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- 1 Incorrect Algorithm
- 2 Reverted to more accepted statement
- 3 "the fully symbolic algebra that al-Khwarizmi would develop much later."
- 4 rewrite
- 5 Contradiction
- 6 "Diophantus got the first knowledge of algebra from India"
- 7 Dating of the 'Dark Ages'
- 8 Vandalism
- 9 Optimization
- 10 General methods
- 11 Misuse of sources
- 12 Epitaph
- 13 diophantus and khwarizmi
The page says:
The answer is determined from two methods: 1. Finding the common multiple of 12, 6, and 7 (which is 84). 2. Taking 14 (the age up to which would be considered a boy; one-sixth of his life) multiplied by 6, which equals 84.
The first method doesn't seem to make sense. It doesn't include, for instance, the information that he died four years before his son, which affects the answer.
The second method relies on knowledge that 14 is an important age in Hellenistic cultures, which isn't necessary.
The reference correctly shows how this problem is solved.
Reverted to more accepted statement
The documentary sources cited in this article refer to Diophantus as an ancient Greek Mathemetician. Alledging he was of Babylonian birth or not Greek is not supported.
"the fully symbolic algebra that al-Khwarizmi would develop much later."
This is not true, al-Khwarizmi's algebra was fully rhetorical, even the numbers were spelled out! I have inserted a direct quote from "A history of mathematics" by Carl B Boyer into the article (with reference) and have removed the factually incorrect statement. self 06:10, 16 October 2006 (UTC)
I am working on a major rewrite of the article. I would like to ask people not to make (large) edits in the next couple of days as it could conflict with my rewrite. Thank you. S Sepp 23:04, 10 January 2007 (UTC)
- Rewrite complete. S Sepp 22:50, 11 January 2007 (UTC)
Diophantus and the Arithmetica were lost in Europe for about 1500 year, says the article. Then it later says, Byzantine mathematician Maximus Planudes has written "Thy soul, Diophantus, be with Satan because of the difficulty of your theorems". So which is it? How would the medieval Planudes know about Diophantus' theories if they were lost in Europe? —The preceding unsigned comment was added by Rwflammang (talk • contribs) 19:33, 24 January 2007 (UTC).
"Diophantus got the first knowledge of algebra from India"
- "According to some historians of mathematics, like Florian Cajori, Diophantus got the first knowledge of algebra from India"
has three references to it. One of the references says nothing of the sort and so I have removed it as a reference. Furthermore the reference that I have removed,
- "Heeffer, Albrecht, The Reception of Ancient Indian Mathematics by Western Historians, Ghent University, Belgium."
explicitly says on page 16 that,
- "The origin of the algebra of Diophantus still needs an explanation, but it is very doubtful that it is to be found in Pythagoras."
So one of the references for the statement that says that Diophantus' algebra came from India actually says that the origin is unknown! So I am adding the sentence "although other historians disagree." and using the above scholarly paper as a reference.
I will try to confirm the other two references. It would be appreciated if the user who added those two references would write the relevant direct quotations from those sources. _selfworm_ ( Give me a piece of your mind · Userboxes · Contribs )_ 04:32, 12 March 2007 (UTC)
The other two references are also inaccurate. The reference "Notes on Indian Mathematics. A Criticism of George Rusby Kaye's Interpretation" does not even mention Diophantus (this work can be read at JSTOR). And the only sentence in the second reference, "Florian Cajori, A History of Elementary Mathematics, 1898", that makes any mention of Diophantus and Indian mathematics is the following:
Frequently he follows a method resembling somewhat the Hindu "false position"; a preliminary value is [...] (page 36)
But this is a far cry from "Diophantus got the first knowledge of algebra from India". Indeed, this sentence does not make any mention, implicitly or explicitly, of any transmission of information. So, the alleged sources for this assertion do not support the assertion (and in the first case above, it actually goes against the assertion). selfwormTalk) 23:06, 19 September 2007 (UTC)
Furthermore, this information is almost certainly false. The Mesopotamians and Egyptians had Algebra long before the Indians, and due to the proximity of Greece to Mesopotamia and Egypt, and its remoteness to India, Greece most likely got its Algebra from Mesopotamia and/or Egypt (which is currently the most popular theory).
Also, seeing as how little is known about Diophantus and the origin of his work, I have trouble believing that a line of transmission from India to Greece could be established. And I have never read anywhere (except for Wikipedia) that Diophantus got his Algebra from India. selfwormTalk) 23:13, 19 September 2007 (UTC)
- Selfworm, I agree with your assessment and I took out the shoddy passage. Cajori's book is available online, and consulting the index & searching through show that he does not make the claim the article ascribes to him. Moreover, Heeffer's article, while it does deal with speculation about Indian origins, significantly finds that all such speculation derives from Wallis 1685, which no one would confuse with a work of scientific history! Wareh 00:17, 20 September 2007 (UTC)
Dating of the 'Dark Ages'
'After Diophantus's death, the Dark Ages began...'
The Dark Ages began in 298? And really, isn't the phrase 'Dark Ages' just a little bit out-dated? Someone should come up with a good paragraph that captures the intent of the passage (viz. that Diophantus' popularity waned for a while after the fall of the western Roman Empire) but that doesn't use such a simplistic phrase (or at least fixes its beginning in 476 or something). Cal 18:11, 4 October 2007 (UTC)
- In what sense is the usage "Dark Ages" dated? The intent, is clear -- a rejection of pagan pre-scientific influences on intellectual culture without any novel production of their own by early medieval Europeans. You are right in that the date is not strictly correct since Pagan influence continued until the early 6th century CE, however, the beginnings of the rejectionism of pagan influences would have started around this time. So some sort of language like "precursors to the Dark Ages" might be more accurate. Qed (talk) 23:55, 31 March 2012 (UTC)
Looks like there has been a fair amount of vandalism in the past couple of weeks that is not getting reverted. I am not a regular contributor here but, to those who are, you might want to think about protecting the page.
Methods for solving algebra-esque problems til the time of Descartes rely on optimization. The integer solutions are arrived at by trial-and-error at first and were later (some of them) able to be abstractly encoded, especially in the modern era as algebraic rings, cycles, permutative matrices, modularity, etc.
Still proofs in this area require methods common in optimization theory - especially in Diophantine's own time prior to more abstract formulaic methods - as are ubiquitous in any field dealing with local-global ranges variation.--Euanthes (talk) 20:18, 4 March 2010 (UTC)
- What? What about Muḥammad ibn Mūsā al-Khwārizmī and his "Compendium on Calculating by Completion and Reduction"? He describes the basic algebraic method, long before Descartes ever encountered it. Qed (talk) 23:49, 31 March 2012 (UTC)
- It should be mentioned here that Diophantus never used general methods in his solutions. Hermann Hankel, renowned German mathematician made the following remark regarding Diophantus.
“Our author (Diophantos) not the slightest trace of a general, comprehensive method is discernible; each problem calls for some special method which refuses to work even for the most closely related problems. For this reason it is difficult for the modern scholar to solve the 101st problem even after having studied 100 of Diophantos’s solutions
and the ref (at least I think its the ref: I rescued it from a version ages back) is Hankel H., “Geschichte der mathematic im altertum und mittelalter, Leipzig, 1874. (translated to English by Ulrich Lirecht in Chinese Mathematics in the thirteenth century, Dover publications, New York, 1973. If no-one has said this since 184, it is unlikely to be very true. Etc William M. Connolley (talk) 11:44, 20 February 2011 (UTC)
Misuse of sources
This article has been edited by a user who is known to have misused sources to unduly promote certain views (see WP:Jagged 85 cleanup). Examination of the sources used by this editor often reveals that the sources have been selectively interpreted or blatantly misrepresented, going beyond any reasonable interpretation of the authors' intent.
A script has been used to generate the following summary. Each item is a diff showing the result of several consecutive edits to the article by Jagged 85, in chronological order.
- The only edits of significance that Jagged made to this article were regarding Diophantus' ethnicity, namely, to prove that he wasn't "Greek", and nothing more. As the page history shows, this was something of an obsession. Of the sources he used, 3 were from the 19th and early 20th century and hence quite old, and the only recent source didn't have a page number. Given this user's history of falsifying sources, I am removing the claims on ethnicity, as was similarly done by another user for Heron of Alexandria. Athenean (talk) 17:44, 3 May 2011 (UTC)
- For reference the Greek epitaph by Metrodotus is here: http://archive.org/stream/greekanthology05newyuoft#page/92/mode/2up, problem 126. I will remove the Latin and hopefully someone who can write Greek will replace it. 188.8.131.52 (talk) 18:01, 15 August 2012 (UTC)
diophantus and khwarizmi
The recent addition comparing Diophantus and Khwarizmi could potentially be valuable but http://www.crystalinks.com/diophantus.html is a blog page and therefore is not a reliable source. Tkuvho (talk) 12:30, 18 November 2014 (UTC)