Talk:History of calculus

Page contents not supported in other languages.
From Wikipedia, the free encyclopedia
WikiProject iconVital articles: Level 5 / History Start‑class
WikiProject iconHistory of calculus has been listed as a level-5 vital article in History. If you can improve it, please do.
StartThis article has been rated as Start-class on Wikipedia's content assessment scale.
WikiProject iconMathematics Start‑class Mid‑priority
WikiProject iconThis article is within the scope of WikiProject Mathematics, a collaborative effort to improve the coverage of mathematics on Wikipedia. If you would like to participate, please visit the project page, where you can join the discussion and see a list of open tasks.
StartThis article has been rated as Start-class on Wikipedia's content assessment scale.
 Mid This article has been rated as Mid-priority on the project's priority scale.

Wiki Education Foundation-supported course assignment[edit]

This article was the subject of a Wiki Education Foundation-supported course assignment, between 7 January 2020 and 14 April 2020. Further details are available on the course page. Student editor(s): TW1010.

Above undated message substituted from assignment by PrimeBOT (talk) 23:35, 16 January 2022 (UTC)Reply[reply]


What are some sources for the following:

In 1704 an anonymous pamphlet, later determined to have been written by Leibniz, accused Newton of having plagiarised Leibniz' work. That claim is easily refuted as there is ample evidence to show that Newton commenced work on the calculus long before Leibniz could possibly have done. However, the resulting controversy led to suggestions that Leibniz may not have invented the calculus independently as he claimed, but may have been influenced by reading copies of Newton's early manuscripts. This claim is not so easily dismissed and there is in fact considerable circumstantial evidence to support it. Leibniz was not known at the time for his probity, and later admitted to falsifying the dates on certain of his manuscripts in an effort to bolster his claims. Furthermore, a copy of one of Newton's very early manuscripts with annotations by Leibniz was found among Leibniz' papers after his death, although the exact date when Leibniz first acquired this is unknown.

None of this is mentioned on the St. Andrews bio for Leibniz. The article, as it currently stands, is very pro-Newton and very POV. Some mention of Newton's own forged letters and so forth should be included. Also, some mention of Newton's abuse of his power as president of the Royal society should mentioned: he appointed the committee to investigate the issue of priority and then wrote the final report himself (anonymously). --C S 07:51, Dec 18, 2004 (UTC)

The origin of all that was a large piece of public domain text copied into the calculus article (from a book about 100 years old). If we are going to mention the priority quarrel, someone should look into more current scholarship. I'm not sure it is right to imply that it is of no interest, and is just 'antiquarianism'. It tends to show that the academic conventions of fair dealing were not in place, at that time. Charles Matthews 08:58, 18 Dec 2004 (UTC)

-- (talk) 20:26, 29 October 2012 (UTC)Reply[reply]

From Infinitesimal Calculus[edit]

Content from former Infinitesimal calculus moved into History of Calculus. Peter Grey 21:32, 23 Jun 2005 (UTC)

Newton, Leibniz Controversy[edit]

I tried to edit and reorganize this article to be a little cleaner. Also, I deleted some statements about the Newton - Leibniz controversy that I feel were dubious. I am not the foremost expert on this subject, but I do know some about it. Unfortunately, much of what is left is rather vague and uninformative. If someone has some good sources on this subject, please provide them! If people can provide good sources for some of the statements I deleted, by all means, reinsert them! Grokmoo 05:05, 7 February 2006 (UTC)Reply[reply]

I wish that you (and everyone) would move deletions of that sort to the discussion page. Some controversies, including this one, are still being argued after the elapse of centuries, but that doesn't inherently mean that old arguments have no merit at all -- they can be good starting material.

I mean, think about it -- I have several books concerning the history of calculus, and if I'm in a wikipedia mood, I might see your deleted material here on TALK, check various things in my books, and attempt to insert material into the article that is backed-up by my references.

But since you simply deleted the controversial phrasings, where does that leave people like me? The wording that bothered you is completely gone; we have no idea what it was about. We can no longer simply react and improve, instead we must spontaneously generate new material, which is much, much harder, in many senses, and tends to be of high quality only when done by a true expert on the topic, whereas simple fact-checking of controversies may eventually be done by the mere enthusiast, if you see what I mean.

In summary, clearly bad or wrong stuff should of course be deleted, but merely questionable but possibly-a-good-springboard material should be moved, at most, until it can be improved.

Think about it -- if you could have improved it, rather than deleting it, you would have, but by deleting it (and calling attention to your deletion), you are asking for volunteers who are more expert than you to exert more effort than you -- not that I'm in that category, but why demand so very much from those whom you are envisioning will correct your deletion???

Don't expect more than incremental improvements. Make edits in a way that inherently supports incremental improvements. Dougmerritt (talk) 04:27, 24 September 2008 (UTC)Reply[reply]

I'd say that we should forget the controversy and move on. Here in Finland we always tell that 'Leibniz and Newton were...' and if someone asks, we tell that the order of the names is just alphabetical. So I suggest that in the context of differential calculus the names of Leibniz and Newton are always presented in alphabetical order.

Linkato1 (talk) 14:27, 15 March 2012 (UTC)Reply[reply]


I have deleted the following... The method of integration can be traced back to the Egyptians, in the Moscow Mathematical Papyrus circa 1800 BC, which gives the formula for finding the volume of a pyramidal frustrum.

This is misleading in many ways... First of all. Well before the Egyptians the people from ancient Mesopotamia had deduced formulas for the volume of the frustum of a pyramid. Secondly. In neither case do we have evidence that the "method of integration" can be traced back to either of these civilizations. It is true that one cannot prove the result using finite geometrical constructions Paul Dehn 1902 however this is not to say that the result was derived by purely speculative means.

Regardless we have no evidence that the Egyptians ever used any methods of calculus.

"Paul Dehn" seems to be a mistake for "Max Dehn". — Preceding unsigned comment added by (talk) 12:56, 26 January 2012 (UTC)Reply[reply]

In February 1933 while on a visit to the United States, Einstein decided not to return to Germany due to the rise to power of the Nazis under Germany's new chancellor.[55][56] He visited American universities in early 1933 where he undertook his third two-month visiting professorship at the California Institute of Technology in Pasadena. He and his wife Elsa returned by ship to Belgium at the end of March. During the voyage they were informed that their cottage was raided by the Nazis and his personal sailboat had been confiscated. Upon landing in Antwerp on 28 March, he immediately went to the German consulate where he turned in his passport and formally renounced his German citizenship. — Preceding unsigned comment added by (talk) 20:31, 29 October 2012 (UTC)Reply[reply]


There is a referenced sentence in "Indian mathematicians":
"In 499 CE, the mathematician-astronomer Aryabhata used a form of infinitesimals to express an astronomical problem in the form of a differential equation."

with the reference being Aryabhata the Elder
But the referenced article says nothing of the sort. selfworm - just downgraded to version 0.4B! 07:50, 6 March 2007 (UTC)Reply[reply]

I have removed the ill-referenced sentence after waiting a day. selfworm__ ( Give me a piece of your mind · Userboxes · Contribs )_ 23:59, 6 March 2007 (UTC)Reply[reply]

This now seems to be a crucial section. See the news here.

"The beginnings of modern maths is usually seen as a European achievement but the discoveries in medieval India between the fourteenth and sixteenth centuries have been ignored or forgotten," he said. "The brilliance of Newton's work at the end of the seventeenth century stands undiminished — especially when it came to the algorithms of calculus.
"But other names from the Kerala School, notably Madhava and Nilakantha, should stand shoulder to shoulder with him as they discovered the other great component of calculus — infinite series."
"There were many reasons why the contribution of the Kerala school has not been acknowledged," he said. "A prime reason is neglect of scientific ideas emanating from the Non-European world, a legacy of European colonialism and beyond."

Since the Western-bias has been decried as a weakness of Wikipedia, I suggest this section be given top priority. -JTBurman 19:01, 14 August 2007 (UTC)Reply[reply]

I think it's just a statement told by a person not a historian. Obiwana (talk) 12:42, 23 December 2022 (UTC)Reply[reply]

Analytic geometry[edit]

The Analytic geometry section does not belongs in the history of calculus article since firstly, Analytic geometry has traditionally not been a part of calculus and secondly, it is woefully underdeveloped in comparison to the main article Analytic geometry. I have removed this section and placed an internal link to Analytic geometry in the see also section. selfwormTalk) 18:06, 17 July 2007 (UTC)Reply[reply]

Go ahead and remove, if someone wants to come back and develop it later they can do so.--Cronholm144 18:43, 17 July 2007 (UTC)Reply[reply]
Very well, I will remove it and if someone disagrees with its remove then they can undo the change and discuss it here. selfwormTalk) 20:07, 17 July 2007 (UTC)Reply[reply]

Symbolic methods[edit]

This section makes very little sense to me. Not only does the wikilink point to an article on symbolic methods in invariant theory, almost certainly wrongly, but after reading it, I cannot even deduce what is the subject of the section. The few mathematical statements that are in it are rather confused (e.g. "the analogy between successive differentiation and ordinary exponentials" and Grassman's "theory of complex numbers"). What is the relevance for history of calculus, if any? Arcfrk 20:12, 14 August 2007 (UTC)Reply[reply]


I've removed this paragraph:

The method of exhaustion was rediscovered in China by Liu Hui in the 3rd century AD, who used it to find the area of a circle. It was also used by Zu Chongzhi in the 5th century AD, who used it to find the volume of a sphere. (ref cited: Helmer Aslaksen. Why Calculus? National University of Singapore.)

The claim is not supported by the given reference (which is a course syllabus and does not qualify as a reliable source anyway). Similar claims are also not found in the articles about these gentlemen, which should be the primary locations.  --Lambiam 08:58, 28 November 2007 (UTC)Reply[reply]


A recent addition has greatly expanded the coverage of Newton and Leibniz's contributions. However, its use of the term "Calculus" is ahistorical and the explanation of the etymology in the very paragraph,

"the Calculus has become a popular term for a field of mathematics based upon their insights"

is wrong: it was not until the mid-twentieth century that the expressions "Differential calculus" and "Integral calculus", which in their turn are descendants of "Calculus of infinitesimals", "Calculus of fluxions", and so on, lost their adjectives. Let us not project the convention adapted by most authors of recent college textbooks back into the seventeenth century. Arcfrk (talk) 05:13, 31 March 2008 (UTC)Reply[reply]

I wrote something on this in this thread: Talk:Integral#Please have someone refer this post of mine to the English wizardspermalink (skip to the last paragraph). Since this keeps coming back (see Talk:Calculus/Archive 2#The Calculus and Talk:Calculus#The Calculus), it would be nice if we could write a paragraph or so about this shift in usage either here or in the main Calculus article. It may be hard to find citable sources, though.  --Lambiam 19:55, 31 March 2008 (UTC)Reply[reply]


Where is his treatise?Likebox (talk) 22:56, 12 December 2008 (UTC)Reply[reply]

Construction of a misleading narrative[edit]

The article overall appears to try to weave a misleading historical narrative out of various threads that used calculus-like ideas throughout the world in ancient and modern times, as if to suggest that they were all somehow a part of the development of what is today known as calculus. Even if this were ultimately true, it is unsupported by sources: the cited Katz source states that it is not known whether and how much the predecessors of Newton and Leibniz were aware of the results of the earlier Indian and Islamic mathematicians. The article goes way too far to avoid a "western" bias that now it contains virtually nothing of what might be called the "mainstream" treatment of the history of calculus. I think the article should be rewritten entirely from a good, standard source, like the definitive (if a bit dated) Boyer source that is currently referenced. The stuff about Indian/Islamic/Chinese mathematics should of course be dealt with, but not presented as part of the same historical narrative unless there are reliable sources to serve as a guide on precisely how to do this. Otherwise, connecting these historical facts into a misleading narrative is WP:OR par excellence. Sławomir Biały (talk) 13:49, 21 July 2010 (UTC)Reply[reply]

I hope you don't mind me renaming this section. "Article problem" could apply to a lot of discussions so I have come up with something more specific.
In terms of your actual complaint, I think you have a very good point, but I think I would split it into two points
  1. The validity of statements and implications made in the article.
  2. Whether, true or not, such statements should be given so much space near the top of this article. i.e. Are we giving themWP:UNDUE weight?
I think the first issue could perhaps be improved by renaming the section currently called "precursors to calculus". I'm not sure what to "Discoveries prior to calculus" maybe. And then a certain amount of explanation would have to go near the start of that section. Something like "Some of the concepts of calculus, such as infinitesimals, were explored to a certain extent by earlier mathematicians. The extent to which any of these developments influenced Newton and Leibniz is disputed but there was certainly no rigorous study of the topic until the 17th century."
I think the second issue could perhaps best be solved by moving the section to lower down the article. e.g. immediately above "See also".
Another thing, which Sławomir Biały hasn't mentioned is that the lead of the article talks a lot about what calculus is and not much about the history of calculus. e.g. it doesn't mention Newton and Leibniz. If we gave the article a proper lead then everything else could be seen in the proper context.
Yaris678 (talk) 17:36, 21 July 2010 (UTC)Reply[reply]
Yaris, I don't think that any historian of mathematics ever claimed that Newton and Leibniz were influenced by Chinese or Indian "precursors". The "revisionist" view, which is to some extent supported by the evidence, is that some discoveries that are now seen as part of Calculus had independently been made much earlier. However, they remained so isolated that, for example, the work of Kerala school was largely unknown in India itself. Of course, all sorts of fringe views may show up on Wikipedia, sometimes because of nefarious edits and sometimes because the most accessible sources on the internet are rarely the most scholarly ones. Arcfrk (talk) 05:40, 22 July 2010 (UTC)Reply[reply]
Sure, my main point was that we could write an introductory paragraph for that section, putting it into context. My example of the sort of text this could contain might not have been the most knowledgeble but then by discussing it like this and referring to sources we can come up with something better.

Responding to Sławomir's very valid argument about misleading historical narrative, I'd like to propose to farm out the section "Precursors to calculus" into a separate article. I see no connections between that part and the rest of the article, and it would be a pity to lose some reasonably researched material simply because it appears under the wrong heading. Arcfrk (talk) 06:07, 22 July 2010 (UTC)Reply[reply]

I was gonna suggest putting it in a separate article too, but you would still have the issue of what to call it. I think moving it to near the end of the article is better but I'm not too bothered either way. Yaris678 (talk) 10:44, 22 July 2010 (UTC)Reply[reply]
Actually, thinking about it, there is the potential for a separate article to become a POV fork. So it's probably best to keep it all in one place if we can. Yaris678 (talk) 10:48, 22 July 2010 (UTC)Reply[reply]
I don't know about the rest of the multicultural material, but the calculations in Archimedes come to close to what was done in the 17th century (and later) as to rub one's eyes in disbelief. It would be a mistake to "farm" Archimedes out as suggested above. On the other hand, it would be good to clarify just what the status of the other pre-Barrow material is. Tkuvho (talk) 11:17, 22 July 2010 (UTC)Reply[reply]
I would also be happy to see a one-article solution if possible. I should have added here that with this edit I fixed what I believed to be the worst of the article's excesses: reorganizing the "precursors" geographically rather than chronologically, and eliminating language like "...the next big development in calculus was... discovered by the Kerala school." However, I do think that further remedy is desirable, and that the main line of the history deserves much more focus than it currently has. Probably the best way to give the article an appropriate focus is to move the "Precursors" section to the very end. Sławomir Biały (talk) 12:09, 22 July 2010 (UTC)Reply[reply]
Good idea. Some of them are not even precursors of the calculus by any stretch of the imagination. Calculating the volume of a pyramid? I would suggest leaving Archimedes as a true precursor, and moving the rest of this material to a comments section at the end. Tkuvho (talk) 12:38, 22 July 2010 (UTC)Reply[reply]
I reorganized the page in accordance to what I saw as a consensus here. No doubt there will be further reogranisations. Tkuvho (talk) 11:17, 25 July 2010 (UTC)Reply[reply]

Archimedes of Syracuse[edit]

I included Archimedes in the title of the subsection on ancient greek mathematicians because Syracuse is not technically speaking in Greece. Tkuvho (talk) 04:29, 26 July 2010 (UTC)Reply[reply]

Well, the whole issue "who should be considered Greek" is murky: arguments have been made that at least some mathematicians of the Alexandrian school, including Diophantus, weren't ethnically Greek. On the other hand, I agree that section titles should be kept simple. Arcfrk (talk) 05:32, 26 July 2010 (UTC)Reply[reply]
This issue is expanded upon in the article on Greek mathematics. I think treating Archimedes as Greek is fine for our purposes. Yaris678 (talk) 11:53, 26 July 2010 (UTC)Reply[reply]
When titling the section, I was aware of precisely this issue. Alexandrian Greece would have been a better choice in retrospect, I think. Sławomir Biały (talk) 19:07, 26 July 2010 (UTC)Reply[reply]
Alexandrian Greece? Does that mean Greece at the time of Alexander the Great? I don't think that helps. Yaris678 (talk) 17:26, 27 July 2010 (UTC)Reply[reply]


If we are to attribute the fundamental theorem of calculus to Barrow, such an attribution should be sourced. Tkuvho (talk) 13:12, 14 December 2010 (UTC)Reply[reply]

See the wikipedia page on the fundamental theorem of calculus. (talk) 17:17, 14 December 2010 (UTC)Reply[reply]
The claim is similarly unsourced there. Do you have a source? Tkuvho (talk) 17:31, 14 December 2010 (UTC)Reply[reply] (talk) 17:41, 14 December 2010 (UTC)Reply[reply]
Not quite. The article says The first full proof of the fundamental theorem of calculus was given by Isaac Barrow.. Your ref says The fundamental theorem of calculus is the recognition that differentiation and integration are the inverse of each other. This is a key realization in mathematics and it was provided by Barrow in his Lectiones.14 It is a critical building block in the development of calculus, which was later formalized by Newton. From that, you can't tell if Barrow just realised it or proved it. Certainly the "later formalized by Newton" suggests Barrow didn't prove it William M. Connolley (talk) 17:57, 14 December 2010 (UTC)Reply[reply]
The source for this seems to be D. J. Struik, A Source Book in Mathematics, 1200-1800 (Princeton: Princeton University, 1986), page 262. If someone has access to this, could they look it up? Tkuvho (talk) 18:11, 14 December 2010 (UTC)Reply[reply]
By the same reasoning, Newton did not prove anything about calculus either, as it is well known that the rigorous foundations only came later. If this is the viewpoint you wish to adopt, then we can change "proved" to "discovered". (talk) 19:55, 14 December 2010 (UTC)Reply[reply]
The question is not who proved the fundamental theorem of calculus, but rather what the sources out there say about who proved the fundamental theorem of calculus. Unless you have a source saying that Barrow did it, we cannot make such a claim here. Tkuvho (talk) 07:58, 15 December 2010 (UTC)Reply[reply]
We have a source which says that Barrow discovered it; we can change the verb to "discovered" if you object to the word "proved". Note that we don't have any sources supporting the assertion that Newton proved it, as was previously claimed. (talk) 08:24, 15 December 2010 (UTC)Reply[reply]
The problem is that your source goes on to imply that what Barrow fell short of what Newton did in the context of the fundamental theorem of calculus, and to conclude that in fact we cannot attribute the discovery of the calculus to Barrow, if I understood it correctly. This is not necessarily the final word, as it could be that Struik and company are insufficiently appreciative of Barrow's geometrical methods. Be that as it may, the source you provided tends to undermine your case. Tkuvho (talk) 08:36, 15 December 2010 (UTC)Reply[reply]
You may find a more careful discussion of Barrow's work in the translation Geometrical Lectures of Isaac Barrow By Isaac Barrow, J. M. Child. Page 31 reviews the results. The proof is in chapters X and XI. See here: —Preceding unsigned comment added by (talk) 17:23, 15 December 2010 (UTC)Reply[reply]
You should indicate the page number in the footnote. Tkuvho (talk) 18:14, 15 December 2010 (UTC)Reply[reply]

(Outdent) Is this a translation of his work itself? It seems that wouldn't work as a supporting reference. I think we should use this one: The History of Calculus Arthur Rosenthal, The American Mathematical Monthly, Vol. 58, No. 2 (Feb., 1951), page 83, who clearly gives credit to Barrow. Thenub314 (talk) 21:42, 4 May 2011 (UTC)Reply[reply]

Excellent, please add it in. Tkuvho (talk) 04:40, 5 May 2011 (UTC)Reply[reply]


I find the dates in the opening to be rather inappropriate. I know of no other history article that inserts dates needlessly in such a way, and I can think of no motivation other than the bias the article towards Newton. The article already has a bit of bias towards Newton, in that it arranges the names "Newton and Leibniz" out of alphabetical order. As it is generally agreed both of them developed calculus independently, I think issues of priority should be relegated to the calculus dispute page. It is worth pointing out that someone could have just as easily inserted dates in favor of Leibniz, by saying "Leibniz (published in ...)". (talk) 17:37, 14 December 2010 (UTC)Reply[reply]

non-European antecedents of the calculus[edit]

There appears to be a disagreement regarding Indian contributions to the calculus. Edits in this direction should be placed in the section Please avoid further edit-warring. Tkuvho (talk) 04:32, 24 April 2011 (UTC)Reply[reply]


This [1] is nationalistic POV-pushing. The addition is unsourced, untrue, and its placement in the lede totally against WP:UNDUE. I have consequently removed it. Athenean (talk) 04:58, 24 April 2011 (UTC)Reply[reply]

Well we do acknowledge Indian contributions in the section, so the additions are not completely unsourced. As I recall, there were some impressive power series developments that anticipated modern European ones by quite a number of years. Tkuvho (talk) 05:03, 24 April 2011 (UTC)Reply[reply]
That may well be, however, the tenor of the additions is highly tendentious, and the way they were added in the lede is a case of WP:UNDUE. As for the non-European section, I don't see such a section in any other history of mathematics articles. Significant advances by non-European cultures should simply be worked into the rest of the article rather than being in a separate section by themselves. It's as if there is "western calculus" and "non-western calculus", almost apartheid-like. I also note that much of the section is unsourced or extremely poorly sourced, which is not surprising since the main contributor to the article is none other than Jagged 85. Instead of tendentious edits to the lede, what needs to be done is to go over the non-European section carefully, throw out what is unsourced or poorly sourced, and what has nothing to with calculus (e.g. the frustum stuff), and merge what is significant (e.g. the Madhava series) into the rest of the article. Athenean (talk) 06:06, 24 April 2011 (UTC)Reply[reply]
One rationale for keeping them separate is that, according to a majority of scholars, they have had little influence on the development of analysis as it actually happened. I agree that irrelevant material should be deleted, of course. Tkuvho (talk) 06:22, 24 April 2011 (UTC)Reply[reply]

14th century Indian differentiation[edit]

A recent edit attributes the concept of differentiation to a 14th century Indian astronomer. Whoever is knowledgeable on this subject please comment on this attribution. Tkuvho (talk) 08:04, 1 May 2011 (UTC)Reply[reply]

The cited source doesn't mention differentiation. It also doesn't mention iterative solutions to nonlinear equations (although there is an iterative solution for some special equations, and this is how he arrived at a series expansion of π). I've edited the text accordingly. Sławomir Biały (talk) 14:43, 1 May 2011 (UTC)Reply[reply]
This is dodgy. Someone has added the text, but the reference remains the same. Furthermore the ref (which is only a web page) says Historians have claimed that the method used by Madhava amounts to term by term integration. which seems very weak (if you want someone to judge the claim, you want a mathematician, not a historian); and it itself contains no refs. I've removed it as essentially unverified William M. Connolley (talk) 15:54, 1 May 2011 (UTC)Reply[reply]
I have no objection to the removal of the statement. However, I'd like to emphasize that MacTutor is generally regarded as quite a reliable source on the history of mathematics, so please let's not paint this with the "only a web page" brush. Also, it does have references of its own; see [2]. Sławomir Biały (talk) 16:23, 1 May 2011 (UTC)Reply[reply]
Agreed. But whilst it has refs of its own, it has no refs for that statement William M. Connolley (talk) 16:35, 1 May 2011 (UTC)Reply[reply]
I'll grant that. I wasn't sure how to handle the unattributed statement either. I just wanted to make sure we're on the same page. Sławomir Biały (talk) 18:47, 1 May 2011 (UTC)Reply[reply]
Also "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 so I've removed it. Re [[Yuktibhāṣā]], I didn't find that text on the mactutor page, so I'm not sure why the ref is there William M. Connolley (talk) 15:54, 1 May 2011 (UTC)Reply[reply]


I removed

In 17th century Japan, Japanese mathematician Kowa Seki[unreliable source?][dead link] made a number of contributions, namely in methods of determining areas of figures using integrals, extending the method of exhaustion. While these methods of finding areas were made largely obsolete by the development of the fundamental theorems by Newton and Leibniz, they still show that a sophisticated knowledge of mathematics existed in 17th century Japan.

as sourceless William M. Connolley (talk) 15:56, 1 May 2011 (UTC)Reply[reply]


Per the ongoing Jagged 85 cleanup, I checked the sources in the articles, and found a lot that was questionable. Specifically:

  • Regarding ancient Egypt, calculating the area of a pyramidal frustum is not calculus, or anywhere close to calculus. It is geometry.
  • In the section on China, the Pythagorean theorem likewise has nothing to do with calculus. The section was entirely unsourced, even though bold claims about calculus were made.
  • In the India section, Joseph's book was completely misused. First, the claim that Aryabhatta used a differential equation is complete bunk. The search term "Aryabhatta" and "differential equation" do not even appear in the book [3]!
  • The sources on Manjula and Bhaskara II were similarly misused. I rephrased the article per the sources. Athenean (talk) 18:10, 3 May 2011 (UTC)Reply[reply]
Thanks. Re Indian, The mathematician Manjula, in the 10th century, was aware of differentiation doesn't sound plausible. One of the refs appears to be [4], but a similar one [5] doesn't mention this claim at all. Is [6] really reliable, or is it just some blokes web page? Also, the details there are less than sketchy: Evidence suggests Bhaskara was fully acquainted with the principle of differential calculus, and that his researches were in no way inferior to Newton's,, with no refs provided William M. Connolley (talk) 21:11, 3 May 2011 (UTC)Reply[reply]

As far as MacTutor is concerned, this is not their regular history page, but rather a "project" by a bloke named Ian Pearce. This link is definitely unreliable. Tkuvho (talk) 14:07, 4 May 2011 (UTC)Reply[reply]

Yes, see It's a student writing. That page isn't a "reliable source" in the meaning of the act. Charles Matthews (talk) 14:26, 4 May 2011 (UTC)Reply[reply]
The Indian section turns out to have originated in Jaggedese [7] so I removed it because it means none of the refs can be trusted (unless someone has fixed it later; sorry I may have missed that) William M. Connolley (talk) 14:46, 4 May 2011 (UTC)Reply[reply]

Ignorance of the Indian contributions to calculus[edit]

This article by all mean is WESTERN BIASED. There is now well documented evidence that many important results in calculus like power series expansion of pi and so on were given by Kerala School of Mathematics 300 years before Newton or Leibniz. What is wrong in acknowledging that. It is definitely not acknowledged and everything is written from Western perspective emphasizing NEWTON-LEIBNIZ war. Does this mean other parts of the world need to write their own evidence-based history of calculus?.Chenna001 (talk) 10:27, 6 May 2011 (UTC)Reply[reply]

Chenna, please sign your comments. The consensus among editors seems to be that the addition you proposed should be in the non-european section of the article. Tkuvho (talk) 08:24, 6 May 2011 (UTC)Reply[reply]
Incidentally, I was not the one who removed the Indian subsection. I just restored it a few minutes ago. The great Indian mathematical tradition should be represented here, while avoiding excesses of ethnomathematics. I look forward to a productive collaboration. Tkuvho (talk) 08:34, 6 May 2011 (UTC)Reply[reply]
OK. I restored Indian section. For whoever removed the entire section, I would like to mention that such intolerance will make things only worse. For those who are complaining about sources, you cannot expect that things in AMerican or European journals can only be credible. There are sources which are original about which we do not need any recommendations. For example, the book YukthiBhasha discusses a lot of mathematical material and it is preserved in a fine condition from ancient times. Now when the original source exists, if you(those who are deleting stuff citing no credible source or something like that) again persist for some document written by westerner talking about YukthiBhsha to take YukthiBhasha seriously, then you can judge yourself about your own "western bias". Chenna001 (talk) 09:27, 6 May 2011 (UTC)Reply[reply]
It may also be more appropriate to rename this whole topic as Western History of Calculus and start another topic with Eastern History of Calculus.Chenna001 (talk) 09:32, 6 May 2011 (UTC)Reply[reply]

For whoever removed the entire section: this page isn't write-only you know; please bother to actually *read* it too. As I said above, The Indian section turns out to have originated in Jaggedese [7] so I removed it because it means none of the refs can be trusted. I've removed it again. If you wish to restore it, please state clearly that you have personally verified all the references that you restore. And please drop the nonsense about "war" (note: C later silently removed this [8]) William M. Connolley (talk) 10:28, 6 May 2011 (UTC)Reply[reply]

The point is that not all the sources cited there are from Ian Pierce. You also need to read what I have written there. I do not need some westerner telling me that Yukthibhasha is a book in this world. I am restoring it on these grounds. If you want to say something is unreliable then prove it to be unreliable. You cannot state something is unreliable as if you have complete knowledge about everything. Also, you cannot say somebody is bloke if you don't like what he/she writes. It would be best if you maintain some respect for others. This is not a place for your personal opinion.Chenna001 (talk) 10:41, 6 May 2011 (UTC)Reply[reply]
Thank you for removing your talk of "war". But can you not see that I do not need some westerner... is equally unacceptable? The point is that not all the sources cited there are from Ian Pierce. No, that isn't the point. Please cast your eyes up above to the section about the Jagged cleanup. The *point* is that most of that text comes from Jagged, who is known to abuse his sources. Unless you have personally verified that the sources you've re-inserted actually say what it claims, please don't re-insert them again William M. Connolley (talk) 11:05, 6 May 2011 (UTC)Reply[reply]
Chenna, please keep in mind that most editors here are interested in the important Indian contribution to mathematics, and agree with you that certain original contributions preceded European discoveries. Avoiding blanket anti-western rhetoric will help your cause. Tkuvho (talk) 11:09, 6 May 2011 (UTC)Reply[reply]

I think it's better to rewrite the Indian section from reliable sources. I'm a bit of a novice when it comes to the History of Mathematics, but even Morris Kline's "Mathematical thought from ancient to modern times" acknowledges some of the discoveries of Indian mathematicians. That might be a place to start. There shouldn't be a need to rely on questionable sources like the Pearce paper. Sławomir Biały (talk) 11:33, 6 May 2011 (UTC)Reply[reply]

Thanks everybody. I will check relevant sources myself and re-write stuff later. I am having my exams now...Chenna001 (talk) 19:29, 6 May 2011 (UTC)Reply[reply]

(outdent) Here is a reference which I haven't read, but I will if someone doesn't beat me to it "Was Calculus Invented in India?" by David Bressoud, College Mathematics Journal, Vol. 33, No. 1, Jan., 2002. He seems to cite a few other papers about it which might give some more details. If it helps with the current dispute the opening sentences are: "No. Calculus was not invented in India. But two hundred years before Newton or Leibniz, Indiana astronomers came very close to creating what we would call calculus." Thenub314 (talk) 19:37, 6 May 2011 (UTC)Reply[reply]

PS The author then give a description of the power series expansions that Chenna001 mentions, so I am not trying to be dismissive to Indian contributions to calculus. Just want to give some reliable sources to base them on so we don't need to argue about it. Thenub314 (talk) 19:53, 6 May 2011 (UTC)Reply[reply]
PPS Here is the JSTOR link for anyone interested who has access to JSTOR: [9]

Jaggedalia, part 2[edit]

At ghosts of departed quantities, a few editors are attempting a whiggish rewriting of the history of the calculus. George Berkeley criticized both the infinitesimal and fluxional procedures of the calculus, which he claimed amounted to the same thing. Weierstrass and his followers in the 1870s did 3 things: (1) they largely accepted Berkeley's critique of infinitesimal procedures; (2) they sought to eliminate infinitesimals; and (3) they developed infinitesimal-free foundations for analysis, namely foundations based on the real numbers and epsilontics. Then in the 1960s, Robinson came along and restored infinitesimals to respectability, in particular removing whatever logical inconsistencies were present in dy/dx style definition of derivative. He was thus the first one to resolve the paradox of the infinitesimal procedures criticized by Berkeley.

The paragraph above is agreed to by all the historians I have read. Now a few editors have come along and rewritten history. The page ghosts of departed quantities no longer mentions Robinson. Instead, it claims that Weierstrass resolved Berkeley's paradoxes. This does not compare favorably with Jagged's efforts, to the extent that Jagged at least left the old material in while adding his new material. Some input would be appreciated. Tkuvho (talk) 13:36, 25 May 2011 (UTC)Reply[reply]


The following comment was recently deleted: "Fermat also obtained a technique for finding the centers of gravity of various plane and solid figures, which influenced further work in quadrature". What the comment did not mention is that these results, like those on maxima and minima as well as tangents, of Fermat were applications of his method of adequality. Fermat's role as a pioneer of calculus is indisputable. I don't think we can err by overemphasizing Fermat in this section. The comment should be restored and expanded upon (incidentally, it was originally added by another editor). Tkuvho (talk) 08:49, 16 December 2011 (UTC)Reply[reply]

I also support the reinsertion of the removed text, as well as further expansion of the section "Pioneers of modern calculus". More detail rather than less is called for here. Other topics this article could touch upon include the development of the integral (e.g., Riemann and Lebesgue) and some more information on the contributions of Cauchy and Weierstrass to its foundations. — Myasuda (talk) 14:25, 16 December 2011 (UTC)Reply[reply]
Currently the material is poorly organized. Thus, Bolzano is mentioned before Newton and Leibniz. Some restructuring may be in order. Tkuvho (talk) 13:10, 29 December 2011 (UTC)Reply[reply]
Agreed. Much of the article should be restructured and expanded. In addition to chronological issues, the hatnote for the Leibniz–Newton calculus controversy would be better placed in the "Legacy" subsection (which should probably be renamed). And the post Leibniz and Newton material needs to be significantly elaborated upon. — Myasuda (talk) 21:40, 29 December 2011 (UTC)Reply[reply]
Great, give it a try. Note also the section which is two sections below.Tkuvho (talk) 09:23, 30 December 2011 (UTC)Reply[reply]

Two different methods[edit]

The method of exhaustion and the method of indivisibles are two genuinely different methods, contrary to what the page currently states. Tkuvho (talk) 12:58, 29 December 2011 (UTC)Reply[reply]

World as infinite aggregate[edit]

The page currently claims that Leibniz viewed the world as an infinite aggregate (of monads), as well as "aggregate of infinitesimal points". Is there a source for this claim? Tkuvho (talk) 10:44, 28 February 2012 (UTC)Reply[reply]


I am surprised there is mention of Johannes Kepler's work on Wine Barrels. This work was fairly important in the evolution of calculus, see Roberto Cardil (MatematicasVisuales), "Kepler: The Volume of a Wine Barrel - Kepler's Era," Convergence (January 2012), DOI:10.4169/loci003499 Rhodydog (talk) 21:25, 9 August 2022 (UTC)Reply[reply]

The work mention in the first bit about Kepler "Stereometrica Doliorum" is about that problem. NadVolum (talk) 20:47, 14 December 2022 (UTC)Reply[reply]

Orphaned references in History of calculus[edit]

I check pages listed in Category:Pages with incorrect ref formatting to try to fix reference errors. One of the things I do is look for content for orphaned references in wikilinked articles. I have found content for some of History of calculus's orphans, the problem is that I found more than one version. I can't determine which (if any) is correct for this article, so I am asking for a sentient editor to look it over and copy the correct ref content into this article.

Reference named "ReferenceB":

I apologize if any of the above are effectively identical; I am just a simple computer program, so I can't determine whether minor differences are significant or not. AnomieBOT 13:02, 5 February 2023 (UTC)Reply[reply]