Wikipedia talk:WikiProject Mathematics

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Draft:Sabir Gusein-Zade[edit]

Hello. I wrote Draft:Sabir Gusein-Zade and it has been rejected twice. If someone here would like to help me to improve it so that it can be accepted I would be really grateful. Sorry about my bad English (it's not my native tongue you know...), I won't try to create articles again, but it will be sad to me if my work there (albeit modest) be deleted after the six months deadline... By the way, it seems that pages marked as "Draft:" are not shown by Google or Wikipedia searches in standard mode, making it difficult for other interested people to find them and maybe help to improve the drafts. Sincerely, --Rodrigo 189.6.212.77 (talk) 05:00, 2 April 2015 (UTC)

Suggest you use this link as a reference and mention his being editor-in-chief of MMJ. He clearly passes WP:PROF but this is not immediately apparent from the draft. —David Eppstein (talk) 05:24, 2 April 2015 (UTC)

Thank you for the suggestion and the link! I've just made an addition to the draft http://en.wikipedia.org/w/index.php?title=Draft%3ASabir_Gusein-Zade&diff=654669582&oldid=654592460 --Rodrigo 189.6.193.44 (talk) 18:51, 2 April 2015 (UTC)

Current activity page[edit]

What's going on with the Current activity page today? Its format is changed and most of it is blank. Michael Hardy (talk) 16:44, 3 April 2015 (UTC)

See User talk:Jitse's bot. Apparently the bot is feeling under the weather. It cleared out both this page and Wikipedia:Pages needing attention/Mathematics/Lists‎. —David Eppstein (talk) 17:16, 3 April 2015 (UTC)

Lancaster Edit-a-thon[edit]

Hi all; I'd like to let you know there will be a mathematical Wikipedia edit-a-thon this Wednesday at 3:30-6pm (UK time), in Lancaster University during a mathematics conference, as part of the 150th anniversary celebrations of the London Mathematical Society. The event page is here:

Wikipedia:WikiProject Mathematics/Lancaster University Edit-a-thon 8 April 2015

So feel free to join in online, and/or keep an eye on that page for any relevant activity. Cheers! Mark M (talk) 19:15, 6 April 2015 (UTC)

Article "Montgomery reduction": Change its presentation to "Montgomery multiplication"[edit]

Hello Wikipedia Mathematics community,

I would like to propose a change to the article Montgomery reduction. The article is about a certain method for fast modular multiplication invented by the mathematician Peter L. Montgomery.

I'm a very newly registered user here on Wikipedia. (See my user page for a brief self-introduction.) I only learned of the subject of Montgomery multiplication via the Wikipedia article, and I am not an expert in the field. However, having now studied the subject for a few weeks I think I now understand the subject reasonably well, and I think I see a few ways to improve the article.

However, even if I now think I understand the subject reasonably well, I still preferred to seek discussion before I make edits, not only because I am completely new on Wikipedia, but also because I am new to the Montgomery multiplication subject. I.e., what I seek is the input of people who have contributed to the article and who are more familiar with the subject than I am. (For example, it may be that I am unfamiliar with the terminology or label under which the subject is classified in certain fields such as cryptology.) About 2 weeks ago I already posted on the article's talk page, but no one responded there, which is why in my attempt to seek discussion I am now posting this here.

In this posting, I would like to address the following set of very related problems with the article Montgomery reduction:

Properly speaking, the "Montgomery reduction" in the title of the WP article is in fact only a subroutine used internally inside the fast modular multiplication method invented by Montgomery. (In his 1985 paper, Montgomery used the desgination REDC() for this reduction subroutine.) Montgomery's fast modular multiplication method as a whole is properly called Montgomery multiplication. Moreover, this REDC() subroutine (= the algorithm performing "Montgomery reduction") is a subroutine that is specific to Montgomery multiplication, i.e. it is not a general-purpose algorithm that can be taken out of Montgomery multiplication and applied outside of it.

In the bulk of the text, the WP article actually in effect explains the complete Montgomery multiplication, and not only the REDC() subroutine for the Reduction step. (That the article explains the complete Montgomery multiplication is of course very logical, since it would be hard to explain the Reduction subroutine without explaining also the complete Montgomery multiplication.)

However, looking at the title, the lead section, and the section "Formal statement" in the beginning, the WP article seems to be presented as a description of "Montgomery REDUCTION" only.

I think this is a case of naming something for one of its parts.

(Note also that (at present) there does not exist a separate WP article titled "Montgomery multiplication".)

A very related problem with the article is the confusion between the following terms:

  • Montgomery algorithm;
  • The REDC() function (or algorithm);
  • Montgomery step;
  • Montgomery multiplication.

This terminology problem is IMO very much related to the improper "pars pro toto" title. The problem is a lack of clear distinguishing between terms and hierarchical algorithm elements in the beginning of the article (and in its whole presentation which includes its title). In my view, a reader new to the subject is from the beginning led to misunderstanding of terms and into confusion about what are the different algorithms and how they fit together. (At least, it caused me some confusion on first reading.)

The measure I would like to propose, to solve all these related problems in one go, is to change the presentation of the article from "Montgomery reduction" to "Montgomery multiplication".

This would involve the following:

  • Change the title to "Montgomery multiplication" (or to something similar like "Montgomery's method for fast modular multiplication").
  • Rewrite the lead section, to clearly disinguish the terms mentioned above (including mentioning there explicitly that the REDC() reduction function is a subroutine inside Montgomery multiplication, and including mentioning that "Montgomery algorithm" is ambiguous and can stand for either the REDC() algorithm or for a complete Montgomery multiplication step), so that all these terms are briefly identified and distingished right from the start. (This would also IMO make clear formulation of the bulk of the article text much easier.)
  • Inside the article, rename the section "Formal statement" (which is about the REDC() reduction function) to something like: "Formal statement of the REDC() Reduction function".

I think that ideally the change would probably include also a small amount of rearranging/reordering of the structure of the article. E.g., move the sections "Formal statement" and "Description of Algorithm" into a section that deals with the the REDC() subroutine. Note that all the Examples in the article already are about Montgomery multiplication as a whole, and not about only the Reduction specifically. The section "Rationale" also in effect already explains Montgomery multiplication as a whole, and seems to me to need only very small editing work to adapt if the article presentation would be changed to Montgomery multiplication as a whole.

The Wikipedian Gronk Oz made the suggestion that it would be also a possibility, instead of changing the Montgomery reduction article, to add a separate new article titled "Montgomery multiplication". I would also like to invite your views on this idea. Questions: Does the subject merit two different articles? Was the intention of the creators of the existing article to discuss the Reduction exclusively, or to explain Montgomery multiplication as a whole (and if so why did they title it "Reduction" and not "Multiplication")?

Another thing I would welcome comments on is the following: This is only my speculation, but I could imagine that it could be possible that in some circles (maybe cryptology?), Montgomery's method for fast modular multiplication might conceivably be generally referred to under the label "Montgomery Reduction", same as many other things are commonly referred to under "pars pro toto" names. This might be a reason to consider keeping the the title "Montgomery reduction" intact. However, I am new to the subject and I have no knowledge of circles that use the "pars pro toto" label of "Montgomery reduction" when talking about "Montgomery multiplication". I invite people who have knowledge of circles that use this "pars pro toto" naming for this subject to speak up and comment.

There are no doubt many more kinds of improvement that could be made to this article. However in order to keep things focused, with this posting I seek discussion at first only on this specific issue.

Also, what I would like to discuss at this point is at first only the question of whether the change (or small package of changes) I am proposing is sensible or desirable. I.e. to reach a consensus decision on whether it would be good if the presentation of the Montgomery reduction article is changed to "Montgomery multiplication", leaving the bulk of the article text (including all Examples) intact. Addressing how exactly to implement this change (and when and by whom, etc.) seems then to me a later step.

I would like to acknowledge W.carter from the Teahouse, for pointing me to the Mathematics Project talk page, and Gronk Oz for enthusing and helpful discussion. (Any mistakes in the above are my own.)

With best regards, --MRaccoon (talk) 14:11, 7 April 2015 (UTC)


I'm no expert either, but I know someone who has thought about Montgomery multiplication before, and I've always heard him refer to "Montgomery multiplies" or "Montgomery multiplication". I doubt that there is enough material for two separate articles, so I think that the article ought to be moved. You should do this yourself, and right now! The general principle here is be bold. You should feel free to reshape the article however you please (as long as you are honestly trying to make it better, something which doesn't seem to be a problem in your case). It sounds like you know enough about the subject to write a much better article. Ozob (talk) 14:25, 7 April 2015 (UTC)
@Ozob: Hello Ozob, thank you for your comment, which is much appreciated. Thanks for taking the time to comment, and for commenting so quickly. Your opinion is pretty decided and definite, which is a great encouragement.
I am impressed by the discussions between you and MarcusMaximus on your user talk page, about differentials and coordinate systems (of which much is unfortunately over my head; I can just understand its significance, and I have always regarded both subjects as pretty fundamental). Given that, your information that you know one person who refers to Montgomery's invention as "Montgomery multiplication" and not "Montgomery reduction" sounds to me like a significant data point.
I had seen the BOLD, and I completely understand how it is imporant in the Wikipedia mechanism; but opinions seem to differ as to the degree to which it is allowed for new users to actually be BOLD. Plus I have (had) initially a little hesitation caused by my own "ethical" concern that one shouldn't interfere in stuff that others have created, no matter how loudly they say that it is allowed. However, with your comment you have now pretty much changed me over to an expectation that everything will probably be OK and that I will probably go ahead and make the changes I proposed.
As regards "right now", that seems a separate question. I'm a bit on the "slow and deliberate" side there. I am in no particular hurry myself, so I am feeling rather that it woudn't hurt me to wait a few more days before I post a "Move request". That would allow more people to comment here on the proposal. I would like to repeat my invitation to anyone who has contributed to writing the article to speak up and comment; and in particular I would urgently like to hear from anyone who has information that the subject is in some circles commonly referred to under the name "Montgomery REDUCTION" (and not "Montgomery multiplication").
Thanks to you and to all, and with best regards, --MRaccoon (talk) 19:43, 7 April 2015 (UTC)


I agree with Ozob, that you are able to dramatically improve the article. Do not worry about interference with others stuff: In WP, nobody is owner of anything, and the best articles result of the interference between of many editors.
About the title, I have also heard about "Montgomery multiplication", never about "Montgomery reduction". As changing a title may be more difficult for a new user, I was intended to change the title myself, leaving to you to adapt the content. However, looking on the articles linking to it (button "what links here" on the left), it seems that "Montgomery modular multiplication" would be a better title. Therefore, I'll move the article to this title, leaving a redirect, and also create a redirect "Montgomery multiplication". If you do not agree to include "modular" in the title, it would not be difficult to move again. In any case, you seem the best to adapt the content of the article. D.Lazard (talk) 21:42, 7 April 2015 (UTC)
@D.Lazard: Hello D.Lazard, many thanks for your comment, and for your encouragement. Thanks for your feedback on the naming of the subject. I see that you have now changed the title to "Montgomery modular multiplication".
I think it is a good idea to include the word "modular" in the title. I believe that prevention of misinterpretation up front is one of the main methods for achieving clarity of exposition in a text, and that it is better to be too verbose than to risk misinterpretation. It seems to me that it is good very early on to explicitly state the "obvious" fact that the subject falls under modular arithmetic, because for many readers it may not be obvious, and stating it may prevent many misinterpretations by readers unfamiliar with the subject. It also makes the subject easier to explain and the bulk of the text easier to formulate, because you have already eliminated possible misinterpretations up front and do not need to deal with those possible misinterpretations much more in the bulk of the text. So as for me I quite agree with the fuller title including the word "modular", and I am very happy with the title change you made. I agree that adding the redirect from "Montgomery multiplication" is important (I checked that both redirects are working correctly).
I now intend to wait for a day or two to see if there are other comments on the title change. Thereafter I will then go ahead and carry out the edits in the article text that I proposed. (Or possibly I may begin putting in some few preliminary edits in the lead section sooner.) Many thanks for your encouragements and support, and With best regards, --MRaccoon (talk) 10:39, 8 April 2015 (UTC)
PS (off topic): No one owns anything, I knew that of course, but it is indeed a fact that bears repeating (for me). I had previously only been used to company wikis (containing internal company information like internal software documentation), where in effect every page had an "owner" in the sense of one person who is responsible for that page. There, if you wanted to change something in an existing page, the unwritten but quite definite rule was that you always discuss it first with the person responsible for the page.
Wikipedia demonstrates that it is (apparently) possible to run a wiki without the "ownership responsibility" mechanism, and exclusively on the basis of the mechanism of social control. I am finding that a quite interesting and curious phenomenon of sociology. It tells you something interesting about how people work (one gets the impression that with humans, social control is more influential than anything else). Philosophical questions related to it fairly leap out at me (e.g. implications for politics). Being located politically on the side of "classical liberalism" and very far away from socialism, I'm finding a world lacking the "ownership responsibility" mechanism definitely very curious (to put it very mildly). The "no one owns anything" is taking me a minute to get used to (e.g. also the idea that what I write is then not my responsibility any more and is "common property" and can in principle freely be hacked and mashed up by anyone), but as regards how it works for practical matters here on Wikipedia I think that I got it now. Sorry for the off-topic post. --MRaccoon (talk) 14:19, 8 April 2015 (UTC)
Well, as long as we're off topic...
Social pressure is not the exclusive means of control on Wikipedia. If it were, the project would fall apart. If you want to further your study of Wikipedian sociology, see Wikipedia:Vandalism, Wikipedia:Disruptive editing, Wikipedia:Blocking policy, and Wikipedia:Arbitration Committee.
I think of Wikipedia as a charitable endeavor. Legal ownership of Wikipedia rests with the Wikipedia:Wikimedia Foundation (WMF), and I see my work here as a kind of charitable donation (the actual legalities are more complicated: I retain ownership of my words and grant WMF a license to use them. However the spirit is that of a charitable contribution). Once I've charitably contributed my words, I lose control over them. WMF takes my charitable contributions of words and distributes it to needy minds across the globe. It also allows others to make their own charitable contributions on top of mine. If I don't like the direction an article has taken, I'm free to make another charitable contribution. This perspective is, I believe, consistent with both classical liberalism and socialism. Ozob (talk) 04:17, 9 April 2015 (UTC)
Hello Ozob and all,
Ozob, thanks for your comment. I'm discovering that in my previous comment I may have used the term "social control" somewhat inaccurately. I'm pondering this some more. For this off-topic sociology subject, I'm considering creating a section on my talk page for it, and then replying further there (after I have given the subject some more thought).
On the Montgomery subject, while writing out a formulation of the whole thing for myself I'm discovering that I'm not completely clear myself yet about one or two small points of the mathematics of the thing. It may take me a few days more to get this clear to myself. After I arrive there, and in case I am not sure at that point how to integrate my new stuff into the article, I will then seek discussion again (here or on the article's talk page).
Thank you and with best regards --MRaccoon (talk) 09:29, 12 April 2015 (UTC)

Steiner generation of a conic[edit]

Please could some one check the discussion on Steiner's theorem. User Wcherowi changed the sence of Steiner's thorem twice in such a way that it does not comply with Steiner's "Vorlesungen,...., Teil 2, p.96". Wcherowi's Steiner theorem is not the base of what he calls " sometimes referred to as Steiner's definition of conics or the projective generation of conics". Steiner (!) did proof the generation: see his lecture "Jacob Steiner’s Vorlesungen über synthetische Geometrie, B. G. Teubner, Leipzig 1867 (bei Google Books: [1]), 2. Teil, p. 96 ". Wcherowi changed the reference to Steiner's Vorlesungen such that it is wrong.--Ag2gaeh (talk) 08:01, 9 April 2015 (UTC)

The addition to this citation was accidentally omitted when I reverted. I have now fixed the citation. Comments on the above mentioned discussion are welcome. Bill Cherowitzo (talk) 16:22, 9 April 2015 (UTC)

Draft:Ricci soliton[edit]

This draft was prepared last October by Mbw314 (talk · contribs), who never submitted it for review and has not edited since. It qualified for speedy deletion under WP:CSD#G13 as an abandoned draft, but I have postponed that in case it is worth keeping, or can be developed. Comments welcome. JohnCD (talk) 16:35, 12 April 2015 (UTC)

I think it is worth keeping. It passes my BS and OR detectors (but I have no idea of what the thingies are). A Google search gives plenty of seemingly trustworthy hits. A couple of more references and an inline citation or two, and I think we have decent stub article. YohanN7 (talk) 17:50, 12 April 2015 (UTC)

This is an extremely important topic in global analysis. I'm surprised there is not already an article. Sławomir Biały (talk) 17:55, 12 April 2015 (UTC)
I concur with Sławomir, this is a quite notable topic. Ricci solitons are covered briefly in Ricci flow, but are deserving of their own article. Here is an example secondary review article on Ricci solitons. --Mark viking (talk) 18:59, 12 April 2015 (UTC)

Wikipedia talk:Articles for creation/Poincaré Separation Theorem[edit]

Dear mathematics experts: here's an old AfC submission on a mathematical subject. Is this a notable topic, and should the page be kept and improved instead of being deleted as a stale draft?—Anne Delong (talk) 17:38, 13 April 2015 (UTC)

This looks notable to me. The theorem is discussed in many books on matrix mathematics and has an entry in the CRC Concise Encyclopedia of Mathematics, Second Edition. If it is notable enough for a published encyclopedia, it is notable enough for us. --Mark viking (talk) 18:06, 13 April 2015 (UTC)
Notable. It also appears in Horn and Johnson "Matrix analysis". Sławomir Biały (talk) 19:35, 13 April 2015 (UTC)
Thanks, Mark viking and Sławomir Biały. It's in mainspace now at Poincaré separation theorem.—Anne Delong (talk) 21:37, 16 April 2015 (UTC)

Help checking accuracy of the statements in an article[edit]

Sorry guys, I don't know where to ask help from fellow mathematicians in wiki. Several users (including me) have disputed the statement in Eigenvalue perturbation and its proof. Can someone check it? Best, Taha (talk) 21:27, 16 April 2015 (UTC)