Wikipedia talk:WikiProject Mathematics

Extraneous solution

The surprisingly new article titled extraneous solution could use some work. Michael Hardy (talk) 13:50, 17 January 2008 (UTC)

Is that not just words, with standard dictionary definitions, put together? --Cheeser1 (talk) 20:02, 17 January 2008 (UTC)

I'm afraid you've lost me. I don't understand your question at all. Michael Hardy (talk) 03:44, 18 January 2008 (UTC)

I believe Cheeser1 is suggesting that an extraneous solution is nothing but a solution that is extraneous, and as such is not deserving of its own article. CRGreathouse (t | c) 16:06, 18 January 2008 (UTC)

Right. We have an article on cats and an article on purple, but no article purple cats, because purple cats are just cats that are purple. --Cheeser1 (talk) 00:45, 19 January 2008 (UTC)

Some work?! Dr. Hardy, I would normally defer to your expertise - but, holy moly, this article is garbage. The two examples listed in the article would fit better in an article entitled "elementary school misunderstandings about how to do math". Seriously! See article talk page for discussion. I'm thinking deletion, but I don't formally propose such things, and I usually don't support them. But, this is pretty bad. Tparameter (talk) 01:06, 19 January 2008 (UTC)

Looks to me like this is a very special case of what goes on in invalid proof, which is honestly one of the messiest articles I've ever seen. Abusing multivalued functions or nonexistent operations (logs, square roots, "division" by zero, etc) to get more solutions than there should be for something (or, in some instances, concluding that the "right" solution equals the "wrong" solution like 1=0). I've spent some time considering how to clean it up, but have no idea where to even start. --Cheeser1 (talk) 02:07, 19 January 2008 (UTC)

I have heard the term used to describe solutions outside of the domain. For example, imaginary numbers when the domain is defined as being the reals. Then the imaginary solutions would be "extraneous". However, a colleague just told me that the term is also used as a misnomer to describe non-solutions derived with invalid methods, and also almost-solutions not in the domain BECAUSE they result in division by zero - which also happens to be the first example in the article which I criticized. Tparameter (talk) 08:09, 19 January 2008 (UTC)

But the point is, these are simply solutions that are extraneous. I don't know that this is article-worthy. --Cheeser1 (talk) 08:48, 19 January 2008 (UTC)

That's what I thought - but, there is some discussion on the talk page that extraneous solutions are not necessarily solutions in the first place. I've investigated unreliable definitions on the internet that corroborate this definition (to include certain non-solutions). Tparameter (talk) 16:27, 19 January 2008 (UTC)

They are solutions, but just to the wrong equation. A more apt example might be "fat cat" which is an idiom. They are not truly cats (and not necessarily fat). It's still just a dictionary definition. But "extraneous solution" really does mean a solution that is extraneous - to the given equation, or to some equation you get along they way (by using some operation like squaring). --Cheeser1 (talk) 16:35, 21 January 2008 (UTC)

This concept is specifically discussed often enough in modern high school algebra textbooks that it deserves its own article. Extraneous solutions arise naturally in some contexts; for example, when eliminating fractions produces a quadratic equation. I haven't looked at the article yet to say whether it's good but it should exist. Dcoetzee 18:07, 31 January 2008 (UTC)

Archimedes is on the main page again

Archimedes has made it to the Main Page, there may be some edits to watch for. BTW did we lose the convention for bolding main page articles, they all seem to be bold. --Salix alba (talk) 21:10, 29 January 2008 (UTC)

I noticed that Gauss said the three most impactful mathematicians were Archimides, Newton, and...a guy I'd never heard of. I think the real take-away is that I'd like to understand the broader ramifications of quadratic reciprocity :-) Pete St.John (talk) 22:43, 29 January 2008 (UTC)

That "supposed quote" by Gauss struck a discordant note with me. With a few mouse clicks, it can be traced to a sentence in E.T.Bell (the actual expression used was "epoch making"), and as the regulars will no doubt remember, his assertions should be taken with a pot load of salt. Incidentally, Gauss famously left deeply emerged in thought after Riemann's inaugurational lecture "On the hypotheses which lie at the foundation of geometry". Thus Riemann's insight was so revolutionary that it left Gauss speechless I don't think that an endorsement from Gauss is either necessary or appropriate for the article about Archimedes, though. Arcfrk (talk) 00:46, 30 January 2008 (UTC)

Ir'a in Jacobson's Algebra. This doesn't prevent it from being folk history, of course, but just because Bell said something doesn't prove it's wrong. Septentrionalis PMAnderson 15:59, 30 January 2008 (UTC)

Arcfrk, I've heard as a list of "greatest mathematicians of all time": Archimides, Newton, and Gauss. I wouldn't even want to pick between Gauss and Euler, and I wouldn't know how to meaningfully compare Archimides to Wiles; but it helps to broaden our understanding of history. Gauss isn't just the "de-gauss button on a CRT, if you remember CRTs" guy, and Archimides isn't just the "run-naked-from-a-bathtub" guy; so while the comparisons may not be scientific, I think they have pedagogical utility. And really it's just amazing that Archimides imagined and implemented definite integration so well as he seems to have. Pete St.John (talk) 19:33, 30 January 2008 (UTC)

Isn't it amazing that each of them was also (and maybe, primarily) an applied scientist? Anyway, my point was that a proper place for that saying of Gauss is in a collection of Gauss quotes (that's also where MacTutor puts it). Was there anyone, ever, who did not think that Archimedes was the greatest scientist of antiquity? Arcfrk (talk) 20:26, 30 January 2008 (UTC)

Some of the libraries in antiquity had fewer books than a modern university has undergraduate programs. It's a bit harder to be so eclectic today. But anyway, the quote speaks to the significance of Archimides as a mathematician; you are right, everyone knows he was a great scientist and engineer (he sank a fleet of ships! sorta) but lot's of people don't know, but should, that he was a great mathematician as well. Pete St.John (talk) 20:39, 30 January 2008 (UTC)

That mathematical contributions of Archimedes are not appreciated is a sad story that had started already during his lifetime. But the question is, what is the best way of bringing that out? MacTutor article boldly claims that

The achievements of Archimedes are quite outstanding. He is considered by most historians of mathematics as one of the greatest mathematicians of all time.

If that could be reliably sourced, it would do the job. Arcfrk (talk) 21:06, 30 January 2008 (UTC)

My lecturer's notes have 'easily one of the greatest mathematicians of antiquity, and of all time', but I fear he has never bothered to publish his opinions. If I remember, I'll check a few books for quotes tomorrow. Algebraist 00:35, 31 January 2008 (UTC)

I consider any generally reliable source to be citable, if the fact itself is not questioned; in this case, there is no reason to doubt that Gauss would have considered Archimides a great mathematician, so it is not necessary to scrutinize the published source (Bell). Biographies aren't mathematics and don't have the same standards of rigor, but Bell, like Seutonius, is citable (though historians think of Seutonius as gossipy, sorta the People Magazine of his day, and not a social scientist by modern standards. Did you know that Augustus covered himself with sealskin during rainstorms because he was afraid of being hit by lightning? I would have thought it was because sealskin is waterproof). Pete St.John (talk) 00:51, 31 January 2008 (UTC)

I added the following reference to the one book on history which is within my reach at the moment: Calinger, Ronald (1999). A Contextual History of Mathematics. Prentice-Hall. p. 150. ISBN 0-02-318285-7. Shortly after Euclid, compiler of the definitive textbook, came Archimedes of Saracuse (ca. 287-212 B.C.), the most original and profound mathematician of antiquity. That book also states that Gauss restricts to Archimedes along with Newton the term summus. -- Jitse Niesen (talk) 11:36, 31 January 2008 (UTC)

Constructible number

It is tempting to use this terminology because of the intuition that it conveys (within a certain context), but is such use widely accepted? The article lists no references. Arcfrk (talk) 09:45, 31 January 2008 (UTC)

I'm fairly certain this book, which is as far as I know a reasonably well-established text on the subject matter, uses such terminology. I could be wrong, I'm no expert on which books or which terminology is commonly used. --Cheeser1 (talk) 09:54, 31 January 2008 (UTC)

See Constructible Number at MathWorld. I've added this and two other references to the article. Gandalf61 (talk) 10:07, 31 January 2008 (UTC)

I believe it is widely used in textbooks on abstract algebra (in the Galois theory section, for instance Hungerford's Abstract Algebra: an introduction). MathSciNet gives two articles with this in the title, both referring to the geometric concept, both research level. I think it is safe to say the term is widely accepted, though perhaps not widely used outside of textbooks and a few articles providing new insights on a problem solved completely in the 19th century. JackSchmidt (talk) 17:47, 31 January 2008 (UTC)

Least squares objectionable rewrite

Petergans, a retired specialist in least squares (among other things), rewrote the article on linear least squares from a more specialized point of view which is harder to understand. Now he wants do the same thing for Gauss-Newton algorithm (a nonlinear least squares algorithm). See Talk:linear least squares and Talk:Gauss-Newton algorithm .

While experts are welcome on Wikipedia, rewriting articles from their point of view and making them not comprihensible to others is I think not good. Can we have a discussion here on that, to keep the conversation in one place and have it be seen by more folks? Oleg Alexandrov (talk) 16:01, 31 January 2008 (UTC)

one place and have it be seen by more folks? Oleg Alexandrov (talk) 16:01, 31 January 2008 (UTC)

Dear Oleg and Petergans,

If I were an external reviewer, I would say that the new article is not ready for prime time.

Aside from Oleg's criticism, I have the additional criticism that the new article inserts statistics into every possible nook and cranny. This obscures the main idea and should have been segregated to its own subsection.

Petergans, wikipedia needs experts like you, but it's a learning process (or at least it was for me). I must say I'm not familiar with all the articles on Wikipedia, but please compare your linear least squares and numerical analysis, integral or Eigenvalue, eigenvector and eigenspace, I think that's the direction we're going as a whole in the Wikipedia math project.

Sincerely,

Loisel (talk) 16:53, 31 January 2008 (UTC)

• I echo Mr. Alexandrov's sentiments and cite the policy Wikipedia:Make technical articles accessible as validation. I remain hopeful that a sustained appeal to the MTAA policy would temper the editor's viewpoint. -- DanielPenfield (talk) 17:02, 31 January 2008 (UTC)
• Least squares should definitely be presented with the statistical motivation. I can find some strictly math sources that do it this way if that would help. However, the current presentation is too immediately steep, as many have noted.

Rather than call this an objectionable rewrite, I think it should be a call for help writing a layman's introduction. There is no need to undo the edits, but there is certainly need to introduce the concepts more gradually. Even the old text was wrapped up in technicalities; they were merely technicalities more familiar to mathematicians (linear algebra and vector calculus, roughly speaking, sophomore level courses). The new material appears a little more advanced at face value, but most of the concepts I picked out were covered in our local sophomore level engineering statistics course.

The material on the normal equations could profitably be moved to its own section. They have nothing to do with the definition or motivation of least squares; they merely motivate a wide variety of other numerical linear algebra which can solve well conditioned least squares problems.

A history section might be very interesting, as Gauss's invention of numerical linear algebra more or less began by solving this statistical problem.

Also, should someone leave a note on Petergans talk page, since the discussion is here, he is mentioned by name, and he is likely not a project member? JackSchmidt (talk) 18:10, 31 January 2008 (UTC)

I left a note for Petergans, inviting him to join this discussion. EdJohnston (talk) 18:33, 31 January 2008 (UTC)

I had posted a note on the three article talk pages at which he announced the rewrites. I agree putting an extra note on his own talk page is good too. Oleg Alexandrov (talk) 18:49, 31 January 2008 (UTC)

Thank you for alerting me to the discussion on this page. Let me explain my motivation for proposing the major project. It stems from the fact that I'm an experimentalist (chemistry), not a mathematician. The earlier linear least squares article would be all but incomprehensible to most chemists, if not others like physicists and biologists. So naturally, I have slanted my draft articles towards the experimentalist, that is, towards the application of least squares methods rather than their purely mathematical basis. Here we have a dilemma. The chemist will not be familiar with specialist mathematical notation, and the mathematician will find the applications aspect difficult!

A second motivation was the apalling lack of consistency in notation across related articles. In particular I feel it is important that both least squares and regression analysis be presented in more or less consistent notation. Otherwise it looks as though they are completely separate topics, which they are not.

Thirdly, the current Gauss-Newton algorithm totally misses the point, that it deals with a sum of squared residuals, as is clearly stated in the lead-in of the introductory article, least squares. There's nothing wrong with the maths, but it's not about the Gauss-Newton method as I know it.

For the moment non-linear least squares resides in User:Petergans/b/sandbox. I will revise it in the light of comments, both here and on talk:least squares or talk:Gauss-Newton algorithm. It can then be moved to its own page, where you guys or any else can tweak it further. The question remains, what to do about Gauss-Newton algorithm, re-write it or over-write it?

1. At present it is likely to be comprehensible only to mathematicians. For instance, it says that J is the Jacobian, but gives no indication as to what partial derivatives it contains. There are other instances of notation which will be obscure to a non-mathematician.
2. The notation is unique, within least squares and regression topics, to this article.
3. As mentioned above, it makes no mention of residuals.
4. It is illogical to describe the line search modification in the article and not the Levenberg-Marquardt modification.

My draft adresses all four of these issues. Petergans (talk) 22:06, 31 January 2008 (UTC)

As far as the linear least squares article is concerned, it is much more likely that the average reader is familiar with some linear algebra and calculus than with statistical data fitting theory.

I suggest you focus on making that article more elementary, for example, by putting back the old first part, and only later start modifying other articles, such as Gauss-Newton algorithm. Oleg Alexandrov (talk) 04:08, 1 February 2008 (UTC)

I am puzzled as to what, exactly, you guys find more difficult about my presentation than about the older one. Is it the use of matrix notation? Is it the reference to experimental data? Is it the inclusion of statistics? Is it too generalized? Regarding statistics, from my perspective the optimal values of the least squares parameters are meaningless without estimates of the associated uncertainties, which indicate how many digits of the value are significant - the experimentalist needs to know both the results and how reliable they are. Petergans (talk) 08:50, 1 February 2008 (UTC)

Petergan's revision looks instantly familiar to me. This is the presentation you will find in a modern statistical text book (I detect a certain flavour of Mardia, Kent and Bibby, Multivariate Analysis here, perhaps a Leeds connection?). It does have the advantage of explicitly mentioning the error functions which the previous version glossed over. Statistical applications is a major application of this technique so it does deserve some treatment. Perhaps what could be done is create a statistical application section with this presentation. As for the technicality Least squares is really the best place for the the layman's introduction. --Salix alba (talk) 10:46, 1 February 2008 (UTC)

As an aside, the german wp has a featured article about least squares. Jakob.scholbach (talk) 14:44, 1 February 2008 (UTC)

(To Petergans.) One should not start the article with statistical data estimation and experimental errors. Start with solving a given overdetermined linear system, and derive the normal equations, which is plain linear algebra and calculus. Only then, as per Salix alba, create a fancy statistical application section describing the origin of of the linear system in fitting experimental data, the issues of weights, variance, etc. I hope I'll get to this myself at some point, you're more than welcome to do this by yourself if you have the time. Oleg Alexandrov (talk) 16:29, 1 February 2008 (UTC)

Oleg has moved the article from my sandbox to non-linear least squares and placed a redirect in User:Petergans/b/sandbox so that I can no longer use it. This is premature and out of order. Will an administrator please restore my sandbox, remove the article non-linear least squares and the redirect in User:Petergans/b/sandbox, so that I can work on the draft in the light of the discussion here, before "publishing" it. Petergans (talk) 00:24, 2 February 2008 (UTC)

I moved it back to User:Petergans/b/sandbox, to give you some more time to work on it before it's "live". But remember that articles don't need to be perfect, or even close, when they are created. — Carl (CBM · talk) 01:52, 2 February 2008 (UTC)

Sorry, I should have asked (I had the impression you were pretty much done with it and that other people liked it, and I was requested to do the move by an editor on my talk page). When you're ready, let us know. Oleg Alexandrov (talk) 04:26, 2 February 2008 (UTC)

Other language versions

Jakob.scholbach suggested looking at the German version of least squares. I have also looked at the French version. This is how the problem is stated there.

$\chi ^{2}(\theta )=\sum _{i=1}^{N}\left({\frac {y_{i}-f(x_{i};\theta )}{\sigma _{i}}}\right)^{2}=\sum _{i=1}^{N}w_{i}\left(y_{i}-f(x_{i};\theta )\right)^{2}$
Les quantités $w_{i}$, inverses des variances des mesures sont appelés poids des mesures.

(Literal translation) The quantities $w_{i}$, the inverses of the variances of the measurements are called the "weights" of the measurements

Both French and German articles are based on the premise that least squares is applied mathematics, and that therefore the physical circumstances of its applications are an integral part of it. Petergans (talk) 09:48, 2 February 2008 (UTC)

Explain formula idea

I've suggested an idea at Talk:Second-order_logic#Explain formula idea and given an example there. I thought it would be good if there could be an "Explain formula" link next to complicated formula, that would show/hide an explanation. Perhaps a template could be created for this kind of thing. Any comments on this idea? —Egriffin (talk) 16:29, 31 January 2008 (UTC)

Proofs

I recall reading somewhere that only one proof of a certain proposition should be in an article, so how does one choose the proof? For example, in the article Simson line. there exists a more elementary proof than the one given. Should I replace it or not? Nousernamesleft^{copper, not wood} 03:07, 1 February 2008 (UTC)

We have a separate page for discussions of when and how to include proofs in mathematics articles: Wikipedia:WikiProject Mathematics/Proofs. Perhaps it should be turned into a guideline, which then should hopefully also include guidance on when not to include a proof. Examples of articles with many proofs are Pythagorean theorem and 0.999...; you'd almost think there is something fishy with these claims that they should need so many proofs. So a limit of one proof is not a hard and fast rule. But in general, unless there is something particularly illustrative, illuminating or elegant about a particular proof, I'd say: if a proof must be included, keep it as simple as possible (but not more).  --Lambiam 11:27, 1 February 2008 (UTC)

Whether there should be only one or more than one within the article depends on the purpose of inclusion of the proof. With Pythagorean theorem or quadratic reciprocity, the fact that so many different proofs exist is notable. With propositions whose proofs are routine, I'd often want to include only one. Michael Hardy (talk) 15:31, 1 February 2008 (UTC)

Newton's method

I have found that there are two articles on this topic which slightly contradict each other - Newton's method uses the function and 1st derivative. I was taught this at school as the Newton-Raphson method. Then there is Newton's method in optimization which brings in the 2nd derivatives. Is there a generally agreed way to distinguish between the two methods? I would refer to them as first and second order Newton methods. Petergans (talk) 14:24, 1 February 2008 (UTC)

No, the "second order" Newton method is Halley's method. In optimization, one is looking for the zeros of the gradient, as possible locations of extremal points. So by using Newton's method on the system of first derivatives the Hessian turns up. The order of convergence is still quadratic.--LutzL (talk) 15:20, 1 February 2008 (UTC)

Newton's method is for finding a zero of a function. Newton's method in optimization is for finding an optimum of a function. Applying the latter method to a function f is the same as applying Newton's method to its derivative f'.  --Lambiam 09:20, 2 February 2008 (UTC)

Foundations of statistics

Foundations of statistics has been nomited for deletion. As we've seen happen before, the arguments for deletion go something like this:

"I never heard of 'chemistry'. It sounds like some new religious movement. Delete the article or merge 'chemistry' into 'scientology'."

I think maybe I'll try to start a statistics WikiProject. There's no community and Wikipedia work in that field, even by those who know it well, is so uneven because we lack conventions and the like.

Express opinions on that article here. Michael Hardy (talk) 19:23, 1 February 2008 (UTC)

Random article link

Inspired by a post at the village pump, I'm wondering if anyone else thinks there ought to be a link to Jitse's random article tool on Portal:Mathematics, as seen on Portal:Middle Earth for example. (And Jitse: would you mind?) Algebraist 23:20, 1 February 2008 (UTC)

I think it's a great idea! Another place where it can be included is the WikiProject Mathematics main page (either in the "toolbox" on the left side or in the "Resources" on the right side). Arcfrk (talk) 23:58, 1 February 2008 (UTC)

SVD -- primary meaning?

Recently, I noticed that SVD was an article about a sniper rifle, with no reference to any other meanings. When I google search svd, most of the hits on the front page are for Singular value decomposition, a few are for other meanings, and only one (the wikipedia article) is for the rifle.

I moved the rifle article to SVD (rifle) and made SVD a disambiguation page. The creator of the rifle article has since moved SVD (the disambig page) to SVD (disambiguation) and put the rifle article back at SVD with the comment that "google gets enough first page hits to indicate this is a firearm". (Does google tailor your hits based on previous searches?) They did add a link to the disambiguation page at the top, which is good.

Wikipedia:Disambiguation#Primary_topic indicates that when there is a well-known primary meaning or phrase, that topic may be used for the main article with a link to the disambiguation page. Is the rifle really the primary meaning of SVD? Is this worth arguing about? Where would be a good place to have the "extended discussion" that might indicate that there is no primary meaning, and that SVD should be the disambiguation page? -- KathrynLybarger (talk) 06:13, 2 February 2008 (UTC)

I'm not going to comment on the issue you raise. But another more pressing matter is that in the process of moving the pages around, the original page history of SVD was lost. It remained at SVD (rifle), which is now a redirect. An administrator is going to have to fix the problem and re-move the page SVD (rifle) to SVD so that the history is recovered. Any volunteers? Silly rabbit (talk) 06:24, 2 February 2008 (UTC)

I restored the redirect from SVD to the dab page, so that the history now goes with the correct article. No admin powers were needed nor used, though I have them. —David Eppstein (talk) 06:32, 2 February 2008 (UTC)

Thanks! -- KathrynLybarger (talk) 07:10, 2 February 2008 (UTC)

As supporting evidence: SVD matrix: 1.4M Google hits; SVD rifle: 100k Google hits. —David Eppstein (talk) 06:26, 2 February 2008 (UTC)

Accessibility of maths articles

This question has reared its head again at WP:VPP#Mathematics. Algebraist 01:34, 3 February 2008 (UTC)

Policy on technical terms

Do we have a policy or guideline on the use of technical terms? If not, we should.

I was just looking at finite element method, and it uses two technical terms, "Dirichlet condition" and "displacement condition", to refer to the same thing.

I personally think that, as much as possible, a single article should stick to a single notation, and a single technical term per concept. I think listing other terminologies and notations is a good thing, but I don't think that intermixing terminologies and notations within the article, for no good reason, helps in any way.

So do we have such a policy? Where is it?

Loisel (talk) 04:55, 3 February 2008 (UTC)

I don't know that there's a policy, but it seems to me a matter of good writing, not to be unnecessarily confusing. —David Eppstein (talk) 06:26, 3 February 2008 (UTC)

I'm not as familiar as I should be with the MOS, but I believe terminology switching is frowned upon (in the same way switching BC/BCE or British/US English are not really helpful). --Cheeser1 (talk) 06:32, 3 February 2008 (UTC)

The first paragraph of WP:MOS does provide some guidance on this issue. --Sturm 11:07, 3 February 2008 (UTC)

I think that paragraph refers to consistency across articles, and is given by way of rationale for having a Manual of Style. Nevertheless, the same rationale clearly also applies for consistency within an article being desirable.  --Lambiam 21:39, 3 February 2008 (UTC)

"An overriding principle is that style and formatting should be applied consistently throughout an article, unless there is a good reason to do otherwise". --Sturm 21:46, 3 February 2008 (UTC)

I should have read it more carefully.  --Lambiam 22:25, 3 February 2008 (UTC)

I did not find the term "Dirichlet condition" in Finite element method.  --Lambiam 22:25, 3 February 2008 (UTC)

I guess you're right. It says Dirichlet problem, not Dirichlet condition. Also, thanks for the link to WP:MOS, although I have the feeling that some verbiage that directly addresses notation, symbols and terminology would be more convincing when the issue turns up in an edit war at some point in the future. Loisel (talk) 07:13, 4 February 2008 (UTC)

Examples

Is there a standard format and location for numerical examples in mathematics articles? Examples seem to be scattered or non-existant. See: Expected_value - 2 in intro; Standard_deviation - 1st section, step by step; variance - no example. If there is no standard, should we make one? --Zojj (t,c) 01:37, 5 February 2008 (UTC)

I guess there is no standard. Examples, pictures, and simple non-technical explanations are of course very encouraged and as early as possible in articles, as they help elucidate matters, especially in math. Oleg Alexandrov (talk) 04:35, 5 February 2008 (UTC)

Boubaker polynomials refcheck

This article has had a rough start and could use some help. One important part is to improve the references, but this is a big task. An easy first step is to check the provided references to see if they actually support the claims made, and a second is to format the surviving references in a standard fashion. Silly rabbit and I have made some progress on this, but it would be good to have a few more eyes on the project. The topic may be heavily influenced by physics, so those with a dual background would be particularly helpful. As a warning: the original authors may have a WP:COI and may feel they are not being treated WP:CIVILly since their work has been called non-notable and proposed for deletion really quite a few times now. I think this is just an inherent problem with COI edits, and that there has not really been any incivility, but I felt I should warn you about the probable difficulty in finding consensus on the article as a whole. This should not really affect the refcheck, but when you comment on the references, you might want to double check you aren't accidentally insulting someone or otherwise inadvertently inciting something awful. Thanks for any help. JackSchmidt (talk) 05:24, 5 February 2008 (UTC)

There is a problem with two relevant references: Access to them is not free! He who payed them could verify the existence of the contested items.