# Talk:Calculus

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## The history section

Shouldn't the history section have at least some content? I mean, more than the link? --31.45.79.44 (talk) 22:46, 27 February 2012 (UTC)

In the main text we read: "Pierre de Fermat, claiming that he borrowed from Diophantus, introduced the concept of adequality, which represented equality up to an infinitesimal error term. (André Weil: Number theory. An approach through history. From Hammurapi to Legendre. Birkhauser Boston, Inc., Boston, MA, 1984, ISBN 0-8176-4565-9, p. 28.) " I think that this is misleading. Fermat borrowed from Bachet de Meziriac's Latin translation of Diophantus’ Arithmetika the noun adaequalitas and the verb adaequare where they have a meaning in a completely different context, namely solving a special class of arithmetical problems by the method of false position. Fermat, however, uses those words (and the word adaequabitur) in his method of determining maxima and minima of algebraic terms and of computing tangents of conic sections and other algebraic curves. Fermat’s method is purely algebraic. There is no "infinitesimal error term". Fermat uses two different Latin words for "equals": aequabitur and adaequabitur. He uses aequabitur when the equation describes the identity of two constants or is used to determine a solution or represents a universally valid formula. Example:

$x^3+y^3=(x+y)(x^2-xy+y^2)$.

And he uses the word adaequabitur ($\doteq$) when the equation describes a relation which is no valid formula. Example (Descartes' folium):

$x^3+y^3 \doteq 3xy$.

Typical examples are:

$(x+e)(b-x-e)=bx-x^2-2ex+be-e^2$

and

$be \doteq 2ex+e^2$.

Equations which describe relations between two variables (x and y, x and e) were unknown to Vieta. So the 21-year-old Fermat felt compelled to introduce a new concept of equality and called it adaequalitas. Later, when he created his analytic geometry he abandoned this special terminology of his younger days. See my paper Barner, Klaus: Fermats <<adaequare>> - und kein Ende? Math. Semesterber. (2011) 58, 13-45, unfortunately written in German. 91.4.83.79 (talk) 17:28, 7 February 2013 (UTC) Klaus Barner (talk) 14:40, 5 February 2013 (UTC)

Very interesting. Is there perhaps a translation of your article online somewhere? Tkuvho (talk) 16:13, 6 February 2013 (UTC)

Unfortunately there is none. The reason is: my German is sophisticated and requires reading between the lines whereas my English ist rather weak. It is no artical about mathematics but about history of mathematics which requires a better command of English than I have. However I feel that I should produce a raw translation and ask a native speaker to improve it. Klaus Barner (talk) 19:09, 10 February 2013 (UTC)

## balance and accuracy concerning controversy concerning origins?

Article says, "When Newton and Leibniz first published their results, there was great controversy over which mathematician (and therefore which country) deserved credit." but I understand from the Wikipedia article on the controversy itself (to which this should link) that the controversy evolved many years after Leibniz published his results. Also, the slant of the story itself, as it is told here, seems to favor one side (Newton). — Preceding unsigned comment added by Rentstrike (talkcontribs) 18:25, 28 November 2012 (UTC)

## Capitalization of Calculus

It is my understanding that the formal name for calculus is "The Calculus." While the "The" is generally dropped these days, isn't it still appropriate to capitalize the word Calculus?

"A calculus is a way of calculating, so mathematicians sometimes talk about the 'calculus of logic', the 'calculus of probability', and so on. But all are agreed there is really only one Calculus, pure and simple, and this is spelled with a capital C" (emphasis mine) (Crilly, Tony (2007). 50 Mathematical Ideas You Really Need to Know. London: Quercus Publishing Plc. p. 76, 208. ISBN 1-84724-147-6.)

Interestingly, the index of the book does not capitalize the word.

It would seem seems that we should at least mention the issue of capitalization in the article.

Billiam1185 (talk) 01:02, 4 March 2013 (UTC)

## Why is Leonhard Euler not mentioned ?

To be clear, most who add to the mathematical pages have probable forgotten more than I know about maths (I'm British, so I refuse to call it math). However it couldn't escape my notice that when Google put Leonhard Euler up in a Google doodle and specifically mentioned his historical significance to maths and his important work on infinitesimal calculus, that there is no mention of him whatsoever on the infinitesimal calculus page. Is Google incorrect in its highlighting the importance of Euler? Or is his work on infinitesimal calculus not as important as made out on his Wikipedia page? Either one or the other needs correction?

This is definitely an oversight. Euler should be mentioned both on calculus and infinitesimal calculus. Would you like to contribute a comment there? Tkuvho (talk) 15:05, 20 May 2013 (UTC)

## There should be more technical information

Perhaps more examples on this matter. — Preceding unsigned comment added by Pedrovalle (talkcontribs) 13:11, 20 May 2013 (UTC)

## The introduction should include when and who.

I think there should be something in the introduction about when it was invented and (gulp) who invented it. At the risk of being beaten over the head by all the history revisionists and refactorers out there, I think that should be the 17th century, Newton, and Leibniz. --ChetvornoTALK 00:43, 27 July 2013 (UTC)

## Quote hanging on Newton's edge

The Neumann quote box is hanging on Newton's image edge. Can someone fix it? Tried to, but got rolled-back. Formatting problems. --J. D. Redding 00:11, 28 July 2013 (UTC)

## Really?

Come on, people, let's hold the line for general references. We don't have to give in to the inline-cite extremists, not here. For most aspects of the topic, all our refs are going to say the same thing, probably in almost the same words. Save the inline cites for the stuff that's a little particular, and don't make the reader work through a forest of little blue numbers. --Trovatore (talk) 19:14, 4 December 2013 (UTC)

My take on this... someone comes along and makes some subtle changes. Without inline refs it tends to be pretty hard—if not impossible—to check the sources, at least for me, having not significantly contributed to the article in the past. Inline refs make this much easier. - DVdm (talk) 19:22, 4 December 2013 (UTC)
I resist giving in to citation extremists on non-controversial facts, but having some citations are still useful. For instance, the large Principles section of this article has no citations. If a curious student wanted to learn more about principles of calculus, there are zero pointers to a good source or two on this. It's a flaw. I think the more relaxed citation guidelines in WP:SCICITE would be appropriate here: about one general ref per paragraph. --Mark viking (talk) 20:05, 4 December 2013 (UTC)
I am not a citation extremist. But this article doesn't even meet a one general reference per SECTION standard, much less one general ref per paragraph. Stigmatella aurantiaca (talk) 22:48, 4 December 2013 (UTC)

## Orphaned references in Calculus

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 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 "almeida":

• From Madhava of Sangamagrama: D F Almeida, J K John and A Zadorozhnyy (2001). "Keralese mathematics: its possible transmission to Europe and the consequential educational implications". Journal of Natural Geometry 20 (1): 77–104.
• From Indian mathematics: Almeida, D. F.; John, J. K.; Zadorozhnyy, A. (2001), "Keralese Mathematics: Its Possible Transmission to Europe and the Consequential Educational Implications", Journal of Natural Geometry 20: 77–104.
• From Kerala school of astronomy and mathematics: Almeida, D. F.; John, J. K.; Zadorozhnyy, A. (2001). "Keralese Mathematics: Its Possible Transmission to Europe and the Consequential Educational Implications". Journal of Natural Geometry 20: 77–104.

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 21:02, 11 January 2014 (UTC)

## Merger proposal

CLOSED:

Agree to merger of Infinitesimal calculus into Calculus as per wp:consensus and wp:SNOW. Editor familiar with subject should proceed. Non-Administrative closure-- GenQuest "Talk to Me" 05:31, 16 April 2014 (UTC)

The following discussion is closed. Please do not modify it. Subsequent comments should be made on the appropriate discussion page. No further edits should be made to this discussion.

Request received to merge Infinitesimal calculus into Calculus. User:Unsigned request. Reason= unknown. Please discuss here. GenQuest "Talk to Me" 00:16, 30 March 2014 (UTC)

• Support, with qualifications. I think the main use of the term infinitesimal calculus is simply to mean the calculus; that is, the differential and integral calculus, as opposed to, say, the propositional calculus. So I think infinitesimal calculus should ultimately redirect to calculus. However, whether the content should be merged is a different question. Possibly the content should instead be moved to some title such as infinitesimal methods in the calculus, or else merged into nonstandard analysis, before pointing the redirect at calculus. --Trovatore (talk) 00:35, 30 March 2014 (UTC)
• Update I wrote the above without really looking at the current content of infinitesimal calculus. As it stands, there's actually not that much about infinitesimal methods there, so I'm not sure how much there is to start another article with, or to merge to nonstandard analysis. Still, in principle, I stand by my remarks — for example, it could be (I haven't checked) that the article used to be more about infinitesimal methods, and in that case, that previous content could be used in the way I described. --Trovatore (talk) 00:48, 30 March 2014 (UTC)
• Support. There is not enough material specific to the use of infinitesimals in calculus to warrant an entire article on this topic. All the material presently in the infinitesimal calculus article should be in either the main calculus article or in some closely related article (such as on history, on derivatives or integrals specifically, on non-standard analysis, and so on). Ozob (talk) 02:01, 30 March 2014 (UTC)
• Comment Even if there is enough material for such an article, I don't think infinitesimal calculus is the right name for it. Sorry to be picky about it when we're on the same "side", but I really think the point to stay focused on is, where should the search term infinitesimal calculus point? And in accordance with the "common name" principle, I think that term is more used for the integral and differential calculus (regardless of foundations) than it is for the use of infinitesimals in the foundations of calculus. --Trovatore (talk) 03:45, 30 March 2014 (UTC)
• I think infinitesimal calculus should point to calculus. At this point I think that's what the term refers to; saying "infinitesimal calculus" distinguishes differential and integral calculus (considered together) from, say, propositional calculus. To me it also carries a hint of infinitesimal foundations; maybe they're Newtonian or Leibnizian instead of non-standard analysis, but regardless the term itself suggests that infinitesimals make an appearance in the theory somehow. Ozob (talk) 06:36, 30 March 2014 (UTC)
• Support. Theo (Talk) 10:00, 1 April 2014 (UTC)
• Support As far as I know as a math student with no background in history of math, calculus is essentially a shorthand for infinitesimal calculus. -- Taku (talk) 17:20, 1 April 2014 (UTC)
• Support I think infinitesimal calculus should be merged into calculus, with the redirect also pointing to calculus as the most common usage of the term. The infinitesimal calculus article is mostly redundant with calculus article, except for the "Non-standard calculus" and "Smooth infinitesimal analysis" sections--those could be usefully merged into the Calculus#Limits and infinitesimals section, which doesn't even mention the Non-standard calculus article. --Mark viking (talk) 17:38, 1 April 2014 (UTC)

The discussion above is closed. Please do not modify it. Subsequent comments should be made on the appropriate discussion page. No further edits should be made to this discussion.