Talk:History of calculus

message: 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)
thread_title: Sources

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

message: 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)
thread_title:  Newton, Leibniz Controversy 

message: 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 86.176.100.209 (talk) 12:56, 26 January 2012 (UTC)
thread_title:  Egypt 

message: 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)
replies: text: 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)
replies: text: 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)
thread_title:  Analytic geometry 

message: 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)
thread_title:  Symbolic methods 

message: 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)
thread_title:  China 

message: 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)
replies: text: 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)
thread_title:  Etymology 

message: Where is his treatise?Likebox (talk) 22:56, 12 December 2008 (UTC)
thread_title:  Cavalieri? 

message: 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)
replies: text: 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)
replies: text: 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)
replies: text: 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)
replies: text: 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)
thread_title:  Archimedes of Syracuse 

message: 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)
replies: text: See the wikipedia page on the fundamental theorem of calculus. 131.111.184.95 (talk) 17:17, 14 December 2010 (UTC)
replies: text: The claim is similarly unsourced there.  Do you have a source?  Tkuvho (talk) 17:31, 14 December 2010 (UTC)
replies: text:  http://www.lucasianchair.org/17/barrow.html 131.111.184.95 (talk) 17:41, 14 December 2010 (UTC)
replies: text:  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)
replies: text: 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)
replies: text:  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". 131.111.184.95 (talk) 19:55, 14 December 2010 (UTC)
replies: text: 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)
replies: text:  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. 131.111.184.95 (talk) 08:24, 15 December 2010 (UTC)
replies: text: 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)
replies: text:  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: http://www.archive.org/details/geometricallectu00barruoft  —Preceding unsigned comment added by 131.111.184.95 (talk) 17:23, 15 December 2010 (UTC)
replies: text: You should indicate the page number in the footnote.  Tkuvho (talk) 18:14, 15 December 2010 (UTC)

text: Excellent, please add it in.  Tkuvho (talk) 04:40, 5 May 2011 (UTC)
thread_title:  Barrow 

message: 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 ...)". 131.111.184.95 (talk) 17:37, 14 December 2010 (UTC)
thread_title:  Dates 

message: There appears to be a disagreement regarding Indian contributions to the calculus.  Edits in this direction should be placed in the section http://en.wikipedia.org/wiki/History_of_calculus#Non-European_antecedents_of_the_calculus.  Please avoid further edit-warring.  Tkuvho (talk) 04:32, 24 April 2011 (UTC)
thread_title:  non-European antecedents of the calculus 

message: This  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)
replies: text: Well we do acknowledge Indian contributions in the section http://en.wikipedia.org/wiki/History_of_calculus#Non-European_antecedents_of_the_calculus, 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)
replies: text: 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)
replies: text: 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)
thread_title:  POV-pushing 

message: 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)
replies: text: 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)
replies: text:  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)
replies: text: 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 .  Sławomir Biały (talk) 16:23, 1 May 2011 (UTC)
replies: text:  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)
replies: text:  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)

text:  Also  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)
thread_title:  14th century Indian differentiation 

message: I removed 
: In 17th century Japan, Japanese mathematician Kowa Sekihttp://www2.gol.com/users/coynerhm/0598rothman.html 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)
thread_title:  Japan 

message: 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 !
* 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)
replies: text: 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 , but a similar one  doesn't mention this claim at all. Is  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)

text: Yes, see http://turnbull.mcs.st-and.ac.uk/~history/Projects/index.html. 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)
replies: text:  The Indian section turns out to have originated in Jaggedese  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)
thread_title:  Cleanup 

message: 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)
thread_title:  Jaggedalia, part 2 

message: 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)
replies: text: 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)
replies: text: 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)
replies: text: 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)
replies: text: Great, give it a try.  Note also the section which is two sections below.Tkuvho (talk) 09:23, 30 December 2011 (UTC)
thread_title:  Fermat 

message: 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)
thread_title:  Two different methods 

message: 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)
thread_title:  World as infinite aggregate 

message: 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)
replies: text: The work mention in the first bit about Kepler "Stereometrica Doliorum" is about that problem. NadVolum (talk) 20:47, 14 December 2022 (UTC)
thread_title:  Kepler 

message: 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":
From History of logarithms: 
From Science and technology in Iran: 
From Law: Robertson, Crimes against humanity, 90.
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)
thread_title:  Orphaned references in [[:History of calculus]]