Talk:Indian mathematics

Vaishali Ganit(a)?

This page doesn't cite a source for it, and Vaishali Ganit simply redirects back to this page. It isn't mentioned in the main academic publications (e.g. by G.G. Joseph, Kim Plofker, or Takao Hayashi), so I had to do some detective-work...

"Vaishali Ganit" was first mentioned on this page in December 2005; no source was ever provided. There were more details about the supposed contents of this text, all uncited, prior to when the Jain math section was shortened in May 2007. The "false position method" page formerly had an uncited claim that "Vaishali Ganit" contained the first-ever use of this mathematical method. The claim was inserted in 2006, and deleted in 2013 by a user who noticed the suspiciousness. However, the claim had already been credulously carried over into other secondary sources about math history, which still appear in a Google search. I used Google Search's time range tool and found three other mentions of it on pages that appeared to be older than 2005, but Google was wrong: these pages all were created or updated between 2010 and 2016, and appear to have derived their information from Wikipedia.

In conclusion, I can't find even a single reliable source that verifies the existence of a text with a name remotely like "Vaishali Ganit(a)". In fact, it appears that every single mention of it is either from websites that simply copy Wikipedia, or from pages that got their information from Wikipedia. Hence I am deleting the mention of it here. I have the strong suspicion that it is nothing more than a decade-long hoax. Avantiputra7 (talk) 04:42, 26 May 2018 (UTC)

Invented or recorded?

This article had said that the decimal system was invented by Indian mathematicians and recently Deacon Vorbis changed that to say it was recorded by ancient Indians. There followed a bit of back and forth by various editors and I was involved with part of that. Even though it seems to fly in the face of "common knowledge", I do believe that Deacon Vorbis' intent was correct. The statement was cited to Kim Plofker's Mathematics in India, a work in which Plofker tries to set the record straight and point out what is historically known and what is speculation about the history of Indian mathematics. He She does not, as far as I can tell, use the term "invented", instead he she talks about the concept being "developed" and being "recorded" for the first time. In an earlier work he she pointedly remarks that the origin of the concept can not be determined from the historical record. It seems to me that using the word "invented" and citing Plofker for it is very inappropriate. --Bill Cherowitzo (talk) 19:36, 26 June 2018 (UTC)

You are right. I wrote the article long time ago, or wrote most of the readable sections of the article. It was "recorded." That's what Kim Plofker says. I will restore it if it hasn't been done already. Fowler&fowler«Talk» 17:35, 27 June 2018 (UTC)

Plofker is a she. "Recorded" is no put down. There is no evidence that the Indians got the ideas from any other place or civilization. What they first recorded in an orally transmitted Buddhist text is a piece of beauty. Other civilizations had bits and pieces of the puzzle. The Chinese had a place value system. But what is in use today is the Indian system, more importantly the arithmetic in use today, addition, subtraction, multiplication, long division, ..., the bread and butter of primary school math the world over, is the work of unknown mathematicians of the subcontinent. Fowler&fowler«Talk» 18:01, 27 June 2018 (UTC)

My deepest apologies to Kim. I thought that I had read something about her that used the masculine pronoun and was surprised by that, having initially assumed she was female. I agree that there is nothing wrong with the use of "recorded", but another editor claimed that this might imply that the origins of the concept came from elsewhere. I don't see it that way, but I would be willing to add a short clarification to thwart that implication–not quite sure how to do that though.--Bill Cherowitzo (talk) 21:26, 27 June 2018 (UTC)

On vacation

I am on vacation through September. I'd be grateful if David Eppstein, Johnuniq and RegentsPark, Abecedare could keep an eye on this article. I mean, I know you do in any case, but the times are such that more vigilance might be required. Best regards, Fowler&fowler«Talk» 17:01, 16 July 2020 (UTC)

Kerala mathematics

In kerala mathematics section, it is said that the geometric series formula discovered by kerala mathrmaticians were discovered earlier in 10th century by arab mathrmatician ibn al haytham. And i checked the link and no where in the book it is mentioned that alhazen were aware about this geometric series formula. It seems like kerala mathematicians were the first to discover it. So i want you guys to remove that comment. Jino john1996 (talk) 11:52, 15 January 2021 (UTC)

Without thinking too carefully, I reverted your change. I've now reverted myself. Because (a) I don't know for myself; (b) the impressive-looking Edwards ref was added by an anon in 2006, and I have no means of checking it; (c) the Ibn al-Haytham doesn't have anything similar William M. Connolley (talk) 19:05, 15 January 2021 (UTC)

This "we invented it first" sports-spectator view is a bad way to understand the history of mathematics. And the formula for a finite geometric series is in Euclid (Book IX, prop. 35). It's an easy step from there to the infinite one but it is plausible to me that the Kerala mathematicians stated that step before others, because the concept of infinite limits may not have been current elsewhere (but see Zeno). It's that concept, not the specific formula, that is the interesting part. —David Eppstein (talk) 19:11, 15 January 2021 (UTC)

Narayana pandit

Narayana pandit is not a kerala mathematician. He lived and worked in north india . So i have decided to remove that part Jino john1996 (talk) 17:38, 15 January 2021 (UTC)

This change is in agreement with Plofker's Mathematics in India, which puts Narayana in an earlier chapter than Kerala. —David Eppstein (talk) 19:12, 15 January 2021 (UTC)

Sum of integral powers of numbers

Why is the equation 1^k+2^k+3^k .... for large k /n^k+1 is equal to 1/k+1 is attributed to alhazen ? First of all, he only found out the sum of 2nd and 4th powers of finite numbers. It was kerala school who gave a general formula for any integral powers of finite numbers and also made the realization that for infinite n , lower order terms can be neglected and can be written as n^k+1/k+1. It was kerala school who explicitly stated this result. So it should be credited to kerala school only. So i am editing that paragraph. Jino john1996 (talk) 17:33, 24 January 2021 (UTC)

The general formula for finite geometric series is in Euclid, long before Kerala. As I already clearly stated two sections up, but apparently you didn't read that. —David Eppstein (talk) 19:23, 24 January 2021 (UTC)

Again read the comment carefully. I am not talking about geometric formula . We already discussed about that. In this, i am talking the about sum of integral powers which should be credited to kerala school and alhazen should not be mentioned Jino john1996 (talk) 05:41, 25 January 2021 (UTC)

You are of course correct re the formula, sorry. I have no useful knowledge of Alhazen's accomplishments here but we should certainly not be mentioning him without a source. —David Eppstein (talk) 06:00, 25 January 2021 (UTC)

Article's title

If this article showed that in India there is no such thing as counting, or that south of the Himalayas multiplication has no effect, or perhaps that dividing twelve by three gives sixty-five in India, then the current title would certainly be justified.

Isn't it all just mathematics? Where is the article on "Argentinian gravity"? TooManyFingers (talk) 18:13, 11 September 2024 (UTC)

A title suggestion accompanying your criticism would have been a good idea. History of Mathematics in India? Indian contributions to mathematics? Something else?RegentsPark (comment) 20:23, 11 September 2024 (UTC)

I think both of your possibilities are good. There's also already a redirect from "Mathematics in India". Any of those seems (to me) accurate enough and suitable enough, and I wouldn't argue against any of them. People with a stronger connection to the article than I have, might prefer one of them over another, or might have more ideas; I'd be fine with any consensus that prevents the kind of obvious wrong interpretations I complained about. TooManyFingers (talk) 21:43, 11 September 2024 (UTC)

The term "Indian mathematics" is widely used with the meaning of "mathematics in South Asia before the modern era." See Kim Plofker's article in Britannica, Indian mathematics, which ends before East India Company rule in India really took off, i.e. a largely British syllabus came to be taught in the high schools and colleges of the subcontinent.

Britannica editors, however, have added the following short paragraph at the very end: In the 20th century Indians trained in modern Western mathematics contributed significantly to the development of the global conversation of mathematics. The brilliant young mathematician Srinivasa Ramanujan (1887–1920) made important advances in the field of number theory. Mathematician and physicist Satyendra Nath Bose (1894–1974) collaborated with Albert Einstein to develop Bose-Einstein statistics and to predict the existence of Bose-Einstein condensate.
Despite the shift of academic mathematical discussions in India toward more global norms, some numerical terms with origins in ancient Sanskrit remain part of modern India’s daily number system. The terms lakh (Sanskrit: laksha) for 100,000 and crore (Sanskrit: koti) for 10 million are commonly used in India and some neighboring countries in place of million, billion, trillion, and so on. One million is thus written as “10 lakh.” The terms can also be combined, thus “one lakh crore” equals one trillion. When writing these numbers with commas, the rule of three numbers between commas is eschewed for groupings of two. Other unique Indian terms for larger numbers beyond crore exist but are not commonly employed. In India, lakh and crore are often used in financial matters, government statistics, and demographics. Fowler&fowler«Talk» 15:30, 6 January 2025 (UTC)

Aryabhata I's contributions - Trigonometry

Not sure if "Contains the earliest tables ...", "Contains the trigonometric formula ..." is the best verbiage. Would it be better to use "Created" instead of "Contains"? Merlin.anthwares (talk) 14:32, 24 December 2024 (UTC)

Differential coefficient.

What exactly does the article mean by differential coefficient? In the calculus section of the ninth to twelfth century period of Indian mathematics, the article mentions the differential coefficient, without a citation mind you. The issue is that the term "differential coefficient" seems to be just an old phrase for derivative, if it doesn't mean that please correct me. The article mentions that the Indian mathematicians only had preliminary conceptions of the derivative, so the article would be saying that these mathematicians only had a preliminary concept of the derivative, but also discovered the derivative, which is contradictory. From what I know, Indian mathematicians did know about certain derivatives, like that sines derivative is cosine, but did not have a general formation of the concept we know today. Bibbloti (talk) 10:05, 6 January 2025 (UTC)

Sadly that entire subsection (Classical) needs to be rewritten, or more accurately written, as what is there is nothing but a mostly unsourced list. I can't make any promises, but I'll see what I can do. Fowler&fowler«Talk» 15:08, 6 January 2025 (UTC)

Many thanks for that. Bibbloti (talk) 08:43, 7 January 2025 (UTC)