Talk:History of mathematics
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I'm developing some material from zero divided by zero for inclusion here. But its taking some time to work up so I'm putting it here temporarily while it is worked on. Feel free to contribute Barnaby dawson 10:13, 22 Sep 2004 (UTC)
Could somebody please clean up the first lines of 'complex numbers'? They sound rather trivial or non-encyclopedic. Radiant! 22:09, 12 Feb 2005 (UTC)
I disagree with the following sentence "spherical trigonometry was largely developed by the Persian mathematician Nasir al-Din Tusi (Nasireddin) in the 13th century." Other mathematicians wrote about spherical trigonometry before him, including Ptolemy in the 100s AD in his book the Almagest long before the 1200s. NikolaiLobachevsky 21:08:49 12/26/2006 (UTC)
I have been doing some work with the references. Over time they have grown sloppy and have been subject to some vandalism. There are a couple of long quotes that have been put into the notes that do not have full citations (names and dates but no book titles or other bibliographic info). I've decided to pull these out and put them here so that if this information can be found we can decide whether or not to replace them. Bill Cherowitzo (talk) 04:32, 9 January 2015 (UTC)
Pingree 1992, p. 562 Quote: "One example I can give you relates to the Indian Mādhava's demonstration, in about 1400 A.D., of the infinite power series of trigonometrical functions using geometrical and algebraic arguments. When this was first described in English by Charles Whish, in the 1830s, it was heralded as the Indians' discovery of the calculus. This claim and Mādhava's achievements were ignored by Western historians, presumably at first because they could not admit that an Indian discovered the calculus, but later because no one read anymore the Transactions of the Royal Asiatic Society, in which Whish's article was published. The matter resurfaced in the 1950s, and now we have the Sanskrit texts properly edited, and we understand the clever way that Mādhava derived the series without the calculus; but many historians still find it impossible to conceive of the problem and its solution in terms of anything other than the calculus and proclaim that the calculus is what Mādhava found. In this case the elegance and brilliance of Mādhava's mathematics are being distorted as they are buried under the current mathematical solution to a problem to which he discovered an alternate and powerful solution."
(Bressoud 2002, p. 12) Quote: "There is no evidence that the Indian work on series was known beyond India, or even outside Kerala, until the nineteenth century. Gold and Pingree assert  that by the time these series were rediscovered in Europe, they had, for all practical purposes, been lost to India. The expansions of the sine, cosine, and arc tangent had been passed down through several generations of disciples, but they remained sterile observations for which no one could find much use."
Plofker 2001, p. 293 Quote: "It is not unusual to encounter in discussions of Indian mathematics such assertions as that “the concept of differentiation was understood [in India] from the time of Manjula (... in the 10th century)” [Joseph 1991, 300], or that “we may consider Madhava to have been the founder of mathematical analysis” (Joseph 1991, 293), or that Bhaskara II may claim to be “the precursor of Newton and Leibniz in the discovery of the principle of the differential calculus” (Bag 1979, 294). ... The points of resemblance, particularly between early European calculus and the Keralese work on power series, have even inspired suggestions of a possible transmission of mathematical ideas from the Malabar coast in or after the 15th century to the Latin scholarly world (e.g., in (Bag 1979, 285)). ... It should be borne in mind, however, that such an emphasis on the similarity of Sanskrit (or Malayalam) and Latin mathematics risks diminishing our ability fully to see and comprehend the former. To speak of the Indian “discovery of the principle of the differential calculus” somewhat obscures the fact that Indian techniques for expressing changes in the Sine by means of the Cosine or vice versa, as in the examples we have seen, remained within that specific trigonometric context. The differential “principle” was not generalized to arbitrary functions—in fact, the explicit notion of an arbitrary function, not to mention that of its derivative or an algorithm for taking the derivative, is irrelevant here"
- Bill. I traced down the references and restored the citations to the article. This should provide a starting point for further editing. SteveMcCluskey (talk) 15:43, 9 January 2015 (UTC)
Steve. Thanks, I appreciate the effort and knew that it would be easier for someone else to do. I do have a concern about these and other lengthy quotations in the footnotes of this article. It appears to me that some kind of debate (or perhaps just one side of one) is being carried out in the footnotes. I understand that there is some controversy here with some probably overzealous comments made and quoted and then countered by other quotes, and I don't mean to shy away from reporting on such controversy; but I wonder whether this is the appropriate article to do this in and whether or not the "footnote wars" are the right way to handle it. Bill Cherowitzo (talk) 18:22, 9 January 2015 (UTC)
- You're welcome. I agree that the footnote wars do present too many lengthy quotations. When they were added they were probably felt necessary to counter claims by Indian nationalist historians. I suggest trimming the quotation from Bressoud's citation, which is almost a tertiary source. Plofker's comment represents the most recent serious historical study so I'd keep it. The quotation from Katz is excessively long and jumps between Islam and India so really isn't on target for this discussion. I like Pingree's as an analysis by a distiguished scholar, rejecting claims for Indian calculus in the context of a discussion that Asian mathematics was not adequately appreciated by "Hellenophilic" historians. I'll strip the quotations from Bressoud and Katz and leave the remainder. SteveMcCluskey (talk) 20:23, 9 January 2015 (UTC)
start date of indian mathematics per boyer's page 208
it says in the wiki text that history of indian mathematics starts around 2600-1900BC, however the cited source (p 208 boyer edition 1) states:
"Chronology in ancient cultures of the Far East is scarcely reliable when orthodox Hindu tradition boasts of important astronomical work more than 2,000,000 years ago and when calculation leads to billions of days from the beginning of the life of Brahman to about A.D. 400. References to arithmetic and geometric series in Vedic literature that purport to go back to 2000 B.C. may be more reliable, but there are no contemporary documents from India to confirm this".
thus i'm wondering if even the dates 2600BC-1900BC are inappropriate? given that the edit i had to revert tried to extend this from 3000 BC, and the cited text says 2000 BC, i'm having a hard time understanding why it's 2600 BC to 1900 BC.
Boyer does not present any evidence for "All of these results are present in Babylonian mathematics, indicating Mesopotamian influence" and "showing strong Hellenistic influence". He may be correct that these results were there earlier, but "influence" is speculation. Evidence in the form of direct or indirect contact between the Indians, Babylonians and Greeks is lacking. Including material like this is giving undue weight to a badly written source.