Talk:Sharaf al-Dīn al-Ṭūsī

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Derivatives of cubic polynomials[edit]

I have removed the first sentence of the section Treatise on equations because it misrepresents the source cited. More details can be found on an archive of the Mathematics in medieval Islam talk page. An accurate account, written form a neutral point of view, of the various conjectures about how al-Din acquired his knowledge of the maxima of cubic polynomials should eventually be added to the article.
David Wilson (talk · cont) 14:00, 19 March 2011 (UTC)


I removed, piecewise, several WP:COPYVIOs from this article (from [1]) before deciding that it was pretty well all made of that stuff. So I took it all out.

Besides which, the polynomial / derivative stuff was wrong, per what is now in Mathematics in medieval Islam and the discussion there William M. Connolley (talk) 07:49, 27 April 2011 (UTC)

Derivatives of cubic polynomials again[edit]

I have now reverted this series of recent edits. Even though the last of these seems like a reasonable paraphrase of the source cited, the language used by this tertiary source is unfortunately itself quite likely to be misunderstood, unless it is read in conjunction with some of the more scholarly literature on the subject. If you consult that literature—some of which is cited by the source—you will find that al-Ṭūsī left no clue as to how he found out that the maximum of the function b x − x3 occurs when x = √(b/3). It's certainly plausible that he might have discovered this fact by some process similar to taking a derivative and setting it equal to zero, and some scholars have argued that he must have done so. But, as others, notably J.P. Hogendijk and J.L. Berggren, have pointed out, there are other ways that he could have discovered this fact without having had to use the derivative at all. Thus, for Wikipedia to state as undisputed fact that al-Ṭūsī discovered some sort of derivative, even implicitly, would be a blatant violation of its policy on maintaining a neutral point of view. All of this has already been discussed extensively here and here.
David Wilson (talk · cont) 10:06, 19 February 2017 (UTC)

I agree with the above. My edit was intended to bring the paragraph in line with the source, but I wasn't that happy with the source's phrasing in this instance. So I don't mind the removal of my edit, but I do think that something needs to be said about al-Ṭūsī's mathematical contributions. Perhaps a copy of what you included in the Differential calculus page. My general feeling is that a controversy needs to be discussed and not hidden. If we don't include something, I fear that we shall be dealing with this POV pushing for a long time. --Bill Cherowitzo (talk) 18:52, 19 February 2017 (UTC)
I agree with Wcherowi, something must be said about that in the article, that's why i added a line about his supposed implicit use of a derivative and i made sure to show the two points of view (Rashed and Hogendijk).— Preceding unsigned comment added by Wikaviani (talkcontribs) 00:31, September 4, 2017 (UTC)

And again[edit]

The disputed claim that al-Dīn_al-Ṭūsī discovered the derivative of cubic polynomials has just been re-added to the article by this edit, with a citation to a source which is undoubtedly reliable, but which does not support the claim. I shall therefore be reverting the edit. I refer the editor who made it to one of Wikipedia's guidelines which says you should only cite a source directly if you have read that source yourself. An account of what the cited source actually does say can be found here.
David Wilson (talk · cont) 00:28, 11 June 2017 (UTC)

Edit warring and removal of sourced materials[edit]

I reverted edits by user Wcherowi as his edits where unsourced and look like edit warring with anonymous user University of St Andrews is a reliable source and R. Rashed is also a reliable source about this topic and these two sources are cited in many good articles on Wikipedia. Please user Wcherowl, if you have different reliables sources claming something else, bring them on the talk page and do not remove sourced informations. — Preceding unsigned comment added by 2a01:e34:ee9d:a200:f039:9ff8:3983:5318 (talk) 11:57, September 3, 2017‎ (UTC)

The two sources cited in the edits by the anonymous user from IP were the University of St Andrews's MacTutor website, and an article, Innovation and Tradition in Sharaf al-Dīn al-Ṭūsī's Muʿādalāt, by J.L. Berggren in the Journal of the American Oriental Society. However, some key claims made in the material added by these edits are egregious misrepresentstions of these sources, and simply not supported by either of them. To wit:
  • "He also developed the concepts of a derivative function … ". This is cited to the Mactutor article, but nothing remotely like that is stated anywhere in that article. What it actually says is:
"Basically using the derivative of this expression, al-Tusi finds [where] the maximum occurs …
"Of course al-Tusi's use of the derivative of a function, without of course saying so, is very interesting. The paper [11] attempts to discover the origin of this implicit use of the derivative, which the author claims arises from algebraic proofs based on analytical procedures. The paper [12] suggests that a rather different approach, not one analogous to the modern derivative, lay behind Al-Tusi's method. The papers [10] and [14] contribute to this discussion; see also [2], [3] and [4] for further insights.
Moreover, Berggren's article actually contradicts the notion that even an implicit use of derivatives in al-Tusi's work can be considered an established fact.
  • "He understood the importance of the discriminant of the cubic equation to find algebraic solutions to certain types of cubic equations." This is cited to Berggren's article, which nowhere uses the term "discriminant" for any purpose, let alone as the name of something which al-Tusi supposedly recognised the "importance" of. The Mactutor article does use the term "discriminant" once:
"Then Al-Tusi deduces that the equation has a positive root if
D = b3/27 - a2/4 ≥ 0
where D is the discriminant of the equation."
but nowhere says anything about al-Tusi "understanding" its "importance". In fact, the statement in the MacTutor article is a little misleading, in that al-Tusi never expressed inequalities in forms like A – B ≥ 0. Since he didn't recognise that an expression of the form A – B made any sense if A < B, he never rewrites inequalities such as A ≥ B or A ≤ B in the forms A – B ≥ 0 and A – B ≤ 0 which we recognise today as being equivalent.
Your reversions of user Wcherowi's edits were therefore completely unwarranted.
David Wilson (talk · cont) 08:46, 4 September 2017 (UTC)

Hi, In the source it's stated that Roshdi Rashed (who is a reliable source on that topic) writes that Al-Tusi is the founder of algebraic geometry (..."represents an essential contribution to another algebra which aimed to study curves by means of equations, thus inaugurating the beginning of algebraic geometry"). this has been removed from the article and i would likely ke to know why. If no legit explanation is provided, i will edit again the article with this statement. More, users Wcherowi and Wikaviani edited the article by saying that the implicit use off a derivative of cubic function was claimed by Rashed but challenged by Hogendijk and Berggren, and this has been removed to although being true... an explanation eoylb br welcomed...

Your comments are a little out of date. The article has been changed (before you wrote this, but maybe a tie time-wise) in what I think is a positive way. Wikaviani and my edits have never been removed from the article, but there is some difficulty with looking at earlier versions of the page at the moment (I hope that this gets fixed). --Bill Cherowitzo (talk) 22:30, 5 September 2017 (UTC)
I'd say mentioning algebraic geometry is justified, but I'm not sure about "founder of". Perhaps this quote might be useful. Wiqi(55) 22:44, 5 September 2017 (UTC)

I changed the phrase with algebraic geometry to one closer to the source. But i think that the statement "He is credited as having turned trigonometry from a tool used in astronomy into a mathematical subject in its own right" is wrong as the one who performed this change was NASIR al din al Tusi and not SHARAF al din al Tusi. I looked at the source cited and there nothing about Sharaf's work in the field of trigonometry... if there is a concensus about this point, i will remove that sentence.

If it is the wrong al-Tusi then by all means remove the sentence. I reverted your change for two reasons. First of all the St. Andrews citation is not an independent source since all they are doing is citing Rashed's comment. That article had already been cited three times and there was no need for a fourth reference to it. Rashed's comment seems to me to be a bit of hype (or perhaps just how others are using his comments) and I would like to see some independent source also make this claim before reinstating it. --Bill Cherowitzo (talk) 01:49, 6 September 2017 (UTC)

For anonymous user who opened this topic about "edit waring": there is nothing such that here, we're just discussing some issues in the article to make it the more accurate possible. I agree with user wcherowi when he says that we should remove Tusi's supposed work in trigonometry as it does not appear in the source cited. But i do not understand why we should change Rashed's sentence about Tusi as the beginner of algebraic geometry and write instead "lefts his mark". I think that if we cite a source, we should remain as close as possible to it and not change it arbitrarily.--Wikaviani (talk)

I don't want to be engaged in an edit waring, but i changed again the phrase about algebraic geometry. If we cite Rashed, let's cite him properly... — Preceding unsigned comment added by 2A01:E34:EE9D:A200:C4AC:5CC0:900A:7C11 (talk) 21:33, 6 September 2017 (UTC)


The current reference cited in the article as justification for the statement "He understood the importance of the discriminant of the cubic equation to find algebraic solutions to certain types of cubic equations"—namely J.L. Berggren's article Innovation and Tradition in Sharaf al-Dīn al-Ṭūsī's Muʿādalāt—does not support it. Berggren's article contains not a single mention of the term "discriminant", and as far as I can see there is nothing whatever in the article to indicate that Berggren would agree with the statement. Unless someone can supply a decent source to justify the statement within a few days, I shall remove it from the article.
David Wilson (talk · cont) 16:17, 15 September 2017 (UTC)

I have managed to track down a statement by Roshdi Rashed which can be used to justify including in the article at least an attribution to Rashed of a statement to the effect that al-Tusi "understood the importance of the discriminant" of cubic polynomials. In my opinion, however, this attribution needs to be qualified by stating certain facts about al-Tusi's treatment of cubic equations which might be regarded as casting some doubt on the accuracy of Rashed's statement.
David Wilson (talk · cont) 18:04, 16 September 2017 (UTC)

Citation check needed[edit]

One of the sources currently cited in the lead as support for the statement that al-Tusi was Persian is page 247 of the 2008 second edition of Helaine Selin's Encyclopaedia of the History of Science, Technology, and Medicine in Non-Western Cultures The only searchable edition of that encyclopaedia available in Google Books appears to be the 1997 first edition, whose page 247 contains nothing whatever about al-Tusi. Jan Hogendijk's article on al-Tusi on p.894 of the same edition merely says that he was born "Tus (Iran)", which is far from ideal as a citation to justify the statement that he was Persian.

The Minor planet center web page cited at the end of the lead is also very far from ideal, in my opinion. Although it does say specifically that al-Tusi was Persian, and is published under the auspices of the prestigious Harvard-Smithsonian Center for Astrophysics, it is nevertheless a page about astronomy, not the history of mathematics, and I don't believe it's author's opinions on the latter subject should be assumed any more authoritative or reliable than that of any other well-educated layman.

Since I have convenient access to a printed copy of the cited 2008 edition of Selin's encyclopaedia in a local University library, I will check it later today.
David Wilson (talk · cont) 16:21, 18 September 2017 (UTC)

I have now checked the source, which says "This [i.e. the linear astrolabe] was invented by Iranian mathematician Sharaf al Dīn al-Tūsī … ". The article, Astrolabe, in which the text appears, seems to be a verbatim copy of the same article which appears on pp.74–75 of the 1997 edition of the encyclopaedia.
Since I've no idea whether the terms "Persian"and "Iranian" can be considered completely synonymous or not, I have replaced the former with the latter in the article.
David Wilson (talk · cont) 04:59, 19 September 2017 (UTC)
According to our article Iran the terms are interchangeable especially in cultural contexts. Iranians have always used Iran and there was a movement at one time to have everyone drop Persia in favor of Iran, but this has not prevailed. My preference would be for Persian since that conveys (for me, and I now realize that this is mistaken) a more historical flavor. --Bill Cherowitzo (talk) 05:28, 19 September 2017 (UTC)
I have no preference one way or the other between "Iranian" or "Persian", as long as a good source can be found to support the choice. I am, however, fairly strict in what I consider a "good" source. I had earlier found some books in Google Books which described Sharaf al-Din al-Tusi as "Persian", but for various reasons I didn't find any of them satisfactory. However, I've now found this source, which seems to me to be impeccable, and describes our al-Tusi as a "Persian astrolabe maker". So I would be perfectly happy for this source to be added to the references and cited as justification for changing the description back to "Persian".
David Wilson (talk · cont) 07:48, 19 September 2017 (UTC)