Talk:Mathematics in the medieval Islamic world/Archive 1

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Archive 1

Archive 2

i didnt know half this stuff —Preceding unsigned comment added by Decora (talk • contribs) 02:43, 29 January 2009 (UTC)

The religion of Islam does not include math, there is no connection. Mathematicians who were living in regions where Islam was the dominant religion , does not imply that they were Islamic mathematicians . The term makes no sense , but is rather used in some sort of vain attempt at associating the glory of the accomplishments of mathematicians and scientists with the religion of Islam. The fact of studying the Qu'ran makes no impact on one's mathematic ability. The same goes for any other association of a faith with a scientific field. Thus editors who are going around weaving terms like Islamic mathematicians are using Wikipedia as a soap box.--CltFn 06:07, 28 April 2006 (UTC)

Talk on talk pages to gain consensus before moving. Add an NPOV if you are worried about these issues... you may be right but you need to discuss. Here's my problem. If anything is "good" you say it's not Islamic based and if it's "bad" like the invasion of Iberia you say it is Islamic. This is just adding systemic bias to Wikipedia because you don't have a coherent system for when to include religion as an influence... and when to not. We will get some discussion here before this is moved again and we will get discussion about how this should be dealt with over the whole gamut of articles. Thank you. gren グレン 07:31, 28 April 2006 (UTC)

I oppose the move. See also Talk:Islamic science. --Striver 10:26, 28 April 2006 (UTC)

I oppose the move as well. Islamic mathematics is a well-defined term to historians of mathematics with a precise meaning. It's pretty clear tha CtlFn again has no idea what he is talking about. If you don't like the name of this term, so be it, but don't start using Wikipedia as a soap box yourself. —Ruud 13:23, 28 April 2006 (UTC)

Islamic mathematics and Arabic mathematics are modern historical terms for the mathematical sciences in Islamic civilization from the beginning of Islam (A.D. 622) until the 17th century. Although most of the mathematicians in this period of Islamic civilization were Muslims, some prominent mathematicians had other religious backgrounds (Christian, Jewish, Zoroastrian). Arabic was the main scientific language but not necessarily the native language of a mathematician, who might have been Persian, Turkish, etc. (Definition by Prof. J. P. Hogendijk)

This is a discussion we really need to have. I completely oppose CltFn's arbitrary moves and changes on things he does not need acceptable but this does not make him wrong. What we need to discuss is "is there an Islamic mathematics?" Who uses that phrase? How is it used between different parties? Do Muslims uses it to glorify Islam while secular scholars use it as a term of convenience? If so we cannot conflate those differences as the same. Is attributing these mathematics to the Arabs any different than making it Islamic mathematics? Is it just changing it from a religious pride issue to an ethnic pride issue? What do mathematics historians call this? Personally I don't know what the title of this article will be but I'm pretty sure we'll need to have a section describing the fact that Islamic mathematics is a term in use but so is Arab mathematics. It is not one or the other and the supporters of each term have their biases. Arab nationalists want to glorify the Arabs while "Islamic nationalists" (for lack of a better term) want to use this to glorify Islam. We need to recognize that this is not a straightforward discussion of one is true the other isn't. Both have merit and both are propaganda. We could go for "Mathematics arising from the Middle East" however that is not a term commonly used and would therefore be hard to justify its usage. Let's have a serious discussion and not let this get into reverting before we have done that. gren グレン 18:51, 28 April 2006 (UTC)

Historians of mathematics use the terms Arabic mathematics or Islamic mathematics. I don't know who coined these terms, but I think it is far more likely that they were invented by ignorant Westerners than nationalistic Arabs or Muslims. This article should clearly mention that not all mathematicians that fall under this category were Arabs or even Muslims, but it is definitly not Wikipedia's task to "correct" unfortunatly chosen terminology. —Ruud 19:09, 30 April 2006 (UTC)

invented by ignorant Westerners ? Sounds a bit strong for a guess--CltFn 02:02, 15 May 2006 (UTC)

Ruud / R. Koot, you removed {{accuracy}}. I have re-added it in the sense of making it totally disputed. I am doing this because I think CltFn would make the point that we don't have proof that these mathematicians were Muslim. Therefore what you have would be inaccurate. I don't want to debate this as a fact or whatnot but please do me the favor of not removing this. I will make sure this doesn't digress into a revert war but in order to do that we must address the argument of CltFn which is by no means unfounded. Therefore please do not remove those tags and let us discuss it first. As we come to a decision we can remove the tags. Revert warring will not be tolerated though for anyone here. If you start reverting without involving yourself in the discussion you should probably receive a short block. gren グレン 18:51, 28 April 2006 (UTC)

I removed the {{accuracy}} tag as the reference I added made it clear that there are no factual accuracy problems with the current article, and that adding two tags was just CtlFn trying to make a WP:POINT. I don't understand your reasoning ("[...] that we don't have proof that these mathematicians were Muslim") though, as the article states that Islamic mathematics refers to mathematics "including Arab and Persian mathematicians, as well as other Muslims and non-Muslims"? —Ruud 19:16, 30 April 2006 (UTC)

It seems that the debate involving the {{TotallyDisputed}} tag centers around whether Islam was influential in the development of mathematics. This is silly.

The connection between religion and mathematics is well-known in the history of mathematics. The followers of Pythagoras held the religio-spiritual belief that everything was number. Religious aspects of the theory of number appear in the Theaetetus and the Timaeus of Plato. Even as late as in the 17th century, Leibniz would have said that the invention of calculus was a vehicle for peering into the mind of God.

Even in the early 20th century, Western mathematics has been highly influenced by Western philosophical thought, and philosophical thought does and should include religion. Only after the separation of logic into its own category (apart from mainstream mathematics) in the middle of the 20th century did the connection between Western mathematics and Western philosophy cease entirely.

Now, I am not an expert in medieval mathematics, but I am quite knowledgeable about the philosophy of mathematics. The suggestion that Islamic thought had nothing to do with the development of medieval mathematics seems highly improbable to me, and I believe that the {{TotallyDisputed}} tag should be removed. --Wzhao553 08:15, 11 May 2006 (UTC)

Agree, the NPOV concerns were easily debunked and I have already adressed the factual accuracy concerns. No one has voiced any concerns since. —Ruud 00:59, 15 May 2006 (UTC)

There is no connection between religion and mathematics that I can see, by the way what exactly is Islamic thought and what does it have to do with Mathematics. This seems to be obvious to you , so , how about explaining this to other wikipedia editors who may not be see the connection. .--CltFn 01:51, 15 May 2006 (UTC)

Agree that religion and mathematics are subsets of philosophy, but it is wrong that religion is the mother of mathematics. They may both derive from the same sense of awe and religiosity, but to say that the teachings specific to one form of religion give rise to mathematics is silly. As someone who has studied Islam, knows the language, and is fully familiar with the Hadith and the teachings of the various schools of jurisprudence, I can say that nowhere did I ever see in any of the teachings anything remotely concerned with mathematics. If you can point to something in the haditha or the Quran that might suggest otherwise, it would be a great addition to the article. But I am certain no such connection exists. The only connection is the consanguineity between the spiritual need to understand the world and the expression of that understanding in either mathematical terms or in the folk mythologies of religion. Those who are drawn to one tend also to be drawn to the other, but in no way does learning about angry Abrahamic Gods inspire mathematical revelations.

This idea of "Islamic mathematics" completely ignores and downplays the contributions of pre-Islamic thinkers in India, Babylon, Egypt and other places whose insights were essential for later "Islamic" thinkers to draw their insights. In other words, the people who gave us mathematical insights would have likely done so if the dominant religion were Zoroastrianism or Christianity.

If anything, what Islam provided was not a religion, but a stable government with fixed laws that allowed for trade, economic growth, and division of labor. It was this that allowed a larger number of people to specialize in mathematics and contribute their talents rather than laboring in fields. So if Islam contributed to mathematics, it was only tangentially.KartoumHero (talk) 19:21, 30 October 2009 (UTC)

I would like to open a discusion about renaming this article to Middle-Eastern mathematics as Mathematics has nothing to do with Islam or Judaism or Buddhism or Christianity or any religion , unless that religion provides mathematical principles and datums that would justify such an association. --CltFn 02:16, 15 May 2006 (UTC)

But religion and mathematics are heavily intertwined. Mathematics provided a religious and spiritual world-view for the Pythagoreans. Logical and "mathematical" proofs of the existence of God have been attempted by Anselm, Descartes, Leibniz, Spinoza and many others. Then there's Kronecker's famous quote that "God made the whole numbers; the rest is the work of man." Even proponents of intelligent design have begun to employ probability theory in their arguments against naturalism. Why do you feel that there is no justification for such an association? --Wzhao553 02:31, 15 May 2006 (UTC)

Give me one tenet from Islam that correlates with Mathematics. --CltFn 02:59, 15 May 2006 (UTC)

How about Averroes' attempt to provide mathematical rigor to his theological and metaphysical reasoning by attempting to reconcile Islam with Aristotelian philosophy? --Wzhao553 03:14, 15 May 2006 (UTC)

What tenet from Islam are you referring to? --CltFn 03:24, 15 May 2006 (UTC)

Averroism. --Wzhao553 03:40, 15 May 2006 (UTC)

Yes I see , thanks to this remarkable tenet I can see my math skills increasing already.--CltFn 03:48, 15 May 2006 (UTC)

• Oppose. The term "Middle-Eastern mathematics" is a neologism, while the term "Islamic mathemtics" is as well-established in the history of mathematics as "Renaissance" is in the history of Europe. —Ruud 02:34, 15 May 2006 (UTC)

No need to vote , this is not a vote but a discussion --CltFn 02:57, 15 May 2006 (UTC)

Where did I vote? —Ruud 02:59, 15 May 2006 (UTC)

• Don't rename this. "Islamic mathematics" gets plenty of Google hits; "Middle-Eastern mathematics" only a few, most of which refer to something entirely different. --Lambiam^Talk 08:21, 15 May 2006 (UTC)

The term "Middle-Eastern mathematics" would be incorrect due to several reasons. Islamic mathematicians not only lived in the Middle East, they also lived in Central Asia, North Africa, Spain and India. Mathematics has also been studied in the Middle East since the days of the Egyptians and Babylonians (which already have their own articles), and continued in the days of the Chaldeans, Persians, Greeks, Romans, Syrians, Arabs and Turks. This article refers broadly to the mathematics of the Islamic-dominated cultures, and not just the religion of Islam, in the same way "Greek mathematics" refers braodly to the mathematics of the Hellenistic cultures, and not just the Greek people. Jagged 04:16, 25 May 2006 (UTC)

CltFn re-added the {{Totally disputed}} tag on 2006 May 15 03:01, with edit summary: the dispute is all over the talk page and was mentioned in my comment when I inserted the tag the first time. But as far as I can see, all issues have satisfactorily been dealt with since. What else is left? CltFn should be more specific, especially in light of the fact that the tag was removed by another editor in good standing. --Lambiam^Talk 08:30, 15 May 2006 (UTC)

This bit seems to have an obvious typo:

Al-Haytham (b. 965), also known as Alhazen, in his work on number theory, seems to have been the first to attempt to classify all even perfect numbers (numbers equal to the sum of their proper divisors) as those of the form ${\displaystyle \ 2^{k}-1(2^{k}-1)}$ where ${\displaystyle \ 2^{k}-1}$ is prime.

since ${\displaystyle 2^{k}-1(2^{k}-1)}$ is always 1. I can think of a few things that the author might've meant to write, but I don't know the subject well enough to correct it myself. Staecker 12:00, 15 May 2006 (UTC)

I've corrected the formula, which now reads: ${\displaystyle \ 2^{k-1}(2^{k}-1)}$. --Lambiam^Talk 14:14, 15 May 2006 (UTC)

Supposedly Al-Batanni (868-929) produced the relationship tanx = sinx/cosx

However, it says later that Abu'l-Wáfa (940-998) invented the tangent function.

I dont see how you could get a relationship for the tangent function before the tangent function was invented. Harley peters 17:04, 28 September 2006 (UTC)

Between the two titles "Islamic mathematics" and "Arabic mathematics", the first one is much less misleading. The overwhelming majority of those mathematicians were muslim (at least in name), while only a small minority of them were Arab. I should also remind that the previous move to "Arabic mathematics" (in March 10) wasn't based on any concensus. this page should either move back to "Islamic mathematics" or to "Mathematics in Medieval Muslim World" (which I think is much more accurate). Jahangard 17:57, 17 April 2007 (UTC)

Arabic mathematics and Islamic mathematics are the only two terms used by historians mathematics and therefore the only acceptable titles. Both are misleading as the mathematicians it concerns where neither all Arabs not all Muslim. The term Islamic mathematics has recently been gaining more prominence:

Although many able authors have contributed valuable articles, the work as a whole is flawed, to such an extent that one hesitates to recommend it as a general reference on the subject for non-specialists. The flaws are of an editorial nature, and the first is the title chosen for the work. It is no disservice to Arabs (modern or medieval) to point-out that non-Arabs (principally Persians and Turks) also played important roles in the development of medieval Islamic science, and these roles should be acknowledged in the choice of title. "Islamic" is a very serviceable epithet and should have been used, rather than "Arabic," to describe the science being studied. — J. L. Berggren on Roshdi Rashed's Encyclopedia of the History of Arabic Science. (Journal of the American Oriental Society, Vol. 120, No. 2. (Apr. - Jun., 2000), pp. 282-283.)

but on the other hand seems to attract a lot of frustrated people which believe the name implies a closer connection to Islam than it does in reality (see posts above.) —Ruud 18:57, 17 April 2007 (UTC)

Usually, shorter names and phrases are more common than the longers. However, for controversial names, avoiding the ambiguity and the controversy is much more important than other criteria. Therefore, "Mathematics in Medieval Muslim World" is a much better title compared to the other two. Also, between "Islamic mathematics" and "Arabic mathematics", although both of them can be misleading, the second one is much more misleading, because the overwhelming majority of those mathematicians were not Arab. Anyway, it's better to see the opinion of other wikipedians. Jahangard 22:54, 17 April 2007 (UTC)

How about Arabic and Islamic mathematics thats the title used for this period in History of mathematics. It neatly escapes the conflict and is an acurate description. --Salix alba (talk) 15:39, 22 April 2007 (UTC)

It still has the problems that I mentioned (e.g. ambiguity). Mathematics in medieval Islamic world is the exact description of the topic. I think, Also, titles such as "Medieval Islamic Mathematics" or "Mathematics of Medieval Islam" are fine (the first one is consistent with "Medieval European Mathematics" and the second one is already used in the title of a relevant book). Jahangard 03:46, 23 April 2007 (UTC)

Survey for the requested move

Arabic mathematics → Mathematics in Medieval Muslim World — That's what this page is about. For the detail of the discussion see above. Jahangard 23:07, 17 April 2007 (UTC)

Add  * '''Support'''  or  * '''Oppose'''  on a new line in the appropriate section followed by a brief explanation, then sign your opinion using ~~~~. Please remember that this survey is not a vote, and please provide an explanation for your recommendation.

Survey - in support of the move

• Support per previous discussion. Jahangard 23:07, 17 April 2007 (UTC)
• Reluctant Support The page should be moved from Arabic mathematics (most of these people are not Arab), but I'd still prefer the old title Islamic mathematics. --Mardavich 23:14, 17 April 2007 (UTC)
  • I believe this is a misunderstanding of the meaning of the word "arabic", which refers to language. If it were referring to Arabs, the correct term would be "Arabian mathematics" or "Arab mathematics". In any case, I believe some cool reflection is needed here, and comment further below.
• Support, Islamic mathemaathics is more appropriate. Islamic mathemaathics is also consistent with related WP articls such as Islamic science, Islamic medicine, Islamic astronomy,Islamic astrology ...(Arash the Archer 02:07, 18 April 2007 (UTC))
• Support The page should be movd to Islamic Mathematics, since most of the people here are not Arabic--Pam55 01:47, 19 April 2007 (UTC)
• Support Far less POV title, and is far more accurate. It should be titled Mathematics in Medieval Muslim World. Also note that many of the other articles are open to discussion about being moved as well.--Sefringle 01:51, 15 May 2007 (UTC)
• Support: "Arabic Mathematics" would limit the Mathematics researches to the Arab world, while "Mathematics In Medieval Muslim World" will reflect all the works done in all Muslim territories (Arab, Turkish, Persian). -Ariana310 07:24, 19 May 2007 (UTC)
  • Ariana, it seems from your comment that you did not notice the remark I already made a few lines above concerning the distinction between arabic and Arab/Arabian. I do hope you have taken the trouble to read the many interesting discussions on this page (above and below) before expressing your opinion. Geometry guy 14:33, 19 May 2007 (UTC)

Survey - in opposition to the move

• Veto "Arabic mathematics" and "Islamic mathematics" are the only two terms used to describe this era in the history of mathematics. Wikipedia is not the place to "correct" unfortunately chosen terminology. —Ruud 23:23, 17 April 2007 (UTC)

As I explained before, for ambiguous or controversial names, the popularity of a name is not the main criterion. About the usage, there is already a book with the title Mathematics of Medieval Islam. So, claiming that "Arabic mathematics" and "Islamic mathematics" are the only two terms used to describe this era in the history of mathematics is simply wrong. Jahangard 23:39, 17 April 2007 (UTC)

Anyone who looks hard enough can find exceptions to the rule. Read the comment of the reviewer to see how he names the subject of this book. —Ruud 23:55, 17 April 2007 (UTC)

So what? I've already mentioned that "Islamic mathematics" is more commonly used (mostly because it's a shorter name). I'm saying that 1) For a controversial topic such as this, avoiding the ambiguity is much more important than the usnig the most comon names. (see WP:Name). 2) Terms such as "Mathematics of Medieval Islam" are already used in the related literature, to refer to the topic of this page. Jahangard 00:18, 18 April 2007 (UTC)

It's not a common and accepted usage. —Ruud 00:25, 18 April 2007 (UTC)

As a side note the author of this book is also the author of the article "Arabic mathematics" in Encyclopaedia Britannica. —Ruud 00:34, 18 April 2007 (UTC)

It is not an acceptable usage?!!! That's the title of one of the most important books on this subject. Jahangard 00:55, 18 April 2007 (UTC)

I did not say acceptable, I said accepted. —Ruud 08:19, 18 April 2007 (UTC)

• Rethink required. Now that this issue appears to have cooled down a bit, I think a serious rethink is needed. A month ago, I would not have been in the least bit bothered what this article is called, but since then I have seen the colossal waste of time that can be generated when people attempt to categorize by religion (this is not, I hasten to add, a comment on this discussion). Let me make some remarks.
  1. This article is closely associated with the category Category:Islamic mathematics formally known as Category:Arabic mathematics. I came here because of the current CfD on Category:Jewish mathematicians. One of the arguments used by the Jewish-by-occupation pressure group for the existence of this category is that it is "similar to" Category:Arab mathematicians. The argument is flawed, but it is difficult to counter effectively at the moment, because our own (mathematics) house is not in order. For one thing, Category:Arab mathematicians should probably be renamed, but there is another point...
  2. One of the arguments I would like to employ at the CfD to explain the distinction is that there is no Jewish mathematics (or Category:Jewish mathematics), but there is Arabic mathematics (and Category:Arabic mathematics). Then I click on these links and find myself in an Islamic world. A Jewish editor following these links is hardly going to be impressed.
  3. I do not deny that personal and societal religion has a role to play in scientific and mathematical thought. However, calling this Islamic mathematics is a bit like calling the mathematics of (say) 15th-18th century Europe Christian mathematics. Similarly, although the society was Islamic, I am not convinced that "Mathematics of the Islamic/Medieval Muslim world" is any more helpful a choice of title than "Mathematics of the Christian world" or "Mathematics of the pagan world". It seems to me to be wiser to avoid using religious terms unless there is clear case that religion is central to the description of the topic.
  4. This brings us back to the issue that started this debate: Arabic mathematics is misleading because "The overwhelming majority of those mathematicians were muslim (at least in name), while only a small minority of them were Arab." I sympathise with this point of view, and agree that the established term "Arabic mathematics" is not ideal — however, this concern is actually a misunderstanding of the meaning of the word arabic. The OED defines it to mean "the semitic language of the Arabs" and "of or relating to Arabia (especially with regard to language and culture)". The noun and adjective referring to people is Arabian or simply Arab.

In other words, Arabic mathematics does not refer to Arabs at all, it refers to the indisputable fact that this mathematics was written in Arabic! It was the lingua franca of the time. I understand that many readers (especially non-native English speakers) may miss this point, but the solution is simple: spell out the meaning of the name in the introduction to the article. Please think on it. Geometry guy 12:10, 16 May 2007 (UTC)

You have observed the difference between "Arabic" and "Arab" (or "Arabian"). You should also look at the difference between "Islamic" and "Muslim". This page is not directly about religoius background. This page (and the corresponding category) is about the mathematics of a historical civilization which is called "Islamic civilization", or more precisely "Medieval Islamic civilization" (not "Arabic civilization"). That's why most of the recent works on this subject use "Islamic Mathematics" or "Medieval Islamic Mathematics" or similar terms. To avoid the ambiguity, I had proposed a title such as "medieval Islamic mathematics" (or "Mathematics in medieval Islamic world"). Based on the discussion in this page (and the survey), I moved the page to "Medieval Islamic Mathematics". However, later, the page was moved to "Islamic mathematics", without furthur discussions on the talk page. I should also note that until now, the mathematic pages, are categorized based on nationality (for modern era), ethnicity, or the culture (civilization), not the language. We don't refer to Indian mathematics as "sanskrit mathematics". The same is true for medieval European mathematics which is not called "Latin mathematics" (sometimes the language and the historical culture have the same word, like "Greek civilization"). A title such as "Medieval Islamic mathematics" avoids any ambiguity. It clearly shows the relation to the well-defined term "Medieval Islamic civilization", and after all, this page is about mathematics in that civilization. I should also note that one of the best recent works on this subject have used "Mathematics of Medieval Islam" as the title. About other pages, if it is related to a certain civilization and culture, we can have a page (and a correponding category). For example, if there are sufficient resources on "Mathematics in ancient Jewish civilization", we can have a page on "ancient Jewish mathematics" (related to a certain civilization, not just the religious background of the mathematicians). Jahangard 14:51, 16 May 2007 (UTC)

This difference was not noted before and is the main justification given for support votes in the survey, so I think it needs to be considered.

About the main justification of the previous discussion, I had mentioned that both "Arabic mathematics" and "Islamic mathematics" acn be ambiguous (the first one might be confused with Arabian ethnicity and the second one might be confused with the muslim religious background, rather than the relation to "Islamic civilization"). I explained that the first ambiguity is much more misleading than the second ambiguity (because, after all, the overwhelming majority of those matematicians were muslim, while only a minority of them were Arab). However, I argued that it's much better to have a title which not ambigious (that's why I proposed the move to "Mathematics in Medieval Islamic World" or "Medieval Islamic mathematics"). Also, I agree that we need to think more about the title (we probably need to have another survey, because in the previous survey, the choice between "Medieval Islamic mathematics" and "Islamic Mathematics" is not clear).

Yes you did, and now you are saying it again. I disagree with your assertion about levels of ambiguity, and your justification in terms of numbers, but I have more-or-less said that already too. Anyway, concerning the point of agreement, there appears to be a useful discussion starting at the WikiProject. Geometry guy 18:33, 16 May 2007 (UTC)

Anyway, I followed your suggestion: Islamic is both a redirect here, and a derived adjective in the dictionary, which gives two meanings for Islam: the religion of the Muslims, and the Muslim world. It defines Muslims as followers of this religion, and Muslim (adj.) means "of the Muslims or their religion". This didn't reassure me much. I also don't find it helpful to bring the article's history into the discussion.

As for the more substantive points, I didn't quite get the relevance of sanskrit etc., as the term "Arabic mathematics" clearly is commonly used, along with "Arabic culture" and and "Arabic literature". I admit my final paragraph oversimplified the issue by saying that "Arabic" refers to the language (it does, but not only) — I did this to emphasise that it is not used to refer to the people. I did appreciate the nuances you articulate concerning "Islamic civilization", but ask you (and others) again to think on it. I will too. Geometry guy 16:08, 16 May 2007 (UTC)

My main point was that categorizing mathematics based on the language is not very common. Also, there are some practical problems. The fact is that although most of those mathematical works (in the Medieval Islamic world) are written in Arabic, some Medieval Islamic mathematicians have works in other languages (specially Persian). For example, Jamshid Kashani has written in both Arabic and Persian. In doesn't make sense to separate these works just based on the language. The same thing can be applied in our time. There are many 20-century mathematicians who have written both in French and English languages (or both German and English), and it does not make sense to gategorize their work based on the language, however it still makes sense to categorize works in certain branches of mathematics, based on the school of thought, which is indirectly related to the country or the academic institutes (for example "French school of algebraic geometry" which was heavily influenced by works of Serre and Grothendieck). Jahangard 17:11, 16 May 2007 (UTC)

You misunderstand/misrepresent my comments here. Who is talking about categorizing by language? Not me, and I thought I had clarified. Slicing up mathematics/mathematicians by language is indeed a stupid idea. Anyway, there are enough categorizations: I hope there is not going to be Category:Mathematics/Mathematicians by civilization either!

"Arabic", like "Greek", is a word with nuances covering language, literature and culture. It is just one way to describe the mathematical culture of that era. Islamic and/or Muslim is another way. The mathematicians weren't all Muslim, and they did not all write in Arabic all the time, so what can we do? Reflect on it, and hope consensus finds a good solution. Geometry guy 18:33, 16 May 2007 (UTC)

Yes, Arabic can also refer to a culture, literature, ... . However, this page is about mathematics in a historical civilization/culture which is called "Islamic civilization" or more precisely "Medieval Islamic civilization". Nowadays, nobody call that culture/civilization "Arabic civilization" (In 19-century or early 20-century European texts you may find this term synonymous with "Islamic civilization", but, in recent years this special usage of the term is obsolete and "Arabic culture", or "medieval Arabic culture" may only refer to a sub-category of "Medieval Islamic culture/civilization" not the whole civilization). I still prefer "Medieval Islamic mathematics" because it avoids possible ambiguity. Jahangard 20:53, 16 May 2007 (UTC)

You make several strong assertions here without justifying them, and I have found plenty of material on this page (including some quoted sources) which disagrees with them. Furthermore, I am not so old, and have always heard of the mathematics and mathematicians that gave us algebra and algorithms referred to as arabic. This mathematics did indeed take place in an Islamic civilization, but that does not mean it is necessarily the most sensible name for the category. Finally Wikipedia does not innovate: when you say in recent years this suggests a movement towards replacing terms like arabic by more politically correct (? I am not sure if that is the right phrase, or a fair comment) terms like Islamic. I have nothing against such a trend, but it is not the job of Wikipedia to advance it. This is what policies like NOR and NPOV are intended to avoid. Geometry guy 14:29, 19 May 2007 (UTC)

Discussion by approval?

Jahangard has suggested in the above discussion that

...we need to think more about the title (we probably need to have another survey, because in the previous survey, the choice between "Medieval Islamic mathematics" and "Islamic Mathematics" is not clear).

It will be clear from my contributions here that I share this view. Can I suggest, however, that it might be more productive to have a discussion by nomination and approval, rather than the more adversarial support/oppose approach? In this procedure, editors can nominate possible titles for this article which other editors can support or comment on. Anyone can nominate as many titles as they like, and everyone can support as many options as they wish, in the spirit of approval voting, although as usual, it would not be helpful to call it a vote. This approach might help to generate and refine solutions to the naming problem which has been occupying editors here for so long. Geometry guy 14:51, 19 May 2007 (UTC)

I would suggest summarizing the pros and cons of each title, in an as neutral way as possible, between the nomination and voting phase. —Ruud 23:51, 19 May 2007 (UTC)

I had in mind a more interactive approach. Obviously the nominator would discuss the pros (and if they are truly wikipedian, also some of the cons), but further pros and cons could be added by other users. One reason for this approach is that new ideas for titles could be generated during the process. Also, I emphasise, it is rarely a good idea to have a vote in wikipedia: it is the weight of argument, not the weight of numbers that really matters when trying to find consensus. Geometry guy 00:00, 20 May 2007 (UTC)

In the list of mathematicians in this article we should just bring the lead statement of the coresponding main article without any change or discussion. Ibn al-Haytham article indicates that he was born in Basra which is now currently in Iraq but it doesn't say he was Iraqi. If anyone doesn't agree with this please take it to the main article of Ibn al-Haytham first and if there was a consensus about that we will change here accordingly. (Arash the Archer 00:59, 26 April 2007 (UTC))

Dear Arash,Iraqi does not mean ethnicity Iraq is a country and as long as that person born in that country and have a surname such as Al-Basri then He is Iraqi I did not say he was Arab or Persian I just said he was Iraqi. Arab Iraqi or Persian Iraqi is another issue. Also saying Many/Most of the important mathematicians were Persians is considered POV because some of them their ethnicity is not clear or controversial, also who is going to decide who was important and who wasn’t?!. I can also say many of them were Arabs since at least 40% of them were definitely Arabs. If you still disagree please let me know so we can discuss the issue until we agree:).Thanks--Aziz1005 20:53, 26 April 2007 (UTC)

As I told you before this is not the place to discuss if he was Iraqi or not. There are very good reasons why we can not say he was Iraqi(the main one is that Iraq wasn't a country until 20th century) You should go to Talk:Ibn_al-Haytham if you want to discuss it. In this article we should just bring the lead of Ibn al-Haytham main article.Cheers! (Arash the Archer 21:10, 26 April 2007 (UTC))

Iraq is a country even before the 20th century and it's mentioned in many historical books. Anyway, if you still want to remove the word Iraqi from here as far as it is not mentioned in the main article that could be understood because as you said if there is an issue about that man we should discuss it there, I’ll do a research about Ibn Alhaytham then I can discuss the changes there. However the other sentence (Many/Most of the important mathematicians were Persians is considered) is still POV therefore I still disagree with reverting it back to the article.Salam--Aziz1005 23:20, 26 April 2007 (UTC)

You agreed to delete the word Iraqi according to the Ibn al-Haytham main article, so why do keep adding it? Regarding the other sentence it is no doubt that Many of the most important mathematicians were Persians. It is also not POV to put it in the article since most of people do differentiate between Arabs and Persians and this sentence it illuminative.(Arash the Archer 21:14, 28 April 2007 (UTC))

I reverted just because others who did not want to discuss the issue reverted my edit. Also because you did not respond!=p. I wrote Muslim instead of Iraqi, since the main article hasn't changed. The other sentence is pov because Now the title is Islamic mathematics not Arabic so there is no need to mention that sentence since most of those scientists were Muslims and it's not our job to count how many of them were Persians, Tajiks, Arabs or Turks, therefore it is still considered pov. What do you think?--Aziz1005 00:15, 29 April 2007 (UTC)

Ok, Let me take another look at the article to see if I can replace is with a more NPOV statement.(Arash the Archer 17:31, 29 April 2007 (UTC))

I'm going to rewrite the biographies section to be more concise, in chronological order and based on the lists from Hogendijk and MacTutor. —Ruud 06:14, 30 April 2007 (UTC)

Making the biographies more concise is a good idea. However, I don't think that relating them to modern countries (such as Uzbekistan, Iran, Irak, ...) is meaningful. Instead of that, their ethnicity (Arab, Persian, Turk, ...) should be mentioned. Jahangard 06:29, 30 April 2007 (UTC)

This is the format used by Hogendijk's list and the approximate location where any of the persons on this list seems far more more relevant than the ethnicity people which to ascribe to them. I might change it to a place of birth/death format later, though. —Ruud 06:38, 30 April 2007 (UTC)

I agree with Jahangard, modern countries/nationalities are irrelevant, their ethnicity (Arab, Persian, Turk) should definitely be mentioned, along with city of birth/death (Not modern country).--Mardavich 06:58, 30 April 2007 (UTC)

Could you give some arguments for that, as I don't find this obvious (in fact, I hold the opposite opinion) and have to note that it is quite common to refer to historic geographical areas by their modern name while leaving out any information on the subjects ethnicity. I'd strongly prefer to leave any discussion of the ethnicity of to the full biography, where it can be backed by a number of reliable sources. —Ruud 07:48, 30 April 2007 (UTC)

Well, there was no nationality in the classical times, people were identified by their ethnicities, referring to historic geographical areas as modern countries automatically associates the subjects with that modern nationality, and that's misleading. Since then, the borders have changed and the native populations have migrated and re-migrated many times (someone from Merv or Bukhara would have been an "Iranian" at that time, but not anymore) so Khwarazmi was no Uzbek, Abu al-Wafa was no Iraqi, and Al-Jayyani was no Spaniard. --Mardavich 08:08, 30 April 2007 (UTC)

This page is supposed to be about Mathematics in Medieval Islamic World, not about modern mathematicians with Muslim background (such as L. A. Zadeh). I removed the section about fuzzy mathematics. Jahāngard (talk) 22:22, 5 December 2007 (UTC)

why are we added to the Religion list but not the ethnic group? did not Jews contribute in Islamic Spain? —Preceding unsigned comment added by 74.72.241.66 (talk) 10:16, 14 January 2009 (UTC)

if jew are a ethnic group, does that mean my ethnicity changes when i convert to judaism?86.144.71.206 (talk) 02:50, 23 April 2009 (UTC)

Please note that the post you are responding to is over three months old, and was offered as a one-time edit. Additionally, your post seems tangential and not really in keeping with the idea of article discussion, Wikipedia is not a Monty Python Argument Clinic sketch. - Arcayne (^{cast a spell}) 02:56, 23 April 2009 (UTC)

I have unprotected this page, since it was protected nearly a month ago for edit warring. By the way, everyone should sign posts on talk pages with four tildes. I can't easily tell how long the stuff in the previous section has been there, and usually we look over the talk page before unprotecting articles, so the dates help. CMummert · talk 17:28, 25 May 2007 (UTC)

The section above is being written collaboratively and it would therefore be inappropriate or impossible to sign the comments. —Ruud 20:10, 26 May 2007 (UTC)

It seems CMummert has disappeared or changed their name? -Aquib (talk) 18:51, 16 February 2011 (UTC)

I'm dubious about declaring this clean [1]. RK notes at least one other problem and restores the tag [2]. I think the claim re irrationals was dodgy [3]: what the source actually said was Algebra was a unifying theory which allowed rational numbers, irrational numbers, geometrical magnitudes, etc., to all be treated as "algebraic objects" and this is rather different to Arabic mathematicians were also the first to treat irrational numbers as algebraic objects WMC 21:48, 14 February 2011 (UTC)

I'm beginning to fear that moving most content in the article to a subpage and then selectively moving stuff back in will be a better approach than slowly cleaning up this mess. The real pity is that most statements have some truth at the core, but have been so distorted that any casual reader will be severely misled. —Ruud 14:13, 15 February 2011 (UTC)

It may well be for the best William M. Connolley (talk) 15:54, 15 February 2011 (UTC)

Note: the article in its pre-stub state is available from Talk:Mathematics in medieval Islam/Jagged 85 William M. Connolley (talk) 11:39, 17 February 2011 (UTC)

There is no such thing as Islamic mathematics. What is the point of this article. I don't see how anyone, no matter how politically correct they are, could possibly believe that arithmetic would be different for a Mohammedan than a Christian. 1+1=2 universally. --FDR (talk) 17:26, 31 January 2011 (UTC)

Please read the preceding talk entries answering your question. Just so you know Mohammedan, like Musulmen, is a fairly archaic term Yclept:Berr (talk) 05:31, 16 March 2011 (UTC)

Pjoef (talk · contribs) made many changes to this article, and it is very hard to see what was done. I have attempted to summarize the changes to assist discussion, but now that I have done so I do not think the result is very helpful as it is too complex. Nevertheless, here it is. The early part of the following notes should be accurate, but I lost enthusiasm and might have missed some changes in the later edits.

Pjoef made 45 edits on February 14 and 15, 2011. This permalink shows the state of the article after the last of these edits.

Considering successive edits as a single change, seven changes were made:

diff1

• Insert spaces (two spaces between sentences).
• Place punctuation outside quotes.
• Rearrange citations (splitting to multiple lines).
• Tweak some citations (use "first" field, use "pp", and more).
• Change some page ranges like "pages=60–3" to "pages=60–63".
• Use {{Harv}} to rearrange reference in five places.
• Add links like Aristotle and first visibility of the Moon.
• Incorporate {{quote}} into {{Citation}}.
• Put square brackes around ellipsis, to give [...].
• Move an image (Irakischer Maler von 1287 001.jpg).
• Add {{lang-ar}} and {{lang-lat}}.
• Add {{See also|Algebra}} and {{See also|Arithmetic}} and {{See also|Geometry}}.
• Put "See also" in alphabetical order in two columns.
• Move "Biographies" section.
• In "External links", add {{Refbegin}} and {{Refend}}.
• Add the underlined text in: "development of mathematics, including the early Islamic mathematics".
• Add reference for "MacTutor": Arabic Mathematics: Forgotten Brilliance?

diff2

• Change bare http link in ref by adding a name ([http://example.com Name]).
• Link Saccheri quadrilateral.
• Fix typo.

diff3

• Change some links and URLs.

diff4

• Use {{sfn}} to replace some refs.

diff5

• More citation changes.
• Introduce new text:

  Al-Hassār, a mathematician from the Maghreb (North Africa) specializing in Islamic inheritance jurisprudence during the 12th century, developed the modern symbolic mathematical notation for fractions, where the numerator and denominator are separated by a horizontal bar. The "dust ciphers he used are also nearly identical to the digits used in the current Western Arabic numerals. These same digits and fractional notation appear soon after in the work of Fibonacci in the 13th century.^{[citation needed]}

• Insert new text:

  who were also the first to treat irrational numbers as algebraic objects,[ref name="ReferenceA"/] which was made possible by the development of algebra

• Change subheading from "Cubic equations" to "Dynamic functional algebra".
• Insert new text:

  and was the first to discover the derivative of cubic polynomials

  This was the earliest form of dynamic functional algebra.

• Change text for Al-Hassar including insertions like "developed the modern symbolic mathematical notation for fractions". Seemed to introduce a partial duplication: "Al-Hassār, an Arabic mathematician from the Maghreb...".
• Removed some   between number and unit.

diff6

• More citation changes.

diff7

• More citation changes and some tweaks.

Taken altogether, the amount of content change was small, yet hard to see due to the massive alterations to spacing and citation style. Johnuniq (talk) 07:43, 14 March 2011 (UTC)

Please, see this and this (note: the second link will be archived at the end of this month [March 2011]) –pjoef (talk • contribs) 11:06, 14 March 2011 (UTC)

Good point Pjoef. As I have been saying, there was a lack of AGF and discussion towards consensus when this article was stubbed. It was basically pulled out from under you. -Aquib (talk) 14:21, 14 March 2011 (UTC)

Thank you for your time, John. This is helpful. I am not seeing opinions anywhere in the RFC on the veracity of the assertions re Tusi's use of the derivatives of cubic polynomials (I have linked a source above) and also the term dynamic functional algebra (I linked to an article on the Turing prize for FORTRAN). I have seen nonsense, bollocks, that sort of reply, but something a bit more specific would be helpful. I am not a SMEee, but they too seem worthy of a civil reply. -Aquib (talk) 14:21, 14 March 2011 (UTC)

Aquib, this has been repeatedly pointed out to you, you seem to be suffering from a bad case of WP:IDIDNTHEARTHAT, but once more:

• The term "dynamic functional algebra" doesn't exist. I can see how Jagged managed to invent this term from the source he cites, but it doesn't exist. The source in question certainly doesn't point out any relation to functional algebra.
• See Yadegari, Mohammad (June 1978). "The Use of Mathematical Induction by Abū Kāmil Shujā' Ibn Aslam (850-930)". Isis. 69 (2). {{cite journal}}: Unknown parameter |[pages= ignored (help) for a concise overview of "several archaic forms of mathematical induction" and conclude that Jagged's claim:

  "The first known proof by mathematical induction was introduced in the al-Fakhri written by Al-Karaji around 1000 AD, who used it to prove arithmetic sequences such as the binomial theorem, Pascal's triangle, and the sum formula for integral cubes."

  is very misleading. This what is so typical and so wrong about Jagged's writing: falsely claiming that X was the first to do Y (strongly implying X did Y in the modern mathematical sense of the word) while being completely devoid of any mathematical content.

—Ruud 16:01, 14 March 2011 (UTC)

Worth considering. I didn't catch the place where my source re Tusi and derivatives was refuted. Did I miss it? -Aquib (talk) 17:50, 14 March 2011 (UTC)

Jan Hogendijk (1989), "Sharaf al-Din al-Tusi on the number of positive roots of cubic equations", Historia Mathematica 19, pp. 69-85:

I now investigate the possible relationships between al-Tusi’s definition of D and the derivative. We have f’(m) = [...], but this quantity does not occur in al-Tusi’s argument. This means that al-Tusi does not find m by computing the derivative f’ and by putting f’(x) equal to zero. Therefore the concept of derivative is not implicit here.

—Ruud 20:17, 14 March 2011 (UTC)

Thank you! This explains the objection WMC has to the assertion. However, we can now see the original Tusi assertion is not fabricated, but is rather a matter of dispute among the scholars. I have a very nice source that contradicts this claim, and your source seems to be directly addressing this controversy. Which means, for the purpose of this RFC, the assertion is within the realm of acceptable content and is not a cause for stubbing the article. Another good reason to have a discussion before taking extreme measures. -Aquib (talk) 21:09, 14 March 2011 (UTC)

Well, reveal your cards then... —Ruud 21:43, 14 March 2011 (UTC)

Quoting user:Wiqi55 from the above RFC:

Restore, but with ^{[verification needed]} tags (or another special tag) following each sentence. We can then slowly verify each sentence/statement and either re-phrase to better reflect the cited sources or delete if failed verification. I'm suggesting this approach based on my experience in cleaning Jagged edits in a couple of shorter articles (al-Battani and Abu Kamil). In both cases, the Jagged content was useful as a starting point, and better than starting from scratch. And I have to admit that Jagged can be right some times or almost so (i.e., not all his edits are of the same quality). Once this process is done, we can delete sources and claims that can be proven false or unreliable. I would also suggest saving the hard parts for last, like writing a synthesis for mathematical development, after all cleaning/verification is done.

Aquib (talk) 15:30, 14 March 2011 (UTC)

Not acceptable. Firstly, extrapolating from the current pace at which the cleanup of Jagged's article has been proceeding, this is going to take months at best, most likely more. Factual inaccuracies should not be left out in the open for such a long period. This process can be carried out Talk:Mathematics in medieval Islam/Jagged 85. Secondly, the article suffers from deeper structural issues (e.g. being written from a topical point of view instead of the more logical chronological order) which will likely not be addressed by this solution. —Ruud 15:39, 14 March 2011 (UTC)

First, keeping the article stubbed for months or years is not acceptable. What guarantee do we have the stub won't be in this state 5 years from now? Look at Science in medieval Islam 6 months into its stubbing. Second, rearrangement by chronology is reflective of a certain, shall we say, approach to the study of the History of Science which is not universally accepted. Separate topic. -Aquib (talk) 16:08, 14 March 2011 (UTC)

If you spend all your time forcing us to go round in the same old circles, and refusing to admit that anything is wrong, then yes: this is likely to be a protracted process. If however you actually set to work improving the article, and not getting in other people's way,then we might indeed make some progress. Replacing the entire article with a giant pile of cn's doesn't look like a good idea. A better way forward, if you want to try this, and one that doesn't require anyone's agreement, would be to copy the article, or just one selected section, into a sub-space, add the tags there, and work on it there. when you've finished a given section, ask for an OK, then it can get re-added William M. Connolley (talk) 16:12, 14 March 2011 (UTC)

Pointless. And one of these days, if I have the time, I am going to go back through this page and see if there is a single response to anyone with an opinion different than your own that does not include at least one insult. Why don't you try making your case on its own merits some time? Whew. -Aquib (talk) 18:34, 14 March 2011 (UTC)

And don't think all the static is distracting me from getting an answer on Tusi's use of derivatives in cubic polynomials. I have a good source. -Aquib (talk) 18:38, 14 March 2011 (UTC)

Note: when Wiqi55 said I'm suggesting this approach based on my experience in cleaning Jagged edits in a couple of shorter articles I think some of us thought he meant he had actually used this idea (comes from an editor who has successfully applied the technique. -Aquib (talk) 13:00, 14 March 2011 ). But looking at the article history, and talking to W55, it becomes clear that he hasn't actually used the technique - it is more an idea. It should not be misunderstood as a technique successfully used in practice William M. Connolley (talk) 21:33, 14 March 2011 (UTC)

Rereading Wiqi55s statement I can see he might not have been saying he had tagged the articles, he could have simply been suggesting we could do that. Interesting idea nevertheless. -Aquib (talk) 22:30, 14 March 2011 (UTC)

Further note: that although W55 asserted he had cleaned up Abū Kāmil Shujā ibn Aslam, there was still erroneous material left [4] which he has just restored [5]. Sigh William M. Connolley (talk) 21:35, 14 March 2011 (UTC)

I'm not sure why you are calling that material "erroneous" considering that the cited references clearly supports the claims being made. I'm afraid that this phenomenon of "careless" editing is now spreading, as we're seeing well-referenced and well-cited material being removed from articles for no obvious reason. Also, see the discussion on my talk page concerning my suggested approach. Wiqixtalk 22:18, 14 March 2011 (UTC)

It is erroneous because it says that Al-K invented algebra, which is wrong. But we've agreed this on the talk page already William M. Connolley (talk) 10:04, 16 March 2011 (UTC)

@WMC, the last time I heard you making claims about erroneous material, it was the 5 edits you made just before this article was moved/stubbed. Those edits turned out to be much less significant than what I would have expected as a justification for stubbing. In fact, of those 5 edits, three were regarding Tusi's use of a derivative in cubic polynomials - an assertion that is controversial and turns out to be supported by some academics. In fact, it seems the only real issue identified was the section heading referring to dynamic functional algebra. So maybe you could be certain you are referring to material we would all agree is erroneous before you make this new claim. And maybe you could make this claim somewhere besides the area where we should be discussing a proposed compromise. Thanks -Aquib (talk) 22:41, 14 March 2011 (UTC)

The article should cover a period running not from medieval Islam's start but from medieval Islam's first achievement in Mathematics - for example Al-Khwārizmī's Compendious Book in c820? - or if not then, when? MacStep (talk) 22:55, 14 March 2011 (UTC)

One can argue that Islamic mathematics started with the establishment of the House of Wisdom under Abassid caliph Harun al-Rashid (786) or, slightly later, under his son al-Ma'mun (813). One of the first known contributions was Al-Ḥajjāj's translation of Euclid's Elements. But we actually have a reliable source which errs on the early side with 622. —Ruud 23:19, 14 March 2011 (UTC)

Katz starts his description with the founding of Baghdad (766, he says) and the program of translation of Greek texts begun under Harun (786 on, as you say). Smith starts with the Sindhind, again Baghdad, around 766 William M. Connolley (talk) 23:26, 14 March 2011 (UTC)

"mathematics" Encyclopædia Britannica states it is necessary to know [the history of mathematics] ...in Islamic civilization from the 9th to the 15th century. - I think the weight of references will (eventually) push the relevant period forward a couple of hundred years or so. MacStep (talk) 00:21, 15 March 2011 (UTC)

I think that Al-Khwārizmī is a good starting point. Frankly that's already stretching the definition of "medieval". Of course this would be easier if we had a decent article 'early Islamic/Persian/Arabian mathematics' for the material from, e.g., 622. CRGreathouse (t | c) 15:31, 15 March 2011 (UTC)

The history of Islamic mathematics and astronomy are deeply intertwined. According Struik 'Arabic' mathematics starts with the Absid caliphs al-Mansur, Harun al-Rashid and al-Mamun. Al-Mamun founded the House of Wisdom and its first activity consisted of al-Fazari translating the astronomical texts brought to al-Mansur by and unknown Indian astronomer in 771 or 773. So there's actually some activity a few years before al-Khwarizmi already, activity that forms the basis of his work. I think the foundation of Baghdad (762) would be a fairly natural starting point and very close to first known activity of 771 of 773. —Ruud 15:53, 15 March 2011 (UTC)

Per my recommendation for a Medieval Islamic X naming convention for this and related pages (see Talk:Mathematics_in_medieval_Islam#Excuse_me.3F above and Talk:Mathematics_in_medieval_Islam#Medieval_Islamic_X below), I don't think 622 or 770s would be too early to count as medieval, if the term is broadly used to mean the post-classical period before the Renaissance (keeping in mind that current scholarship is critical of the whole "Dark Ages" notion in no small part because it only coincides with what was happening in Western Europe, whereas Islam had the opposite experience.) Yclept:Berr (talk) 06:59, 16 March 2011 (UTC)

I think we need to settle this without changing the facts on the ground in the process, as they say. I'll just ask and see what they think. -Aquib (talk) 23:49, 15 March 2011 (UTC)

As expected [6] William M. Connolley (talk) 09:53, 16 March 2011 (UTC)

Regarding the naming discussion that took place (apparently) in 2007 (see above in reference to here), I suggest the first step that be taken to rationalize the handling of the Jagged-affected pages is to standardize the naming convention to conform with similar history-of-x pages on Wikipedia.

• Medieval Islamic science
• Medieval Islamic mathematics
• Medieval Islamic metaphysics (page apparently deleted outright using the Jagged cleanup as an excuse)

etc. These pages should all be renamed and grouped together so that they can be more easily found and reviewed by experts, and the folks currently editing them need to get over their Jagged obsession and start focusing on bringing back sound content from the pages that were deleted en masse per WP:BATHWATER. Apologies to Ruud above, but if folks have been editing these pages since 2006-7 they should clearly be able to distinguish questionablely sourced additions from the same editor from quality sourced additions made by other editors in support of the same material. A wikiproject might be the best way to handle this. Yclept:Berr (talk) 06:34, 16 March 2011 (UTC)

• Why, this page is not even listed on the Islam portal under the current (disparate) naming convention. See up top. Yclept:Berr (talk) 06:41, 16 March 2011 (UTC)
• Aaand this naming convention (Medieval Islamic mathematics, etc) is the only one both Jahangard (the person who proposed the current page name for this & science page) and Ruud both separately suggested back in 2007 (above). The only reason it wasn't settled on is because the discussion was sidetracked over the merits of "Arab" vs. "Islamic" due to the number of folks coming in insisting that the label Islamic (cultural/historical term) was "potentially offensive", even though Ruud pointed out that is the accepted term Yclept:Berr (talk) 07:22, 16 March 2011 (UTC)

I don't think now is a good time to talk about re-naming the page. Lets let the current fuss about stubbing die down, hopefully start rebuilding the page (why not help?), then we can have another round of profitless discussion of names William M. Connolley (talk) 10:21, 16 March 2011 (UTC)

Arabic mathematics

Pros

1. Together with Islamic mathematics by far the most frequently used term in academic literature in to refer to this period in the history of mathematics. Of these two Arabic mathematics is probably used the most, however Islamic mathematics is more common in recent literature.
2. This title reflects the fact that a key feature of mathematics in this era was the generation of new mathematical ideas which have become associated with the Arabic language, such as algebra, algorithm and (of course) Arabic numeral.
3. Consistent with the naming of Babylonian mathematics, Egyptian mathematics, Indian mathematics, ...

Cons

1. Not all, perhaps even only a minority, of the mathematicians in this period where ethnic Arabs and is therefore seen as offensive by some people, even though "Arabic" seems to refer to the language used to transmit science during that time.
2. Although Arabic was the dominant scientific language of the Islamic world in that era, the mathematical works were not exclusively written in Arabic. Some medieval Islamic mathematicians have have works in other languages. For example, one of the main works by al-Kashi is written in Persian. Arabic is ambiguous and can refer to both "Arabic language" and "Arabic culture". Even among those mathematicians who have written their mathematical works exclusively in Arabic, many didn't belong to the Arabic culture. For example, Khayyam has written his main mathematical works is Arabic, but he is also famous for his Persian poetry (he is considered as one of the icons of Persian culture).

Quotes

1. Let us begin with a neutral and innocent definition of Arabic, or what also may be called Islamic, science in terms of time and space: the term Arabic (or Islamic) science the scientific activities of individuals who lived in a region that might extended chronologically from the eighth century A.D. to the beginning of the modern era, and geographically from the Iberian Peninsula and north Africa to the Indus valley and from the Southern Arabia to the Caspian Sea—that is, the region covered for most of that period by what we call Islamic Civilization, and in which the results of the activities referred to were for the most part expressed in the Arabic Language. We need not be concerned over the refinements that obviously need to be introduced over this seemingly neutral definition. —Sabra, A. I. (1996). "Situating Arabic Science: Locality versus Essence". Isis. 87: 654–670.

2. In the present case, the problems of the proper "historical" approach are further complicated by the difficulties of defining "Islamic" mathematics. One minor dispute is terminological: since "Islam" is primarily a religious term, it seems inappropriate to use it to qualify a science whch had very little to do with religion (especially when a number of its practitioners in the period in question were not Muslims). I prefer "Arabic," although that term too requires many qualifications. But, even when we allow "Islamic" to stand as a shorthand word for a cultural complex, we are still faced with the fact that the mathematics (like all the sciences) of that culture are simply a continuation of the Hellenistic Greek tradition. One of the most remarkable features of Islamic civilization was the way in which it took over and continued, in a different language and mostly in a different geographical area, the scientific heritage of antiquity, which was moribund in the contemporary Byzantine Empire, and in so doing breathed new life into it. There are a number of brilliant achievements in Arabic mathematics, but it has to be viewed as the direct continuation of the Greek tradition (and indeed is unintelligible without that background). Thus making "Islamic mathematics" a separate subject of study is artificial. Berggren, a scholar with a notable record of investigation of previously unstudied medieval mathematical texts, is of course well aware of all this, and of necessity allots some space to laying out the ancient Greek background to the topics he treats. But I should have liked to have seen in the book a more forceful presentation of the essential unity of Greek and Arabic mathematics. — Gerald J. Toomer on J. Lennart Berggren's Episodes in the Mathematics of Medieval Islam. (The American Mathematical Monthly, Vol. 95, No. 6. (Jun. - Jul., 1988), pp. 567-569)

Islamic mathematics

Pros

1. Together with Arabic mathematics by far the most frequently used term in academic literature in to refer to this period in the history of mathematics. Of these two Arabic mathematics is probably used the most, however Islamic mathematics is more common in recent literature.
2. Consistent with the naming of Babylonian mathematics, Egyptian mathematics, Indian mathematics, ...
3. Consistent with Islamic science, Islamic medicine, Islamic astronomy,Islamic astrology ...
4. "Islamic" refers to "Islamic civilization" which is a well-defined term.

Cons

1. Seems to put some people into an "OMG Islam!!!1111!1!1"-mode, or at least causes them to misinterpret this as "the mathematics of Islam", while "Islamic" in this context merely refers to the Islamic civilization.
2. How relevant is it that the culture of the time was primarily Islamic, when there were, for example, many Jewish mathematicians who contributed to the mathematics of the period? (This learnt at a recent CfD!)

Quotes

1. Let us begin with a neutral and innocent definition of Arabic, or what also may be called Islamic, science in terms of time and space: the term Arabic (or Islamic) science the scientific activities of individuals who lived in a region that might extended chronologically from the eighth century A.D. to the beginning of the modern era, and geographically from the Iberian Peninsula and north Africa to the Indus valley and from the Southern Arabia to the Caspian Sea—that is, the region covered for most of that period by what we call Islamic Civilization, and in which the results of the activities referred to were for the most part expressed in the Arabic Language. We need not be concerned over the refinements that obviously need to be introduced over this seemingly neutral definition. —Sabra, A. I. (1996). "Situating Arabic Science: Locality versus Essence". Isis. 87: 654–670.

2. Although many able authors have contributed valuable articles, the work as a whole is flawed, to such an extent that one hesitates to recommend it as a general reference on the subject for non-specialists. The flaws are of an editorial nature, and the first is the title chosen for the work. It is no disservice to Arabs (modern or medieval) to point-out that non-Arabs (principally Persians and Turks) also played important roles in the development of medieval Islamic science, and these roles should be acknowledged in the choice of title. "Islamic" is a very serviceable epithet and should have been used, rather than "Arabic," to describe the science being studied. — J. Lennart Berggren on Roshdi Rashed's Encyclopedia of the History of Arabic Science. (Journal of the American Oriental Society, Vol. 120, No. 2. (Apr. - Jun., 2000), pp. 282-283.)

Arabic/Islamic mathematics

(Or similar titles such as Arabic and/or Islamic mathematics.)

Pros

1. Covers both of the most frequently used terms in academic literature with a neutral point of view.
2. The combination of the two titles suggests that this is an historical period article, rather than an ethnic or religious one.

Cons

1. Has the potential to offend both the readers who would dislike "Arabic mathematics" and also the readers who would dislike "Islamic mathematics"!
2. It is quite uncommon, if not unprecedented, to give articles multiple titles on Wikipedia. Those are given the lead section.

Arabic and Persian mathematics

Pros

1. Covers the two main cultures involved. Persian suggests period and arabic suggests it's not ethnic (but see Con no. 2 below!)
2. Fairly concise, descriptive, would work for the category, and also suggests an option for handling Category:Arab mathematicians.
3. Usual advantage of avoiding names with religious connotations.

Cons

1. Nonstandard.
2. There were mathematicians in this period who where neither Arab nor Persian (but for example, Turkish or Moorish). Unlike "Arabic mathematics" it would be quite difficult to explain that "Arabic and Persian" does not refer to the ethnicity of them but to something else instead.

Medieval Islamic mathematics

Pros

1. Seems to be regarded as less offensive than "Islamic mathematics" by some people.
2. Consistent with "Medieval European mathematics" (but see con #2).
3. A similar title is used in one of the most important books on this subject: Episodes in the Mathematics of Medieval Islam.

Cons

1. Medieval is only a temporal adjective and is superfluous as there is no "Ancient Islamic mathematics" or "Modern Islamic mathematics".

(History of) mathematics in (the) (medieval) Islamic civilization/world

Pros

1. Seems to be effective at avoiding upsetting some people in the way "Arabic mathematics" or "Islamic mathematics" does.

Cons

1. Would be inconsistent with the current naming of Egyptian mathematics, Greek mathematics, Indian mathematics, ...
2. Would be inconsistent with the naming of other article son historical topic (e.g. the article on World War II is located at World War II, not History of the Second World War.)
3. While a great title (of a chapter) for a book, Wikipedia is not a book but an encyclopedia. An encyclopedia is a list of terms followed by a description of that term (is this necessarily true for an online wikipedia which easily uses "redirects"?). The terms which people will encounter in literature, and then perhaps decide to look up in Wikipedia, are "Arabic mathematics" and "Islamic mathematics". An encyclopedia should not concern itself with "fancy" titles and is a descriptive work, not a prescriptive work and should therefore not try to "correct" unfortunately chosen terminology which is in common use by historians.
4. Some of these variations do not lend themselves well as suitable names for the associated category.
5. The lead section of this article would still start out "In the history of mathematics, Islamic mathematics or Arabic mathematics refers to ..." as these are the terms used in the relevant literature.

(History of) mathematics in (the) (medieval) arabic era/culture

Pros

1. Titles such as these, as in the previous suggestion, have the potential to avoid upsetting some people, by making it clear that the term "arabic" refers to a cultural/linguistic rather than ethnic phenomenon.
2. It is worth searching for titles which avoid the word "Islamic" (why?), yet do not lend themselves to other misinterpretations.

Cons

1. Same inconsistency issues as above (how important is consistency?).
2. The arabic era could be confused with the Arab empire, which is a sub-period, as far as I understand.
3. Arabic culture still has the potential to be confused with Arab/Arabian culture. That historical culture is often called "Islamic culture" (or "medieval Islamic culture") and "Arabic culture" is mostly used in another meaning (refering only to the culture of Arabic world).
4. Some of these variations do not lend themselves as suitable names for the associated category.
5. The lead section of this article would still start out "In the history of mathematics, Islamic mathematics or Arabic mathematics refers to ..." as these are the terms used in the relevant literature.

(History of) Mathematics and Islam

Pros

Cons

1. This refers to a totally different topic than that discussed in this article.

(Medieval) Middle Eastern mathematics

Pros

1. Using a geographical term is less divisive than using a term with ethnic or religious connotations.

Cons

1. No reliable sources have been identified which use this term to refer to this period in the history of mathematics.
2. Morocco, Spain, and Central Asia are not part of the Middle East.

Excuse me?

Am I the only person who finds this discussion surrealistic? Aquib (talk) 18:57, 16 February 2011 (UTC)

Why? Seems legitimate to me. Question is, who wrote this section? The signatures are missing, as are any replies. Yclept:Berr (talk) 06:22, 16 March 2011 (UTC)

Medieval Islamic mathematics would seem to be a better term, along with (-->) Medieval Islamic science, etc. Then people would actually be able to, y'know, find the page which some folks feel is better left stubbed because they think it takes months to edit to varify or remove sourced claims from an already written article. Good thing they aren't working for a scholarly journal with that attitude! Yclept:Berr (talk) 06:14, 16 March 2011 (UTC)

Good point! -Aquib (talk) 14:50, 16 March 2011 (UTC)

Err, are you worried that people might not find this page, but instead find Medieval Islamic mathematics? That doesn't make sense, since that redirects to this page. And could you drop the accusations of bad faith, perhaps? William M. Connolley (talk) 14:58, 16 March 2011 (UTC)

Out of curiousity... the K pic for the cubic solution: am I right that it is not "constructible" in the traditional sense (because you can't draw parabolas?) so doesn't (in theory) allow geometrical solution William M. Connolley (talk) 23:04, 16 March 2011 (UTC)

Not using a straight-edge and compass, but it's seems possible using other devices: http://mathdemos.gcsu.edu/mathdemos/conic_via_locus/. —Ruud 23:17, 16 March 2011 (UTC)

By the way, solving the problem geometrically, means your solving ${\displaystyle {\frac {x^{2}}{a}}={\sqrt {\left({\frac {b}{2a^{2}}}\right)^{2}-\left({\frac {b}{2a^{2}}}-x\right)^{2}}}}$, if you square both sides, work out the polynomials, and simplify you get ${\displaystyle x^{4}+a^{2}x^{2}-xb=0}$, divide by ${\displaystyle x}$ to get the algebraic equation back. —Ruud 00:01, 17 March 2011 (UTC)

The Request fr arbitration has been filed -Aquib (talk) 06:39, 21 March 2011 (UTC)

There has been some dispute in the Rfc above about the verifiability of the following sourced statement:

"In the 12th century, the Persian mathematician Sharaf al-Dīn al-Tūsī was the first to discover the derivative of cubic polynomials, an important result in differential calculus.

which had appeared in the Differential Calculus section of a pre-stubbified version of the article. A slightly different version of this statement was removed from another section of the article on the grounds that it sounded "totally made up" to the editor removing it, even though that editor had apparently not checked the source cited to confirm that his assessment was accurate. Another editor has given two sources which he apparently thinks provide sufficient justification for the statement. However, one of those sources does not at all justify the statement as it is actually worded, and the other is completely worthless—at least for the purposes of citation as a reliable source.

In view of all this I am rather bemused that no-one seems to have bothered checking the source actually cited, which is an article, "Innovation and Tradition in Sharaf al-Dīin al-Ṭusi's al-Mu'ādalāt ", by J. L. Berrgren, in Journal of the American Oriental Society, 110 (1990), pp.304–9. I have now read this source, which is undoubtedly reliable by Wikipedia's standards, and can confirm that the above-quoted text from this Wikipedia article blatantly misrepresents it, in that it states as an undisputed fact something—namely that al-Dīn al-Ṭusi discovered the derivative of a cubic polynomial—which the cited source makes absolutely clear is no more than a conjecture proposed by one expert on al-Dīn al-Ṭusi's work to explain how the latter acquired his knowledge about the maxima of certain cubic polynomials. Moreover, although Berrgren, the author of the cited source, does think that the conjecture is reasonable, he also thinks that another explanation, which doesn't rely on al-Dīn al-Ṭusi's knowing how to compute a derivative, is nevertheless more likely.

The first of the two other sources that have been offered as supposedly supporting the above-quoted statement is page 97 of History of Mathematics: Highways and Byways by Amy Dahan-Dalmèdico and Jeanne Peiffer. The passage which was cited as supposedly supporting the statement was the following:

"The discussion, in effect, is almost always based on the search for maxima [not "maxims", as originally quoted] and for that Sharif Al-Din used expressions corresponding to the first derivative for polynomials. ....

"He referenced the role of the discriminant [not "determinant", as originally quoted] in cubic equations.

But the somewhat vague circumlocution, "Sharif Al-Din used expressions corresponding to the first derivative for polynomials", used in this passage, does not at all mean the same thing as, nor does it imply that, Sharif al-Din discovered the derivative of cubic polynomials, Moreover, the text originally omitted from this quotation (as indicated by the ellipses) says:

"Although this idea is never so indicated and the extant manuscript still does not permit determination of the source of these deep results their presence must be noted."

Precisely what this means is anybody's guess, but having now read Berrgren's article, I would surmise that Dahan-Dalmèdico and Peiffer are here acknowledging the fact—which is stated explicitly by Berrgren—that al-Din did not actually perform the operations of determining an expression for the derivative (at least, not in his known surviving works).

The second source offered as supposedly supporting the disputed statement was Encyclopedia of Ancient Egypt issued by an organisation going by the name of "MobileReference". However, this organisation appears to be in the business of aggregating Wikipedia articles and regurgitating them as e-books for downloading to mobile devices. If you compare the page cited with the last four paragraphs of the Algebra section of this version of Wikipedia's article, you will find that they're almost (or perhaps completely—but I haven't checked every single jot and tittle) word for word identical. The source is therefore clearly worthless as a citation to support statements made in Wikipedia.
David Wilson (talk · cont) 14:33, 18 March 2011 (UTC)

David, thanks for your detail analysis of the section, one of the most constructive comments in the last few days. Do you have a suggestion as to how this section could be worded to acuratly reflect the sources? --Salix (talk): 17:43, 18 March 2011 (UTC)

Yes David, thanks. My assertion is it is a notable claim. How would the claim be worded and balanced in order to avoid undue weight? Thanks -Aquib (talk) 18:08, 18 March 2011 (UTC)

You need to read what David wrote. The problem is not undue weight. The problem is that the claim is *wrong* William M. Connolley (talk) 18:27, 18 March 2011 (UTC)

You need to exercise common courtesy and focus your remarks on the topic rather than suggesting I did not read his post. Try arguing facts, not personalities. -Aquib (talk) 00:48, 19 March 2011 (UTC)

It is best to focus on the issue. WMC asserted that what David wrote shows that the claim is wrong. Do you disagree? If so, you need to say why. If you agree, how could rewording possibly help? Articles should not record every conjecture. More importantly, the big issue under discussion is whether the article warrants stubbing. If David's analysis is correct, it shows exactly the problem that requires stubbing because it is important that Wikipedia not record false information as if it were verified fact. Johnuniq (talk) 04:26, 19 March 2011 (UTC)

Could you clarify of make explicit where the "it" in "My assertion is it is a notable claim" refers to? —Ruud 01:19, 19 March 2011 (UTC)

Thanks, David. I think every assertion made by Jagged should be handled like this. As for al-Tusi and his derivative, we should follow the example given in the last four paragraphs of this MacTutor article (which mentions a few additional papers about the subject). Wiqixtalk 19:51, 18 March 2011 (UTC)

@Wiqi, thanks for turning up this article and the citations it uses, they should be useful. -Aquib (talk) 01:31, 20 March 2011 (UTC)

A clarification of my position

For those interested in understanding my position on this question of the claim al-Din discovered the derivative of cubic polynomials. This is an important point from my perspective, and I do not believe my message has yet been clearly communicated.

1. It does not matter whether this claim is true. What is true is I have a reliable source that says Rashed has argued that Sharaf Al-Din discovered the derivative of cubic polynomials and realized its significance for investigating conditions under which cubic equations were solvable. If there is something wrong with this one, just let me know and I will get another. I am not a mathematician, but I can Google lots of books and scholarly works debating this issue. I don't have JSTOR, and the conclusions of my source article may very well be that he didn't. It is not criticial to my position. I have a reliable source that says Rashed argues he did. This is notable. In addition, judging from the amount of material swirling around this topic, it is important. These facts justify its inclusion, and I am confident that given time I can produce many similar sources. According to neutrality policy, this justifies the inclusion of the material in the article, in proportion to the weight it carries in the scholarly community. I have seen no acknowledgement from the other editors that it is even a legitimate scholarly point of view, but it has a lot of scholars talking about it. How can that be?

2. This claim was removed from the article with an edit summary stating that sounds totally made up. It is not totally made up, and its removal without checking its reliability is a violation of neutrality policy. It is a perfect example of why we should not delete cited material without checking it. I do not know how much weight this claim should be given, yet, but it is a significant claim and should not have been removed. The fact this claim sounded totally made up to one editor largely contributed to the article's stubbing.

3. How much of this is going on right now across the affected articles?. This is a blatant example of what can happen when there are no checks or controls in place to curb destructive editing. The normal WP policies and procedures designed to prevent this sort of problem simply do not apply any more. The cleanup is operating outside the normal bounds of our encyclopedia. One mistake like this is bad. 100 are horrifying. A sustained effort to clean up articles with no safeguards in place could eventually tilt the POV of vast sections of the encyclopedia.

I am not here to argue whether the claim is true. To take an a position on the validity of this claim is essentially to synthesize a conclusion based on conflicting, reliable sources. The claim is notable, and therefore deserves inclusion. If we were operating under the normal rules, a simple remedy would be to tweak the statement to make it more generally acceptable or include opposing views. Any other conflicting claim from a reliable source is perfectly welcome.

Aquib (talk) 05:38, 19 March 2011 (UTC)

Aqib wrote:

"What is true is I have a reliable source that says Rashed has argued that Sharaf Al-Din discovered the derivative of cubic polynomials and realized its significance for investigating conditions under which cubic equations were solvable. If there is something wrong with this one, ... "

Well this is just Berrgren's article, this link to which I have already given in my discussion of it above. There's nothing wrong with it, but it did not support the statement that was actually made in, and removed from, the article. I agree that the statement should not have been removed from the pre-stubbified version of the article until the source had been checked (the stubbification itself is a separate issue, which I would prefer not to be drawn into discussing at this time). But the fact remains that had the source been checked, its failure to support the statement actually made in the article would have justified the immediate removal of that statement anyway.

There remains the question of whether an accurate account of the various conjectures—including, but not limited to, Rashed's—proposed to explain how al-Dīn came by his knowledge about the maxima of cubic polynomials should be included in the article. I have no opinion on this at the moment. It's certainly significant enough to be included in the article on al-Dīn himself. But I expect that an accurate account, written from a neutral point of view might need to be so lengthy that including it in this article would be according it too much weight.

David Wilson (talk · cont) 12:30, 19 March 2011 (UTC)

Thanks for taking the time to look into this David. You are right, the citation does not directly support the claim. Let me boil down my position a bit more. The claim is not totally made up, as it appeared to be in the eyes of one expert. To one such as myself unfamiliar with the subject, the fact that the development of calculus predates the Renaissance is significant. If an expert can make a mistake like this, under these circumstances, what will become of the rest of the cleanup targets? We are throwing the baby out with the bathwater. -Aquib (talk) 13:50, 19 March 2011 (UTC)

The "bathwater argument" gets thrown around a lot here, so let me quote from the actual essay:

Well, if this is the case, the deletion process is not the route to take to solve the problems. That's what the talk page is for. Deletion of an article is damaging to Wikipedia and should only be used as a last resort. Content removal can be used to weed out problematic areas. Other adjustments can be made, which may include the addition of information and sources. It may take a lot of work. But it is well worth it!

(Emphasis mine) Might I instead direct your attention to Wikipedia:Verifiability. —Ruud 15:05, 19 March 2011 (UTC)

Posible rewording

Heres an attempt at a rewording inspired by the MacTutor treatment

In the 12th century, the Persian mathematician Sharaf al-Dīn al-Tūsī investigated cubic polynomials. For example, in order to solve the equation ${\displaystyle \ x^{3}+a=bx}$ with a and b positives he found the maximum point of the curve ${\displaystyle y=bx-x^{3}}$ to be ${\displaystyle x={\sqrt {\frac {b}{3}}}}$, using what would nowadays be regarded as the derivative of the function. There is academic debate over quite how he arrived at his expression.

I'd also suggest this goes in section entitles Cubic equations where this and the work Omar Khayyám of could discussed.--Salix (talk): 13:23, 19 March 2011 (UTC)

My understanding from reading Berrgren's article is that the academic debate includes the issue of whether al-Dīn could in fact be appropriately described as having used the derivative of the function. So I would suggest something along the following lines:

In the 12th century, the Persian mathematician Sharaf al-Dīn al-Tūsī developed a novel approach to the investigation of cubic equations—an approach which entailed finding the point at which a cubic polynomial obtains its maximum value. For example, in order to solve the equation ${\displaystyle \ x^{3}+a=bx}$, with a and b positive, he would note that the maximum point of the curve ${\displaystyle y=bx-x^{3}}$ occurs at ${\displaystyle x={\sqrt {\frac {b}{3}}}}$, and that the equation would have no solutions, one solution or two solutions, depending on whether the height of the curve at that point was less than, equal to, or greater than ${\displaystyle a}$. His surviving works give no indication of how he discovered his formulae for the maxima of these curves. One scholar has argued that he must have obtained expressions for what would be recognized today as the derivatives of the functions whose maxima were being sought. However, other explanations, which would not entail his explicitly having to calculate a derivative, have also been proposed.
(See Note RF)x

David Wilson (talk · cont) 14:50, 19 March 2011 (UTC)

This seems more reasonable, but still favours Roshed's conjecture, not mentioning explicitly Hogendijk's explanation, while Roshed's conjecture has had the most severe critique. —Ruud 15:04, 19 March 2011 (UTC)

How about replacing the last two sentences with:

"Various conjectures have been proposed to account for his discovery of them."

with citations to the relevant sources? I wouldn't be able to cite Rashed, Hogendijk or al-Daffi and Strolys directly myself yet, because I haven't read the relevant works. I could cite them indirectly by citing Berrgren, and indicating that he cites them, but it would obviously make more sense if they could be cited directly by someone who has actually read them.

David Wilson (talk · cont) 15:59, 19 March 2011 (UTC)

That seems like a good idea. I've only read the article by Hogendijk and the review by Berggren. I would only cite the latter (pp. 308-9) as it nicely summarizes all the other work. —Ruud 16:19, 19 March 2011 (UTC)

No, this still blatantly misrepresents the sources: Roshed conjectured that a derivative might have been used, Hogendijk explicitly states a derivative was not used, al-Daffi offers another explanation not using a derivative. According to Berggren, Roshed's conjecture is not well supported by the primary sources, Hogendijk's explanation is by far the most plausible, and al-Daffi's explanation possible. Now, all four are respected historians of Islamic mathematics, so I agree this warrants a thorough discussion at the article on Sharaf al-Dīn al-Tūsī (mentioning the historians by name, their positions and their critiques.) This discussion cannot be summarized in such a form as to remain accurate, neutral, and concise enough to be put into an overview article. I have not seen any such claim of al-Tusi "using derivatives" in the standard works on the history of mathematics. Also, you, somewhat implicitly, suggest rebuilding this article in a topical fashion: topical histories belong in the "History" section of that topic, overview articles need to be ordered chronologically so the influences earlier contributors had on later contributors becomes more clear. —Ruud 15:00, 19 March 2011 (UTC)

I agree with Ruud that the exact interpretation is unclear, and that doing justice to the issue - which would indeed be an excellent thing to do - would occupy far more space than it warrants on an overview page (if it were certain, or even probable, that derivatives had been used, that would certainly be worth a place; but as the most probable interpretation seems to be that they weren't, then the final text won't be all that exciting). So, yes, this should be done on the al-Tusi page in detail, and once we have a stable text there it can be referred to here William M. Connolley (talk) 15:49, 19 March 2011 (UTC)

@Salix and David, I find these suggestions constructive and useful. The fact Berrgren characterizes Rashed as arguing that Sharaf Al-Din discovered the derivative of cubic polynomials is significant in terms of describing the strength of Rashed's conviction. -Aquib (talk) 01:25, 20 March 2011 (UTC)

Note this type of equation, of course, always has an odd number of (real) solutions, i.e either 1 or 3. All the best: Rich Farmbrough, 10:54, 27 April 2014 (UTC).