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Citation Needed

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Please provide a citation for Madhava being "considered the father of mathematical analysis" . . . I know of no printed sources that make a reasonable claim of this . . . the father of analysis as we know them today are more likely to be consider Karl Weierstraß, as he was interested in the basis of the Calculus . . . before his time, there were no clear definitions regarding the fundamentals of calculus, and thus theorems could not be properly proven. Madhava in contrast, like many before him, merely introduced the idea of infinity to certain classes of functions, like many after him would do before analysis was put on a firm footing. Arundhati bakshi 18:45, 24 March 2006 (UTC)[reply]

See Mathematical analysis and it's talk page for more detail (and a printed source for the claim). Also see [1] highlighting all pioneers in analysis - it considers Madhava the founder of mathematical analysis in contrast with Weierstrass as father of modern analysis. Weierstrass' page also says the same. --Pranathi 00:29, 6 April 2006 (UTC)[reply]
Then he should be mentioned as the father of an older form of mathematical analysis. Kerhwos (talk) 14:54, 15 September 2021 (UTC)[reply]

Put on Kerala School

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Hi, I put these questions on the Kerala school.

Could we get some cleanup on the maths stuff?


  • 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
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?
What radius?
What diameter?
What circumference?
  • Power series of angle θ (equivalent to the Gregory series).
??? What does this mean?
Ok. As solutions to quadratics? Cubics?
As solutions to ...
Which transcendental number?
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
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 01:57, 12 May 2006 (UTC)[reply]

Obvious Thing

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Okay in the article, the expansion for pi/4 is a direct result of the Madhava-Gregory series(theta=pi, n=1), but the article points to some expansion of the arctangent as the source. Is this a mistake?

Disputed

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None of the questions under Put on Kerala School have been answered.

To give an example, the article claims that Madhava invented the fundamental ideas of:

  1. Infinite series expansions of functions.
  2. Power series.
  3. Taylor series.
  4. Maclaurin series.
  5. Trigonometric series

First question, were these expansions really infinite as claimed? Further, for some functions he gave what looks like the first terms of a Taylor or Maclaurin series of that function. That is a nice accomplishment. But the fundamental idea of a Maclaurin or Taylor series consists of giving the rule how to develop a function into a series. No evidence that he knew this is given. -- Zz 17:56, 29 March 2007 (UTC)[reply]

Tag removed

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Just added a number of facts, such as the location of Sangramagrama, the uncertainty regarding which of the results are specifically attributable to Madhava (including a sketch of some of the arguments), ensuring that the reader is aware of the degree of doubt on this matter.

Removed many of the indirect references (e.g. several instances of the Mactutor pages) with journal articles. Merged the "bibliography" section into references (though some people may disagree, I feel this is cleaner - you get a sense of what the text does; if we need to repeat the citations in a bibliography, it should have annotations).

Also added a citation for integration along with the original malayalam text.

As for the disputed facts, I think among the examples given, with citations to various texts, we have many examples of these three :

  1. Infinite series expansions of functions (mostly trig functions)
  2. Power series : all are power series expansions
  3. Trigonometric series : many involve the trig functions in the expansion

The following two however appear to be unlikely:

  1. Taylor series.
  2. Maclaurin series.

Since these express functions as powers of the derivative for a general function, it is unclear that the understanding of higher-order derivatives was sufficiently understood. While derivatives are being computed, it is not clear whether power series of derivatives were used. Unless other facts come to light, I am removing reference to these two. mukerjee (talk) 17:42, 6 September 2007 (UTC)[reply]

Transmission to Europe

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I have no expertise in this matter, but the section This is due to wrong understanding of the authors concerned. It was almost impossible for the Jesuits in the sixteenth century, who are experts with the eminence of Mādhavan or his disciples, to study Sanskrit and Malayalam and to transmit them to European Mathematicians, instead of they themselves claiming the credit for the discovery. is very unclear. Who is misunderstanding whom? What is impossible? Were the Jesuits able to understand Mādhavan but unable to transmit them? Were they experts in Sanskrit and Malayam or not? Can anyone offer something to clarify it? Moreover, it reads to me like original research. Perhaps it would be clearer to say acknowledge priority in discovery of the relevant work to Mādhavan etc. but to state that there was no actual evidence that this knowledge was transmitted to the West; therefore the question of tranmission to Europe is simply unresolvable without more evidence. Rob Burbidge (talk) 09:51, 18 May 2011 (UTC)[reply]

I asked pretty much the same questions when reading those sentences. They make almost no sense. There are quite a few grammar issues (and shaky claims) in the current article. The part you pointed out is just the worst of it. 24.220.188.43 (talk) 14:53, 2 September 2011 (UTC)[reply]
At 2019-12-08 there is the sentence "... uncertain ... whether any of these ideas were transmitted to the West, ... calculus was developed completely independently by Isaac Newton and Leibniz." If transmission is uncertain then transmission is possible. In that case Newton or Leibniz could have benefited and the sentence is inconsistent. And incidentally, "it" is unnecessary in most sentences. Many sentences can be rewritten in a simpler form without "it". For example: "Transmission of these ideas to the West is uncertain." Regards, ... PeterEasthope (talk) 15:13, 8 December 2019 (UTC)[reply]

Usage of "we"

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I added a tone tag, because the article uses the plural third person ("we") very frequently, e.g. "We find Madhava's work on the value of π cited in..." This is not in keeping with the style guidelines. I'd fix it myself, but I'm supposed to be working instead of reading about approximations of Pi, let alone repairing a Wikipedia article! :D --13.12.254.95 (talk) 16:04, 15 March 2012 (UTC)[reply]

Spelling of Sangamagrama

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Currently,[2] and since the very beginning,[3] the title of this article is: Mādhava of
Sañgamāgrama

However, if you’d like to spell Sangamagrama with diaereses diacritics, the correct spelling would be
Saṅgamagrāma

ñ vs. ṅ is relatively unimportant (though inaccurate), but -māgrama is simply wrong and confusing when it’s actually -magrāma. Since the title is wrongly spelled, we’re going to have to move this article sooner or later, to simply “Madhava of Sangamagrama” or maybe “Mādhava of Saṅgamagrāma” or...??? Any suggestions? —Gyopi (talk) 11:46, 15 August 2012 (UTC)[reply]

Additional comments: There are typos in the current title. One can see the rigorous transliteration Saṅgamagrāma in the first line of page 101 of On an Untapped Source of Medieval Keralese Mathematics, or by searching Mādhava Saṅgamagrāma on books.google.com. The spelling in the current title Sañgamāgrama is simply wrong.(*1) If the name of the place is transliterated rigorously, the title will be Mādhava of Saṅgamagrāma.

However, the new title of the article should be Madhava of Sangamagrama without diacritics, in accordance with WP:TITLE: “Titles are those that readers are likely to look for.... Such titles usually convey what the subject is actually called in English... Titles usually use names and terms that are precise enough to unambiguously define the topical scope of the article, but not overly precise.” If you look at a similar page, the page title for Āryabhaṭa is Aryabhata without diacritics as well, Nīlakaṇṭha Sōmayāji is Nilakantha Somayaji, and Kēraḷa is Kerala. The page Madhava of Sangamagrama already exists as a redirect to this article, and I can't simply move Mādhava of Sañgamāgrama to Madhava of Sangamagrama. I'll request the move to Madhava of Sangamagrama unless someone says otherwise.

(*1) If you check Malayalam alphabet, it's not difficult to tell that the original spelling സംഗമഗ്രാമ reads Sa(ṁ)GaMaGRāMa; except the reason why (ṁ) is transliterated as ṅ before g is a bit complicated (explained in ISO 15919). Similarly, if you check Devanagari, संगमग्राम reads Sa(ṁ)GaMaGRāMa. —Gyopi (talk) 03:03, 16 September 2012 (UTC)[reply]

I think it's possible to move this article to Madhava of Sangamagrama if I use Template:Db-move first. But then, the move should be non-controversial or consensual. So please say now if you don't like this move. Thanks! I mean, the typos are obvious and there's nothing to talk about, but there might be someone who prefers the rigorous title Mādhava of Saṅgamagrāma... — Gyopi (talk) 03:20, 16 September 2012 (UTC)[reply]

Additional verification:

  • Bag, A. K. (1980), Indian Literature on Mathematics During 1400–1800 A.D. (PDF), Indian Journal of History of Science 15 (1): 80. “Mādhava (c. 1400) of Saṅgamagrāma near Cochin was a well-known scholar in astronomy and mathematics.”
  • Shirali, Shailesh A (1997), Nīlakaṇṭha, Euler and π (PDF), Resonance: 33. “In the text Yuktibhāsā, the series is credited to Mādhava of Sangamagrāma (1350–1410), who lived almost a full century before Nīlakaṇṭha.”

So I’m moving this now. — Gyopi (talk) 03:30, 23 September 2012 (UTC)[reply]

Picture needed.

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No picture provided nor can i find one on the web. — Preceding unsigned comment added by Srathi00 (talk • contribs) 14:26, 6 November 2014 (UTC)[reply]

Sorry didnt see this section Imagetoimageless (talk) 09:29, 21 August 2020 (UTC)[reply]

It is probably important to have known paintings of this particular mathematician. This image was commissioned from the mathematicians city.

The sphere, arched integral (tree) on the left of sphere to show his contribution to mathematics is all encapsulated in this image. A lot of detail in the painting pertains to the era. There are no other known genuine image with such detail other than this. This mathematicians contribution has already been diminished. An image is essential to understanding the person, era and conscious simplicity. Ultimately this only improves the page.

The image is shown without breaking open license, adhering to Wikipedia policy etc... While thanking previous editors, wouldn't you agree the page require a further contribution, constant improvement Imagetoimageless (talk) 09:29, 21 August 2020 (UTC)[reply]

Image added Imagetoimageless (talk) 10:57, 21 August 2020 (UTC)[reply]

Plagiarism

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Much of this article is taken word for word from this biography, particularly the section on infinite series. HGilbert (talk) 12:14, 15 March 2015 (UTC)[reply]

Copyright violation is a serious problem and we should definitely remove instances of it; thanks for bringing it up. But I cannot actually find any sentences taken word-for-word from the MacTutor site (except the phrase "Madhava gave three forms of Rn which improved the approximation", which is fairly generic, and explicitly cited with the MacTutor site as reference). Also, this article is much longer than the MacTutor biography, so I don't think it's possible that most of this article is taken from there. Could you give examples, or simply remove whatever you think is copied, and then we can reinstate them from proper sources? Shreevatsa (talk) 16:50, 15 March 2015 (UTC)[reply]

Yes, that is one sentence copied. Others are:

  • "The most convincing is that they come as the first three convergents of a continued fraction which can itself be derived from the standard Indian approximation to π namely 62832/20000."
  • "Madhava also gave a most accurate table of sines, defined in terms of the values of the half-sine chords for twenty-four arcs drawn at equal intervals in a quarter of a given circle." HGilbert (talk) 17:28, 15 March 2015 (UTC)[reply]
I've removed or rewritten those. There isn't anything more, as far as I can tell. Shreevatsa (talk) 20:40, 15 March 2015 (UTC)[reply]
You have only rephrased, instead of rewriting them. Kerhwos (talk) 14:42, 15 September 2021 (UTC)[reply]
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Image requirement

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It is probably important to have known paintings of this particular mathematician. This image was commissioned from the mathematicians city.

The sphere, arched integral (tree) on the left of sphere to show his contribution to mathematics is all encapsulated in this image. A lot of detail in the painting pertains to the era. There are no other known genuine image with such detail other than this. This mathematicians contribution has already been diminished. An image is essential to understanding the person, era and conscious simplicity. Ultimately this only improves the page.

The image is shown without breaking open license, adhering to Wikipedia policy etc... While thanking previous editors, wouldn't you agree the page require a further contribution, constant improvement. Imagetoimageless (talk) 09:26, 21 August 2020 (UTC)[reply]

Sorry didn't realise that a previous editors had already discussed that a picture/image would be ideal. I have added entry to that Imagetoimageless (talk) 09:31, 21 August 2020 (UTC)[reply]

I've again removed this; there's no indication where it's from, who it's supposed to be of, or, if it is supposed to be of Madhava, whether there's any reason to believe it's even remotely accurate. –Deacon Vorbis (carbon • videos) 13:51, 23 August 2020 (UTC)[reply]

I have discussed with other editors. They have queried that the artist, subject has to be attributed. The comments will be addressed as asked. However it is if consensus I assume that all paintings of pre- photography era cannot be clearly said to define the exact physical qualities of the person. However the subject is madhava. The artist will have to attribute it directly to the subject. Have directed this to the artist. However, shall we agree that one the attribution to subject ( madhava) , era and license is resolved, it's self resolved? Thanks Imagetoimageless (talk) 19:26, 24 August 2020 (UTC)[reply]

Imagetoimageless In articles about people who lived before photography, we do use paintings and drawings, some created long after the death of the subjects. But in those cases it is well known or easily cited that the image is at least intended to represent a particular person, and there can be discussion of which image (when several are available) best represents or illustrates the person in question.
Can you cite sources that say that this particular image is intended to represent Madhava? If you do, we can consider how reliable those sources are. DES (talk)DESiegel Contribs 15:07, 27 August 2020 (UTC)[reply]
Oh and, in line with WP:BRD, please do not reinsert the image, now that it has been challenged, without first obtaining a consensus to do so in this discussion. DES (talk)DESiegel Contribs 15:09, 27 August 2020 (UTC)[reply]
I am from Kerala, and that image doesn't seem to pertain the time or place as the uploader claims. It is a very generic look of a Namboothiri Brahmin. Most Wikipedia articles rely on portrait drawn at the life time of the person (eg: Isaac Newton, Shivaji)And Articles like Aryabhata uses image of statue from a reputed Indian astrophysics institute(IUCAA) with a clear disclaimer “there is no historical record of his appearance”. Some random drawing can't be used as image on Wikipedia ChandlerMinh (talk) 06:13, 29 August 2020 (UTC)[reply]
Good points. I was hoping to learn from Wikipedia as to whether Madhava was Hindu, Muslim, or something else. Whoever rendered that portrait of him seems to have been under the impression that he was a Vedic Hindu, the flavor of Hinduism preferred by Namboothiri Brahmins. If that impression was reliable, that would presumably rule out Muslim. On the other hand Islam entered India via the Malabar Coast including Kerala as early as the 6th century CE. Does anyone have anything more concrete? Vaughan Pratt (talk) 17:46, 29 April 2024 (UTC)[reply]
Mādhava was not Muslim: the name Mādhava is a Hindu one, and is one of the names of Krishna. Little is known of Mādhava himself, but we can reasonably draw inferences from the fact that most of his students/disciples were Namputiri Brahmins: see File:Kerala_school_chain_of_teachers.jpg. According to https://www.jstor.org/stable/23497280 by P. P. Divakaran (note that Prof. Divakaran is also from Kerala, and has done substantial work into the Kerala mathematicians in recent years):

Mādhavan and his Followers

In the chaotic aftermath of this ‘100 year war’, the Cera kingdom broke up into a number of principalities, of which the most powerful was that ruled by the Zamorin (samutiri) dynasty from Calicut. This period also saw a renewed influx of brahmins and their rise to a position of social and cultural preeminence. The southern part of the Zamorin’s domain became a particularly favoured area for Namputiri settlements. It is in this region, on either bank of the river Nila (more commonly known now as the river Bharata), that there emerged, beginning in the second half of the 14th century, a succession of astronomers and mathematicians of truly exceptional quality. They formed a tight-knit group, all linked together by the traditional teacher-disciple bonds. There was at least one father-son pair among them, Parameśvaran and Dāmodaran. Most were Namputiris of one variety or another. According to local tradition, three were native to one village and two taught at the same temple school. Virtually all lived in close geographic proximity and produced their work within a time span of roughly two centuries.

The most original and creative of this brilliant lot, by the acclamation of those who followed him, was also the first: Mādhavan, said to be of Sangamagramam.8 Mādhavan has remained a somewhat shadowy figure. We know nothing about his life except that it spanned the second half of the 14th century and the first quarter of the 15th and that the great astronomer Parameśvaran was his disciple.

The footnote (8) above says:

It is possible to make the case that Mādhavan or his family was a recent arrival from up north. He is said to have been an Emprantiri (brahmins recently arrived from coastal Karnataka, an established staging area on the migrant route).

So while we may not have a clear answer about Mādhava himself, we can fairly conclude from his name, and from his students (and the nature of close-knit communities at the time) that he was (in your terms) "a Vedic Hindu". Hope that answers your question. (But we shouldn't include an unattributed image in this article though!) Shreevatsa (talk) 00:55, 30 April 2024 (UTC)[reply]
Here's what I said when this image came up on WT:WPM:
The oldest source TinEye finds is from The Telegraph, a Calcutta newspaper, with the caption "A digital image of Madhava drawn up by the Madhava Ganitha Kendram, a voluntary association working to revive his works, with inputs provided by descendants of the mathematician-astronomer". The copyright status of the image is not clear, so it should perhaps be deleted on that basis, but it is clearly not intended to be an impersonation, anachronism, or cultural insult. Here is another 2014 article about the painting, which was commissioned by the Kerala State Science and Technology Museum (KSSTM) in Thiruvananthapuram. My guess is that both the museum and the voluntary association would be happy to have their painting used widely to represent Madhava as an alternative to leaving him "faceless", but it would be worth trying to find their contact info and ask them directly for a copyright release. –jacobolus (t) 03:46, 30 April 2024 (UTC)[reply]

IP removal

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We have an IP that has removed information twice supported in reliable sources and replaced it with information also supported. The issue here is the removal of sourced information and replacing it with an older source. The removed information is from a journal and website from 2007 and retrieved in 2020, respectively[4]. Their information is sourced to a journal from 1995 [5]. I have refrained from further escalating this but these edits appear disruptive even if they are in good faith. --ARoseWolf 20:49, 26 September 2022 (UTC)[reply]

Don’t add image

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Little is know about his life. So don't add random image from internet here. WP has certain rules ChandlerMinh (talk) 19:17, 11 February 2023 (UTC)[reply]

The image people keep wanting to add is a copyright violation that shouldn't be on Commons anyway.... XOR'easter (talk) 20:44, 28 May 2023 (UTC)[reply]

Copy edit

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Recently user @Krishnachandranvn: has added a lot of content to this page especially in the “Madhavan, the person” section . Since this is an encyclopaedia I would like to request Krishna Chandran to make those sections as succinct as possible. The Wikipedia Manual of Styles suggests to not use many unnecessary words. The articles present form is like as if it is written like a blog. ChandlerMinh (talk) 19:22, 11 February 2023 (UTC)[reply]

Kerala school of astronomy and maths

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I recently removed some unsourced or junk reference which doesn't support Wikipedia source guidelines."Science and technology in free India" (PDF). Government of Kerala—Kerala Call, September 2004. Prof.C.G.Ramachandran Nair. Retrieved 2006-07-09. is broken and not reliable so I've removed it and MAT Cancius link isn't really a reliable source for citing in Wikipedia so I removed it. Leveinhockerkerala (talk) 05:55, 14 September 2023 (UTC)[reply]

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