Wikipedia talk:WikiProject Mathematics/Archive/2008/Aug

Sasquatch principle

Could someone take a quick look at this article? It has been tagged and PRODded as a hoax, looks implausible, and first searches find nothing about it or the supposed author "Jonas Arbetman"; but it just might be genuine. JohnCD (talk) 20:23, 1 August 2008 (UTC)

The statement and proof of the theorem seem fine to me (shorter: the ideal class group is a group and if a^n = a^(n+1), then a=1). The journal article is not a mathematics article, but rather a math education article. It is not indexed by either Mathematical Reviews or Zentralblatt MATH, but it does appear to be an often cited journal for mathematics education. I don't have time at the moment to search the education literature for the article (1983 is not available online from the publisher), but I think checking the reference is the best idea. I think it very likely that it is not a hoax. I suspect this is some sort of double play on words; like the squeeze theorem but with some sort of implied humor. The implied humor is lost on me without the original article.

Since the topic itself strikes me as non-notable, I did not remove the prod. JackSchmidt (talk) 20:46, 1 August 2008 (UTC)

Since the article is properly sourced, I don't see why it is regarded as a hoax. On the other hand the result is a trivial consequence of one of the characteristic properties of Dedekind domains (invertibility of all fractional ideals). At the same time, it is a relatively technical result for which no applications are given -- the "example" of taking $n=1$ is especially feeble. I support deletion. Plclark (talk) 21:59, 1 August 2008 (UTC)

It is being suggested that the name Sasquatch principle is a hoax; does the source use it? But that's not the only question; an article on an uncited neologism would be almost as bad. Septentrionalis PMAnderson 22:11, 1 August 2008 (UTC)

Asking whether the name of something can be hoax smacks of philosophy: is it possible to pretend to call something by a certain name? I know what you mean -- hoax or not, such a strange name should come with an attribution from a reputable source. But in this case I think the article itself is not notable and will probably be deleted, rendering this moot. Plclark (talk) 23:55, 1 August 2008 (UTC)

It is certainly possible to pretend that something is conventionally called by a certain name. Michael Hardy (talk) 00:03, 2 August 2008 (UTC)

I agree. It can be a hoax to claim that something is widely called by a name that it is not. I have been battling a group of trolls on Pareto principle with a similar modus operandi recently. That said, I couldn't find the original article cited by Sasquatch principle to tell whether it actually supported what it was claimed to; the online archives only go back to 1995. —David Eppstein (talk) 00:31, 2 August 2008 (UTC)

Just a note -- this article has been put up for deletion. RayAYang (talk) 19:54, 3 August 2008 (UTC)

Tracking down specific changes to an article

Hello all. I'm wondering if there's a way to figure out from the history of an article in which specific diff a particular change was made. In other words, if I want to know who added a sentence in an article (that may have been there for years), how can I do this without sorting through a pile of diffs trying to narrow it down by hand? VectorPosse (talk) 11:06, 2 August 2008 (UTC)

The editor's index gives wikiblame and User:AmiDaniel/WhodunitQuery. Algebraist 11:48, 2 August 2008 (UTC)

This is probably obvious, but if you do it by hand, binary search can be very helpful. —David Eppstein (talk) 16:02, 2 August 2008 (UTC)

Pythagorean theorem

Can anyone help reason with the person who's lecturing me in condescending fashion at talk:Pythagorean theorem? I'm being told that the "proper" mathematical term for the sides of a triangle that meet at a right angle is "catheti" and "legs" is something one should say only to children, and "the other two sides" is insufficient for an encyclopedia. Michael Hardy (talk) 23:58, 3 August 2008 (UTC)

The term "cathet" is used in Russian for the other two sides. I have never heard "catheti" even though it may be the correct form grammatically. The person may be suffering from OCD. Katzmik (talk) 09:42, 4 August 2008 (UTC)

Assessment scale

The 1.0 Assessment Team is currently having a cleanup of the plethora of Classification templates that WikiProjects use to assess the pages within their scope. I notice that WikiProject Maths is the only project to use the {{bplus-Class}}, dating from a time before C-Class. I was wondering if, now that the 7-point scale that WPMaths has used for a while has now been implemented wikipedia-wide, this project thought it would be a good idea to adopt the C/B system rather than B/B+. This would essentially involve running a bot (I'd be happy to organise one) to reclassify all your B-Class articles as C-Class, and then all your B+-Class articles as B-Class. This would then deprecate the {{Bplus-Class}} template and classification level.

I'm not entirely sure how your B/B+ scheme correlates with the new grading criteria recently implemented by the 1.0 project, so it's possible that this won't be a good idea (that is, if your 'B-Class' articles already meet the standards for generic B-Class articles, it would be crazy to downgrade them all to C-Class). I'm keen to hear the views of project members on this issue. Happy‑melon 10:29, 4 August 2008 (UTC)

Hello. did you read the discussion at [[1]]? The B+ rating is used for articles that exceed the B rating but are not quite GA. So as you say, it would make no sense to downgrade it to B and then downgrade the B rated ones to a lower grade. --C S (talk) 10:41, 4 August 2008 (UTC)

I know that there is bad blood between WPM and GAC. But perhaps this may be a good time to get our B+ articles reviewed and (with luck and some effort) promoted to GA status. We currently have 81 B+ articles. I'm sure at least some of these (such as exterior algebra which I have worked on recently) are at GA level already, or nearly so. Is there a champion for the cause? siℓℓy rabbit (talk) 12:33, 4 August 2008 (UTC)

Easy as pi?

Since nobody here seems to follow the village pump, I thought I'd post a link to this proposal here:

Wikipedia:Village pump (proposals)#Easy as pi?

Jkasd 04:54, 5 August 2008 (UTC)

The proposal seems based on a few common misconceptions. One is that since the person was unable to understand something, only experts that already know the topic could understand it. Another is that because understanding a paragraph took more than one reading, it must be written badly. I think we would all be doing ourselves a big favor if we as a group wrote up one of those well-written FAQs like the kind that exist for USENET. There is no shortage of volunteers hear who are able to cogently explain these issues. It's just that nobody has gotten around to doing it, so my counter proposal to the above is to get started on such a document.

On a related note, recently I started taking a closer look at the articles that are tagged for various cleanup duties. For the most part, this tagging is done frivolously. For example, a stub on a Japanese mathematician got tagged because somebody didn't understand what this person had worked on. The discussion linked above by Jkasd indicates that more people are going to be going on tagging sprees in the future. I think if we actually want to improve the encyclopedia, we need to discourage this. I know that for me personally, after spending a few hours trying to figure out why some articles were tagged as "needing context", I no longer have the time and energy to actually work on adding context to the articles that need it. This tagging is a drain on our resources, and it is being done by people who often take only seconds to play a dozen such tags and never come back to look at the articles. --C S (talk) 05:53, 5 August 2008 (UTC)

Initial rating requested

I would like to request initial rating for the newly created articles Bass-Serre theory, Kurosh subgroup theorem, Rostislav Grigorchuk, Grigorchuk group and Grushko theorem. Thanks, Nsk92 (talk) 16:00, 4 August 2008 (UTC)

For Grushko theorem see my comment on the article talk page. Katzmik (talk) 10:13, 5 August 2008 (UTC)

Barber paradox

I never thought of myself as defender of barbers' rights but if you are interested in foundations please see my comment at talk:russell's paradox. Katzmik (talk) 11:54, 5 August 2008 (UTC)

Discussion on the Viète's formulas name

There is a discussion at Talk:Viète's formulas as to whether the article in question should be renamed to Vieta's formula. Outside input is welcome. Oleg Alexandrov (talk) 07:15, 6 August 2008 (UTC)

avoiding personal attacks

I have glanced over the wiki contributions made by arcfrk over the past two years, and find them on the contrary very helpful, contrary to the wording of the odd attack at the discussion page of differential geometry of surfaces. Katzmik (talk) 12:56, 6 August 2008 (UTC)

Are you sure you mean Arcfrk? His only edit in the last month there was this one, which seems perfectly civil to me. What "attack" are you talking about? Can you supply a diff? Paul August ☎ 16:14, 6 August 2008 (UTC)

I think Katzmik means complaints about Arcfrk not by Arcfrk. Katzmik, yes, there has been an ongoing clash between Mathsci and Arcfrk. But I was under the impression that this has quited down since about Jul 7 08. Are you referring to more recent edits? Perhaps it would be good to go over that talk page and erase anything that might look personally offending. What's the standard procedure for doing that? Oded (talk) 18:18, 6 August 2008 (UTC)

After looking at Talk:Differential geometry of surfaces I would suggest that Mathsci use perhaps a bit more civility. I found the pattern in some of his comments to be rather accusatory and patronizing. It could be just me reading it this way, since written text is notoriously hard to interpret, but perhaps more efforts could be done there to keep the discussion cordial. Oleg Alexandrov (talk) 02:20, 7 August 2008 (UTC)

Agree. Paul August ☎ 19:50, 7 August 2008 (UTC)

Hmm. I am not sure where I have made personal attacks. It's hard to know how to react when an editor rejects the standard linear ODE for describing parallel transport or suggests using existence theorems on isothermal coordinates as an elementary explanation of Gaussian curvature. In all cases, however, Katzmik's suggestions have been (or are being) incorporated in slightly modified form into the article as it continues to be revamped. Having looked at Katzmik's articles on his own research area, I realize that Katzmik's idiosyncratic WP editing style is to create an approximate initial point which, after successive iterations by other editors, eventually becomes encyclopedic. It took me a while to work this out and I am sure that most mathematics editors would initially find problems with edits like this until they came to grips with his methods. I have noticed that, although unconventional, the substance of every proposal he makes, even if not the precise form or occasionally brusque manner of delivery, are extremely valuable. Most of the discussion on the Differential geometry of surfaces talk page was transferred from my talk page, where he was posting messages every few minutes while I was trying to figure out how to make mainspace edits. As regards civility, we seem to be having a friendly non-mathematical discussion on his talk page, where I revealed my "inner Gromov groupie" to him after he made an allusion to this edit of mine [2] on the talk page of DG of S here.

I think my ongoing responsiveness in my edits to the mainspace article to his invariably insightful comments should speak for themselves. I also refactored the second version of my response to Arcfrk's proposal of a possible split (which I agree with - see above). At the moment I am preparing a segment on "rolling without slipping or twisting" to expand and provide sources for silly rabbit's additions and I have spent almost half a day trying to find a proper complete reference for the method (referred to in one unreferenced sentence in an Appendix of Arnold's classical mechanics book, now added by me to the references) for constructing parallel transport by approximating paths by piecewise geodesic paths. I had hoped my own copy of Aleksandrov and Zalgaller would help, but not so far ... Any help would be appreciated! Mathsci (talk) 09:07, 8 August 2008 (UTC)

I think the original post in this thread referred to this edit of yours[3](specifically, the first and the last sentences), which, I am happy to see, you redacted[4]. Nsk92 (talk) 14:11, 8 August 2008 (UTC)

I'm not so sure. That was 2 days ago. I think Oded was explicitly mentioned in the edit summary :-) Meanwhile I have cleared up the mystery of Arnold's sentence, thanks to the account in Berger's Panorama. Arnold's sentence, repeated when he generalized it to the case of a Riemannian n-manifold was an "exercise for the interested reader" ... I'll give an obvious method of solution in a footnote (using the Sobolev or L² energy norm on paths). Mathsci (talk) 17:26, 8 August 2008 (UTC)

Template:Nobel icon proposed for deletion

A TfD has been convened, as to whether to prohibit all the little gold icons in Nobel prizewinners' infoboxes. Jheald (talk) 09:04, 7 August 2008 (UTC)

Of course, as far as I know, only one mathematician has ever won a Nobel prize. siℓℓy rabbit (talk) 14:21, 7 August 2008 (UTC)

Maybe two ? Gandalf61 (talk) 14:57, 7 August 2008 (UTC)

Why maybe? So he didn't win it for Principia; so what? Septentrionalis PMAnderson 17:02, 7 August 2008 (UTC)

Maybe he was a philosopher and logician, not a mathematician? Algebraist 17:06, 7 August 2008 (UTC)

You cannot win a Nobel prize for your mathematics, but you can win one for applying it to Economics, Physics, Chemistry, or whatever. JRSpriggs (talk) 17:16, 7 August 2008 (UTC)

Of course, Russell won the Nobel prize for literature. So it doesn't count. ;-P siℓℓy rabbit (talk) 19:39, 7 August 2008 (UTC)

Perhaps three? Richard Pinch (talk) 21:26, 7 August 2008 (UTC)

Rather arguably, maybe even four? But calling him a mathematician is pushing it, even though he studied math. Ozob (talk) 22:28, 7 August 2008 (UTC)

The prize in Economics is not really the Nobel Prize. It is a prize whose name was chosen to be easily confused with the Nobel Prize. Oded (talk) 01:25, 8 August 2008 (UTC)

RFC at St. Petersburg paradox

For whoever is interested in such things: I'd like to draw your attention to Talk:St. Petersburg paradox#Request for comments: punctuation after displayed formula. The issue in question is: should a sentence ending on a displayed formula have a period after the formula?  --Lambiam 18:18, 8 August 2008 (UTC)

Feynman subscript notation

I've just removed the use of "Feynman subscript notation" from curl, since I've never seen it before and don't see the point of it. I've noticed it's also used a couple of times on vector calculus identities, and thought I'd ask here before removing it from there as well, just in case it is a real notation and I'm just missing the point of it. It uses subscripts on nablas to indicate which vector they act on, eg. $\nabla _{A}(\mathbf {A} \cdot \mathbf {B} )$, whereas I would just write $\nabla \mathbf {A} \cdot \mathbf {B}$ (possibly with brackets, but I think it's standard for gradient to take precedence over dot product). Does anyone else know why such a notation is being used? --Tango (talk) 00:55, 8 August 2008 (UTC)

I reverted your change to Curl (mathematics). You changed the meaning of the formula. You changed

$\mathbf {v\ \times } \left(\mathbf {\nabla \times F} \right)=\nabla _{F}\left(\mathbf {v\cdot F} \right)-\left(\mathbf {v\cdot \nabla } \right)\mathbf {F} \ ,$

to

$\mathbf {v\ \times } \left(\mathbf {\nabla \times F} \right)=\left(\mathbf {v\cdot \nabla F} \right)-\left(\mathbf {v\cdot \nabla } \right)\mathbf {F} \ ,$

which is different. To see the difference, I will translate these to 3-D tensor-index notation where I am using the Einstein summation convention and ignoring the difference between covariant and contravariant because this is a Cartesian coordinate system in Euclidean space

$\epsilon _{ijk}\,v_{j}\,\epsilon _{klm}\,F_{m,l}=v_{n}\,F_{n,i}-v_{p}\,F_{i,p}\,$

$\epsilon _{ijk}\,v_{j}\,\epsilon _{klm}\,F_{m,l}=v_{n}\,F_{i,n}-v_{p}\,F_{i,p}\,$

In other words, you are contracting with the wrong tensor index of the gradient of F. OK? (By the way, I have not checked whether any of these formulas are correct or not.) JRSpriggs (talk) 02:44, 8 August 2008 (UTC)

Yeah, by the way, please, for my sanity, as well as the sanity of many readers who aren't physicists, don't use the Einstein notation for sums. Einstein was a genius, but I'm not, and what little typing you save by omitting $\sum _{i}$ is completely defeated by the people you lose omitting it. Also, I think there are many conventions and they are not always compatible. Sometimes you sum across repeated indices depending on whether or not they're in superscripts or subscripts, and then you don't know anymore what's an exponent and what's an index... Loisel (talk) 04:36, 8 August 2008 (UTC)

OK, I checked and the first (original) version is correct, but the second (Tango's version) is wrong. In fairness, I should say that if Tango had instead used $\mathbf {(\nabla F)\cdot v}$ to replace $\nabla _{F}\left(\mathbf {v\cdot F} \right)$, then he would have been OK.

To Loisel: Whenever the Einstein summation convention is used, superscripts are never exponents except for "2" representing a square. The explicit use of the digits "0", "1", "2", or "3" as indices is very rare, so you can almost always be sure that a superscript two stands for a square. If you pay attention to the context, you can always tell. Practice makes perfect.

To me, the summation signs are really just clutter which make it harder to read formulas.

When using Cartesian coordinates in flat three dimensional space, $g^{ij}=\delta ^{ij}\,$ (where δ is the Kronecker delta), so $A_{i}B_{i}=A_{j}g^{jk}B_{k}\,$ is just a further abbreviation. JRSpriggs (talk) 07:09, 8 August 2008 (UTC)

Again, I realize you're smart like Einstein, but there are many people who aren't. I kid, but seriously, there's one thing I have learned relatively recently: help your reader. Give details so that the reader can understand easily. If you're writing an article for physicists, please go ahead and use the Einstein notation. But there are lots of Calculus students who will understand $\sum _{i}a_{i}b_{i}$, but not $a_{i}b_{i}$. Loisel (talk) 06:02, 9 August 2008 (UTC)

I agree with JR that explicit summation symbols can clutter more complicated formulas (where multiple indices are contracted, or where there are many summands being contracted on different indices). However, I also believe that the summation convention is abused on Wikipedia to the point where I have seen formulas use this convention to express contraction on a single index. This thread illustrates perfectly that, whereas those who are familiar with the notation may view the summation signs as unnecessary, it may be a significant barrier to understanding for those unfamiliar with the notation. So, in the interests of WP:MTAA, I think that the summation convention should be avoided in articles where it is unreasonable to expect the majority of readers to be conversant with the summation convention (for example, the article Cross product). siℓℓy rabbit (talk) 16:32, 9 August 2008 (UTC)

Forgive my ignorance if this is a stupid question, but isn't $\mathbf {(\nabla F)\cdot v} =\mathbf {v\cdot (\nabla F)}$? Am I missing something? VectorPosse (talk) 10:01, 8 August 2008 (UTC)

This would be true if F were a scalar, but it is a vector field and in general $\nabla \mathbf {F} \not =(\nabla \mathbf {F} )^{T}$. siℓℓy rabbit (talk) 12:11, 8 August 2008 (UTC)

I think by the end of this thread, I'm going to feel really dumb, but if $\mathbf {F}$ is a vector field, I don't even understand what is meant by $\nabla \mathbf {F}$. I understand an expression like $\nabla \cdot \mathbf {F}$, but the result is not a vector field. VectorPosse (talk) 17:46, 8 August 2008 (UTC)

Think of $\nabla \mathbf {F}$ as representing the Jacobian matrix (rather than a gradient). There is a little more to it than that to do with covariance and contravariance of vectors, but if you do everything in an orthogonal coordinate system, then it amounts to the same thing. siℓℓy rabbit (talk) 17:50, 8 August 2008 (UTC)

To VectorPosse: See Dyadic tensor. In 3-D, there are three ways to multiply two vectors: the dot product which yields a scalar; the cross product which yields a vector; and the tensor product which yields a dyad, also called a rank two tensor or square matrix. In tensor-index notation, these products of $A_{i}\,$ by $B_{j}\,$ are: $({\vec {A}}\cdot {\vec {B}})=g_{ij}A_{i}B_{j}\,$; $({\vec {A}}\times {\vec {B}})_{i}=\epsilon _{ijk}A_{j}B_{k}\,$; and $({\vec {A}}{\vec {B}})_{ij}=A_{i}B_{j}\,$ itself. $\mathbf {(\nabla F)}$ is a dyad. Traditionally, a dot product on the left and a dot product on the right affect different factors in the dyad. JRSpriggs (talk) 05:22, 9 August 2008 (UTC)

Thanks! I learned something new today. VectorPosse (talk) 12:06, 9 August 2008 (UTC)

As have I, thank you indeed! (And thank you VectorPosse for asking the questions I was going to ask.) --Tango (talk) 15:17, 9 August 2008 (UTC)

Vacuous truth

Our article on vacuous truth, until April or so of this year, was about the concept that I assume most people here understand as the phrase's referent: Conditionals that are true because their antecedents are false, and universals that are true because the domain of the universal quantification is empty. But then someone revised it so that it now seems to be more about analytic truth, or logically necessary truth, in general. I think this is wrong but I didn't want to just revert a long series of changes. I left a message at the article's talk page but have seen no response. Does anyone have suggestions as to the best way to proceed? --Trovatore (talk) 21:33, 9 August 2008 (UTC)

The only major change I can see since the beginning of April is to the first paragraph. I'm not sure it was a particularly good change, but it hasn't substantially changed the subject of the article. Could you provide some diffs for the changes you're talking about? --Tango (talk) 22:07, 9 August 2008 (UTC)

[Here's http://en.wikipedia.org/enwiki/w/index.php?title=Vacuous_truth&diff=next&oldid=206038832] where it started to go seriously wrong, as far as my understanding of the concepts goes.

Apparently there's a reference for this usage so it should probably be treated. But I don't think it's what's most generally understood for vacuous truth.

Let me give a couple examples of the concepts as I know them:

1. The assertion all squares are rectangles is not vacuous, because there do exist squares. What it is, rather, is an analytic truth, a statement "true by virtue of its meaning". Whether it's also a logically necessary truth I'm not as sure.
2. On the other hand, the assertion all flying unicorns in Canada are zebra-striped is a vacuous truth, because Canada has no flying unicorns. But it's not an analytic truth, because zebra-stripedness is not part of the meaning of "flying unicorn in Canada". Nor is it a logically necessary truth — or at least I don't see how you can refute, by logic alone, the existence of a non-zebra-striped flying Canadian unicorn.

Note that the second statement is not even "devoid of content", which the article now uses as part of the definition; it has content because it wouldn't be true if there were non-zebra-striped flying Canadian unicorns, which there logically could be. It's "vacuous" because it appears to assert zebra-stripedness of some object, but in fact does not. --Trovatore (talk) 06:42, 10 August 2008 (UTC)

Ok, so you are just referring to the first paragraph. You're right that it was incorrect (and has now been fixed) - whoever wrote it was confused between something being tautologous and it being vacuously true. --Tango (talk) 17:56, 10 August 2008 (UTC)

What is clear is that the article used to be on what a mathematician would call a "vacuous truth", e.g. "all squares that are not squares are rectangles" is vacuously true. This is the typical way a mathematician would encounter the term. Now the article is on a variety of concepts as explained above. --C S (talk) 09:09, 10 August 2008 (UTC)

I've edited the first paragraph to get rid of the idea that vacuous truth is the same as analytic truth.

In the mean time, would it be unreasonable to use more realistic examples instead of statements about flying unicorns and the like? If I want to ascertain that no cell phones will ring in my classroom during my class, I may seek an assurance that "All cell phones among the audience are turned off". That statement may be true because there are no cell phones there, and that's certainly good enough for my purpose. No flying unicorns are invloved. Talk of flying unicorns makes the whole concept seem vacuous, and that's not what we should do. Michael Hardy (talk) 14:09, 10 August 2008 (UTC)

I had posted on the talk page of the article (and I wish that this thread had responded there instead of here). The trouble with editing out the old version is that it had solid references backing it up, one of which I verified. I also agree that this definition of vacuous is definitely not the one I am used to seeing, and I am happy for the edit. But I think some effort should still be made to incorporate the other viewpoint. siℓℓy rabbit (talk) 14:17, 10 August 2008 (UTC)

Is a classroom with no cellphones any more realistic than the flying unicorn example? Good point though. --C S (talk) 00:30, 11 August 2008 (UTC)

If we're going to include both notions, then we should make a VERY SHARP distinction between them---don't leave anyone an opportunity to get confused as a result of the article. Michael Hardy (talk) 20:52, 10 August 2008 (UTC)

Lead summary template

An experimental lead summary template is was being trialled at Abelian group. Theresa Knott is inviting comments at Talk:Abelian group. Gandalf61 (talk) 21:10, 11 August 2008 (UTC)

List of important publications in statistics

List of important publications in statistics is on AfD. Is there a reason for that that would not apply equally to list of important publications in mathematics, list of important publications in computer science, list of important publications in biology, list of important publications in physics, list of important publications in economics, list of important publications in psychology, etc., etc.? Opine at Wikipedia:Articles for deletion/List of important publications in statistics. Write Keep, Delete, Comment, or the like. Don't just say "Keep" or "Delete"; explain your reasons. Michael Hardy (talk) 06:14, 13 August 2008 (UTC)

Differential geometry of surfaces

Back in January, I created this article by importing a few sections from the article "Surface" and adding a modicum of motivations and history. Since then, it has been greatly expanded by the initial writer, MathSci, and presently appears to be a hodge-podge of definitions and facts ranging from special chapters of surface theory to general Riemannian geometry. Sections on surfaces of nonpositive curvature and, especially, parallel transport and connections, strike me as completely out of place (both can be stand-alone articles). A couple of highly competent editors are looking over the article, but this may be insufficient to form a consensus on the appropriate scope and level of generality and to prevent POV pushing, so help from others would be greatly appreciated. Arcfrk (talk) 16:25, 5 August 2008 (UTC)

Is this supposed to be limited to infinitely differentiable embeddings of two dimensional manifolds into three dimensional Euclidean space? JRSpriggs (talk) 00:04, 6 August 2008 (UTC)

This article was created almost entirely from material written by me. It has been gradually revamped by me, JackSchmidt and silly rabbit. They seem happy with the present form, which follows closely the exemplary account of Marcel Berger, itself an updated commentary on the original work of Gauss. This is standard 3rd year undergraduate material and has been for example the content of a 3rd year DPMMS course on the Geometry of Curves and Surfaces, given at the University of Cambridge, presented in Pelham Wilson's recent C.U.P. book "Curved Spaces" as well as older classic texts (eg Eisenhart's 1909 book). Another standard presentation of the theory of connections on surfaces at a beginning graduate student level was added at the end, to reflect the content of 3 now classic texts by Singer & Thorpe, O'Neill and do Carmo. The aim was to present this material in an approachable way, aimed at non-experts. It carefully outlines the theory of Elie Cartan in the simplest possible case, sometimes assuming the surface is embedded in Euclidean space for simplicity and added clarity, just as all three text books do. (The article contains a reference to the fact that surfaces can always be locally embedded in R⁴ in the general case and in R³ in the analytic case.) Singer & Thorpe's account has been followed quite closely also, but with input also from the standard encyclopedic text of Kobayashi and Nomizu. The initial article - assembled as a hodge podge by Arcfrk - still has a second paragraph by Arcfrk in the lede unrelated to any of the content in the article, It has an opening section, now entitled "Overview", lifted from Surfaces, which was actually more appropriate there, as it is not about the differential geometry of surfaces. The section on examples (constant curvature surfaces, ruled surfaces, etc) needs expanding mostly by wikilinks. The undergraduate and the graduate courses could be split as two separate articles, after some minor rewriting of the material on the Gauss-Codazzi equations. JackSchmidt and silly rabbit have been enthusiastic during the revamping, which was requested with the specific remit of making the material as approachable and readable as Differential geometry of curves, a much easier subject. The article still has "underconstruction" templates, so is still being reworked. I am sure that with the other editors that are actually working on and looking over the revamping of the article, decisions on splits can be made when the time is appropriate. This talk page is probably not quite the right place to dicuss this kind of thing on wikipedia. On the other hand WP:AN/I would have been worse. Thanks, Mathsci (talk) 06:09, 6 August 2008 (UTC)

What I was asking for is a very brief statement of what the intended scope of the article is. JRSpriggs (talk) 12:17, 6 August 2008 (UTC)

Well it would seem to be 3-fold:

• a summary of the contents of a standard undergraduate course on DG of S up to Gauss' theorema egregium and the Gauss-Bonnet theorem
• a summary of the contents of a standard introductory graduate course on DG of S covering the use of connections through differential forms on the frame bundle a la Cartan up to Gauss-Codazzi, using embedded surfaces as motivation
• a brief encyclopedic survey of any other related topics in the DG of S

The other constraints are that it should be written to be as accessible to as wide an audience as possible, so fairly self-contained, and that it should largely follow standard textbooks for the first two points. Someone asked for it to be as user friendly as Differential geometry of curves. Mathsci (talk) 13:23, 6 August 2008 (UTC)

The last part of the article on "Riemannian connection" has now been extensively reworked (as encouraged by silly rabbit):

• to apply to arbitrary oriented surfaces (as possibly proposed by JRSpriggs)
• to treat the example of the 2-sphere and Maurer-Cartan forms in detail
• to include material on "rolling without slipping and twisting"
• to separate out material on embedded surfaces where it improved clarity (as proposed by Katzmik)
• to define parallel transport using the geodesic curvature of a curve
• to include comments on the Arnold construction of parallel transport (as proposed by Katzmik)

Because of the natural break between 19th century/undergraduate and 20th century/graduate material, I am quite happy to see this last part made into a separate article, possibly called "Riemannian connection on a surface" or some variant of that, like "Riemannian geometry of surfaces". Mathsci (talk) 09:49, 14 August 2008 (UTC)

Although I support a split, the distinction between "Differential geometry of surfaces" and "Riemannian geometry of surfaces" seems a little too arbitrary for my taste. The title of the new article should be chosen to try to accurately reflect its contents so that readers can easily determine whether they want to click through to the article or not, and don't have to get mired in details to find out. Your suggestion of "Riemannian connection on a surface" seems better. Or just "Connection on a surface" — which also leaves some room for potential future expansion. siℓℓy rabbit (talk) 14:02, 14 August 2008 (UTC)

Thanks for the reply. I also prefer "Connection on a surface", because as you say it is unambiguous and leaves open the possibility for adding material on projective, conformal and spin connections later. Mathsci (talk) 15:52, 14 August 2008 (UTC)

On second thoughts, because of the present introductory form and intent of the article, it seems best to call it Riemannian connection on a surface, as this will allow sections to be subdivided. This does not preclude other types of connections being mentioned or a future name change. Projective connections would seem to be best discussed in an article "Connection on a Riemann surface", which could also contain an account of the theory of Atiyah and Bott. Regarding conformal connections, there is a general problem at the moment with wikipedia's coverage of Teichmuller theory. I was surprised to find that the Beltrami equation was not discussed (I put in a brief description in Isothermal coordinates) nor various other constructions of Teichmuller space, one of which involves the conformal class of a metric and Poincaré's theorem (also inserted by me in Surfaces). There are plenty of articles and books summarising this. Teichmuller space does not seem properly encyclopedic, nor for that matter Quasiconformal mapping. It's also quite odd that Uniformization theorem contains a reference to a 2004 Harvard Ph.D. and one article on Ricci flow. There are no other references: neither Paul Koebe nor Henri Poincaré are mentioned. Mathsci (talk) 05:00, 15 August 2008 (UTC)

List of basic mathematics topics

The List of basic mathematics topics seems fairly poorly maintained, and looks like a project assembled by someone with only a glancing familiarity with mathematics. Personally, I think it should look more like Lists of mathematics topics which is far more comprehensive and useful as an encylopedic resource. I'm not sure what, if anything, to do about this. Opinions are welcome. siℓℓy rabbit (talk) 23:24, 6 August 2008 (UTC)

Perhaps List of basic mathematics topics should be scrubbed, started again and this time the name changed to List of elementary mathematics topics and the content restricted to school mathematics, with a link at the bottom of the page to List of mathematics topics. And the List of mathematics topics#Basic mathematics section of List of mathematics topics replaced with a link to List of elementary mathematics topics. Delaszk (talk) 15:51, 13 August 2008 (UTC)

Proposal to rename optimization category

The word Optimization can be used outside the context of optimizing a mathematical function, so I propose that the Category:Optimization be moved to Category:Optimization (Mathematics). That way people won't put articles and categories like Hardware tuning into the Optimization (Mathematics) category. Delaszk (talk) 16:00, 13 August 2008 (UTC)

Good idea, bad name. Category:Mathematical optimization would be better, but is there anything that improves on that? CRGreathouse (t | c) 16:49, 13 August 2008 (UTC)

The hard part will be changing all the articles and subcategories to point to the new category name. You will probably want to recruit a bot to do that. JRSpriggs (talk) 01:47, 14 August 2008 (UTC)

There's a standard bot for that, if the rename is approved at WP:CfD. — Arthur Rubin (talk) 02:06, 14 August 2008 (UTC)

Also the new category should be made a subcategory of a more general "Optimization" category which would also include stuff like Hardware tuning. JRSpriggs (talk) 09:16, 14 August 2008 (UTC)

Mathematical optimization get 396,000 hits on Google, so it seems a reasonable enough name. The proposal has now been submitted to WP:CfD. The entry is at Wikipedia:Categories_for_discussion/Log/2008_August_14#Category:Optimization Also agree that a more general category should be added.Delaszk (talk) 22:22, 14 August 2008 (UTC)

Steiner chain

An article titled Steiner chain just appeared, written by user:King of Hearts. I was surprised that that was never there before. Two things:

(1) It's still a bit stubby; anyone who can add more should take a look;

(2) Not many articles link to it. Are there others that should? If so, please add the links.

Michael Hardy (talk) 04:54, 15 August 2008 (UTC)

Two Peer Reviews

150 years & still begging for mathematicians. ;)

M'lords, if you would be so kind, I'd like to beg a peer review of Newton's theorem of revolving orbits. I realize that the article is more the province of physics than of mathematics, but it would be a gracious gesture. Also, Isaac Newton is covered by the Mathematics WikiProject — perhaps you might want the chance to review his theorem?

I'd also like to put in another plea for reviewing the problem of Apollonius. I'll be re-making some images into SVG's, but otherwise the article might be ready for FAC? As always, any suggestions or advice you had would be very welcome.

Thank you in advance, and hoping that you enjoyed the sly caption, Willow (talk) 20:49, 7 August 2008 (UTC)

Willow, your moving images cause my computer to suffer memory overflow. Please have them only move when one clicks on them. JRSpriggs (talk) 02:48, 8 August 2008 (UTC)

I second that. Actually there is very little value-added since most of the images have already finished their animation by the time the page loads for me. (Ok, so I have a slow connection.) Of course, one way to fix this (the wrong way) is to make the images move continuously. I prefer JR's suggestion. siℓℓy rabbit (talk) 04:22, 8 August 2008 (UTC)

Thank you both (and Ozob!) for looking at the Newton article. :) I'm sorry about the memory-intensive GIF animations, which I thought would be helpful for people who found the equations difficult to follow and just wanted to get the gist. (As an aside, the planets do move continuously.) I'll see what I can do to make the animations more computer-friendly. Thank you again, Willow (talk) 13:34, 8 August 2008 (UTC)

Maybe it's only Image:Newton_revolving_orbit_3rd_subharmonic_e0.6_240frames_smaller.gif, but this does not appear to move continuously on my browser. siℓℓy rabbit (talk) 13:39, 8 August 2008 (UTC)

As one solution, I've replaced the animated GIF images with OGG Theora video files. I hope that the animations will run smoothly for you all now, and that you'll have the opportunity to review the article. Thank you in advance! :) Willow (talk) 18:16, 15 August 2008 (UTC)

Hoffman and Johnson

There is a dispute on Talk:Navier–Stokes existence and smoothness as well as Talk:d'Alembert's paradox, on the inclusion of material from a paper and book by Hoffman and Johnson. Since most of the discussion is between two editors, Egbertus and me, I would be very glad if someone else could contribute to the discussion. -- Crowsnest (talk) 11:25, 10 August 2008 (UTC)

Unfortunately, after having been informed of NPOV and COI policies by what must be 5 different editors now, Egbertus has simply started resorting to reversions after failing to convince a single soul of the appropriateness of inclusion. In fact, even after receiving painstaking explanations, Egbertus is now accusing everyone of NPOV violations in an information suppression campaign. I don't know how this makes sense: that we are all in cahoots to put down Hoffman and Johnson, but nonetheless I think more eyes are needed here. There is also ample evidence that the initial material was included by Hoffman and Johnson and Egbertus, despite seemingly being very invested in the promotion of this work, has refused to answer queries on his/her relation to these persons, which raises further questions. --C S (talk) 20:04, 12 August 2008 (UTC)

It's now clear that Egbertus is unwilling to follow Wikipedia policies. S/he simply does not agree with using third party sources. S/he also seems to have started engaging in editing the articles, then waiting until nobody is apparently watching, then including the disputed material yet again. Is there nothing that can be done to stop this? Can an admin warn Egbertus to stop such behavior? I understand this is not a blockable offense, but on the other hand, this is an SPA with a definite COI (no denials at all and some coordinated effort with an account admitted to be one of the authors). What can be done here? --C S (talk) 11:22, 15 August 2008 (UTC)

The article d'Alembert's paradox is now also heavily slanted toward the point where when one reads the article one believes "hey, this thing is unresolved...nobody knows anything!" when in fact, from reading the referees rejection reports of the disputed paper (conveniently posted on the senior author's website) it seems this is an extremist and unconventional viewpoint. --C S (talk) 11:24, 15 August 2008 (UTC)

Who says this isn't a blockable offense? WP:Block policy#Disruption lists 'persistently violating other policies or guidelines' as grounds for a block. There's even a specific clause about COI SPAs. Algebraist 11:38, 15 August 2008 (UTC)

Hi. Yes, thank you! I found a similar statement elsewhere in the COI pages. I guess I was under the "not blockable" impression because the COI warning template does not at all mention the possibility of a block. I have posted a summary at Wikipedia:Conflict_of_interest/Noticeboard#promotion_efforts_at_d.27Alembert.27s_paradox_and_.22related.22_articles which should hopefully resolve the situation. (I apologize for the disorganized nature of the summary but there is way too much discussion to summarize neatly and I have little time to do so). All I wish is that a stern warning be given by an admin. Something that is sterner than simply "oh by the way, if you have a possible COI, you should be careful", which has already been issued on Egbertus' talk page. I hope that will be enough to get Egbertus to desist in this activity. --C S (talk) 12:10, 15 August 2008 (UTC)

Newberger's summation formula

Newberger's summation formula is a orphan article—linked to only from the list of mathematics articles—that has been nominated for deletion. The grounds cited for deletion are pretty weak: only that its evident flaw have not been attended to for two years. Michael Hardy (talk) 04:37, 15 August 2008 (UTC)

Post opinions at Wikipedia:Articles for deletion/Newberger's summation formula. Michael Hardy (talk) 16:25, 15 August 2008 (UTC)

Michael Atiyah

is up for peer review. Comments to Wikipedia:Peer review/Michael Atiyah/archive1 or talk:Michael Atiyah. R.e.b. (talk) 14:47, 15 August 2008 (UTC)

differential geometry of surfaces

Administrator Oleg Alexandrov has encouraged me to place the following comments at this page. The content of the comments is solely my own responsibility and do not engage Oleg in any way.

The notions of connection, parallel transport, and covariant derivative are all interrelated and of central importance in a number of fields, including differential geometry and gauge theory.

As far as the differential geometry of surfaces is concerned, a number of editors have already voiced the opinion that the subsection on connections is vastly overblown given the simple construction of parallel transport given in Arnold's introductory book. The construction is completely elementary and similar to the calculation of pi using approximation by polygonal curves, which must go back to the ancient Greeks, perhaps even Hindus.

Namely, the case of surfaces is special since there is only one extra direction in addition to the tangent direction. For this reason parallel transport is uniquely determined by knowing the geodesics.

Essentially what needs to be decided is whether [[differential geometry of surfaces]] should be an alternative introduction to differential geometry, with the case of surfaces particularly in mind, or whether it should more seriously try to focus on the surfaces themselves.

The material on connections is interesting and could be moved to a different page. Katzmik (talk) 11:58, 15 August 2008 (UTC)

In short, there exists a content dispute on what should be in the differential geometry of surfaces article. Interested geometers are welcome to comment on the article talk page, while avoiding recent issues with incivility there. Oleg Alexandrov (talk) 15:42, 15 August 2008 (UTC)

I do like the new version of differential geometry of surfaces, shaping up to look like a great article. I can't see a problem with summary style section on connections as they apply to surfaces as a with a {{main}} link at the top of the section, to an appropriate page on the general case. There are many people who are specifically interested in surface especially in applied domains, so its good to treat this well, others with a higher dimensional bent will more appreciate a more general approach. --Salix alba (talk) 10:31, 16 August 2008 (UTC)

Using the summary style is a definite improvement. Illustrations in "Examples" also add a lot to the article. Nonetheless, I feel that only first paragraph of the section "Riemannian connection" is directly relevant for the theory of surfaces, the rest of the section reads like a blurb for the theory of connections. Gauss's approach based on the first and second fundamental forms and Darboux–Cartan's method of a moving frame form two traditional alternatives for foundations of the theory of surfaces, and both should be clearly explained and compared in the beginning of the article. Structure equations for a surface in a moving frame then naturally lead to the theory of connections in Riemannian geometry; conversely, the use of connections provides conceptualization for structure equations and certain computations with the curvature (cf the 1st and 3rd paragraph). Arcfrk (talk) 13:21, 16 August 2008 (UTC)

Concerning the scope: the larger issue ("the content dispute" mentioned by Katzmik and Oleg) still stands. The present version is, on the one hand, rather textbooky in style, and on the other hand, not very systematic in structure. My opinion is that this article should be a coarse-grained introduction to the problematics of the differential geometry of surface theory. The Springer EOM entry Theory of surfaces demonstrates one possible approach, although it's too sketchy by Wikipedia standards. Chapter 4 of Hilbert and Cohn-Vossen provides a masterful non-technical account (a little long for us). Berger's "A Panoramic view of Riemannian Geometry", on the other hand, seems totally unsuitable as a template: it has completely different goals and only spends a little over 80 pages out of 850 total on surfaces (Section 1.6 and Chapter 3), with the choice of material dictated by the overall goals. Arcfrk (talk) 13:21, 16 August 2008 (UTC)

Concerning the mode of presentation: Wikipedia provides excellent "infrastructure" for treating special topics and techniques, and we already have key elements in place (all topics needed for this article already have their own articles of at least the start class). Conversely, cramming all sorts of auxiliary material in a single article (as Mathsci evidently prefers to do) tends to lead to severe problems with maintanence, especially, with coordinating multiple forks scattered over different articles and makes the articles hard to edit as a contibutor and follow as a reader. Arcfrk (talk) 13:21, 16 August 2008 (UTC)

Differential form

Differential form could use some work. See also talk:differential form. Michael Hardy (talk) 00:39, 17 August 2008 (UTC)

Deletion sorting

Per a comment I noticed elsewhere in passing, I've proposed the creation of a deletion sorting subpage for mathematical topics. Feel free to comment at Wikipedia talk:WikiProject Deletion sorting#Mathematics. —Ilmari Karonen (talk) 14:08, 18 August 2008 (UTC)

The page Wikipedia:WikiProject Mathematics/Current activity already includes them. Since there are so few mathematics deletion discussions, I think it makes more sense to include them with the science ones. — Carl (CBM · talk) 14:41, 18 August 2008 (UTC)

Need reviewer for Good Article in geometry

Hi, I've just nominated the problem of Apollonius as a Good Article. If one of you would be so good as to review it, I'd be very grateful. I think you won't be too disappointed with its quality, since I've been working on it since January. Well, strictly speaking, I created the stub back in May 2006, but I didn't start improving it until this year. Anyway, thank you very much for taking the time to do the review! :) Willow (talk) 19:48, 18 August 2008 (UTC)

Congratulations on getting us another mathematical Good Article! —David Eppstein (talk) 01:11, 20 August 2008 (UTC)

reals vs complex in the lead of articles

I am working on Positive-definite matrix with a few other editors and the following question has come up. If a concept is well defined over the complex numbers/matrices, should the article start with the real case and then go on to the complex case, or should the text focus on the complex case and mention that the real case is just a special case of this. The arguments for Real first is that it is easier to understand if you haven't had more than two years of college maths. The argument for the complex case is that it is the most general, and once you are comfortable with complex numbers, it's very easy to see how to make the claims more specific. I would argue that since Wikipedia's math articles are (ostensibly) not intended for those doing graduate studies in maths, the real case should be first. Is there already a policy on this? If not, I'd propose that there should be one. Where would I propose this? Pdbailey (talk) 19:26, 15 August 2008 (UTC)

missing the point, from the beginning. the reason for dealing with the complex case first, in this particular article, is because it is simpler and cleaner, not because it is more general. this is not unusual. real operator algebras and real algebraic geometry are, for instance, both trickier than their complex counterparts.

and the statement "once you are comfortable with complex numbers, it's very easy to see how to make the claims more specific", coming from you, i am sorry to say, is somewhat annoying, after you introduced mistakes in the article by carelessly and blindly replacing C with R. Mct mht (talk) 21:31, 15 August 2008 (UTC)

Mct mht, please post any responses regarding this particular topic back at the talk for PD matrix. You stopped responding when you claimed that the fact that symmetry needs to be imposed is prima face evidence that the Real case is problematic and I asked you how the Hermitian requirement differed from the same. Pdbailey (talk) 19:06, 16 August 2008 (UTC)

I think there should not be any stated policy for this. In some cases it makes sense to begin with the reals, and in other cases with the complex. Also, for some articles it makes perfect sense to assume familiarity with advanced concepts, while for others you want to assume as little as possible. Oded (talk) 03:32, 16 August 2008 (UTC)

I agree with Oded. Wikipedia is not a bureaucracy and issues like this can easily be addressed on a case-by-case basis according to the needs of the article, its readers, and the encyclopedia. Geometry guy 09:37, 16 August 2008 (UTC)

Agreed - this should be decided on a case-by-case basis. If the real case is a special case of the complex case then it might make sense to introduce the complex case first, and then specialise to the reals. But there are other topics (such as derivative) where the real case is more general, and so should be introduced first. Gandalf61 (talk) 10:41, 16 August 2008 (UTC)

Agreed, case-by-case is best. Often the complex case and the real case are identical, just with the words "complex" and "real" swapped. In those cases, I would suggest discussing the real case first, so as not to scare people away, and then mention that the complex case is exactly the same. In cases where there is a difference between the cases, it needs to be decided based on the details of the article. --Tango (talk) 18:23, 16 August 2008 (UTC)

This is obviously a policy (real where there is only minor differences, complex where it is easier), and one that is agreed upon, why not make it formal? This is helpful when you are editing a page and arguing with someone who just likes complex numbers better when the articles claims are essentially identical--I can understand this since many articles are written for and by graduate students, but then they are not accessible for others. Pdbailey (talk) 19:11, 16 August 2008 (UTC)

Let's be careful here. Sometimes the real and complex versions are very different. As noted, real and complex differentiation. Another example: bilinear forms, where the real theory has many more applications, since the complex theory most often used is the theory of sequilinear forms (this difference underlies much of the argument over postive-definite, I think). Richard Pinch (talk) 19:54, 16 August 2008 (UTC)

And even if there are only minor differences, Oded said (and I agree) that it makes sense to treat only complex if a topic is so technical that this wouldn't hurt accessibility. I don't see a need for a policy. -- Jitse Niesen (talk) 20:09, 16 August 2008 (UTC)

It is formal as something that like is going to get. It's part of the mathematics MoS: "A general approach is to start simple, then move toward more abstract and technical statements as the article proceeds." This is just common sense, and there is no need to make a guideline specifically for this situation. By the way, I don't think you're helping your case by claiming that a complex treatment requires graduate study. Complex numbers are already used in just as sophisticated ways in undergraduate engineering curricula. --C S (talk) 20:30, 16 August 2008 (UTC)

Thanks to all who responded, I agree with all these contributors, this is not a good policy given the strength of existing policies. C S, I did not claim that complex numbers are introduced in graduate studies--after all, I was solving PDEs in college with complex Eigenvectors in my chemistry classes. I only claimed that most of the math articles appear to be written by and for graduate students. Pdbailey (talk) 04:30, 17 August 2008 (UTC)

I never claimed you made any such ridiculous claim. I said you claimed that a complex treatment of "positive definite matrix" required graduate study. At least, I figured that was an implication of the remark: "I would argue that since Wikipedia's math articles are (ostensibly) not intended for those doing graduate studies in maths, the real case should be first." I have no idea why you would say this if you did not think graduate study was required. I even said "complex numbers are already used in just as sophisticated ways in undergraduate engineering curricula". You would seemingly agree with this from your last remark. In any case, a claim such as you just made that "math articles appear to be written by and for graduate students" is hardly bolstered by your comments thus far. Indeed, given that you believe a complex treatment is approachable by undergrads, to then claim that not doing the real case first is a sign of articles being written for graduate students, that is an argument I cannot understand. --C S (talk) 23:46, 20 August 2008 (UTC)

New policy proposal and draft help

Wikipedia:Scientific standards

I have drafted a new proposal and would like help in clarifying, adjusting, adapting, and improving it. It is based on five years of work here at Wikipedia (not always the prettiest, I might add). I think it summarizes the opinions of a great majority of editors as to how to handle scientific situations. This proposal serves as a nexus between WP:NPOV and WP:RS for cases where we are dealing with observable reality. It is needed because there are a lot of editors who don't seem to understand what entails best-practices when writing a reliable reference work about observable reality. I don't pretend that this version is perfect, and would appreciate any and all additions, suggestions people may have for getting to some well-regarded scientific standards.

Note that these standards would apply only when discussing matters directly related to observable reality. These standards are inspired in part by WP:SPOV but avoid some of the major pitfalls of that particular proposal. In particular, the idea that SPOV even exists is a real problem. However, I think it is undeniable that we should have some standards for writing about scientific topics.

See also WP:SCI for another failed proposal that dovetails with this one. I hope this particular proposal is more in-line with the hole I see in policy/guidelines for dealing with these situations.

ScienceApologist (talk) 19:58, 19 August 2008 (UTC)

I definitely support the ideas underlying your proposal. Moreover, I believe I support the proposal itself, but I think the undefined term "observable reality" has the potential to be problematically broad. (For instance, it is at least arguable that paparazzi engage in observable reality, but I doubt you intend them to come under the scope of your proposal.)

On the other hand, I am pretty sure that mathematics does not deal in observable reality per se (again, it would be strange to deny that any human activity had some kind of connection with observable reality, but this connection plays no part in the methodology of mathematics). I rather think that mathematics brings its own issues vis a vis reliable sources and the like, that to my knowledge have not yet been sufficiently engaged here. For instance, is a complete, correct proof "original research" and therefore inappropriate? What if it is supported by an external link to informal writing on some mathematician's webpage? (What if that mathematician is also the editor of the article?)

My own feelings here -- which are still tentative -- are that by definition a correct mathematical proof is verifiable, so that I think including proofs in articles (even when not accompanied by a citation to a specific source) should not be categorically discouraged. On the other hand, I think there are very often good expository reasons to discourage proofs, especially ones which are moe than a few lines long. I also think that mathematical material that would be acceptable if added by someone else should generally be acceptable when added by the author, although of course the correctness and notability are up to challenge. Finally, I think that mathematical assertions which are reliably sourced but are (by consensus of sufficiently interested and qualified editors) incorrect should be removed from wikipedia. My understanding is that this is explicitly against certain wikipedic philosophies, but nevertheless I think it is appropriate. Comments? Plclark (talk) 23:11, 19 August 2008 (UTC)

And what if the article itself is about a proof? E.g. proof that holomorphic functions are analytic. Michael Hardy (talk) 00:14, 20 August 2008 (UTC)

I think that the problem comes from what people mean when they say observation. In some sense, the anecdotal report of eyewitness testimony may seem like some to be "observable reality", but it is in fact not. Part of the scientific method relies on replicability. The paparazzi photo and the usual suspects line-up defy the traditional standards of replicability for obvious reasons. On the other hand, mathematical proofs can be replicated. This makes them, in a phenomenological sense, subject to these guidelines more than popular culture, for example. Does this make sense? ScienceApologist (talk) 23:21, 19 August 2008 (UTC)

To Michael: since you ask, I see no good reason why this article is called "proof that X" rather than just "X". Do you? To ScienceApologist: to me the term "observable reality" does not inherently connote replicability (especially since, as I said, I am not exactly sure what it means!): are there not conceivably one time only natural phenomena? My point is that we are being drawn into a discussion on the philosophy of science. It's an interesting discussion (and, for what it's worth, I find all your positions eminently philosophically defensible; my point is that they are, like any philosophical position I have ever encountered, also "philosophically attackable"), but an interesting discussion is probably not what you want when you are trying to set clear guidelines. I recommend that you speak of replicability more explicitly in your proposal. Finally, although I hadn't thought of it that way, I heartily agree that the replicability of mathematical proofs is an important part of the phenomenology of mathematics. (I still think that a separate discussion of wikipedia policies vis a vis mathematics would be useful.) Plclark (talk) 01:07, 20 August 2008 (UTC)

Well, an article "Proof that X", or "proof of Y's theorem" would be presumed to contain the proof. An article "X" or "Y's theorem" might well discuss the history, failed attempts, earlier weaker versions, applications, but refer to the literature for the proof (think X = Fermat's Last Theorem, for example). Richard Pinch (talk) 07:20, 20 August 2008 (UTC)

Well, sure. But only about half of proof that holomorphic functions are analytic is devoted to the proof. The other half is devoted to the other sort of material you mention. Moreover, I would expect a "proof that X" article to refer back to an "X" article, and this one doesn't. Plclark (talk) 10:29, 20 August 2008 (UTC)

I don't think that mathematical proofs are replicable so much as verifiable. This makes a difference, and it's relevant to why a proof might be included in Wikipedia. Richard Pinch (talk) 07:20, 20 August 2008 (UTC)

Again I'm not completely clear on the terminology. What distinction between replicability and verifiability do you have in mind? Plclark (talk) 10:29, 20 August 2008 (UTC)

What I mean is that to verify a scientific experiment I have to repeat it, in other words, to do exactly the same thing all over again. But a proof can be verified mechanically, at least in principle: I don't have to discover it all over again, or even understand it. However, I don't claim that this terminology is standard. Richard Pinch (talk) 18:38, 20 August 2008 (UTC)

parallel transport on surfaces

I rewrote the section on Riemannian connection at differential geometry of surfaces in a way more relevant to the case of surfaces. Please take a look. Katzmik (talk) 10:24, 20 August 2008 (UTC)

Probability distribution

Here's the worst opening paragraph I've read in a long time, at probability distribution:

A probability distribution describes the values and probabilities associated with a random event. The values must cover all of the possible outcomes of the event, while the total probabilities must sum to exactly 1, or 100%. For example, a single coin flip can take values Heads or Tails with a probability of exactly 1/2 for each; these two values and two probabilities make up the probability distribution of the single coin flipping event. This distribution is called a discrete distribution because there are a countable number of discrete outcomes with positive probabilities.

Sigh.... Michael Hardy (talk) 16:53, 20 August 2008 (UTC)

I think it is better now. Oded (talk) 02:03, 21 August 2008 (UTC)

General relativity is a featured article, not just A-class

Salix alba (talk · contribs) just updated the list of good articles. While looking at that, I noticed that general relativity is listed as an A-class article. Actually, it is a featured article as you can see by looking at the article itself. "General relativity" should not be confused with introduction to general relativity which is also featured and correctly listed as such. Would someone please check over the whole list! JRSpriggs (talk) 20:37, 20 August 2008 (UTC)

I've updated some of the lists (anyone can do this). Entropy, Algorithm, Number and Trigonometric functions could do with having their ratings reassessed. I would quible as to whether general relativity and introduction to general relativity really count as mathematics rather than physics.

Wikipedia:Featured article candidates/Trigonometric function is worth looking at for a hint of what the FA process used to be like. For some reason recent mathematician promotions all start with E - Emery Molyneux, Emery Molyneux Edward Wright Emmy Noether. --Salix alba (talk) 23:05, 20 August 2008 (UTC)

A mathematical specific citation template

Following a discussion on my talk page I'm wondering if there is a desire for mathematics specific citation template.

Copied from talk page:

Thanks for your edit at differential geometry of surfaces. The truth is that I am not completely happy with this format, since it does not agree with the standards in the mathematical literature. Namely, the standard format as represented by Math Reviews citations and followed by virtually all math journals, is as follows:

1. author name

2. title of article

3. name of journal

4. year of publication

5. page numbers.

Now I am not arguing that there is anything intrinsically better about such order, merely that this happens to be the format used in math publications. I find the other format confusing. The other format happens to be the format used in the physics literature and is appropriate to articles in physics.

I frequently get confused by the physics format and come away from a citation thinking that it does not provide the year of the publication, as it does not appear in the usual space.

I raised this issue once at WP math but the discussion quickly degenerated into a debate whether manual entries are better or automated entries are better. The following points were obscured in that discusssion:

1. the proof of the usefulness of any automated system is whether it can be easily adapted to new situations. Thus, if the citation format cannot be easily equipped with a flag that would switch from the physics format to the mathematics format and back, then there is something wrong with the citation format.

2. there are not twenty or so formats. Rather, there are two main formats, one mostly used in math and the other mostly used in physics. There are variations in italization, punctuation, etc., but for the most part math journals use the Math Reviews format. Katzmik (talk) 12:54, 20 August 2008 (UTC)

I do take your point,and personally I would prefer a mathematical style. The advantages of the citation template seem to outway the stylistic differences, in particular the ability to use hyperlink in the document. The page in question has generally used the citation template so its more consistent with that page. In theory it would be possible to produce a new citation template with a mathematical style it woulf hen be a case of changing {{citation|...}} to {{math-citation|...}}, it might be worth mentioning this on WT:MATH to see what people feel about this. --Salix alba (talk) 17:32, 20 August 2008 (UTC)

Instead of introducing a new template {{math-citation}}, perhaps it would be possible to modify the existing one by outfitting it with a flag? I would suggest the "up" position to be math, the "down" position to be physics, but we might be outnumbered here :-) Katzmik (talk) 08:32, 21 August 2008 (UTC)

There seem to be two main ways to do this. Create {{math-citation}} mainly by cut and paste from {{citation}} and change order appropriately (fairly easy). Or modify {{citation}} to accept a style parameter (harder). --Salix alba (talk) 10:40, 21 August 2008 (UTC)

I seem to be missing something here. When did Wikipedia become a mathematics journal? Geometry guy 11:59, 21 August 2008 (UTC)

Many wikipedia users, as well as contributors, are mathematicians. They are used to a certain format in bibliographic citation. There is an unmistakable tradition as I summarized above to place the year toward the end of the citation, contrary to the format adopted at citation. Is it a legitimate request to have the mathematical public accomodated? Katzmik (talk) 12:18, 21 August 2008 (UTC)

I, for one, strongly favor this idea -- in either of its forms. Just to get it going I slightly prefer the {{math-cite}} form. CRGreathouse (t | c) 12:24, 21 August 2008 (UTC)

If you know your way around templates please go ahead and create one. Katzmik (talk) 12:34, 21 August 2008 (UTC)

I hacked something together; examples here. In the process I determined that it probably isn't needed at all. The formats actually aren't that different. CRGreathouse (t | c) 15:24, 21 August 2008 (UTC)

Since when do only physics and math articles use citations? Every field of research has its own journals, each with its own convention for citing articles. (For an example look at the major difference between the conventions of the two biggest journals out there Nature and Science.) I don't think wikipedia would be served well, by having all lot of different conventions, used through out the site. On the other hand, the status quo is that there is a whole bunch of different conventions used through out the site, so I don't see much harm. (TimothyRias (talk) 12:51, 21 August 2008 (UTC))

I think it's better to just use {{citation}} as a black box and (essentially) ignore how its output is formatted. It's a lot of work to maintain a citation template, and the extremely slight benefit of rearranging the order of the citation data doesn't justify the cost. — Carl (CBM · talk) 13:27, 21 August 2008 (UTC)

I agree. Wikipedia has two predominant reference formats, represented by {{citation}} (which follows Harvard) and {{cite book}} et al. (which follow Chicago/MLA). We don't need another one. Wikipedia articles should accommodate their entire readership, especially as an article can be within more than one domain. I'm surprised at the idea that professional mathematicians cannot cope with the year being in a different place than it is in mathematical journals. Geometry guy 13:46, 21 August 2008 (UTC)

It would indeed be surprising if anyone had said that they "cannot cope". Instead, what is claimed is that it would be more convenient. Personally I would rather the computer do the work (through some template or script) to adapt to what I find useful than that I do the work. I believe that many people reading mathematics articles are likely to be used to the mathematics style, and would also find it convenient to be accomodated in this way. Richard Pinch (talk) 16:53, 21 August 2008 (UTC)

I'd expect most people reading the article to be more than able to adapt to the convention being used. The minor (debatable) convenience of serving a particular convention to a certain subclass of users, does in my view not weigh up to disadvantages brought by having multiple templates. (such as not benefiting from improvements to other templates. (TimothyRias (talk) 07:56, 22 August 2008 (UTC))

I feel consistency with the other parts of Wikipedia is more important than consistency with some subset of math journals. Our target audience isn't mostly people who read math journals, anyway. To reduce this to absurdity: in print chemistry journals, often the title of a reference is omitted, and the journal name is highly abbreviated, and of course (since it's print) there is no link to anything online, making the reference only usable to people who understand the abbreviations and either have a physical copy of the journal or access to an online table of contents for that journal. Do we want to encourage the chemists to develop their own project-specific citation guidelines that make the Wikipedia citations equally difficult to use? No? Then why should we expect math to be treated any differently? —David Eppstein (talk) 17:31, 21 August 2008 (UTC)

The maintenance problems convince me that the minor stylistic differences does not warrent the creation of a new template. If its really a big problem you could actually reformat the citation data using the COinS metadata produced by the {{citation}}. Proving I've got way to much time on my hand I hacked together a monobook script which parses this data User:Salix alba/mathcite.js which could be customised to any format you want. --Salix alba (talk) 14:29, 22 August 2008 (UTC)

That's a wonderful idea. — Carl (CBM · talk) 15:36, 22 August 2008 (UTC)

Great! This is the way to get the computer to do the work. Geometry guy 15:58, 22 August 2008 (UTC)

universal natural number

With this edit a user has added to the article about the number 3 the (fairly obvious) fact that any natural number can be expressed as a power series of 3. The user adds that because of this fact, 3 is called the "universal natural number". Based on a quick google search, it doesn't seem like this is standard terminology. Can anyone confirm or refute this claim? I've left it in for now with a request for a citation. -- Rick Block (talk) 18:20, 21 August 2008 (UTC)

I see it's been (properly) reverted already, but what the edits seem to be describing has its own article: balanced ternary. —David Eppstein (talk) 18:30, 21 August 2008 (UTC)

I guess 3 (number) should link to balanced ternary. I'm not sure where though. Algebraist 18:35, 21 August 2008 (UTC)

(ec)Any natural number can be expressed as a power series in any (>= 2) base; that's the point of positional notation. Even if we restrict ourselves, for some reason to 0, -1 and +1 as coefficients, it's still true of 2 as well as 3. This is not only an unsourced neologism, but a totally pointless one. I've removed it. Algebraist 18:32, 21 August 2008 (UTC)

(ec - at least we're all agreeing with eachother!) It's clearly nonsense - the same can be said of any natural number greater than 1, it's just expressing the number in base 3 (actually, as David says, it's balanced ternary rather than regular ternary, but I don't think that's really significant). --Tango (talk) 18:33, 21 August 2008 (UTC)

Small typesetting issue

At lack-of-fit sum of squares, I changed the first of these two formats to the second:

$\sum _{i=1}^{n}\sum _{j=1}^{n_{i}}{\widehat {\varepsilon }}_{ij}^{2}$

$\sum _{i=1}^{n}\sum _{j=1}^{n_{i}}{\widehat {\varepsilon }}_{ij}^{{}\;2}$

Is it just my browser, or do others see the superscript "2" getting uncomfortably stabbed by the \widehat before the additional tiny spacing is added? Michael Hardy (talk) 16:31, 22 August 2008 (UTC)

It's not just you. The formulas are just .png images -- I can't even get them to change to anything else by changing preferences. The latter does look better, pity about the code though.

I bet if Knuth saw that it would mean another month's delay on his AoCP. Heh heh heh.

CRGreathouse (t | c) 16:56, 22 August 2008 (UTC)

To me it looks like the "2" is too close in the first and too far in the second. How about

$\sum _{i=1}^{n}\sum _{j=1}^{n_{i}}{\widehat {\varepsilon }}_{ij}^{\,2}$

instead? Ozob (talk) 18:37, 22 August 2008 (UTC)

For the Time Being I've implemented that format in both lack-of-fit sum of squares and Studentized residual. Michael Hardy (talk) 18:54, 22 August 2008 (UTC)

That looks best to me. It's a pity TeX can't sort out the spacing on its own for something like that. --Tango (talk) 21:44, 22 August 2008 (UTC)

I'd use \hat instead of \widehat:

$\sum _{i=1}^{n}\sum _{j=1}^{n_{i}}{\hat {\varepsilon }}_{ij}^{2}$.

I think \widehat and \widetilde and friends are too big when put over a single letter. -- Jitse Niesen (talk) 13:11, 23 August 2008 (UTC)

Need name for theorem

Back in the 1970s when I was in graduate school at the University of Maryland, Prof. Donald Sweet (who died that same year) told me of a theorem which generalized a result which I discovered empirically. While looking at Wythoff's game (which I had re-invented, and only recently learned the name of), I had noticed that every positive integer is either $\lfloor k\phi \rfloor$ or $\lfloor k\phi ^{2}\rfloor$ for some integer k, but never both. Donald told me that whenever ${\frac {1}{\alpha }}+{\frac {1}{\beta }}=1$ for positive irrational reals α and β, then this same phenomenon occurs. That is, each positive integer is either $\lfloor k\alpha \rfloor$ or $\lfloor k\beta \rfloor$ for some integer k, but never both. Does anyone know the name of this theorem or have a link to an article on it? Do you know of any generalization to more than two irrationals? JRSpriggs (talk) 06:52, 24 August 2008 (UTC)

See Beatty sequence. Joseph Myers (talk) 09:37, 24 August 2008 (UTC)

To Joseph Myers: Thank you for this information. I have added a link to Beatty sequence to the Wythoff's game article. JRSpriggs (talk) 20:58, 24 August 2008 (UTC)

a vote on citation?

Concerning the above discussion of a math citation format, it seems as though there are arguments on both sides. Perhaps we can try to formulate a proposal that would be acceptable to most people. One particularly important observation concerns the need for a certain uniformity throughout wiki. This concern obviously would have to be addressed in any proposal.

It seems to me that if a style parameter is added to an existing template, this would have the advantage of both preserving uniformity, and proving flexibility that is generally an important feature of any useful piece of software. Can we have a vote on the suitability of such a proposal? Katzmik (talk) 08:50, 22 August 2008 (UTC)

Please no voting. Wikipedia is not a democracy, and voting is invariably devisive. Geometry guy 09:32, 22 August 2008 (UTC)

But one often has bulleted lists of opinions on proposed policies, each beginning with support or oppose. It's not "voting" since one doesn't simply enumerate support and oppose votes; rather, each is accompanied by a rationale. Michael Hardy (talk) 16:31, 22 August 2008 (UTC)

Sure, but this is something of a last resort when other methods (mostly good discussion) have not reached a consensus. The thread above has plently of good ideas and good discussion. Geometry guy 18:16, 22 August 2008 (UTC)

Well, no; there are some situations in which it's the preferred first resort—in particular, in pages whose purpose is to promulgate Wikipedia policies. It might be preferred in other places where the issue being debated is a change in standard conventions. (Also in AfD discussions, requests for adminship, etc.) Michael Hardy (talk) 18:57, 22 August 2008 (UTC)

I agree, there are a few pages which need to and should use the support/oppose approach, but this isn't one of them. Geometry guy 19:07, 22 August 2008 (UTC)

There's no point in voting for this anyway. If the people in the project who actually work on maintaining these templates feel it is too much work with no real benefit to have multiple templates, it's a Pyrrhic victory to impose a consensus on them. The next time some software update breaks something or you want to add something to the template, if the maintainers don't want to bother, what have you gained? --C S (talk) 00:19, 24 August 2008 (UTC)

At this stage it is not completely clear to me whether there is a large consensus for adding a style parameter to be able to conform the the Math Reviews format, or not. Before we go to the systems people with a request for a modifition, we should sort out our own differences. I did not get a very clear sense from the above whether Geometry guy and C S oppose a vote on procedural grounds, or whether they don't like the idea of a style parameter? Katzmik (talk) 08:56, 24 August 2008 (UTC)

The slightly different order in the citation method does not seem to present any problems. What does present problems is when editors add content without any sources. There are whole articles without sources. This applied for example to restricted representation which had little or no content and no references - it was a vague essay. The citation method has the advantage that one can use harvnb in footnotes and harvtxt in the text. This is particularly useful for the format of wikipedia which is quite unlike what would be written in a journal - more like a book. It's extremely easy to copy over refs from mathscinet, and add urls - the order is irrelevant. Mathematics editors should be encouraged to add sources when they edit as this seems to be the main source of problems in mathematics articles on wikipedia: it sometimes can be almost impossible to know what people are talking about when they make vague references to desired content or its significance. Mathsci (talk) 08:47, 28 August 2008 (UTC)

For an handy tool to get well-formatted citations, including the option to parse Bibtex code (such as from MSN), have a look at the zeteo tool (which I wrote). Jakob.scholbach

Dodgy edit?

This is over my head, I'm afraid. Would someone like to take a look at this edit to Booth's multiplication algorithm? It's hard to believe that the description in the article up to this point required this much correction. Deor (talk) 22:45, 27 August 2008 (UTC)

The edit looks plausible to me. -- Jitse Niesen (talk) 10:48, 28 August 2008 (UTC)

It seems correct to me: It works in the example multiplication given below. Ozob (talk) 16:38, 28 August 2008 (UTC)