Talk:History of calculus

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Contents 1 Sources 2 From Infinitesimal Calculus 3 Newton, Leibniz Controversy 4 Egypt 5 India 6 Analytic geometry 7 Symbolic methods 8 China 9 Etymology

[edit] Sources

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)

[edit] From Infinitesimal Calculus

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

[edit] Newton, Leibniz Controversy

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)

[edit] Egypt

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.

[edit] India

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)

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)

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)

[edit] Analytic geometry

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. selfworm^Talk) 18:06, 17 July 2007 (UTC)

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)

Very well, I will remove it and if someone disagrees with its remove then they can undo the change and discuss it here. selfworm^Talk) 20:07, 17 July 2007 (UTC)

[edit] Symbolic methods

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)

[edit] China

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)

[edit] Etymology

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)

I wrote something on this in this thread: Talk:Integral#Please have someone refer this post of mine to the English wizards^permalink (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)