# Wikipedia talk:WikiProject Mathematics/Archive 48

## Wranglers

The 2nd wranglers cfd has been closed as delete and the closer has declined an invitation to re-open. Perhaps someone would like to start a DRV on both the wranglers categories. The first was deleted on the argument '1. This is a valedictorian category. 2. We have deleted a valedictorian category (risible cfd). 3. So we must delete this one.' Occuli (talk) 14:49, 23 March 2009 (UTC)

There is now a DRV on the categories for Wranglers, a travesty mathematicians will doubtless wish to remedy. Occuli (talk) 13:55, 24 March 2009 (UTC)
It was closed, with the decision being to restore the categories. They now exist again at Category:Senior wranglers and Category:Second wranglers. One could quibble about the capitalization, but it was a quibble of that nature that led to the original deletion... —David Eppstein (talk) 00:03, 1 April 2009 (UTC)
Is there a central discussion for these categories somewhere? Moving them to the capitalized names is a trivial task that only requires a template to be set up. Bots will handle the actual category changes on the pages. Tothwolf (talk) 19:40, 1 April 2009 (UTC)
Yes, Categories for Discussion. That's exactly what set off this whole situation — a trivial recapitalization request two months ago for these two categories morphed halfway through into a suggestion that they be deleted, because the people who regularly participate in the discussions at CfD are not mathematicians and didn't understand the difference between this honor and being selected as valedictorian of one's local high school. And they probably still don't, so I would urge caution in trying it again. —David Eppstein (talk) 20:37, 1 April 2009 (UTC)
While we're on the topic, I see we have a page List of Wranglers of the University of Cambridge. This is not in fact a list of Wranglers (of whom there are a great many, most of whom, such as myself, are not notable) but rather a list of Senior and Second Wranglers. Should it be moved to List of Senior and Second Wranglers of the University of Cambridge, or would that be too clunky? Algebraist 20:45, 1 April 2009 (UTC)
Well, yes, but I meant is there a central discussion location outside CFD/DRV? I could set up the templates to move the articles over to the capitalized names but I wouldn't want it to catch anyone off guard or anything. Tothwolf (talk) 20:48, 1 April 2009 (UTC)
No, I don't think there is. Algebraist 20:51, 1 April 2009 (UTC)

(break)
Ok, here are links to the various CfD and DRV discussions that I could find:

I also uncovered this discussion:

I can't help but wonder if the Tripos Wranglers category should have gone to DRV as well?

If no one here objects, I'll be WP:BOLD and point the soft redirects the other way so the bots will recategorize articles under Category:Senior Wranglers and Category:Second Wranglers.

--Tothwolf (talk) 23:23, 1 April 2009 (UTC)

I'm not sure if we really need to go through another round of discussion for a simple renaming. Is there any controversy about the capitalisation change? If not then an application of WP:IAR could be appropriate. Total number of articles is within the scope of WP:AWB so don't need to get bots involved. --Salix (talk): 16:32, 2 April 2009 (UTC)

Tothwolf: I don't think Category:Tripos Wranglers should be restored. Being a high-ranking wrangler is important (or was, while they were still ranked). Being a plain wrangler is no more important than getting a first in any other degree, and as far as I know this has always been the case. Algebraist 17:16, 2 April 2009 (UTC)
Algebraist, well, I wondered about it because it was deleted in pretty much the same manner as the other two categories and was listed in the 2008-01-16 CfD which was also where Senior wranglers and Second wranglers were first listed. The Wrangler (University of Cambridge) and Wooden spoon (award) articles both cover the third degree and just going by Wrangler (University of Cambridge) being in the top 3 was a very high achievement. Tothwolf (talk) 20:13, 2 April 2009 (UTC)
The top three, maybe, but all of them? I'd want to see some sources for that being important. Algebraist 00:30, 3 April 2009 (UTC)
I'm out of my element here with the terminology and your reply has me confused. Based on what I saw in the CfD archives I thought Category:Tripos Wranglers had previously been used for third-ranking wrangler articles but maybe this wasn't the case? Was this category actually used much more broadly? Tothwolf (talk) 01:32, 3 April 2009 (UTC)
See Cambridge Mathematical Tripos. My understanding: "tripos" is the name of the exam; a "wrangler" is anyone who takes the exam. A "third wrangler" would be someone who places third in the exam, but a "tripos wrangler" is just a redundant way of writing "wrangler". —David Eppstein (talk) 02:51, 3 April 2009 (UTC)
Ah, it would seem to be redundant to Category:Senior Wranglers and Category:Second Wranglers then. Unless there happen to be lots of existing articles that wouldn't fit into those two categories I can't really see a need for it. A Third Wranglers category might be useful for navigational purposes depending on the number of articles though. Tothwolf (talk) 03:56, 3 April 2009 (UTC)
Salix, exactly. I just wanted to make sure I wasn't misreading or overlooking something before I made any changes and I also wanted to make sure people involved with these knew what was going on so no one would be surprised. Tothwolf (talk) 20:13, 2 April 2009 (UTC)

Done Now we just have to wait for the bots to recategorize the articles. Usually it only takes a day or two but sometimes it takes a little longer. Tothwolf (talk) 00:24, 3 April 2009 (UTC)

## Euclidean algorithm and Fermat's Last Theorem

I'm still hoping to interest the talented mathematicians here in improving the Euclidean algorithm article. I've had a few nibbles, but basically I've been alone in transforming this into this. Does anyone want to help significantly before I submit it to GAN, and thence to FAC? I've more that I want to add, of course, but a fellow editor or two would make it more fun. It's an important article, don't you agree?

It's wonderful to see that Wiles's proof of Fermat's Last Theorem is getting attention, but please let me call your collective attention to Fermat's Last Theorem itself? It seems as though it could be improved significantly with relatively little effort from the people here. It's a rewarding article, since the problem is one of the most engrossing of the last four centuries, one that has inspired much of algebraic number theory (the current WPM collaboration) and captured the public's imagination. I'll be glad to work on it myself, in a few weeks, but as a biochemist, I feel poorly qualified, especially relative to the many mathematicians here. Proteins (talk) 07:41, 28 March 2009 (UTC)

Recently Lagelspeil has been undertaking the huge task of working on an article on the mathematics of Wile's proof. As part of his/her work, he unfortunately deleted significant chunks of the FLT article, including the story behind Wiles and his proof, and a brief overview of his approach. Whether or not there is a separate in-depth article on the Wiles proof, it is clearly inappropriate to remove this content. I have restored these deletions and provided a link to the more in-depth math article. --C S (talk) 08:17, 28 March 2009 (UTC)
I don't think anyone will be ashamed if you bring up the FLT article to FA status. Rather, I would imagine many (including myself) would be highly pleased. Indeed, I don't seem to have as much time as I thought for the knot theory FA nom and had to withdraw it. One thing it lacks is a brief section on applications in biology (including understanding actions of enzymes on DNA and using knot invariants as protein shape descriptors). I wish someone with a good knowledge of biochemistry would add one. --C S (talk) 08:33, 28 March 2009 (UTC)

I'll be delighted to help you as best I can with the knot theory article. By lucky coincidence, I have a little collection of knot-theory articles on proteins and nucleic acids. (I'm not sure whether anything has been published on polysaccharides.) Give me a few days to dig them up. And thank you for taking my unhappily critical comments about the FLT in the best possible way; I'll be happy to help in making FLT a good article, hopefully with your and others' help. Proteins (talk) 19:32, 28 March 2009 (UTC)

Misc. comment: Lagelspeil has been blocked as a returning banned user, so don't expect any further work from him/her on Wiles' proof of the FLT. --C S (talk) 00:40, 3 April 2009 (UTC)

## Indefinite sum and indefinite product

Does anyone have a view on the two new articles List of indefinite sums and List of indefinite products ? I have found some (minimal) sources that use the term "indefinite sum" to mean the inverse of the forward difference operator - enough for me to give this article the benefit of the doubt - and added them to the article. But I can't find any useful sources for the term "indefinite product", and I am beginning to wonder whether this is a neologism/OR. I have left a note on the author's talk page. Gandalf61 (talk) 15:55, 1 April 2009 (UTC)

This is definitely not original research; I've seen it in the context of computer algebra. For example the Mathematica documentation for the Sum and Product functions uses the respective terms "indefinite sum" and "indefinite product". Googling gave this hit in a book about Maple. Fredrik Johansson 16:51, 1 April 2009 (UTC)
Thanks for the reference. I've added it to the article. Charvest (talk) 17:11, 1 April 2009 (UTC)

The term "indefinite sum" seems self-explanatory, in view of the way the term "indefinite integral" is used. Just do for sums what "indefinite integral" does for integrals and that's it. Michael Hardy (talk) 15:05, 2 April 2009 (UTC)

Agreed, but being self-explanatory does not, AFAIK, obviate the the requirement to conform to WP:V by providing reliable sources. Happily, this requirement has now been met for both articles, and they have also been given better titles and some context. Thanks to everyone who helped. Gandalf61 (talk) 09:05, 3 April 2009 (UTC)

## Complexity

I find maths very interesting, I am trying to understand many more complex aspects of maths and in my mind this is the best website to use. However, sometimes I feel you need a Masters degree in Calculus to understand many of the pages. Somehow even the most simple articles are turned into mind blowing formulae and all sorts of complicated explanations. On many articles, there are no examples that actually involve numbers to demonstrate somethings use. For example, I find functions hard to understand, I thought I had the grasp of it after reading a book so I came onto here and after reading I am now more confused. It's easy to forget this is an encylopaedia and sometimes behind all of the info there still needs to be a simple, easy to understand description. 95jb14 (talk) 18:21, 2 April 2009 (UTC)

That's a fair criticism. I also think that many articles could use more/better illustrations.
Did you have any particular examples in mind?
CRGreathouse (t | c) 19:05, 2 April 2009 (UTC)
Thanks for responding. These are a few examples: Integral (too complex in intro, lacks example), Function (mathematics) (same reason) and Limit (mathematics). I won't be on in about ten minutes after writing so feel free to reply but I probably won't respond before tomorrow. If need be, leave a comment on my talk page - this could be a long discussion!!!! 95jb14 (talk) 19:56, 2 April 2009 (UTC)
Readability for basic mathematics articles is something that we need to work on. It can often be difficult in an article to strike the right balance between formalism and intuition, between generality and important special cases, and between advanced and elementary viewpoints. The authors of the function (mathematics) article have clearly worked very hard to strike a balance between all of these competing objectives, and they've done an admirable job, but the result is a huge conglomerate of competing ideas and viewpoints struggling for attention. I'm not sure that anyone reading that article would be able to understand it unless they were already familiar with all of the different concepts of a function.
My attitude towards these problems is that it often works well to have an elementary article and an advanced article on the same topic. For example, about a year and half ago I wrote an article entitled Euclidean subspace that covers subspaces of Rn from an elementary standpoint. This makes it possible for the article on linear subspaces to be primarily about subspaces of an abstract vector space, while still having an article that is accessible to non-mathematicians.
I suspect that the same thing would work for the function (mathematics) article: some of the content could be split off into a function (calculus) article, which would present functions from the elementary standpoint common in calculus classes. In addition to providing a readable article for those who don't know anything about sets, I imagine the main function (mathematics) article would be better off if it didn't have to struggle so much to include both elementary and advanced ideas. Jim (talk) 18:44, 5 April 2009 (UTC)
I like the idea of two (or even more) levels. But I wonder, could these levels coexist in a single article? (Simple - first, of course.) Boris Tsirelson (talk) 19:12, 5 April 2009 (UTC)
Splitting an article into an "easy" and "hard" version is often a bad idea. Here are some reasons:
• It leads to duplication of effort to maintain both
• It makes it hard for other people to figure out which article to link to. Readers following links are likely to end up in the wrong place.
• The "easy" version often ends up reading more like a textbook than an encyclopedia article. We aren't supposed to "teach" like a textbook would.
It's often better to just make the introductory parts slightly more accessible and put the truly general or esoteric stuff at the end, even if it means that the initial parts are not fully general. — Carl (CBM · talk) 00:38, 8 April 2009 (UTC)

In general, I don't think it's reasonable to expect that a reader with no idea whatsoever about a topic can pick up an article in an encyclopedia and understand exactly what is going on. This has never been true in other encyclopedias, like Brittanica, and those have a much more elementary presentation than we do. it is not our role to provide numerous worked-out examples; even proofs should only be included when there is really encyclopedic interest in them.

Of course articles, like function (mathematics) should be written to be as accessible as possible – but not any more accessible than that. Readers should not expect wikipedia to replace a good textbook, because the role of any encyclopedia is to provide an overview for people who have a vague idea what is going on, and provide a reference for people who know a topic but need to check a particular fact. — Carl (CBM · talk) 00:38, 8 April 2009 (UTC)

I recall an engineer that told me: some engineers succeed to do, others succeed to explain convincingly, why they could not do. :) That was rather a joke, but seriously: Wikipedia is not a firm; if no one volunteers something (say, examples or explanations), it cannot be enforced. On the other hand, given that Wikipedia has no deadline and a lot of volunteers, assume that some want to explain. Should they be discouraged? Or even prevented? Boris Tsirelson (talk) 05:47, 8 April 2009 (UTC)

## Speedy deletion

The article Steven Roman has been tagged for speedy deletion if anyone wants to comment. Charvest (talk) 22:36, 5 April 2009 (UTC)

I've untagged it. It looks reasonably likely to pass a full AfD if it comes to that. —David Eppstein (talk) 23:13, 5 April 2009 (UTC)
thankyou Charvest (talk) 09:28, 6 April 2009 (UTC)

On a related subject, Yousef Alavi has been proposed for deletion. I'm not certain he passes WP:PROF, so I haven't unprodded his article myself, but others may want to take a look. —David Eppstein (talk) 20:57, 7 April 2009 (UTC)

Unprodded. "Yousef Alavi" OR "Y Alavi" "graph theory" gets a high number of hits on google web, google books and google scholar. Charvest (talk) 21:16, 7 April 2009 (UTC)

## Herbrand's theorem

I stumbled upon this article and noticed it is missing a math ratings template. Thanks! momoricks (make my day) 07:10, 8 April 2009 (UTC)

## Aliquot

I've been engaged with a bit of a dispute with Milo Gardner on Aliquot regarding whether his additions concerning Egyptian fractions are sufficiently relevant to include in the article. More eyes would be welcome. If there's discussion of the issue it should probably be on the talk page there. —David Eppstein (talk) 17:36, 8 April 2009 (UTC)

## J. Michael Steele

Is he notable enough? He claimed that he invented shattering, which is not true. At best, he and his advisor were the first who used the term shattering in his PhD dissertation in 1975 in relation to the process defined by V&C 6 years earlier. Are there any other accomplishments which necessitate presence of the article about this mathematician? (Igny (talk) 17:02, 10 April 2009 (UTC))

The named professorship is an automatic pass of WP:PROF #5. We don't have to look for notability ourselves; the committee that gave him that title has already done the looking for us. But if you want a better answer, his six books and papers with over 100 citations in Google scholar (ignoring the antipyrine one which appears to be by someone else) would probably be a good place to start. Judging by my past experience with AfDs of academics, those publications would very likely be enough to give him a pass of WP:PROF #1, and the presidency of IMS #6. Any single one of those criteria would be enough to keep the article. —David Eppstein (talk) 17:07, 10 April 2009 (UTC)
Ok, ok you convinced me. Two points: this article is more of a stub then because it lacks details about his accomplishments. Second point, there is a significant number of professors who got honorable titles of various degrees, likely numbered in thousands in USA only. I could name a few from my department who are distinguished enough and who do not have an article on WP. (Igny (talk) 17:29, 10 April 2009 (UTC))
So why not write more articles on equally-deserving academics who are not properly represented here, and/or fix up this one to better represent his accomplishments? —David Eppstein (talk) 17:41, 10 April 2009 (UTC)
(a)I do not know much about Prof. Steele. to contribute, (b) I did not want to fight AfDs which I expected to follow. (Igny (talk) 18:05, 10 April 2009 (UTC))

## History of matrices

I'm currently trying to write a good article on matrices. One of the still weak points is the history section. Does anybody know a good reference for this topic? Thanks, Jakob.scholbach (talk) 20:09, 10 April 2009 (UTC)

Try Matrices and determinants and Thomas Muir: History of determinants r.e.b. (talk) 20:28, 10 April 2009 (UTC)

Jakob, I think you can read French-language texts. Try Les matrices : formes de représentation et pratiques opératoires (1850-1930) which seems complete, with a lot of sources, some of them in English. --El Caro (talk) 07:16, 11 April 2009 (UTC)

## Poll: autoformatting and date linking

This is to let people know that there is only a day or so left on a poll. The poll is an attempt to end years of argument about autoformatting which has also led to a dispute about date linking. Your votes are welcome at: Wikipedia:Date formatting and linking poll. Regards Lightmouse (talk) 11:45, 11 April 2009 (UTC)

Please forgive my complete lack of familiarity with mathematics on Wikipedia, but the article Internal_-_Proof:_Orthogonality_of_Solutions_to_the_General_Sturm-Liouville_Equation looks like it could be deleted, even though it (looks to me like) it contains some salvageable information. Could someone more familiar with the area take a look? Cheers, - Jarry1250 (t, c) 16:07, 11 April 2009 (UTC)

I moved this to Orthogonality of solutions of the general Sturm–Liouville equation, and then someone deleted the new redirect. Michael Hardy (talk) 16:24, 11 April 2009 (UTC)
I am working on the markup for this proof (I am new to Wikipedia and forgot to prepend the page with my account name). This proof is not yet properly typeset, but is closer than the material mistakenly put into the general Wikipedia namespace. When it is ready to go, I will make a proposal to create a page for the proof and link the Sturm-Liouville page to it. I am also working on the markup for a proof of the orthogonality of Associated Legendre Functions for fixed m. (see separate entry on this talk page). Dnessett (talk) 17:32, 11 April 2009 (UTC)

## Polynomial recurrence

Polynomial recurrence has been prodded for deletion 76.66.193.69 (talk) 06:54, 25 March 2009 (UTC)

I added a little to the article mentioning Somos sequences (a different subject, one that I think we should have an article but don't now, and one that is an example of the type of recurrence described by the polynomial recurrence article). However I haven't unprodded it yet because I'm not convinced this is important terminology. —David Eppstein (talk) 18:27, 26 March 2009 (UTC)
A big problem with this article is its title. "Polynomial recurrence" is a well-known non-trivial notion in Ergodic Ramsey Theory. Look at Vitaly Bergelson's website (math.ohio.edu), for example. In contrast, the definition of this article is a trivial one, probably not deserving a separate name and article. At least, the title should be changed. Polynomial recursion would be much better, I think. A bit of a problem is that I see there exist some more papers using the term "polynomial recurrence" in this meaning... So maybe a disambiguation page is necessary? --GaborPete (talk) 06:01, 3 April 2009 (UTC)
"Recursion" would be quite incorrect. This is about recurrence relations. But whether it deserves to be separate from the main recurrence relation article is not obvious to me; I'm leaning towards a merge. —David Eppstein (talk) 06:50, 3 April 2009 (UTC)
Wow. I have used "recursion" for recurrence relation in all my life, without having heard (or noticed?) the expression "recurrence relation"... It might be the influence of my Hungarian mother tongue (rekurzió), but it's still strange, given that I have been working in North America for 8 years now (with degrees from Cambridge, UK, and Berkeley, CA). Anyway, I vote for this article to be merged into recurrence relation. But is it OK to do it without a redirect? "Polynomial recurrence" should really be about Ergodic Ramsey Theory, I think, but I'm biased, since I'm interested in that area. --GaborPete (talk) 09:00, 3 April 2009 (UTC)
To David Eppstein: A recurrence relation is one way of defining a primitive recursive function. So the use of "recursion" is appropriate. JRSpriggs (talk) 12:56, 3 April 2009 (UTC)
I too have encountered "recursion" in this sense often; in particular the terms "recursion equation" and "recursive sequence" seem fairly frequent. My impression was that it's old-fashioned, and "recurrence" is more common and what we should call it now. Shreevatsa (talk) 13:16, 3 April 2009 (UTC)
Perhaps my greater care at distinguishing "recursion" from "recurrence" comes from my computer science background. But to me, "recursion" is a computer programming concept involving subroutines that call themselves. There are no computer programs, no subroutines, in a recurrence, only an equation relating certain values of a sequence to certain other values of the same sequence. One can trivially construct a recursive algorithm to compute the values of a recurrence, but it's usually the wrong way to compute them (dynamic programming is much more efficient). —David Eppstein (talk) 14:20, 3 April 2009 (UTC)
Yes, I know — I should have mentioned that I too, since learning programming, have always hated the use of "recursion" for recurrence (but that I've encountered it sufficiently often to hate it!). In my experience, this use of "recursion" (which is not a reference to the computer programming concept, or to a method for computing the values) is mostly found in old books written long before computer programming was common (and in some translated books). I agree that Wikipedia (and everyone else) should, to avoid confusion with computer programming (but note that the recursion article talks of other things too), not use "recursion", but the more current term "recurrence" — was only explaining why "recursion" might be familiar to User:GaborPete and yet seem incorrect to modern US readers. Shreevatsa (talk) 15:03, 3 April 2009 (UTC)
Well, I find it quite strange that although recurrence relations are much closer to algorithmic recursion, recursive definitions and recursive sequences than to recurrence in dynamical systems and probability, this closeness for you is a reason for calling them differently, rather than similarly. Also from the point of view of English word endings: recursion is a product of something recursive, while recurrence is the state of being recurrent. Of course, one could equally say that the defining relation of a recurrence relation is 1. a recursive relation, or 2. a recurring relation, but then why "recurrence relation" and not "recurring relation"? Anyway, I know I won't change this. But according to google, my version also seems well-established (both in research papers and textbooks), so you shouldn't forbid "linear, polynomial, non-linear recursions". --GaborPete (talk) 03:53, 13 April 2009 (UTC)
Given all this discussion, what should we do with polynomial recurrence? Merge the article to recurrence relation, then a disambiguation page? I volunteer to write the ergodic theory version. --GaborPete (talk) 03:53, 13 April 2009 (UTC)
Merge and dab seems like a fine solution to me. —David Eppstein (talk) 04:16, 13 April 2009 (UTC)

## Proposal for adding proof to Associated Legendre Function article

I spent 2 weeks searching the web, trying to find a proof of the orthogonality of Associated Legendre Functions for fixed m without success. So, working together with a theoretical physicst (retired) we developed one. Some of the proof relies on logic I found on the web and some we developed on our own. We would like to contribute this proof to the Associated Legendre Function wiki page (using a link to a separate page for the proof). It was suggested to me by RHaworth (who seems to be a Wikipedia administrator) that I work with an established editor on this. I am happy to do so. Please contact me if you are interested in working on this. Dnessett (talk) 17:32, 11 April 2009 (UTC)

Please see WP:OR. Wikipedia is not the place for publishing original proofs. It's ok to have proofs in some articles (especially to the extent that it contributes to the reader's understanding, rather than merely supplying a mechanical verification of some fact) but it would be best if you could point to something in the mathematical literature as a published proof of the same fact that you're simply rewording. —David Eppstein (talk) 18:01, 11 April 2009 (UTC)

I am not proposing an original proof. The proof is an amalgamation of steps I found on the web, these fragments being hard to follow. The proof contains a reference to a book that is partially available on Google:books. The reason I am making this proposal is I am learning Quantum Mechanics (with the help of a Theoretical Physicist) and could not find anywhere on the web a proof that the Associated Legendre Functions for fixed m are orthogonal. This is stated on the Associated Legendre Function Wikipedia page, but it is not easy to demonstrate (there are a few calculus tricks that are non-obvious). So, providing a proof would help others who find themselves in the same position understand why these functions are orthogonal. A draft of the proposed proof is at: User:Dnessett/Legendre/Associated Legendre Functions Orthogonality for fixed m. Dnessett (talk) 18:26, 11 April 2009 (UTC)

Since Wikipedia isn't really the best place for proofs, it might be better to put the proof on PlanetMath, and put an external link to the proof in the appropriate Wikipedia article. --Zundark (talk) 18:33, 11 April 2009 (UTC)
I disagree that Wikipedia isn't the place for proofs. We shouldn't insist on proofs for every mathematical fact stated here, but I think it's reasonable to include a proof (or maybe better a sketch of a proof) when it conveys more to the reader than just the validity of the proposition being proved — often a proof will contain important ideas that have more general applicability, and are best expressed in the context of the proof. Alternatively, another reasonable standard is whether a survey article in the Monthly would be likely to include the proof. And some proofs are notable in their own right (for instance, most or all of the proofs in Aigner and Ziegler's "Proofs from the Book" could be considered to meet WP:N, as they are explicitly discussed by a third-party reliable source). My biggest concern with proofs is (as I know from experience) it's easy to commit original research rather than following previously published steps, but it sounds like that's not an issue in this case. —David Eppstein (talk) 19:20, 11 April 2009 (UTC)

I don't know much about PlanetMath, but when I went to its web site and searched for "Associated Legendre Function" I found nothing (there was some material on Legendre Polynomials, but they are a limited subset of Associated Legendre Functions). There is a Wikipedia article on Associated Legendre Functions and it would seem to me appropriate to provide a subpage of that article that proves the orthogonality of those functions (right now it is just stated). These functions are components of Spherical Harmonics, which are used extensively in the solutions of differential equations expressed in spherical coordinates. Speaking from personal experience, I found it hard to accept by fiat that the Associated Legendre Functions are orthogonal. So, I would argue that others who are investigating subjects that use these functions would find a proof of orthogonality beneficial. Dnessett (talk) 18:52, 11 April 2009 (UTC)

For those who may be interested, a first draft of the proposed proof page is found at User:Dnessett/Legendre/Associated Legendre Functions Orthogonality for fixed m Dnessett (talk) 19:07, 11 April 2009 (UTC) [Sorry, I already stated this above. I'm not sure what is the proper etiquette here. Should I remove this redundant comment or leave it, since it is part of the historical record?] Dnessett (talk) 19:20, 11 April 2009 (UTC)

It has been pointed out that the proposed proof not only shows orthogonality of the Associated Legendre Functions, but also provides the normalization constant. Consequently, I have created a new page User:Dnessett/Legendre/Associated Legendre Functions Orthonormality for fixed m that is properly labeled. The old page will remain, but all my future work on the proposal will occur on the new page. Dnessett (talk) 14:28, 12 April 2009 (UTC)

## Honorable titles for Professors

It is somewhat connected to the previous section. There are many honorable titles in academics of various degrees. I wonder which are worthy of inclusion here. In my personal opinion, many of these titles should not be notable enough. In fact, from the experience of people who I know, earning the title is akin to becoming a member of an elite club, not quite notable enough on its own merit. In many cases it says more about the person as a politician rather than as an academician. I am talking about various named professorships, distinguished professors, etc. How about professors who gained other types of recognition/ achievements, like publishing 100+ papers, or 10+ books, or getting a million dollar grant? Where should we draw the line? What do you think? (Igny (talk) 18:33, 10 April 2009 (UTC))

If you don't think that having a title should be sufficient, you should suggest that on WP:PROF.
It's worth pointing out that what's considered a large number of published papers varies depending upon the field. And quality is generally more important than quantity. If someone has published 100+ papers or even 1,000+ papers, but not a single one is interesting, then that person should not have an article. Whereas someone who doesn't like to publish and publishes only interesting work (such as Ofer Gabber or Mariusz Wodzicki) should have an article. (Unfortunately, neither of them do!) Ozob (talk) 20:34, 10 April 2009 (UTC)

I personally haven't met any titled math professors that seem to have achieved their distinction from politics. Rather, I see a number of such people who generally avoid politics and have hefty mathematical reputations. I'd like to know if Igny's assertions are based on either plentiful experience, academic studies, or perhaps s/he has experience in other subjects and certain countries. --C S (talk) 23:28, 10 April 2009 (UTC)

Well, I am not trying to diminish achievements of mathematicians in any way. Any of the recognition is quite an accomplishment, and I actually did not mean to judge it. However, I would like to discuss the inclusion threshold for WP articles of thousands of science professors. The reason of this discussion is actually to avoid AfD battles before they even start. Case in point, article on Estate V. Khmaladze, existence of which was questioned soon after it was created. (Igny (talk) 19:41, 11 April 2009 (UTC))

I agree with Igny's comment. I strongly believe that developing a set of meaningful criteria for inclusion of living mathematicians into Wikipedia is a serious issue that we need to discuss at length. Refering to WP:PROF is a non sequitur. We need to come up with guidelines, or better yet, clear criteria that are suitable specifically for mathematicians, that are consistent with Wikipedia's mission, and that make sense from the practical point of view. So far I mostly see a knee-jerk reaction on a part of a few people ("who are you to question professional merit of my peers"?), which is off the mark, with some overtones of inclusionism, and only occasional rational arguments. I personally prefer to err on the side of caution and not create articles unless there is a good reason to do so (it's not a secret that removing material from WP is harder than adding it, and that many reasonable AfDs fail in the face of entrenched resistance of only a few persons or due to general apathy). Further, it would be nice if we can reach consensus on the kinds of information that should and should not be included into the math biographies.

I will list some things to consider in developing the criteria, and I hope that more than the usual two or three people will contribute their perspectives. Arcfrk (talk) 21:22, 11 April 2009 (UTC)

• We are not in the business of evaluating scientific merit of anyone's work. The committees that oversee appointments for named chairs and professional awards base their judgment on confidential reports that cannot be cited on Wikipedia.
• There is a large number of mathematicians who have made impact within their fields and/or have been recognized through academic honors but who lack significant secondary source coverage. Although notable according to WP:PROF and other guidelines, their inclusion will contradict Wikipedia's policies on sources and verifiability (apart from the obvious difficulty of coming up with encyclopaedic information in the first place).
• There are mathematicians with significant impact on major areas of mathematics who presently lack wikipedia bio articles (shockingly, this includes several winners of Leroy P. Steele Prize for lifetime achievement). Should we, therefore, engage in systematic creation of articles on mathematicians deemed notable according to a certain set of criteria? This seems already to be happening eg with members of national academies and presidents of professional societies.
• Wikipedia is not a directory or indiscriminate collection of information. On the other hand, there are electronic databases, such as MathSciNet and Zentralblatt der Mathematik, that are "closed source" and are viewed both as authoritative and as accurately reflecting the publication record in mathematics.
• Thousands of mathematicians have published articles in the leading mathematics journals such as Annals of Mathematics, Inventiones Mathematicae and a few others (it would be hard to even come up with a generally agreed upon list, but I note that some of the leading journals themselves do not have a WP article yet!). Any attempt to create articles for all of them is bound to result in thousands of stubs with no reason or mechanism for further development.
• Any biographical article is a liability to maintain and a potential source of aggravation for its subject, as evidenced by continuous debates relating to WP:BLP.
• Should the practice of creating red links for mathematicians whose contributions are mentioned in topical articles on Wikipedia or whose work is cited be encouraged or discouraged?
• What is a reasonable quantity of publications in a biographical article? Should monographs or textbooks be given more weight than articles? All too often, the publication list appears to be a fairly random hack (not even based on MathSciNet in some cases). Should we strive to create annotated lists? Or would a link to the person's own publication list on the web be a better solution?
Since Arcfrk asked for contributions from other than the usual suspects, I'll keep it brief, but (1) if there's a problem here, it's true generally of professors rather than specific to mathematicians, so I don't see the point of math-specific standards other than some obvious points such as that MathSciNet is a more appropriate database to use than the alternatives; (2) there's a related recent discussion at Wikipedia_talk:Notability (people)#WP:ATHLETE needs updating in which WP:PROF is cited as appropriately restrictive compared to the situation in professional sports in which walking on the field once counts as being sufficiently notable; (3) I think verifiability is a much bigger problem than notability for our current academic biographies. —David Eppstein (talk) 21:54, 11 April 2009 (UTC)
Here's a proposal. New list: List of basic details for notable mathematicians. It is proposed that redlinks for mathematicians are redirected to their section in this list. The list will eventually include links to each mathematicians homepage, their Mathematics Genealogy Project page, other biographical sources as they are found, list of awards etc. Charvest (talk) 18:29, 12 April 2009 (UTC)
It looks like a useful aid to editing math biography articles, but shouldn't it be in Wikipedia project space rather than in article space? —David Eppstein (talk) 18:43, 12 April 2009 (UTC)
RHaworth thought similarly but chose user space instead. It's now at User:Charvest/sandbox. —David Eppstein (talk) 19:46, 12 April 2009 (UTC)
Now at Wikipedia:WikiProject Mathematics/mathing missematicians. — RHaworth (Talk | contribs) 19:51, 12 April 2009 (UTC)
A funny name! Boris Tsirelson (talk) 20:09, 12 April 2009 (UTC)
At the moment all the redlinks from Euler medal, Godel prize, Polya Prize, Leroy P. Steele Prize and EMS prize are included. The list was formatted and sorted in alphabetical order using Textpad with regular expressions, with some manual adjustments. I can do the same again to incorporate lists of redlinks from other prizes for every prize deemed suitable. Would you say that all mathematicians getting any of the prizes in the category Category:Mathematics awards are automatically notable ? Using textpad was a workaround. It would be better to use a database I suppose. Any recommendations ?Charvest (talk) 21:26, 12 April 2009 (UTC)
Ahem, all? What about Richard Kadison (Leroy P. Steele Prize, 1999)? Also, maybe seeing all these red links will cool down some heads thinking of including more prizes. Arcfrk (talk) 21:46, 12 April 2009 (UTC)
Ok, I missed some. Now added. Charvest (talk) 23:43, 12 April 2009 (UTC)
I've moved the page to Wikipedia:WikiProject Mathematics/missing mathematicians; hope the new name is less funny. Boris Tsirelson (talk) 15:25, 13 April 2009 (UTC)

## Artinian ideal

Artinian ideal has been proposed for deletion via a "prod" tag. It gets 30 hits in google books and 78 hits in google scholar. I have qualms about its deletion because Wikipedia's coverage tends to be broad. But algebra is not my field.

I added the identification of the eponym as Emil Artin. Is it possible that it's actually Michael Artin? Michael Hardy (talk) 16:22, 11 April 2009 (UTC)

If it is, the whole section needs work; we imply that these are named for Artinian rings, which come from the Artin-Wedderburn theorem. Septentrionalis PMAnderson 14:28, 13 April 2009 (UTC)
I figured it out: the article intends to talk about "Artin monomial ideals" in (free) polynomial rings. I just haven't gotten around to correcting it. Arcfrk (talk) 16:34, 13 April 2009 (UTC)

## Continuity property

Should this article exist? Is this a common name for this theorem? Jim (talk) 02:14, 13 April 2009 (UTC)

The name is almost certainly ambiguous. By me, this is a trivial consequence of the Heine-Borel theorem, but I'm not sure our readers will think so. Septentrionalis PMAnderson 03:09, 13 April 2009 (UTC)
The real content of this theorem is expressed in the statement that the continuous image of a compact set is compact and the image of a connected set is connected; everything else follows immediately from the Heine-Borel theorem, as PMAnderson points out. The name looks like a neologism, so it seems better to me to delete this article. I have prodded it. Ozob (talk) 15:28, 13 April 2009 (UTC)
It's not just Heine-Borel: you also need the fact that intervals are connected. Even the compactness part can be done without open covers. When I was an undergraduate we did all this with sequential compactness. Algebraist 16:08, 13 April 2009 (UTC)
Good point, thanks for the correction. Ozob (talk) 00:58, 14 April 2009 (UTC)
I went there and read it and my reaction was to see if it could be redirected to Heine-Borel theorem. But after I looked at Heine-Borel theorem, I decided I'd better not. The H-B theorem article is too technical. I think there is room in the encyclopedia for an article that highlights the special case of H-B that says that the image of a closed interval under a continuous function f ; RR is a bounded set. That could be a new article, or it could be a section at the top of the article on H-B. The H-B article as it is has a number of pedagogical problems. For example, it launches almost immediately into a discussion of pseudocompactness. But pseudocompactness is only interesting in case cases that the H-B theorem does not cover!
I think a good approach would be to fix up H-B suitably, and then redirect Continuity property to there. I'll take a stab at that if nobody else does something sooner. —Dominus (talk) 15:39, 13 April 2009 (UTC)
There are two natural questions here: firstly, how commonly in the literature is the result covered by this article treated as a single result, rather than two separate results (one to do with compactness and one with connectedness)? Secondly, of the sources that do treat this a single result, what name do they give to it? I do not know the answer to either of these questions. Algebraist 16:08, 13 April 2009 (UTC)
I don't know the answers. But I will speculate: I think that the special case I noted above predates the formulation of compactness, and provided the initial motivation for both compactness and for the H-B theorem. Was H-B really discovered in the context of arbitrary metric spaces, as the current Heine-Borel theorem article suggests? I imagine that it was originally a theorem of analysis, not topology, and was generalized later. I will try to do some research on this, and I suggest that we take this part of this discussion to Talk:Heine–Borel theorem. —Dominus (talk) 16:28, 13 April 2009 (UTC)
The compactness-related stuff isn't the issue here: it's covered in our article extreme value theorem. The problem with continuity property is that it is (more or less) a combination of the EVT with the IVT, and this combination may not be notable. Algebraist 16:34, 13 April 2009 (UTC)
Neither Baby Rudin nor Ross's Elementary analysis seem to state this in quite the way the article has it. In Baby Rudin, it's proved in the middle of theorem 4.23; in Ross, I guess corollary 18.3 is the closest, but it doesn't include compactness of the image. Ozob (talk) 00:58, 14 April 2009 (UTC)

## Infobox

Hello, everyone. Does anyone think having an infobox in a math article is a good idea? What I have in mind is something like this (see right):

Technical level Undergraduate Yes Yes Yes. (Dedekind) ≤ 1 Field, Polynomial ring in one variable, Set of integers Euclidean domain UFD, Bézout domain UFD Discrete valuation ring Finitely generated modules over a PID

(This is something I prepared for the purpose of the discussion, so the details are not my concern right now.) If there was a similar proposal before, I'm not aware of it.

Part of the reason I'm proposing this is that I think infoboxs are inherently more accurate than those chains of rings we have in some articles; e.g., one in principal ideal domain article. I understand the motivation behind those chains: to put a topic in a large context. I believe infoboxs can do a better job. -- Taku (talk) 11:26, 11 April 2009 (UTC)

No, I don't think that's a good idea, for several reasons. I don't see the issue with the lede of principal ideal domain; it's easy to read. Here are some reasons I don't support that sort of box:
• Foremost, mathematics is best communicated through the same language we ordinarily use to communicate, which is English sentences. It's not actually any easier to read the infobox than it is to read sentences; in fact, it's harder, because I have to read each line, decide what phrase on the left is actually supposed to mean, and then read the right, and decode any abbreviations there.
• Because of the lack of context and space, it's very hard to convey any subtlety via an infobox. This tends to generate lots of questions and confusion when readers cannot figure out what something in the infobox is supposed to mean. It also leads to erroneous edits by well-meaning users who think something in the infobox is correct, because it is too brief to explain fully.
• Some over-zealous editors tend to put far too much in the infobox. Not having the infobox at all is a good way to avoid this. For example, if we have a "examples" section, I predict some editor will copy all the examples into the infobox. It's very difficult to get agreement on exactly which subset of the examples to include in the infobox, and the time taken for that discussion is better spent on other things.
• More generally, the information in the infobox only duplicates what is in the article, and so it just adds to the difficulty of maintenance.
• Because there is no good reference for the technical level of a part of mathematics, we shouldn't try to assign it one. Is metacompactness a graduate or undergraduate topic? The Gauss–Bonnet theorem?
• Infoboxes are nice for Chemicals, where there is certain data (such as the chemical name and molecular formula) that we know each chemical will have. And they are OK for people, because again there is certain data (birth and death, nationality) that all people will have. But there is no simple collection of bullet points that all mathematical topics share.
— Carl (CBM · talk) 12:09, 11 April 2009 (UTC)
I think it's a very good idea. I don't agree that "infoboxes are inherently more accurate" or that they "can do a better job" than anything, but I do feel that adding infoboxes can be useful. (In addition to the text of the article, not as a replacement.) In particular, the "Examples", "Generalizes", and "Special case of" would be useful to have quickly visible in an infobox for any article. To answer some of CBM's points:
• Everything is best communicated through English sentences, and yet we have infoboxes everywhere on Wikipedia,
• Readers who care will read more than just the infobox, so it's okay if it misses some of the subtleties,
• The question of what is "far too much" for an infobox can be resolved through discussion and consensus as usual,
• I don't see a problem with the infobox duplicating what is in the article (that's what it's meant to do),
• I agree that "technical level" should not be one of the fields of the infobox (but this a detail, let's not discuss this right now),
• It's OK that there isn't a simple collection of bullet points for all mathematics topics, really Shreevatsa (talk) 15:07, 11 April 2009 (UTC)

Let me clarify a few things first. I never meant to suggest we replace text by infoboxes. (I though that was obvious...) I never said the lede of the PID article has a problem, and my infobox idea is going to solve it. All I meant was that an infobox is probably a better idea than a chain of rings currently we have. I never meant to claim infoboxes are "inherently" superior forms of describing math. I agree that an infobox cannot convey some important subtlety, which text can provide better. But that's basically the point of an infobox. While the article can discuss a topic in depth, infobox can provide a summary of the article; they work complementary to each other. I also don't believe math is best communicated via prose. Why do you, for example, put examples in bullet points on a white board when you teach a class? Because, apparently, sometimes leaving some technical details out help students remember essential points. infoboxes duplicate information, but that's exactly the point: putting the same information in different forms help readers digest information. I think this is why infoboxes are popular throughout Wikipedia. We are in bussiness of conveying information after all and we seek to maximize the effectiveness.

As to "technical level" section in my muck-up, I thought that's important because, often, math articles are often accused of not clearly specifying the background necessary to understand them. It is inevitable that some math articles are simply unreadable without proper prior-training. Also, it is important that an article clearly states if the topic that the article discusses is of interest only to researchers or something every math major learns in college. Of course, "technical level" isn't a good way to do. A possible alternative would be "prerequisite". Does anyone have suggestion? -- Taku (talk) 18:25, 11 April 2009 (UTC)

In the article principal ideal domain there is already a bullet point list of examples - in the section titled "examples". But most of the other things in your mock up would only apply to algebraic structures (commutativity, etc), not to arbitrary articles on mathematics.
The idea of having article list "prerequisites" has been discussed many times, and the outcome of the discussions has always been that the lede section should establish the context, and that there is no need to list prerequisites otherwise. — Carl (CBM · talk) 18:41, 11 April 2009 (UTC)

I should have been more specific. I didn't propose to put an infobox that exactly looks like one I put above to every math article. No. Obviously, not every math article needs an infobox, and each article needs a different kind of infobox. The one above should be called "Template:Infobox ring" or something and should be put to articles on rings or rings-like structures. I was interested how people feel about infoboxes in math articles in general, not specific one above. If "prerequisites" is not a good idea, then that's ok. As I said above, I only made that mock-up to generate discussion about infobox. The details could be worked out later if people are for infoboxes. -- Taku (talk) 18:52, 11 April 2009 (UTC)

I don't have a strong opinion about this, but I think the infoboxes may lead to crappier pieces of information than a usual text would. Also, the information you have put in the box up there should mostly be covered by an adequate lead section. (E.g. commutative, Noetherian, domain, a few examples, applications). Jakob.scholbach (talk) 19:57, 11 April 2009 (UTC)

My general feeling is that infoboxes are a very bulky way of conveying very little information, and that they discourage editors from putting the same information in a more readable form into the prose of the article. Also, when placed prominently in an article they get in the way of illustrations. —David Eppstein (talk) 20:01, 11 April 2009 (UTC)

I think infoboxes are really a matter of taste. Obviously the example doesn't work; it would take quite a bit of work to get this right. But done right, they could make our articles a bit more appealing to a wider audience. I don't really see them getting in the way of illustrations – typically we don't have any, and this is unlikely to change any time soon. In that case infoboxes can work as a substitute. What I see as a potential problem is that infoboxes may discourage merging of articles.
E.g. the articles prametric space (could someone comment on the talk page whether that's a translation error for premetric?), pseudometric space, quasimetric space, semimetric space could profit from an infobox for generalised metrics. But it would probably be better to merge the whole bunch. --Hans Adler (talk) 21:54, 11 April 2009 (UTC)
I've moved the article to premetric space, and I agree that all these articles should be merged. Charvest (talk) 22:55, 11 April 2009 (UTC)
I have a religious dislike for infoboxes. Paul August 03:21, 13 April 2009 (UTC)

I don't have anything in particular against Taku's infobox over other infoboxes...but to echo Paul's comment: I have never seen an infobox in an article improve the article. Articles on chemical elements is an interesting example and one I may be easily persuaded are useful. However, looking at the cluttered infobox in carbon, I wonder how useful it really is. --C S (talk) 05:35, 14 April 2009 (UTC)

For what it's worth, mathematics articles on probability distributions already have infoboxes (that's Template:Probability distribution), see e.g. Exponential distribution, Cauchy distribution etc. And I have found the infoboxes useful on several occasions (well, I don't know what skewness and excess kurtosis are, but all the rest have been useful at least once). Not all mathematical topics have similar facts about them that might be looked up often, but for ones which have them, infoboxes are useful. Shreevatsa (talk) 05:58, 14 April 2009 (UTC)

Shreevatsa made a good point; I was completely unaware of infoboxes in probability articles (probably because I don't edit them.) This led me to believe that I didn't start the thread with a right question. Let me ask a slightly different question. Does anyone can think of any math articles that can be benefited from having infoboxes? In particular, do you think ring articles (e.g., PID, UFD, Bezout domain, GCD domain, ...) can use infoboxes to improve the convenience of readers? -- Taku (talk) 11:58, 14 April 2009 (UTC)

I have found the infoboxes on elements and statistical distributions to be useful. I don't think they would be useful in many math articles. For the algebra articles I prefer more of a breadcrumb "monoid - semigroup - group". CRGreathouse (t | c) 14:25, 14 April 2009 (UTC)
Infoboxes seem to be most useful when the item falls into a well defined classification scheme, and have a few well defined properties which people want to look up. Towns, species fit well with this, I certainly find it easier to find the population of a place from the infobox rather than having to parse the text. Polyhedra (eg) is another grouping of mathematical objects where infoboxes prove useful.
I'm undeiced about whether specific rings really fit. Most properties are fairly esoteric which will be of little interest to most readers. --Salix (talk): 15:29, 14 April 2009 (UTC)
Infoboxes are useful for examples of a general phenomenon. All chemicals share certain properties such as the existence of a boiling point and the existence of a freezing point. Similarly, all probability distributions share certain properties such as the existence of a mean and a median. Just where the boiling point or freezing point is depends on the chemical, and just where the mean or the median is depends on the probability distribution. That's where infoboxes are useful: They collect data on examples. If you can find another type of mathematical structure that has many, many examples, then it might be worthwhile to have an infobox for examples of that structure. For example, you might have a group infobox: It would have information such as whether the group is abelian, simple, nilpotent, solvable, and so on. The trouble with this is that in order for it to be useful, you'd have to find a lot of interesting information for all the groups on Wikipedia; if you had only very basic information, such as whether the group is abelian and whether it's simple, then the infobox would be a waste of time and space.
Another thing to consider is that sometimes our articles cover topics where an infobox may not be workable. Consider group of Lie type, for example. There are lots and lots and lots of groups of Lie type. If you wanted to put a group infobox in that article, for just about every entry you'd have to say "Depends on the group". For specific families of these groups, you may be able to answer this question (e.g., most groups of the form PSLn(Fq) are simple), but in general there's nothing to say. So you'd have to pick which articles get the infobox very carefully.
On the whole, I'm not sure infoboxes are worth the effort. It doesn't seem like they would be for rings since classifying rings is an impossible project. Ozob (talk) 15:59, 14 April 2009 (UTC)

## copyvio

The page Talk:Method of lines says it is a copyio. Charvest (talk) 05:38, 15 April 2009 (UTC)

It looks like the writer tried to paraphrase, but failed to do so very well. They also added information not present in the MathWorld article. I have copyedited it some more and trimmed a sentence or two; I think it is OK now. The best way to make it look less like the MathWold demo would be for someone knowledgeable to expand the article on WP. — Carl (CBM · talk) 11:48, 15 April 2009 (UTC)

## New collapsible auto collapsible template for calculus

For practice with templates, I rewrote a calculus template that was collapsible and that you can have open to the correct category. I did add some articles as well to help from a physics perspective. (Being collapsible, the space issue is diminished quite a bit.) I stole the autocollapse mechanism from Template:PhysicsNavigation but I tried to keep the calculus style.

If there is no objections, I am likely to replace this current calculus template with the one I rewrote soon. I don't know enough about the math projects style to push the button without some warning, though. TStein (talk) 19:15, 17 April 2009 (UTC)

Go ahead. I know not much about Wikipedia templates but I see nothing wrong with your changes. --PST 03:23, 18 April 2009 (UTC)

## WAREL back?

I am not familar with WAREL, but it seems clear that Motomuku is a reincarnation of User:Katsushi. --Hans Adler (talk) 10:19, 18 April 2009 (UTC)

## Strange articles

Valya algebra and Commutant-associative algebra — both created by a single purpose account (no other substantive edits), appeared to be hoaxes at the first glance, since I'd never heard these terms before. After investigating a bit, I found out the following.

• Neither of the two EOM articles quoted (devoted to certain non-associative structures) mentions anything related.
• MathSciNet has exactly one instance of "Valya algebra", in a review of an article of some V.E.Tarasov from 1997, the review quotes from the author's introduction. The same review is also the only occurrence of "commutant-associative algebra" in MathSciNet.
• Zentralblatt has no instances of either term.
• Books of Kurosh quoted do not contain references to these structures.
• The book of V.E.Tarasov quoted has not been reviewed either by MathSciNet or Zbl (in fact, it's not even listed there).

I strongly suspect that the other books quoted (e.g. Malcev) contain nothing on the subject and have only been put in in order to lend an air of legitimacy to the topic. The terms appear to have been used by a single author (and possibly, only on a single occasion); as such, I would think that they are not notable, in spite of having appeared in an established (non-mathematical) journal. It is entirely possible that these articles were created with a purpose of promoting a fringe topic. Whether or not that is the case, what would be an appropriate course of action? What are the specific policies that these articles violate that can be quoted in filing AfD? Arcfrk (talk) 02:52, 18 April 2009 (UTC)

WP:V#Burden of evidence says "The source cited must clearly support the information as it is presented in the article." and "Any material lacking a reliable source may be removed, ...".
WP:V#Reliable sources says "Articles should be based upon reliable, third-party published sources with a reputation for fact-checking and accuracy." and "In general, the most reliable sources are peer-reviewed journals and books published in university presses; university-level textbooks; magazines, journals, and books published by respected publishing houses; and mainstream newspapers.". JRSpriggs (talk) 07:01, 18 April 2009 (UTC)
If this is fringe in the sense of something that only the author works on, then perhaps the definitions can be mentioned in an existing article on a related topiic? Of course, if it is fringe in the stronger sense it's probably better to simply prod it and send it to AfD if necessary. Commutant-associative algebra seems to give two definitions for the same term. I am not used to this type of algebra; does the first imply the second? --Hans Adler (talk) 10:12, 18 April 2009 (UTC)

## Proposal to add proof to Sturm–Liouville theory page

I propose to add a subpage to the Sturm-Liouville namespace that proves solutions to the Sturm-Liouville equation corresponding to distinct eigenvalues are orthogonal. I am asking for help from an editor who works on this namespace to work with me on this. The proposed proof is found at Orthogonality proof. To avoid unnecessary suggestions, let me state that this proof is not original research and there does not seem to be consensus whether proofs belong on Wikipedia or not. On the latter issue, I have contacted established editors asking for their views, but have not yet received a response. If I do not hear from anyone by next week, I will just add the subpage and see what happens. Dnessett (talk) 15:31, 15 April 2009 (UTC)

Why not just add it to the article? Shreevatsa (talk) 15:36, 15 April 2009 (UTC)

I am new to Wikipedia and so am being somewhat cautious in adding pages to the main Wikipedia namespace. It was earlier suggested (when I made a mistake that placed an unwelcomed page in the main namespace, see [Internal?]) that I work with an established editor of the Sturm-Liouville namespace. I have attempted to do this, but no one has stepped forward. Dnessett (talk) 16:01, 15 April 2009 (UTC)

After rereading your question, I now realize I didn't understand it on first reading. I am proposing a subpage so that readers uninterested in a detailed proof need not wade through significant text in order to get to the next point. Dnessett (talk) 17:35, 15 April 2009 (UTC)

What is the value of this. The Sturm–Liouville theory article already gives an effective sketch of how to prove this. A detailed proof on this matter seems of very little encyclopic value. If you still decide that this is useful then that proof should be much better explained. (For example explain before hand what the idea of the proof is.) (TimothyRias (talk) 15:56, 15 April 2009 (UTC))

Value: I and another collaborator were motivated to add this proof when I spent two weeks searching the web looking for a proof that Associated Legendre Functions are orthonormal. I failed to find anything except a Google Books excerpt that made significant jumps in logic. When I contacted my collaborator (a Theoretical Physicist helping me to learn Quantum mechanics), he showed me how the orthogonality of these functions follows from the fact that they are solutions to the Sturm-Liouville equation. He then explained why solutions with distinct eigenvalues are orthogonal and noted that this information was also missing on the web. So, we decided to make a contribution to Wikipedia. Effectiveness of sketch: The sketch might be effective for someone experienced with Sturm-Liouville equations, but for me it was not. I expect other students also would have trouble following the sketch. Better explanation: I am open to doing this, although the sketch in the main article serves that purpose. Why would you repeat that in the subpage? Dnessett (talk) 16:25, 15 April 2009 (UTC)

My general feeling is that any article should stand on its own in terms of notability of subject matter, verifiability, etc. So if you are going to have an article solely about a proof (whether it be called a subpage or "Proof of..." or whatever) you need to justify that the proof itself is notable. This seems difficult to do in this case, given your earlier statements that you had trouble even finding a clear writeup of the proof. If it's not notable in itself, and the details of the proof are not central enough to the topic of the main article to include there, then maybe a Wikipedia article isn't the right way to publish this writeup. —David Eppstein (talk) 17:44, 15 April 2009 (UTC)

The situation is this. I (and others, for example, see physics forum discussion, although that discussion is about the sub problem of Legendre polynomials) have found it difficult to understand why the Associated Legendre Functions are orthonormal. This can be shown directly or by noting they are solutions to the Sturm-Liouville equation, which solutions are orthogonal if they have distinct eigenvalues (which then only demonstrates orthogonality, not orthonormality). The proof of the orthogonality of solutions to the Sturm-Liouville equation is non-obvious, even when sketched as it is in the main article. Is it the role of Wikipedia to help people understand the fundamentals of a theory? I don't know. I only know that when I searched for some help on the web, nothing useful showed up. So, if it is the consensus of the Wikipedia community that this doesn't belong here, fine. I will try to find somewhere else to put it. However, I am not sure how an understanding of consensus is developed. So far, only a couple of editors have responded to this proposal. Would someone give me some guidance on the criteria I should use to simply give up on Wikipedia and go elsewhere? Dnessett (talk) 18:27, 15 April 2009 (UTC)

New Thought: After some thought, I wonder if the following would satisfy your objection. As I understand it, you are uncomfortable with articles that are not self-contained. How about creating a section at the bottom of the Sturm–Liouville theory page that contains the proof. This keeps the proof with the material with which it is associated (so there is no problem with self-containment), but it also doesn't disturb the flow of the reader who isn't interested in the detailed proof. A link to the bottom of the page where the proof resides could be put into the main article. Would this answer your objection? Dnessett (talk) 20:24, 15 April 2009 (UTC)

Your proof is a combination of two proofs: (1) eigenvectors of a symmetric operator, corresponding to different eigenvalues, are orthogonal; and (2) the Sturm-Liouville operator is symmetric. Right? Each one separately is available in many textbooks (I guess so). What is really a problem here? Boris Tsirelson (talk) 19:08, 15 April 2009 (UTC)

You make a legitimate point, but your general argument applies to all Mathematical articles on Wikipedia. Wikipedia Mathematical articles are not supposed to contain original research. They are summaries of knowledge already existing in textbooks, papers and other written sources. So, by your criterion all Wikipedia Mathematical (perhaps all Wikipedia) articles would be unnecessary. Also, let me point out that the proof is a summary of that given in the reference at the bottom of the proposal page. That source provides the explicit proof and does not simply state that orthogonality follows from the two properties you note. Dnessett (talk) 19:33, 15 April 2009 (UTC)

To all proofs, not to all math articles... Proofs are included in Wikipedia only if they are especially interesting (more than usual). But even if this statement should be proved in Wikipedia (assume for now that it should), why in the "combined" form? Surely you do not want to prove specifically that (a-3)(a+3)=a2-9. Instead you'd prove that (a-b)(a+b)=a2-b2, and that 32=9. Boris Tsirelson (talk) 19:53, 15 April 2009 (UTC)

Well, I think your argument that: "Each one is separately available in many textbooks..." applies to just about everything on Wikipedia, but leave that aside for the moment. The reason for not dividing the proof into two parts, as you suggest, is it moves the reader away from the main concern. It requires the reader to suspend his/her interest in why solutions are orthogonal and take up the higher level issue of symmetric operators and their properties. Of course, in the final analysis the form of a proof is a matter of taste. But, presenting the proof in the form as it stands in the proposal has precedent (in the referenced book), which argues for keeping it in its current form. Dnessett (talk) 20:12, 15 April 2009 (UTC)

To reply to your earlier question about self-containment, I think that your proposal of making it a section towards the bottom of the article (but above the references) would be an acceptable solution in that regard. However now I'm finding the later concerns about modularity very cogent. If the result can be made to follow in a straightforward way from two mathematical facts that are each independently so important, what is the value added in merging those separate facts into a single combined proof that doesn't mention them? —David Eppstein (talk) 20:34, 15 April 2009 (UTC)

As I suggested to Boris Tsirelson, the value in presenting the proof as an integrated whole is pedagogical. Factoring it into two parts requires the reader to suspend his/her interest in the orthogonality question and move the focus of attention to the theory of symmetric operators. If, as I was, the reader is interested in why solutions to the S-L equation are orthogonal, but not particularly interested (at least at this point) in delving into the theory of symmetric operators, then the separation frustrates his/her interest. If the reader is a graduate student in Physics or Mathematics, then perhaps forcing him/her to consider the general issue would be healthy. But, not every reader of the article will be in this position (e.g., I am not). My interest is convincing myself that the solutions are orthogonal and then returning to my real interest, which is studying Quantum Mechanics. Let me once again admit that the form of a proof is a matter of taste. Some may find the bifurcation of a proof into two parts a cleaner and clearer way of presenting the proof. But, again as I stated previously, the form of the proof in the proposal is similar to that in the reference, which provides some evidence that this approach has merit. Dnessett (talk) 21:01, 15 April 2009 (UTC)

As a side note. Since your interest is learning Quantum mechanics, you should be primarily concerned with learning the simple fact that the eigenvectors of a Hermitian/Self-adjoint/symmetric are orthogonal if there eigenvalues are different. This fact is central to QM since Hamiltonians are suppossed to be Hermitian operators hence solutions of the time-independent schrodinger equation with different energy eigenvalues are orthogonal. (This little fact is presented in any undergrad textbook, although seldom proven rigorously) From a physics perspective it is then clear that legendre polynomials are orthoganal as they appear as (part of) solutions of the Hydrogen atom.(TimothyRias (talk) 20:59, 15 April 2009 (UTC))

I am using Shankar in my studies. The place where the orthonormality of Spherical Harmonics (and therefore the subsidiary issue of the orthonormality of the Associated Legendre Functions) is introduced is in Chapter 12, which covers rotational invariance and angular momentum. The Hydrogen atom is covered in the next chapter. Spherical harmonics are introduced before we get to the section that covers the solution to rotationally invariant problems (which is section 12.6). So, while your point is valid, I (as an example of a student) am in the process of learning the facts you mention. However, since I prefer to understand things as I go along, I dived into the orthonormality question as soon as Shankar stated it (without proof). That may be more detail about my situation than you desired, but it does provide an example of why people reading Wikipedia might desire the proof provided in the proposal. Dnessett (talk) 21:14, 15 April 2009 (UTC)

Another reason to use the existing proof, rather than breaking it up into two parts: The proof in the proposal elaborates the sketch given in the article. To provide a different proof approach would confuse the reader. Dnessett (talk) 03:32, 16 April 2009 (UTC)

Where is the "monolithic" sketch you mean? I fail to find it. Just the opposite: in Sturm–Liouville theory#Sturm–Liouville equations as self-adjoint differential operators I see: "Moreover, L gives rise to a self-adjoint operator. This can be seen formally by using integration by parts twice, where the boundary terms vanish by virtue of the boundary conditions. It then follows that the eigenvalues of a Sturm–Liouville operator are real and that eigenfunctions of L corresponding to different eigenvalues are orthogonal." Just a sketch of a "split" (rather than "monolithic") proof. Boris Tsirelson (talk) 06:00, 16 April 2009 (UTC)
To my regret, I did not find in Wikipedia this important fact: eigenvectors of a symmetric operator, corresponding to different eigenvalues, are orthogonal. Someone should state it in an article about operators (or spectra etc); and the "Sturm–Liouville" article should link there. As a rule, proofs do not appear in Wikipedia, but statements do. Boris Tsirelson (talk) 06:06, 16 April 2009 (UTC)
Have a look at Compact operator on Hilbert space. And I'd like to add that I don't personnally enjoy very much reading pure lists of facts. What I like in math is seeing the properties in action, and to be told WHY things are true, when it can be done in a reasonably short and nice way. --Bdmy (talk) 07:52, 16 April 2009 (UTC)
I see, thanks. However, this one is not immediately applicable to the Sturm–Liouville operator, since the latter is unbounded. It is applicable indirectly, since (roughly speaking) the inverse operator is compact, but the direct way is preferable. In fact, the needed statement "eigenvectors of a symmetric operator, corresponding to different eigenvalues, are orthogonal" is of the sort you like: "can be done in a reasonably short and nice way"; the proof is short (one line, maybe two). In order to keep the argument short and clear, however, one should avoid self-adjointness (irrelevant here) and use only symmetry (weaker than self-adjointness when operators are unbounded). One should also avoid existence of eigenvectors (this is a harder problem). Boris Tsirelson (talk) 08:37, 16 April 2009 (UTC)
Actually I wrote my post before (and I was wrong about that) looking at the article on Sturm-Liouville theory. Now that I saw both the original article and the proposed adjonction, I must say that I am not in favor of adjoining the proposed proof to the article: there is a too strong difference of level and tone between the two. --Bdmy (talk) 08:43, 16 April 2009 (UTC)

There is a larger issue at hand in this discussion that directly affects the proposal. That is, should Wikipedia include proofs? Subsidiary to this question (if it is decided that proofs are legitimate material in a Wikipedia article) is: when is the inclusion of a proof allowable? This is something the Wikipedia community must decide and perhaps there should be a discussion of this issue at some "higher level" before proceeding with discussions about this particular proposal. However, given that such a "higher level" discussion does not yet exist, I would like to contribute the following thoughts. Wikipedia is used by a large number of people for different reasons. At least three categories of Wikipedia users are relevant to the proof question: 1) those who understand the subject intimately, 2) those who basically understand the subject, but need a place to find details in order to refresh their memory, and 3) those who are learning the subject. Users in the first category tend to be those who write articles. Those in the second and third categories tend to be those who read articles. Discussions about what to include and what not to include in Wikipedia articles are dominated by those in the first category, since they are the Wikipedia editors who do the work. Those who intimately understand a subject many times are interested in eloquence and elegance, rather than in transparency. Since they understand the subject, many details seem to them obvious and therefore unacceptable as material in Wikipedia articles. Readers (those in the second and more importantly the third category) are underrepresented in discussions about Wikipedia content. Many if not most don't even know such discussions exist. So, I think it is prudent for those writing the articles to attempt to take the perspective of users in the other categories. What is obvious to Wikipedia article writers in many cases is not obvious to Wikipedia readers. Dnessett (talk) 16:09, 16 April 2009 (UTC)

However, note the distinction between Wikipedia and Wikiversity. Boris Tsirelson (talk) 17:34, 16 April 2009 (UTC)

In regards to the "monolithic" sketch (a term I don't recall using), if you look at the proof sketch and then at the detailed proof in the proposal, you will see that the latter elaborates the former. So, if you think the sketch is in two parts, then it seems to me you would judge the detailed proof to be in two parts. Dnessett (talk) 16:29, 16 April 2009 (UTC)

The sketch explains (shortly) why this operator is self-adjoint, and says: the orthogonality follows. In this sense it is explicitly split. The "monolithic" (or "combined", if you prefer) proof need not mention the notion of self-adjoint operator at all, and indeed, it does not. Boris Tsirelson (talk) 17:40, 16 April 2009 (UTC)

There has been considerable discussion, off and on, as to whether, when, where, and how to include proofs, some of which is archived on these two pages:

I believe that the consensus has been though, that in most cases, proofs are not appropriate. There are exceptions, notable proofs for example (with references) can be appropriate.

Paul August 18:07, 16 April 2009 (UTC)

The topic has occurred here at WT:WPM, too. The original poster may be interested in the discussions Wikipedia_talk:WikiProject_Mathematics/Archive_46#Proofs and Wikipedia_talk:WikiProject_Mathematics/Archive_46#Connected_space/Proofs. But I suggest that further discussion take place at Wikipedia talk:WikiProject Mathematics/Proofs. Ozob (talk) 18:38, 16 April 2009 (UTC)
I looked at the pages you referenced and again found no clear consensus on the issue. However, I have added an entry to Wikipedia talk:WikiProject Mathematics/Proofs asking for clarification. Before my own, the last entry was 28 Dec 2008. This suggests the discussion page is not very active. So, if the discussion on the larger issue takes off there, then I will pursue it before returning to this discussion. However, if that page turns out to be a black hole, then I would like to continue the discussion here. Dnessett (talk) 19:21, 16 April 2009 (UTC)
I briefly read through the two archives you (Paul August) referenced. It seems to me that there was overwhelming support for providing proofs on Wikipedia. Only one or two users objected to doing so. In addition, there seems to be a category devoted to proofs Article Proofs. So, I am puzzled why you believe that the consensus is most proofs are inappropriate. Dnessett (talk) 18:51, 16 April 2009 (UTC)

I googled "Wikiversity Sturm-Liouville". One of the hits is a page on ordinary differential equations Wikiversity ODEs. This page is in a chaotic state, which means adding a proof of S-L orthogonality to it would be premature. So, there seems to be three choices: 1) wait for the page to become coherent enough to contribute the proof, 2) work on the page myself and get it into sufficient shape to add the proof, and 3) continue pursuing the proposal for adding it to Wikipedia. Choosing the first option would mean there would be a significant amount of time before the proof is available to readers. Choosing the second option isn't practical, since I am not an expert in differential equations, nor do I want to put in the significant amount of time it would take to become one. Choosing the third option has the advantage that the proof would be available relatively soon (if the proposal leads to the proof's inclusion), but has the disadvantage that it is not clear that inclusion is either certain or likely. So, I would appreciate some feedback on these options or suggestions of other options. Dnessett (talk) 18:16, 16 April 2009 (UTC)

Make a PlanetMath page? —David Eppstein (talk) 18:34, 16 April 2009 (UTC)

There is a page on PlanetMath that mentions S-L problems (see Eigenvalue problem). However, they are given as examples. There is no page that I could find that addresses the S-L problem directly. Of course, I could work on creating such a page, but I don't feel I have sufficient depth of expertise to do so. Consequently, this option is very much like option 2 in the entry above. Dnessett (talk) 19:21, 16 April 2009 (UTC)

Well, I don't want to sound hostile, because I'm not, but we're here to build an encyclopedia, not to solve your internet hosting issues. If you can't find better places to publish your writeup, that's irrelevant to inclusion here — what's relevant is what it adds to the article here. So I'd prefer to see discussion continue on the basis of whether adding this proof would be an improvement to our S-L article rather than on how quickly the proof could be made available to readers via one option or another. —David Eppstein (talk) 20:49, 16 April 2009 (UTC)

Fair enough. Dnessett (talk) 21:52, 16 April 2009 (UTC)

I wonder if those who hold that a proof must provide significant improvement to an article might suggest some criteria by which this is judged? It's pretty hard to come up with arguments for inclusion when no objective standards for those arguments exist. Dnessett (talk) 23:22, 18 April 2009 (UTC)

First a comment about Wikipedia_talk:WikiProject_Mathematics/Proofs, where I noticed Ozob left a pretty good summary of the state of the consensus. That subpage isn't actually watched by a lot of people. It sounds kinda bad, but it is there simply to appease people who would like more proofs, particularly the instructive kind I think you wish. There is a pretty set "house" style to writing Wikipedia math articles, and it simply does not include writing details of little lemmas. It's going to take more than a discussion here or there to change it. This style is in fact the de facto consensus. Any time someone deviates from this style, their edits will be reverted/discussed/moved to a subpage (which is the reason there are more than a few such subpages). This has been happening for quite a while (probably at least 4 years), so it's fair to call it the consensus. One interesting aspect of all this is that if you invite the consensus of the rest of wikipedia, you may find something quite different: that a great number probably want all proofs deleted ("not a textbook!" he said), even the famous ones. This leads to the situation where people from this wikiproject have to stridently argue for proofs in AFDs (another place to look for the elusive consensus smoking guns). Thus there is a natural relectance to speak out too strongly against proofs (I know this is true for me and a couple others). We don't want to give "them" too much fodder for arguments to delete proof articles.
As for objective criteria, what Ozob write is correct. Different people have ideas of what good summary writing is. I think in a recent discussion somewhere Charles Matthew commented it would be appropriate to include a little proof of even a trivial fact, if it were the case that this little proof would be included in a typical survey article on the subject. An example might be deducing the uniqueness of the inverse for a group from the group axioms (I haven't read any surveys on group theory but I notice group (mathematics) includes this). For the specific example under discussion, I think what you suggest shouldn't be included. It reminds me of math classes where someone might hand in like 30 pages for math homework while someone else turns in one page. First person gets half the points, second person gets full credit. The lesson here is that when one is learning, particularly at the beginning, one is prone to include all kinds of "important points" that are, in the end, not so primary. --C S (talk) 01:32, 19 April 2009 (UTC)

I'm going to avoid the immediate temptation to defend my proposal in light of the opposition expressed by C S, because as David Eppstein correctly writes, the objective of this discussion is to determine whether the inclusion of the proof in that proposal "would be an improvement to our S-L article", "not to solve (my) internet hosting issues." Unless I am mistaken, C S thinks there are no objective criteria that indicate when a proof will improve an article. It's a matter of taste. Is that what others think? Dnessett (talk) 14:18, 19 April 2009 (UTC)

I'm jumping in here without reading the above discussion, which is always risky. But just responding to the last paragraph above — of course there are no objective criteria as to whether a proof, or practically anything else for that matter, would improve an article. How could there be?
I would call it a matter of judgment rather than "taste".
The fetish for objectivity is harming Wikipedia in general. The most important questions about an article, like does it convey its information effectively? and is it a pleasure to read? are all judgment calls. When objectivity is overvalued, so are less important questions like how many inline citations does it have?. --Trovatore (talk) 19:02, 19 April 2009 (UTC)

The comments by Trovatore suggest he advocates the "Bring Me A Rock" approach to developing articles. For those not familiar with this approach it conforms to the secular parable named (not surprisingly) "Bring Me A Rock," which goes something like this. A King tells one of his servants, "bring me a rock." The servant leaves the castle, goes to the river and selects a rock from its bank. The servant thinks it is a nice rock, it is smooth, pleasantly colored and not too big. He brings the rock back to the King. The King looks at the rock, frowns and says, "not that rock, bring me a different rock." Even if the standards for judging what should and what should not go into Wikipedia articles are subjective, it is only fair to articulate them. This allows those who "aren't in the know" to have some way to judge what they should attempt to insert into an article and what they should not. Dnessett (talk) 00:56, 20 April 2009 (UTC)

## Generalisations of metrics

We had lots of stubby articles on generalisations of metrics: pseudometric space, quasimetric space, semimetric space, hemimetric space, premetric space, inframetric. Except for the first I have boldly merged them all into the pre-existing section Metric (mathematics)#Generalized metrics. --Hans Adler (talk) 00:27, 17 April 2009 (UTC)

Nice. Boris Tsirelson (talk) 04:38, 17 April 2009 (UTC)
Thanks – great that the first response was positive. I still half expect to be lynched. --Hans Adler (talk) 10:13, 17 April 2009 (UTC)
Good work. There has been some research going on lately in the theory of such "generalized metrics". In particular, the question asking for necessary and sufficient conditions for a space to be quasi-metrizable is unsolved. I think that soon we probably would have to allocate each concept to its own article but for now I think what you have done looks good. As far as point-set topology is concerned, these are some of the interesting unsolved problems. --PST 14:56, 17 April 2009 (UTC)
Yes, I agree we may have to spin them out again later. But for the moment there just isn't enough information, the confusing naming issues can only be understood when everything is in one place, and merging allowed me to move some of the examples to the most logical location.
I am not sure what to do with Metric (mathematics)#Important cases of generalized metrics, which I am currently not motivated to understand. It would be great if somebody could find a better title for this subsection, or even a home in one of the other subsections.--Hans Adler (talk) 15:12, 17 April 2009 (UTC)

Does anybody have definite information about the intended meaning of the MSC category 54E23: Semimetric spaces? As it is under 54 (General Topology), I expect that it is for semimetric spaces, but last time I looked the annotated MSC didn't make this clear, and many publications on pseudometric spaces (which are also often called "semimetric spaces") were in this category. I asked the MSC2010 team, but never got a response. If we can be sure about the intended meaning it should go into a footnote, to discourage incorrect categorisation. --Hans Adler (talk) 15:12, 17 April 2009 (UTC)

There seems to be enough information on the various generalized metrics to warrant a split from Metric (mathematics). I'm thinking Generalized metric space; what do you say? CRGreathouse (t | c) 03:45, 18 April 2009 (UTC)
Initially I was going to collect everything in User:Hans Adler/Generalized metric spaces. As you can see I went as far as creating the page in my userspace. But then I noticed that we have two articles metric space and metric (mathematics) which need distinguishing features, and when I started it was already one such distinguishing feature that metric (mathematics) discussed generalised metrics. The other reason for not pursuing this was a naming problem: Lawvere coined "generalized metric space" for extended pseudoquasimetrics, and Stephen Vickers and probably others are still using this term. I believe sooner or later they will have their own decent-sized article, and generalisations in an orthogonal direction don't really seem to belong there. This is just an explanation for why I approached it this way. I have no strong opinion either way. --Hans Adler (talk) 07:48, 18 April 2009 (UTC)
I also don't have a strong opinion. I just noticed that the article on metrics was, after merging all the information, mostly about certain generalizations, and that seems a little but too much. CRGreathouse (t | c) 22:53, 19 April 2009 (UTC)

## Unbounded operator

You are kindly invited to see and expand my new stub Unbounded operator (which was redirected to Closed operator, Operator norm, Bounded operator and what not). Boris Tsirelson (talk) 09:04, 17 April 2009 (UTC)

Nice work. It's amazing that we didn't have an article on such an important topic before. -- Taku (talk) 11:19, 18 April 2009 (UTC)
Thank you. I agree that it is amazing. However, see my comments to your edits. Boris Tsirelson (talk) 16:33, 18 April 2009 (UTC)
Good work. It is nice that we have someone knowledgeable about functional analysis around here - many articles in this topic are under-developed as it appears. --PST 14:01, 20 April 2009 (UTC)

## Talk pages of articles

When we post on talk pages of mathematics articles, we are usually unlikely to get a response within a fixed period of time, unless of course the article is frequently viewed. Sometimes however, we may make important comments at talk pages of articles, which might play a role in improving its quality. In this case, I feel it reasonable to create a certain page that is linked to from WikiProject mathematics (page X, for example). When we post an important comment on the talk page of an article, we write the name of the article, along with out signature on page X. And those who watch page X, will be notified of the article at which a comment has been placed, and will be able to reply. This will allow much more progress for even the more specialized articles, and will give us some place to notify people without piling up comments on this page. Of course, if the comment is highly important, it would be best to post here, but any comment which may improve an article is important, and it is best therefore to have a page which notifies people of such comments. Any thoughts? --PST 07:14, 21 April 2009 (UTC)

I think you are addressing a real problem with this question, but I am a bit reluctant to start a new page on this. We can't force people to post there, and we can't force people to watchlist the new page. This problem could be addressed by using this page for your proposal. We could have a perennial thread "Links to discussions" consisting of entries like the following:
Everybody would be encouraged to add new or stalled talk page sections. (Within reason this happens already.) When the list gets too long we can start a new one in a new section, so that the old one is archived automatically. If the experiment fails, at least we don't have additional pages lying around. If it's successful but clutters this page too much, we can still move it to a new page. --Hans Adler (talk) 07:58, 21 April 2009 (UTC)
First of all, it is certainly true that we can't force people to post on "page X" and nor can we force them to watch it. But at least some people will do so, yes? And "some" is probably better than nothing (at least the dedicated members of this project would do so). On the other hand, I agree that we should first test it out on this page to see if it works because this page would be more seen than "page X", in any case. So I believe that we should do as you say. I'll start a new section below to allow people to note any old discussions that they may remember, or any current important ones, and we will base the decision on the result. --PST 09:09, 21 April 2009 (UTC)
OK, I've created the section below. --PST 09:13, 21 April 2009 (UTC)
The other thing to note is that since it will take time to catch up with the old discussions, it would be of great help if people could note down any current discussions they notice that have been neglected. --PST 09:33, 21 April 2009 (UTC)

I have reservations about the suggestion above, but I think one thing that could work is to have a bot check talk pages of math articles and see which ones have recent comments. Then a page, like the current activity page, could be updated. It could have info like how often during a recent span some talk page is updated. I think this is simple and sufficient for the problem being discussed. --C S (talk) 09:44, 21 April 2009 (UTC)

I don't think that would work for the observed problem. Such a list will be dominated by the very active/high traffic talk pages while the problem was with issues raised on very low traffic talk pages. (TimothyRias (talk) 10:39, 21 April 2009 (UTC))
I'm not sure what you mean. Adding automation by a bot means talk pages will get listed regardless of being low traffic or high traffic. Indeed, in a way, if someone lists an entry on a manual list, as initially suggested, that article can't really be truly low traffic. Each entry (whether high traffic or not) would only show up once after the bot detects a recent talk page comment, so it couldn't dominate the others. Each entry would have additional info that could be useful, such as when the comment was made and whether the talk page was updated during a recent span. This would, I expect, even help entries not "dominate" others. The real problem, as I see it, is that people who know enough about this page to be part of this kind of listing project, usually have ways of gaining the attention from experts needed to improve the page. There may be an infrequent contributor who makes an enlightening comment on an article talk page, but since nobody watches that article, it doesn't get noticed at all. A central location that would note a comment was left on such and such talk page is better than nothing at all.
The bot would pick up such comments, from people who may not be aware of a central location to make such listings. With a manual list, once say, people are drawn to that page, will the entry then be removed? And when is it ok to remove? I expect that's problematic. With bot listed info like, "talk page entry made on such-and-such date, and 5 responses during the recent month", it'd be clear to people reading the list that there is perhaps enough traffic to that page, and others can be looked at. Indeed, the bot could do something like shuffle entries according to different sections like "talk page entry within the last 6 months but no response" and "talk page entry within last 6 months with more than 10 responses". Of course, this is a hypothetical bot, but I don't think it really requires a superbot to be able to do this.
One advantage a manual list offers is summaries, but here again, i see no reason why some human helping maintain the list could not add summaries too. The bot could as a default, list the section heading (if any), and this can be further edited and revised by a human if need be. --C S (talk) 11:25, 21 April 2009 (UTC)

I should add that just because I made a suggestion here doesn't mean I think this is a problem that should be addressed, given our limited resources. Consider things like tags that are already added to articles and listed on the current activity page. I don't really see more than a handful of people going through and fixing the problems indicated by the tags. A lot of these tags are added by non-math people which strongly indicates that those are important articles to fix so that non-math people can read them. Rather than creating more mechanisms so that people interested in the intricacies of some advanced topic (of which only a couple people know enough and are motivated to edit) can be notified of it, I'd suggest it's more important to just do the plentiful work that is already available, namely the tagged articles. --C S (talk) 11:37, 21 April 2009 (UTC)

We are having the same trouble, like everyone I suspect, at physics. I will be keeping a close eye to see if this works. Should we not also try to find ways to make the existing mechanisms work as well such as RfC or the cleanup tag? — Preceding unsigned comment added by TStein (talkcontribs)

Thanks User:C S for your comments. I am not sure how to operate a bot (although I have not really looked at them in detail). On the other hand, the procedure below seems to be going well (User:Hans Adler is contributing as well as some other editors). We'll see what other people think and how this goes but if you have an idea using a bot, feel free to get it started. --PST 02:17, 22 April 2009 (UTC)

## proposing deletion of additive map

I feel that the recent article additive map should be deleted. Before taking formal action, let me explain myself and see whether others agree.

1) What is called here an additive map of rings ${\displaystyle R_{1}\rightarrow R_{2}}$ would be referred to by most mathematicians as a homomorphism ${\displaystyle (R_{1},+)\rightarrow (R_{2},+)}$. Since the multiplicative structure of the ring is not being used, it is somewhat strange that the article requires the objects to be rings: why not groups, or semigroups?

2) There is almost no actual content in the article. It is mostly an unmotivated definition.

3) The section on additive maps on a division ring is so incoherently written that I cannot understand it. Moreover, it is easy to show that an additive map from a division ring of characteristic zero to itself is simply a linear map of the underlying ${\displaystyle \mathbb {Q} }$-vector space. (Similarly, an additive map on a division ring of characteristic p is a linear map of the underlying ${\displaystyle \mathbb {F} _{p}}$-vector space.)

4) There are two "references" given to justify that the article is not orginal research. However, the references do not cite anything in the sources but simply list two entire texts, the first of which is 1400 pages long. This is not acceptable bibliographic practice.

Plclark (talk) 15:06, 21 April 2009 (UTC)

We already have an article additive function. Anything worthwhile in additive map should be merged to there. Algebraist 15:14, 21 April 2009 (UTC)
OK. I don't find any material in additive map which is worth merging into additive function. Anyone else? Plclark (talk) 21:22, 21 April 2009 (UTC)
I can't either. I've boldly redirected additive map to additive function. --Tango (talk) 21:35, 21 April 2009 (UTC)
Looks good to me. I'll go ahead and leave my comment anyways:
(ec)I don't see anything worth saving. I think the division algebra thing is trying to say additive maps between division rings can be represented as sums of "rank one tensors", except that if the destination division algebra is commutative, then it is claiming all additive maps are scalar multiplication, which is clearly false. I wonder if they mean to claim that every K-linear map between two central simple K-algebras, is a sum of such "rank one" maps. I wonder if that is true?
Someone might check Lyndon-Schupp to see if it mentions anything like this. I don't see why it would, but if it did, it might be some interesting math. Also it is a much shorter book. Google books does not think it mentions anything about division rings or algebras (or division really!), and while it does discuss some ring theory, I didn't see anything while searching for "additive" either. JackSchmidt (talk) 21:41, 21 April 2009 (UTC)

## Links to discussions (current or ongoing) - see above section

Links (provide a link to the talk page in question, a comment on the discussion in question if the discussion is long, and your username if possible - otherwise just the link will do):

• Talk:Baire_set - a request (by me) that an expert help improve the article - also there have been some (recent) improvements to Baire set - --PST 06:57, 24 April 2009 (UTC)

For the red links that start with the character "0", why are there so many numbers?Math Champion (talk) 03:18, 24 April 2009 (UTC)

Numbers don't normally start with "0". What special page are you using to see the list? — Arthur Rubin (talk) 05:31, 24 April 2009 (UTC)
My guess would be User:Mathbot/List of mathematical redlinks. Cheers, Ben (talk) 06:20, 24 April 2009 (UTC)
Most of those start with "-" or "−". Only five or so actually start with "0". — Arthur Rubin (talk) 06:27, 24 April 2009 (UTC)
My exhaustive sample of two of these -1284 and -1805 both came up with the links relating to Saros cycle. -1284 is on 54 (number)
The Saros number of the solar eclipse series which began on -1284 July 25 and ended on 32 September 3. The duration of Saros series 54 was 1316.2 years, and it contained 74 solar eclipses.
similar to -1805. So it seems that a lot of these are really years of questionably notability. --Salix (talk): 08:09, 24 April 2009 (UTC)
Sorry, I wasn't clear. I mean the numbers in the list that goes from 0 to 9. Math Champion (talk) 00:44, 25 April 2009 (UTC)

## Alan Turing Year

The new page titled Alan Turing Year is moderately orphaned: probably more pages should link to it. Michael Hardy (talk) 17:12, 24 April 2009 (UTC)

## Matrix (mathematics) and Euclidean algorithm for GAN

Done

Matrix (mathematics) is now a Good Article Nominee. Please consider reviewing the article. Jakob.scholbach (talk) 12:31, 18 April 2009 (UTC)

The Euclidean algorithm is also up for GAN, and I would likewise appreciate a review. But please consider "Matrix" first, especially since Jakob helped a lot with improving the EA and I owe him a debt of gratitude. Proteins (talk) 13:21, 18 April 2009 (UTC)
TimothyRias is nearly done with his review of matrix (mathematics) as a Good Article; would someone else be willing to review the Euclidean algorithm? It'd be much appreciated. There's also a request for a peer review in preparation for nominating the EA as a Featured Article, asking especially for advice on the writing (criterion 1a). Proteins (talk) 18:14, 24 April 2009 (UTC)
I passed matrix for GA just now. Congratulations to Jakob and all others editors that were involved with this articles. (TimothyRias (talk) 07:25, 27 April 2009 (UTC))

## Trisk

Resolved

Mathematical eyes would be welcome at Wikipedia:Articles for deletion/Trisk to confirm (or refute) my view that this article is codswallop. Regards, JohnCD (talk) 21:03, 25 April 2009 (UTC)

• Thanks to all who commented, article has been deleted per WP:SNOW as a hoax. JohnCD (talk) 12:32, 27 April 2009 (UTC)

## Epsilonics

Resolved

Could someone with the requisite knowledge ascertain whether this is a suitable topic for an article, if it is a "translation" might be in order. Guest9999 (talk) 23:33, 25 April 2009 (UTC)

It's certainly not a well-written article. What's much worse (since it can't be remedied by re-writing) the definition is not standard (unless unbeknowst to me, I've been on Jupiter for a few decades; I can't entirely rule that out). I'd seriously consider merging it into (ε, δ)-definition of limit. Michael Hardy (talk) 03:59, 26 April 2009 (UTC)
....also, to speak of "finding the right epsilon" sounds weird. Usually, definitions say "for every epsilon, there exists delta,....". So epsilon is given; the problem is to find the right delta, not the right epsilon. Michael Hardy (talk) 04:00, 26 April 2009 (UTC)

The article goes through the proof that

${\displaystyle \lim _{x\to c}(f(x)+g(x))=L+M}$

BEFORE mentioning that that is what is to be proved. Moreover, it phrases the beginning of the argument as if that is already known. As I said: badly written. Whoever wrote it seems to have some idea what the proofs are, but doesn't know how to write them and explain them. Michael Hardy (talk) 04:02, 26 April 2009 (UTC)

A.k.a. "epsilon-delta gymnastics". If it was a homework I'd give it a C. The real question is, is a simple example of this proof technique proper contents for WP? Jmath666 (talk) 07:26, 26 April 2009 (UTC)

I have made significant improvements to the article as well as included some context of this concept in mathematics. The mistake that I have made was to correct the previous version rather than erasing it and re-writing it completely. As a result, there are still possibly some incorrect logical implications within the proof of which I do not know. Therefore, I would probably leave the article as it is now, and let others polish it to perfection. --PST 12:31, 26 April 2009 (UTC)

I see that User:Point-set topologist has made some significant changes to the article. However, the future of the article remains unclear. No one has yet given any justification for the existence of an article whose content is entirely contained in another, more established article. My recommendation, following Michael Hardy, is that the article be merged with (ε, δ)-definition of limit. Plclark (talk) 16:17, 26 April 2009 (UTC)

This concept is also know as "epsilontics" and also includes the epsilon-N definition of a limit. However, reliable sources are thin on the ground and I agree with merging or replacing by a redirect until sufficient sources are found to support an article on the math culture associated with this. Geometry guy 20:07, 26 April 2009 (UTC)

I also think this should be merged into (ε, δ)-definition of limit, since they are on the same topic. The more general topic, of course, is the use of approximation and estimation techniques; that topic is mathematical analysis. — Carl (CBM · talk) 21:45, 26 April 2009 (UTC)

Looking over the discussion here, I went ahead and redirected the article. — Carl (CBM · talk) 15:15, 27 April 2009 (UTC)
Note that there is some information in that article that could be added to the redirect article or at least to some other articles. --PST 00:09, 28 April 2009 (UTC)

## Ideal ring bundle

Ideal ring bundle is an orphaned article. It it's a valid topic, then it needs work. Michael Hardy (talk) 21:04, 27 April 2009 (UTC)

## Base-27 numeral system

Is a base-27 numeral system septemvigesimal or heptovigesimal ? Both articles are unsourced. Clearly a merge is required - but under which title ? Gandalf61 (talk) 10:06, 28 April 2009 (UTC)

Don't know what is actually being used, but the Latin-based "septemvigesimal" makes more sense, as "heptovigesimal" mixes Greek and Latin roots. — Emil J. 10:13, 28 April 2009 (UTC)

## Orphaned article

I've just stumbled across the orphaned article Generating set of a topological algebra. In addition to being linked from somewhere it needs a proper introduction at the very least. Thryduulf (talk) 09:56, 29 April 2009 (UTC)

I have boldly merged the article into topological algebra, which I have also expanded a bit. Incidentally, "topological algebra" might be a better title for the theory. E.g. such an article could discuss the principle of reading the definition of groups, rings, algebras in the category of topological spaces to get topological groups, topological rings, topological algebras. I could not verify the claim about van Dantzig. Because of the general issues around associativity and units for algebras, this claim might be slightly misleading even if basically true. --Hans Adler (talk) 12:43, 29 April 2009 (UTC)

## "Probabilistic interpretation of Taylor series" on AfD

Probabilistic interpretation of Taylor series has been nominated for deletion. I wondered if this should be considered another case of a badly written article being mistaken for a bad article. I've done some cleanup and organizing, but more can be done.

So help improve the article if you can, and opine at Wikipedia:Articles for deletion/Probabilistic interpretation of Taylor series. As usual, don't just say Keep or Delete; give arguments. Michael Hardy (talk) 15:20, 29 April 2009 (UTC)