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This is an old revision of this page, as edited by 93.74.76.101 (talk) at 11:37, 29 December 2014 (→Navier – Stokes Millennium Prize Problem. Alternative Solution: new section). The present address (URL) is a permanent link to this revision, which may differ significantly from the current revision.

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WikiProject Mathematics
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Euclidean algorithm

I have nominated Euclidean algorithm for a featured article review here. Please join the discussion on whether this article meets featured article criteria. Articles are typically reviewed for two weeks. If substantial concerns are not addressed during the review period, the article will be moved to the Featured Article Removal Candidates list for a further period, where editors may declare "Keep" or "Delist" the article's featured status. The instructions for the review process are here. — Preceding unsigned comment added by ‎DrKiernan (talk • contribs)

Seems like more anti-intellectualism from our friends in the wider Wikipedia community (anyone remember the ridiculous affair that the mathematical works of Alexander Grothendieck should be made accessible to laymen?) Now we are told that the article on the Euclidean algorithm should be made understandable to 10 year old children! Sławomir Biały (talk) 13:53, 6 December 2014 (UTC)[reply]
I think commenting on this nomination is worthwhile. Explaining and promoting mathematics to the widest community possible is important. More generally, Wikiarticles can often be structured so that there is something in them for general public as well as, when necessary, something in them for the expert. My thoughts, sincerely, Grandma (talk) 14:27, 6 December 2014 (UTC)[reply]
It's not a particularly good article. Anyone reading the whole thing risks to die from boredom. YohanN7 (talk) 14:54, 6 December 2014 (UTC)[reply]
Parts of it are boring to me as well. Perhaps not the best article to nominate? Or, maybe because it needs work, it would benefit from the scrutiny that comes with nomination? Grandma (talk) 15:07, 6 December 2014 (UTC)[reply]
Why waste time on an article that is already (undeservedly) FA-class? Yes, surely there must be other better suited. But I can't think of a single math article that is very likely to appear as a featured article (except articles about mathematicians). YohanN7 (talk) 15:26, 6 December 2014 (UTC)[reply]
I agree, the article can be improved. Nothing about the FA designation implies that the article is perfect. But the reasons for nominating it for review are thoroughly idiotic (an easily Googled fact tag, and a belief that the article should be accessible to 10 year olds). A review can be constructive, with thoughtful comments that lead to real improvements. But that didn't happen here. Sławomir Biały (talk) 19:00, 6 December 2014 (UTC)[reply]
Can we please keep the rhetoric conducive to teamwork? Thank you, Grandma (talk) 19:29, 6 December 2014 (UTC)[reply]
Grandma, I'm not sure what you hope to accomplish by your continued trolling, but I'm pretty sure "teamwork" is not high on the list. Sławomir Biały (talk) 19:47, 6 December 2014 (UTC)[reply]
Is there any reason to limit the inputs to two integers? I would think that one could start with any finite number of real numbers. Take their absolute values. Sort by size. Remove zero and any duplicates. Then begin a loop where you replace the largest number by the difference between the largest and the second largest and then resort and remove duplicates (if any). It terminates when there is only one number left (the GCD). No guarantees that it will terminate. JRSpriggs (talk) 10:17, 7 December 2014 (UTC)[reply]
The termination is almost exactly the definition of commensurable. This algorithm is not new, but it is slower than computing first the GCD of the two smallest entries, and then iterate (slower because of more operations involving two large integers).
To editor Sławomir Biały: I have not seen anywhere that "we are told that the article on the Euclidean algorithm should be made understandable to 10 year old children". However Euclidean algorithm is one of the rare important mathematical results that can been told to 10 year old children: It suffices to known long division to introduce it in the modern form using Euclidean division, and this is not even needed for the version by subtractions, which requires only to understand what is a divisor. The concept of GCD is not even required as a background, as Euclidean algorithm is the most elementary way to define GCD's and prove their existence (The set of common divisors is not changed when running the algorithm, and at the end, one gets the set of all divisors of the single remaining integer). It is a pity that the article is written in a style which makes elementary notions unnecessarily obscure for the layman. D.Lazard (talk) 11:38, 7 December 2014 (UTC)[reply]
Dr. Lazard, I do not see the problem with the style of the article that others are complaining about. This is not to say that this or that could not be rewritten in a different style, but I don't see any problems with the style that obviously need fixing, especially not to the extent that the article deserves to be dragged to FA review. Making the article accessible to a 10 year old, for whom even a capacity for reading at an advanced level is rather unlikely, is an unreasonable standard for any encyclopedia article, let alone one about a mathematical algorithm. I am aware that some young persons may learn this algorithm from textbooks which are written for one of such a reading and mathematical level, but I highly doubt that an encyclopedia article would benefit from being rewritten in such a style. There is a project "simple Wikipedia" that is more appropriate for such an undertaking. Sławomir Biały (talk) 15:26, 7 December 2014 (UTC)[reply]
Sławomir Biały, where was "understandable to 10 year old children" first brought up with respect to this Euclidean article? Or is this your interpretation of what is expected? Grandma (talk) 16:11, 7 December 2014 (UTC)[reply]
[1] Sławomir Biały (talk) 16:26, 7 December 2014 (UTC)[reply]
And that is not the same as saying that "the Euclidean algorithm should be made understandable to 10 year old children". Some material in the article should, yes, be accessible to the typical reader, and some material can be there for the expert. Grandma (talk) 16:31, 7 December 2014 (UTC)[reply]
"Grandma", for someone who pays lip service to the idea of "teamwork", you have almost nothing to add to a productive discussion. The single "fact" tag for which the article was brought to FAR has been fixed (by me). Apart from some vague statement that the article should be more accessible (the only target anyone has identified is a 10 year old, a clearly ridiculous standard). If no one actally has anything concerte to add, I propose that we close the FAR as resolved. Sławomir Biały (talk) 16:38, 7 December 2014 (UTC)[reply]

I oppose to close the FAR. The article is full of unresolved issues. Here are some of the main ones.

  • Before my today edit, the article did not mention one of the most important applications (important, at least, by the computer time devoted to it), the reduction of fractions. I have added it in the lead, but it deserves a section.
  • Section "Bezout's identity" presents a method for computing it. I do not know if it is WP:OR, but I am sure that nobody uses it, as extended Euclidean algorithm is much more efficient and easier to use.
  • In the applications, the distinction is unclear between the applications of Euclidean algorithm and those of extended Euclidean algorithm. Extended Euclidean algorithm is introduced only after using it several times (such as in "Bézout's identity" section).
  • The section on polynomial Euclidean algorithm is very poor (compare with sections "Univariate polynomials with coefficients in a field" and "Pseudo-remainder sequences" of Polynomial greatest common divisor. It is not even said that polynomial Euclidean algorithm is fundamental for testing multiple roots and polynomial factorization. Undue weight is given to Sturm chains, that are not an application of Euclidean algorithm, but a variant of it (this is not said).
  • The section "Generalizations to other mathematical structures" contains a confusing description of Gröbner bases. It says that it is a Generalization of Euclidean algorithm, which is historically wrong, as the connection between them has been discovered 7 years after the introduction of Gröbner bases. The important fact is not even given, namely that the polynomial Euclidean algorithm and Gaussian elimination are two special cases of Gröbner basis computations.

This only some of the many issues of this article. Considering them as minor would give a bad opinion of our community to external people. D.Lazard (talk) 19:17, 7 December 2014 (UTC)[reply]

These comments should really appear on Wikipedia:Featured article review/Euclidean algorithm/archive1 so it becomes part of the review process.--Salix alba (talk): 23:15, 7 December 2014 (UTC)[reply]

I mean no offense, but this is not a particularly "exciting" article to read. In a sense, it is irrelevant whether the article is understandable to 10-year-old boys and girls since they will not be reading it in the first place. In fact, it is not clear to me what the target audience of the article is. Wikipedia articles are meant for college-educated or college-being-educated "adults"-those who already known gcd. Thus, in principle, it is not necessary to write them like textbooks that are used in elementary schools. But we "could" choose to make the article accessible to children, but then as pointed out above, it's much better to start without gcd; the algorithm is simpler than the concept (I suppose.)

If the article is meant for more sophisticated readers, then it still fails them. I'm thinking of a para from the article like this one (excuse me for a long quote):

The fundamental theorem of arithmetic applies to any Euclidean domain: Any number from a Euclidean domain can be factored uniquely into irreducible elements. Any Euclidean domain is a unique factorization domain (UFD), although the converse is not true. The Euclidean domains and the UFD's are subclasses of the GCD domains, domains in which a greatest common divisor of two numbers always exists. In other words, a greatest common divisor may exist (for all pairs of elements in a domain), although it may not be possible to find it using a Euclidean algorithm. A Euclidean domain is always a principal ideal domain (PID), an integral domain in which every ideal is a principal ideal. Again, the converse is not true: not every PID is a Euclidean domain.

Again, who would be reading this? The majority of non-math major students need not learn about the distinction between lovely ring-alphabets: UFD, PID, GCD, etc. And why is this in the article "Euclidean algorithm"? Especially, the mention of GCD domains is problematic; it's only interesting to students in "ring theory". It's quite remarkable that the existence of GCD can guarantee that the domain is an integrally closed domain. But there is no need for a student to start to think about GCD domains before he (usually not she) learns about integrally closed domains.

In short, it's not clear to me what reader would enjoy reading this article. -- Taku (talk) 22:02, 7 December 2014 (UTC)[reply]

In the UK we start talking about GCD in Key Stage 3, 11 - 14 years old. I would say there is a good number of children in that age group who would try to read this article. So there is a good case for targeting some of the article at that age group. I think it does that quite well. The article much also pass WP:FACR in particular 1b: comprehensive. This means it must include advanced material which such children will not be able to follow.--Salix alba (talk): 23:10, 7 December 2014 (UTC)[reply]

A bit off topic but its not just the wikipeidia community which has problems with maths. Nature has just rejected an Obit of Alexander Grothendieck by David Mumford and John Tate for being too technical.[2] --Salix alba (talk): 09:41, 16 December 2014 (UTC)[reply]

Intriguing: Tsirelson's rogue edits

According to Daqu,

Tsirelson is known for undoing other people's Wikiedia edits without explaining his reasons for doing so.

If you are intrigued, see this edit, with the summary "Added fact about Tsirelson's rogue edits of Wikipedia". See also here and here. --Boris Tsirelson (talk) 09:53, 16 December 2014 (UTC)[reply]

Intriguing indeed. @Daqu: surely you must have an explanation. I see no reverts of your edits unless you have edited as an ip. YohanN7 (talk) 10:53, 16 December 2014 (UTC)[reply]
It surely must be intended as a joke. Unfortunately, on the internet the line between humor and psychopathic behavior is often not very clear. Sławomir Biały (talk) 12:10, 16 December 2014 (UTC)[reply]

Notification of merger proposal

I propose to merge Stern–Brocot tree and Calkin–Wilf tree, as they appear to be exactly the same tree. I have no opinion for the name of the merged article. I notify this project because of the low number of readers and watchers for both pages. I have opened the discussion at Talk:Stern–Brocot tree#Merger proposal. D.Lazard (talk) 18:00, 16 December 2014 (UTC)[reply]

Discussion of the merits of this proposal can continue at that talk page, but I would like to point out a factual error in your announcement here: these are not the same tree as each other. For instance, the children of 1/2 are different. —David Eppstein (talk) 18:33, 16 December 2014 (UTC)[reply]

Notification of Request for comments

I have opened a request for comments at Talk:Euclidean algorithm#Request for comments. D.Lazard (talk) 11:39, 19 December 2014 (UTC)[reply]

Two drafts for review

These two drafts were submitted today and look promising:

Math topics aren't my forte on Wikipedia, so I'm posting these here if anyone has any comments or wants to review them. Thanks, ~SuperHamster Talk Contribs 06:12, 21 December 2014 (UTC)[reply]

Frame (signal processing)

Should the new article titled Frame (signal processing) be merged into Frame of a vector space? Michael Hardy (talk) 21:15, 21 December 2014 (UTC)[reply]

A merge does seem appropriate. For what it's worth, I think the new article frame (signal processing) is written in a much clearer style than frame of a vector space. Sławomir Biały (talk) 15:00, 26 December 2014 (UTC)[reply]
On a related note, Frame (linear algebra) probably should be a disambig page; in fact, it's already written that way. -- Taku (talk) 23:08, 26 December 2014 (UTC)[reply]

Watchlist bug

Is it only me experiencing that this page does not always show up on the watchlist? YohanN7 (talk) 07:03, 25 December 2014 (UTC)[reply]

My guess would be that when Wikipedia is busy changes to a page take some time to be reflected on your watch-list. I doubt that updating watch-lists is the top priority of the system. JRSpriggs (talk) 12:29, 25 December 2014 (UTC)[reply]
Updating watch-lists is obviously one of the main priorities of the "system". It relates directly to user experience. I also didn't ask if my observation is important. I asked if anyone else has seen it. YohanN7 (talk) 11:31, 26 December 2014 (UTC)[reply]
I have not noticed it. But it is unlikely that I would since I rarely look at this page except as a result of it being on my watch-list.
The experience of the general user (who is not an editor) would probably be a higher priority than that of an editor. Only editors are likely to use watch-lists. JRSpriggs (talk) 14:39, 26 December 2014 (UTC)[reply]
Editors are likely to be online browsing, reading and editing 100 times more than mere readers per month Just to make clear what is annoying with this bug: I frequently have to type "Wikipedia talk:WikiProject Mathematics" in the search box. (I am a clumsy typist.) I know, I could create a link on my user page. YohanN7 (talk) 14:19, 28 December 2014 (UTC)[reply]
...or just type WT:MATH in the search box :) No such user (talk) 18:08, 28 December 2014 (UTC)[reply]
Short for WikiTroject MATHematics? Wouldn't work. Wouldn't remember it from one hour to the next. YohanN7 (talk) 18:17, 28 December 2014 (UTC)[reply]
And WT:WPM, documented at the top of this page, has one letter less, and is hopefully more intuitive ;). No such user (talk) 10:58, 29 December 2014 (UTC)[reply]
I have a lengthy list of links at the top of my talk page (most editors put this list on their user page). One of them is a link to this page. So I could just click on the "talk" link to get to my talk page and then click on my link to this page. Easy. JRSpriggs (talk) 00:44, 29 December 2014 (UTC)[reply]

Dear members of the world mathematical community!

Enyokoyama (talk) (15:12, 8 November 2013) has offered the new section http://en.wikipedia.org/wiki/Talk:Navier%E2%80%93Stokes_existence_and_smoothness#Yet_another_solution_proposed.3F As a result of discussing this section http://en.wikipedia.org/wiki/Talk:Navier%E2%80%93Stokes_existence_and_smoothness#Attempt_at_solution.5Bedit.5D has been proposed for improvements to the Navier–Stokes existence and smoothness article:

Attempt at solution

Classical solutions

In 2013, Mukhtarbay Otelbaev of the Eurasian National University in Astana, Kazakhstan, proposed a solution. As an attempt to solve an important open problem, the proof was immediately inspected by others in the field, who found at least one serious flaw.[1] Otelbaev is attempting to fix the proof, but other mathematicians are skeptical.


Alternative solutions

Terence Tao in 18 March, 2007 announced[2] three possible strategies of an alternative solutions if one wants to solve the full Millennium Prize problem for the 3-dimensional Navier-Stokes equation. Strategy 1 “Solve the Navier-Stokes equation exactly and explicitly (or at least transform this equation exactly and explicitly to a simpler equation)” is used in these works:

The author of these brief notes Alexandr Kozachok (Kiev, Ukraine) has offered (in February 2008 – Internet , in 2008, 2010, 2012 – INTERNATIONAL CONFERENCE reports, in November 2013 and February 2014 - INTERNATIONAL journal) two exact transformations to the simpler equations. These transformations are executed by well-known classical methods of mathematical physics. Therefore not only some professionals, but also educational, social and many other sites have republished or paid attention to these works .

Read more http://en.wikipedia.org/wiki/Talk:Navier%E2%80%93Stokes_existence_and_smoothness#Attempt_at_solution.5Bedit.5D

However the Wiki editors can not deny “Alternative solutions” but only block any information about this work.

Therefore let's formulate your position for editing of the “Attempt at solution” section http://en.wikipedia.org/wiki/Navier%E2%80%93Stokes_existence_and_smoothness#Attempt_at_solution 93.74.76.101 (talk) 11:37, 29 December 2014 (UTC)[reply]

  1. ^ Moskvitch, Katia (5 August 2014). "Fiendish million-dollar proof eludes mathematicians". Nature. doi:10.1038/nature.2014.15659.
  2. ^ "Why global regularity for Navier-Stokes is hard". What's new. Retrieved 22 December 2014.
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