Possibility_of_transmission_of_Kerala_School_results_to_Europe should be looked at closely.  It has all the telltale signs of ethnomathematics, including name-dropping e.g., unspecified "research at the CNRS".  The existence of trade routes is of course important, but couldn't influence travel in the opposite direction along such trade routes?  Could, for example, Diophantes have influenced the Indians via trade routes?  Fermat said he got his idea of adequality from Diophantes.  Tkuvho (talk) 04:52, 10 May 2011 (UTC)
replies: text: Well, that part is either from Bressoud or Katz.  I don't think they were name dropping, just allowing for all possibilities, but remaining skeptical.  Fowler&fowler«Talk» 05:09, 10 May 2011 (UTC)
replies: text: Did you ever get a chance to check out what kind of work is going on at the CNRS and what conclusions may have been reached?  If Bressoud and Katz are both sceptical why should we have a section that implies that there is some truth in such alleged transmissions?  Tkuvho (talk) 12:10, 10 May 2011 (UTC)

text: PS There is also the question of the transmission of al-Haytham's work to India. Fowler&fowler«Talk» 14:20, 10 May 2011 (UTC)
thread_title:  Misuse of sources 

message: The page should be pruned of Pearce's text.  Tkuvho (talk) 02:50, 10 May 2011 (UTC)
replies: text: It is now. :) Fowler&fowler«Talk» 12:01, 10 May 2011 (UTC)
thread_title:  Ian Pearce's pseudohistory 

message: Indian mathematics of this period is entirely rhetorical, ie. no symbolism was used.  The equivalent of formula were written out in words (and without brackets whose absence can lend to ambiguity).  This should be stated at the beginning of the article.  Thus the statement that they had no symbol for factorial is a trivial consequence of this.
The trigonometric formulae given in the article cannot possibly be directly derived from the verbal expressions given in the source material since they only hold true when expressed in radians, which ASAIK were not invented until the early eighteenth century by Roger Cotes.
The reference to induction is irelevent, obfuscatory, and presentist.  It would be better to say simply and with greater clarity that some results were probably conjectured to be true on the basis for a small few values of n, (assuming that is the case) but lacked the technical apparatus to prove them.  Similarly the use of the terms rectification and quadrature when length and area under curve would do.
The editor who used the term theorem does not understand its meaning.  It would be better to refer to formulae or identities and to again stress what was then then their conjectural status.
This article trips itself up claiming results and then almost immediately attributing them to earlier "Arabic mathematicians".  If these two results are mentioned then they should be put at the end and it be stated that they were probably discovered independently. 
IMHO the remarks about radians are sufficient to warrant the article be scrapped and rewritten by an expert in the subject, not by POV-er ignorami  — Preceding unsigned comment added by 86.27.193.180 (talk) 17:16, 13 August 2012 (UTC)
replies: text: The article has had a troubled history. Do feel free to try to improve it William M. Connolley (talk) 21:31, 13 August 2012 (UTC)
thread_title:  Trigometric Series And Radians 

message: This book by G.G. Joseph has been removed from sources:
*"
It is "For Sale Only in South Asia" according to the price sticker on the copy owned by my university. There are problems with some of its mathematics: page 71 and 72 discuss a geometric series and a summation is said to vanish because terms "become negligibly small and can be ignored". Further, in the discussion of trigonometry (page 84) the development of Indian Sine corresponds to trigonometry in Greece using chord length to gauge angles. (compare Survey of Almagest by Olaf Pedersen). Perhaps a second edition, cleaned up and available around the globe, will be posted. — Rgdboer (talk) 21:56, 11 June 2018 (UTC)
replies: text: "For sale only in South Asia," has nothing to do with the content's quality. Many publishers (which includes Oxford and Cambridge) sell cheaper editions in South Asia.  Those are not for sale elsewhere, as the publishers usually sell more expensive editions in the more  upscale markets.  As far as I am aware Joseph's book has a higher priced international edition.  If your university is not in South Asia, then I'm not sure how it managed to get the edition it has.  Joseph's book does have problems.  I haven't looked at it in a long time, but if it is being cited, then it is not a good idea to remove it and the citation.  In the World Cat list of library holdings, it shows up in 839 libraries world wide, including Harvard, MIT, Brown, Northeastern, etc  Fowler&fowler«Talk» 03:59, 30 September 2018 (UTC)
thread_title:  A Passage to Infinity 

message: Anything that have relations to Calculus during the islamic Golden Age was Alhazen’s work. Which, I suppose, is not as extend as the contributions of the Kerala School  — Preceding unsigned comment added by ChandlerMinh (talk • contribs) 15:34, 6 January 2020 (UTC)
thread_title:  “Transmission of ideas from Islamic mathematics to Kerala”? 

message: Does the Kerala School have manuscripts that can be dated to to its time or that are older than 17th century? Few days ago a 'Vedic mathematician' on twitter argued with me that Archimedes doesn't exist before Common Era because there was no manuscript before 10th Century that mentions Archimedes's name. ChandlerMinh (talk) 21:10, 10 January 2020 (UTC)
thread_title:  Manuscripts ? 

message: I have changed “Transmission” to “Possible transmission”. Given that many mathematicians of west showed no qualms in praising the results of Indians, it would be irrational to claim that the transmission happened. Leibniz himself was a self proclaimed admirer of the Chinese mathematics and philosophy.  So those people trying to “steal” ideas from India seems outright ridiculous. ChandlerMinh (talk) 06:38, 23 August 2021 (UTC)
thread_title:  “Possible” transmission