Wikipedia talk:WikiProject Mathematics/Archive/2012/Jun

Bell's theorem
The article on Bell's theorem has been hijacked by crackpot Joy Christian and his cronies. Any attempt to remove references to Christian's discredited work (not published in any peer-reviewed journa, and shown o be fundamentally flawed by a long list of authorities in the fieldl) is immediately "undone" by Christian himself or his supporter Fred Diether. Conflict of Interest!

But if nobody cares about this article better to leave it to the crackpots. Richard Gill (talk) 18:31, 29 May 2012 (UTC)


 * Here's a silly question. If authorities have taken the trouble to point out the flaws in Christian's work--i.e. if Christian's work has received significant coverage in reliable sources--does that make it notable? I guess you're hoping that the answer is no, but the question does need to be asked. Jowa fan (talk) 03:18, 30 May 2012 (UTC)


 * It certainly can do okay or give it enough weight in an another article for inclusion I don't believe that is true in this case though. Dmcq (talk) 07:40, 30 May 2012 (UTC)


 * Generally, in an article about the crackpots, notability is the most relevant criterion. However, in an article about a mainstream scientific topic, we should not treat fringe views, as this often gives them equal WP:WEIGHT. The goal of an encyclopedia article on something like Bell's theorem is to give the reader a treatment of the subject as it is understood by the vast majority of standard, peer reviewed sources.  Sławomir Biały  (talk) 14:46, 30 May 2012 (UTC)


 * Thanks, Sławomir, I think that applies in this case. Jowa fan (talk) 00:10, 31 May 2012 (UTC)

Richard Gill called me “crackpot Joy Christian.” I wonder what his criterion of crackpot is. I let the readers judge for themselves. Here are my credentials: Dr. Joy Christian obtained his Ph.D. from Boston University in Foundations of Quantum Theory in 1991 under the supervision of the renowned philosopher and physicist Professor Abner Shimony (the “S” in Bell-CHSH-inequality). He then received a Research Fellowship from the Wolfson College of the University of Oxford, where he has remained affiliated both with the college and a number of departments of the university. He is an invited member of the prestigious Foundational Questions Institute (FQXi), and has been a Long Term Visitor of the Perimeter Institute for Theoretical Physics, Canada. He is well known for his contributions to the foundations of quantum and gravitational physics, including quantization of Newton-Cartan theory of gravity, generalization of Special Theory of Relativity to incorporate the objective passage of time, and elimination of non-locality from the foundations of quantum physics. A partial list of his publications can be found here: http://arxiv.org/find/all/1/au:+Christian_Joy/0/1/0/all/0/1 — Preceding unsigned comment added by 86.148.6.36 (talk) 22:03, 31 May 2012 (UTC)

As for the paper in question, "Disproof of Bell's Theorem", http://arxiv.org/pdf/1103.1879v1.pdf, is published in my peer-reviewed book, http://www.brownwalker.com/book.php?method=ISBN&book=1599425645, and is widely discussed on the Internet. My work has also been cited in several *published* articles, at least two of them in the Physical Review (not to mention its citations in some lesser known journals). I have given invited talks about my work on several occasions during the past five years. The book itself is only just published, and citations to it will undoubtedly follow in due course. On the other hand ALL of Richard Gill’s misguided, erroneous, and unpublished arguments against my work have been comprehensively debunked, many times over, not only by me but also by several other knowledgeable people on the FQXi blogs. I myself have given a systematic refutation of his misguided arguments in the following two papers: http://arxiv.org/abs/1203.2529 and http://arxiv.org/abs/1110.5876 -- Joy Christian — Preceding unsigned comment added by 86.148.6.36 (talk) 22:13, 31 May 2012 (UTC)


 * Whether or not you are a crackpot, your book is not peer-reviewed, and your result is not generally accepted. If discussed in peer-reviewed articles, it may be mentioned as a claimed disproof of Bell's Theorem.  — Arthur Rubin  (talk) 07:18, 1 June 2012 (UTC)

@Arthur Rubin: My book IS peer-reviewed. My work IS cited and discussed in Physical Review and other journals, and NOT as negatively as you are trying to suggest. You have no proof of what you are claiming. You are clearly biased.

On a different note, I urge the Wikipedia community to remove Richard Gill’s slanderous name claiming from his post above. As you can judge from my qualifications I listed above, his name calling has no justification whatsoever. -- Joy Christian — Preceding unsigned comment added by 86.148.6.36 (talk • contribs)


 * Your book IS NOT peer-reviewed. That would mean the publisher submitted it to your peers for review before publication.  If it were reviewed in Phys.Rev., that would not constitute peer review; it might indicate notability, but not reliability.
 * As for Gil, he shouldn't have called you a crackpot. However, there are people much more established than you are who call you a crackpot, so I'm tempted to modify the places where you were called a crackpot to "so-called" crackpot.  — Arthur Rubin  (talk) 08:18, 1 June 2012 (UTC)

@Arthur Rubin: My book *IS* peer-reviewed. There are also people who call me a genius; so perhaps you should refer me as a “so-called genius.” -- Joy Christian — Preceding unsigned comment added by 86.148.6.36 (talk) 08:38, 1 June 2012 (UTC)


 * Nonsense. If your book was peer-reviewed, your publisher would have said so.  And you need a cite that people call you a genius.  — Arthur Rubin  (talk) 08:40, 1 June 2012 (UTC)


 * Nonsense. My book *was* peer-reviewed, and my publisher does say so.  I do not have to cite people who call me a genius. One can see that from my one-page paper itself:  http://arxiv.org/abs/1103.1879  — Preceding unsigned comment added by 86.148.6.36 (talk) 09:18, 1 June 2012 (UTC)


 * From your one-page paper itself I see that indeed, your idea of what is stated by Bell theorem is far from that of Bell. Thus, treating you as the next genius after Bell, I'd rename your paper as follows: "Disproof of Christian strengthening of Bell theorem". Boris Tsirelson (talk) 11:33, 1 June 2012 (UTC) :-)

Boris, I respectfully disagree (if I understand you correctly). Bell claimed that no functions of the form A(a, L) = +/-1 and B(b, L) = +/-1 can reproduce correlations of the form E(a, b) = -a.b. “This is the theorem” (his exact words). What Bell did not realize is that this claim is true if and only if the co-domain of the functions A(a, L) and B(b, L) is NOT a unit parallelized 3-sphere, S^3. My one-page paper shows an explicit construction of the fact that when the co-domain of A(a, L) and B(b, L) is taken to be S^3, the correlations are inevitably E(a, b) = -a.b. I urge you to have a look at this longer paper to see my compete argument: http://arxiv.org/abs/1201.0775. Thanks. -- Joy Christian — Preceding unsigned comment added by 86.148.6.36 (talk) 12:10, 1 June 2012 (UTC)


 * Ah, now I see, thank you for the clarification; I was not able to understand your text "as is", but now I know what did you really mean. Well, then we agree: “This is the theorem” was said by Bell about (+/-)-valued functions. For vector-valued functions, this is exactly what I called "Christian strengthening of Bell theorem"; and it is wrong, of course, so you are able to disprove it, of course. But in fact, for vector-valued functions it was "disproved" by Bell himself, in the same (historic) article; by doing this he showed that quantum spin measurements can indeed violate Bell inequality. Boris Tsirelson (talk) 13:24, 1 June 2012 (UTC)


 * I am afraid you still haven’t understood what I have shown. The functions A(a, L) and B(b, L) both Bell and I are postulating for measurement results are (+/-)-valued functions only, but the co-domain I am using is S^3 instead of the real line. In other words, A(a, L) and B(b, L) for me are maps of the form +/- 1 = A(a, L) = R^3 x H maps to  S^3, where H is the hidden variable space. So A(a, L) and B(b, L) in my model are pure binary numbers, +1 or -1. They are not vector-valued, although they have been constructed out of a product of two bivectors. The difference is in the co-domain of these functions only, not in the actual values of A and B, which are still scalars, +1 or -1. Note that scalars, +1 and -1, are as much a part of the 3-sphere as the bivectors are. – Joy Christian  — Preceding unsigned comment added by 86.148.6.36 (talk) 14:20, 1 June 2012 (UTC)


 * Yes, I haven’t understood. Yes, the two-point space {-1,+1} can be treated as embedded into the sphere (as a pair of opposite points), but this embedding does not change their correlation.
 * Anyway, the discussion becomes too specific for this page. If you like, we can continue it on my (or your) talk page. Boris Tsirelson (talk) 15:05, 1 June 2012 (UTC)


 * I have added some explanation of my model on your talk page. -- Joy Christian

Whatever the outcome of this discussion, it is clear that we should not cite Joy Christian's self-published work (WP:SELFPUB). There has been a long tradition of criticism of Bell's theorem from the fringes of physics. If mention of this is to be included in the article, it should be sourced to a reliable secondary source documenting such criticism and the replies of the scientific mainstream (WP:NPOV,WP:PSTS). Otherwise, including criticisms sourced to the primary literature is considered to be original research, and is forbidden by Wikipedia policy. Sławomir Biały (talk) 13:51, 1 June 2012 (UTC)

Bell's Theorem (bis)
Comments on Talk:Bell's_theorem will be appreciated. Thanks. History2007 (talk) 00:42, 1 June 2012 (UTC)
 * As a brief aside, I just wanted to say that the whole episode is a bit amazing and embarassing, and I'm sad to see geometric algebra caught in the middle :( Rschwieb (talk) 01:18, 1 June 2012 (UTC)

I urge the Wikipedia community to remove Richard Gill’s slanderous name claiming from his post above. As you can judge from my qualifications I listed above, his name calling has no justification whatsoever. -- Joy Christian — Preceding unsigned comment added by 86.148.6.36 (talk) 06:13, 1 June 2012 (UTC)
 * Both of you, would you mind going and bothering Wikipedia talk:WikiProject Physics instead? I don't know what we have to do with the matter. --Trovatore (talk) 08:42, 1 June 2012 (UTC)
 * It is a physics result, but it is mainly based on simple maths and logic rather than needing any great understanding of physics. I see the notification here as being reasonable. The 'discussion' should definitely be at the articles talk page though. Dmcq (talk) 08:48, 2 June 2012 (UTC)

betterexplained?
I don't recall http://betterexplained.com/archives/ being discussed in this space so I would like to raise the issue of whether this is a reliable source. Also, would it be appropriate to cite it in a footnote in the lede of an article. Tkuvho (talk) 07:29, 1 June 2012 (UTC)


 * A similar question with regard to http://plato.stanford.edu/ In this latter case, there are some serious factual errors.  The chronic problem with these websites is that they are by no means peer reviewed.  The peer review process certainly does not eliminate all errors, but its absence does not help, either.  Tkuvho (talk) 07:33, 1 June 2012 (UTC)
 * We use many non peer reviewed sources such as textbooks and Stanford's Encyclopedia of Philosophy is comparable to that and hence a reliable source.


 * As far as betterexplained.com is concerned I wouldn't regard that as a reliable source and it's beyond me why you even would want to compare that to Stanford's Encyclopedia of Philosophy. They have hardly anything in common other than being available online.--Kmhkmh (talk) 09:12, 2 June 2012 (UTC)

MathJax issue
I'm not sure if this is a known issue, but there seem to be some inconsistencies in the way the Wikimedia parser processes TeX and MathJax. Consider $$a<b$$ :
 * $$a<b$$

versus $$a\lt b$$
 * $$a\lt b$$

If MathJax is enabled, the first equation does not display correctly but the second one does. If "Render as PNG" is enabled the first equation displays correctly, and the second generates a parse error "Failed to parse (unknown function\lt)". This seems to be quite bad, since half of users will see one or the other of the two errors! Sławomir Biały (talk) 14:19, 31 May 2012 (UTC)


 * Now after writing this, the first equation seems to dispay correctly. Strange.   Sławomir Biały  (talk) 14:20, 31 May 2012 (UTC)


 * Perhaps related to this bug, though I don't see exactly how that would cause it.-- JohnBlackburne wordsdeeds 14:35, 31 May 2012 (UTC)
 * Yep. The first problem is bug 36059. Helder 15:12, 31 May 2012 (UTC)

In light of the fact that MathJax is "still experimental", I don't think the preferences page should also say that it is "recommended for most browsers". These two directives seem to be incongruous. Sławomir Biały (talk) 16:39, 31 May 2012 (UTC)


 * Obviously, this is the wrong place to complain about it (and that fixing this bug, pointed out even before the release, has been described as not being of a high priority). Just in case you missed it, the perceived editor-developer divide is being debated for a while now. Nageh (talk) 17:02, 31 May 2012 (UTC)
 * I don't want to join a fight particularly. It seems like this recommendation would be a trivial thing to change in the next update.  Sławomir Biały  (talk) 17:39, 31 May 2012 (UTC)
 * Worth bearing in mind that the "math" tags are not handled well by MathJax - they're deprecated. If you want to use MathJax then go the whole way. Then you can use dollar signs as delims or backslash-openround, backslash-closeround instead. But dollar delims IMO make more sense because they're not as fiddly to type as backslash-openround, backslash-closeround. --Matt Westwood 07:34, 3 June 2012 (UTC)

Shouryya Ray on AfD
See Articles for deletion/Shouryya Ray.

Is this person notable?

Are the news media's claims about him true or merely sensationalist exaggerations that help sell newspapers?

Opine at the page linked to above. Michael Hardy (talk) 16:45, 3 June 2012 (UTC)

Lester Dubins
I was surprised that we had no article on Lester Dubins. I've just created one. It needs further work, both within the article itself and in other articles that ought to link to it. Michael Hardy (talk) 17:31, 3 June 2012 (UTC)

pi: 9th Top-priority FA article for project
The pi article has been nominated for Featured Article status. If successful, this will be the ninth Top-priority FA article for the Mathematics project. Editors familiar with the FA criteria are welcome to provide input at Featured article candidates/Pi/archive1. --Noleander (talk) 12:33, 15 May 2012 (UTC)
 * The pi article mentions the series:
 * $$ \pi = + \frac{2\times3\times4} - \frac{4\times5\times6} + \frac{6\times7\times8}  - \frac{8\times9\times10} +  \cdot \cdots $$
 * A reviewer at FAC asked what the origin of this series is (who, when). Does anyone have a reliable source that identifies the origin of this series?   Sources are available that define the series, so that is not a problem:  it is the origin that is needed.  Thanks in advance. --Noleander (talk) 20:01, 15 May 2012 (UTC)


 * I notice a lot of references to Eric Weistein's website, including the reference for this series. I wouldn't consider him a reliable source on anything.  It's probably worth trying to find a better source.   Sławomir Biały  (talk) 20:12, 15 May 2012 (UTC)
 * Weisstein is used as a source only for "motherhood" factoids: formulae that are represented in hundreds of math texts (e.g. definition of polar coordinates).  I don't mind changing those cites to hardbound math books, but I'm pretty certain that there was consensus within the Math project that Weisstein is a valid RS for simple or basic math-related facts.   Is that not true?   Of course, Weisstein should not be used as a source for contentious or complex material. --Noleander (talk) 20:22, 15 May 2012 (UTC)
 * If MathWorld is not an acceptable RS for basic math facts, I have at hand A guide-book to mathematics by 	 Bronshteĭn and  Semendiaev  (H. Deutsch, 1971).  Any objection to using that for area of a circle, etc?  --Noleander (talk) 20:40, 15 May 2012 (UTC)
 * ... also, just to clarify, the issue here is not the validity of the series (it is documented in many RSs) but rather: does any editor here know of additional detail about the origin of that series, so that additional detail could be incorporated into the article?   At the moment, the article does not contain any statement about the origin of that series. --Noleander (talk) 20:24, 15 May 2012 (UTC)
 * All right, I think we are in good shape now: user:RJHall found a source for the above mentioned series.  And, following the sage advice of user Sławomir Biały, I'm eliminating the use of MathWorld as a source in the article (just a couple more to go).  So, no more help needed on this issue.  --Noleander (talk) 22:56, 15 May 2012 (UTC)

Hello everyone! I would appreciate if a few people could lend their expertise over at the nomination page, even if it is just to confirm that one little section is not a piece of nonsense. I am just concerned about the little things, the off emphasis here, the obscure odd fact inserted there, that have a way of getting into even (or especially?) meticulously-researched articles, and that bespeak inexpertness. For example, detailed discussions of $\pi$'s relationship to the Mandelbrot set fractal and the sinuosity of a meandering river (which are above my head) appear in the middle of other content, like a discussion of Euler's identity (the importance of which even I can understand) or the Fourier transform (which I have at least heard of). It just strikes me as a little fishy, though for all I know the article is perfectly well balanced. Which is why I'm asking for some help. Thanks! Leonxlin (talk) 19:33, 31 May 2012 (UTC)

Pi has passed its nomination! Leonxlin (talk) 01:27, 6 June 2012 (UTC)

Some/several MathJax-Formulae are not displayed (correctly)
Hello

Did I do something wrong/incomplete? I use Firefox 12.0 (enabled Java & Javascript) on Linux as my browser but sometimes/often mathematical formulae are not or are wrongly displayed. E. g. in the page in the table-style of all these matrices there appears a literal "amp;" for the column separator, or in section "Classification", subsection "Elliptic transforms" the formula "0 \le \mbox{tr}^2\mathfrak{H} &lt; 4.\," is not interpreted at all - it is displayed rawly! (This is the first formula in this article, several follow, but the formulae before seem to be displayed correctly). Thanks in advance for any useful help. Achim1999 (talk) 14:22, 5 June 2012 (UTC)
 * This is a known bug in the software. Any equation with <, > or & in will not work with the current MathJax. It has been patched in the source so it should not be too long until it that is rolled out. For now you can use User:Nageh/mathJax which is a working implementation of MathJax.--Salix (talk): 15:33, 5 June 2012 (UTC)
 * Thank you very much. Now I "only" have problems to create my "custom skin file", but I will try. :-)
 * Achim1999 (talk) 16:16, 5 June 2012 (UTC)
 * Well it seems to work, the fiel must be named "vector.js" not "skin.js".
 * At least the rendering is now better and my described errors has gone. The new mistake I observed is: the fraction lines are unusually thick and what is very bad, are too short. So, certain formulae like in the subsection "Determining the fixed points" of the Moebius transformation article become unreadable. A further bug in MathJax, I guess. :-/ Achim1999 (talk) 16:28, 5 June 2012 (UTC)
 * Thats odd, Moebius transformation looks fine for me. It could be a browser related bug, which browser are you using? You might want to bring this up at  User talk:Nageh/mathJax.--Salix (talk): 16:52, 5 June 2012 (UTC)
 * Yepp, I'm afraid you are right. As I wrote at the beginning of this section, I used Firefox 12.0 under Ubuntu (at work). Now I'm logged into another system (my private) running Gentoo & Firefox 3.6.17. The same section now looks okay. Here fraction(line)s are displayed fine. :-/ Achim1999 (talk) 17:53, 5 June 2012 (UTC)
 * If its a browser bug it might be worth discussing it with the MathJax people . That would help them sort it out for anyone else who gets the same problem.--Salix (talk): 21:59, 5 June 2012 (UTC)

Poincare's definition of manifold
I added Poincare's original definition of a differentiable manifold at Manifold. Poincare defined a manifold as a subset of euclidean space which is locally a graph (see details there). This definition is arguably more accessible to a general reader than the more abstract definition involving atlases, charts, and transition functions. The lede could profit from focusing on the subset-of-R^n definition instead of the abstract definition. However, another editor feels that the reader does not need the crutch of Euclidean space to understand the concept of a manifold, and my changes to the lede were repeatedly reverted. Which definition should the lede be based on? Tkuvho (talk) 11:37, 4 June 2012 (UTC)


 * Having the historical definition in a section on history makes sense, but for example that definition makes it quite hard to see that the graph of the absolute value function, as a subset of $$\mathbb{R}^2$$ is a manifold (not differentiable at 0), or the unit circle as a subset of $$\mathbb{R}^2$$ (not locally a graph).


 * A similar thing happens with the concept of function; the historical definitions were simultaneously more limited in some ways and more broad in other ways than the modern definition, so we can't start the article with them. &mdash; Carl (CBM · talk) 12:09, 4 June 2012 (UTC)


 * I for one have serious difficulty understanding what is meant by the wording. Use of the term "graph" in place of "function" confuses.  Also the implication that every manifold is globally embeddable in a Euclidean space should not be implicit in the (modern) definition, even if this is (nontrivially) provable.  So, no, not Poincaré's definition in the lead.  — Quondum☏ 12:35, 4 June 2012 (UTC)


 * The lede as it currently stands (i.e. using a map on the surface of the earth as an example) is utterly perfect. My vote is: leave it like it currently is - non-mathematicians will be able to access it admirably from there. --Matt Westwood 13:38, 4 June 2012 (UTC)


 * @Carl: the graph of the absolute value function is not really relevant as it is not a smooth manifold (actually as an abstract Riemannian manifold it is perfectly differentiable at 0 also). The circle is indeed locally a graph, either over the x-axis or over the y-axis.  As Whitney proved, the two definitions are exactly equivalent.  This means that the atlas definition is only different from Poicare's definition in that it is harder to follow.  It is neither more limited nor more broad.
 * @Quondum: y=f(x) is a function; the set of points (x,y) satisfying y=f(x) is its graph in the plane. I think most calculus students are more comfortable with the notion of a graph of a function than with transition functions between charts.
 * @WestwoodMatt: The current lede does not really tell you what a manifold is. Note that the abstract definition ends up using differentiable functions in the end, as well: the transition functions have to be differentiable functions.  The only difference is the abolition of intuition in the abstract definition, according to Arnold.  Tkuvho (talk) 13:45, 4 June 2012 (UTC)
 * A circle is not locally a graph, there's no neighborhood of the 3 o'clock point around which the curve passes the vertical line test. It could be that you mean that the circle is the image of the real line under a suitable embedding, but that is not what "is the graph" means, because the circle is not the graph of that embedding (the graph is at best a noncircular subset of $$\mathbb{R}^3$$). Whitney's theorem is about embeddings of manifolds, but the embeddings are not generally graphs of functions. &mdash; Carl (CBM · talk) 19:08, 4 June 2012 (UTC)
 * In this setting, a graph means that there exists locally an affine coordinate system in which the manifold is a graph. Nevertheless, under the naive meaning of "graph" as it is used elsewhere in mathematics, it is clearly problematic to say this.   Sławomir Biały  (talk) 19:36, 4 June 2012 (UTC)
 * @Carl: you are correct that Whitney's theorem is about embeddings of manifolds. Indeed embeddings are locally graphs of functions by the implicit function theorem (that's the content of the implicit function theorem).  Tkuvho (talk) 14:27, 5 June 2012 (UTC)
 * Sławomir Biały already mentioned what you seem to be ignoring, which is that you are not talking about things that are locally graphs of functions in the usual sense of the term. The "original definition" of a manifold is not going to be more enlightening if it requires readers to apply unusual or field-specific definitions to the terms it uses. As it is usually considered, the implicit function theorem doesn't apply to the side points of the unit circle, because a certain matrix isn't invertible at those points. In fact they use this as an example in implicit function theorem. &mdash; Carl (CBM · talk) 02:21, 6 June 2012 (UTC)
 * Carl, what you seem to be ignoring that our page implicit function theorem is only a special case of a more general implicit function theorem applicable to any smooth submanifold or regular parametrisation thereof. Thus, whenever the gradient of the defining expression is nonzero, the implicit function theorem applies.  I explained this in terms of your example, namely the circle, at Manifold.  I usually defer to your judgments when it comes to issues of mathematical logic.  Have some common sense to acknowledge that this is not a field you are an expert in, and that your original opposition was based on a misconception.  No "unusual or field-specific definitions" here. Tkuvho (talk) 11:27, 7 June 2012 (UTC)
 * I am quite happy to believe that the way you're using the terminology is common in the area. I'm simply saying that it is not as clear to people outside the area as one might think. &mdash; Carl (CBM · talk) 11:44, 7 June 2012 (UTC)

I do not like the definition through graphs of functions, because it is less intuitive (at least for me) and it uses implicitly the implicit function theorem, which is far of being trivial (it is needed to show that a circle, defined as usual by its implicit equation, is a manifold). On the other hand, I do not like either the use of "scale" in the first sentence of the graph, because it appears in neither formal definition. Thus, I propose for the first sentence: "In mathematics (specifically in geometry and topology), a manifold is a mathematical object that, near each point of it, looks like Euclidean space". This has the advantage to be very close to the definition by charts (except that nothing is said on the transition maps, which are needed only for technical reasons). In fact the definition by charts and atlas is simply a formalization of this informal definition. D.Lazard (talk) 16:12, 4 June 2012 (UTC)


 * @D.Lazard: Thanks for your input. I respect your sentiment in "not liking" the implicit function theorem.  However, this theorem is standard for an advanced calculus course.  The lede shouldn't be an occasion for pleasing the personal tastes of this or that editor, but rather dictated by the goal of greatest possible accessibility.  Certainly the chart definition is an indispensible technical tool, but again the goal of the lede is not necessarily to provide technical tools. Rather, it is to give the reader an idea of the subject matter of the page.  Tkuvho (talk) 16:22, 4 June 2012 (UTC)


 * @Tkuvho: I agree with you that the lead should "dictated by the goal of greatest possible accessibility". But it should, in a non technical formulation, be as close as possible as the technical definition. I "like" the implicit function theorem, what I do not like is to use it implicitly where it is not really relevant. IMO, the "greatest possible accessibility" implies to use only mathematical notions which are unavoidable for given an idea of the subject. Here "near every point" is unavoidable because neighborhoods appear in every definition. On the other hand, "scale" is not needed. The definition through graphs involves a (at least partial) choice of coordinates, which is also not needed. D.Lazard (talk) 16:57, 4 June 2012 (UTC)
 * I didn't put the "scale" in. Feel free to delete it.  As far as choice of coordinates is concerned, it is unnecessary.  One can use a coordinate plane in the ambient R^n without the need to choose new coordinates.  Tkuvho (talk) 14:30, 5 June 2012 (UTC)

I don't really think the lead is perfect at present. In fact, it seems to be worse than the version from three years ago. I'd like to discuss possibly bringing back this earlier revision of the lead. In any event, I don't think it is a good idea to emphasize Poincare's original definition of manifold. Not many sources do this, and at least the motivational examples section of the article would need to be rewritten from this point of view. Sławomir Biały (talk) 16:37, 4 June 2012 (UTC)
 * The current version of the lede expects the reader to know what a homeomorphism is, what a topological space is, and what a neighborhood is. Is this more accessible than the graph of a function? Tkuvho (talk) 11:30, 6 June 2012 (UTC)
 * I think you are arguing that "graph of a function" would be easier to understand for people outside the area. I do know what a manifold is, but I don't find the "graph" explanation clearer even for one-dimensional manifolds, and it's much harder for me to visualize a 3-dimensional manifold as a graph of a function than as something locally homeomorphic to $$\mathbb{R}^3$$. (And either way we have to know what a neighborhood is, because it's "locally a graph of a function".) &mdash; Carl (CBM · talk) 11:44, 7 June 2012 (UTC)

May I point out that this whole discussion should be taking place at talk:manifold, not here.TR 12:28, 7 June 2012 (UTC)

List of scientific constants named after people
The List of scientific constants named after people may not be notable, according to a recent tag put at the top of the article. Apparently what is needed is a literature citation showing that the topic of scientific concepts named after people has received attention from the authors of refereed publications. Michael Hardy (talk) 02:49, 9 June 2012 (UTC)
 * You should add a further category "political naming enforcement" for this page or have you not meet scientific constants fighting for naming of different people names? :-/ Achim1999 (talk) 15:15, 9 June 2012 (UTC)

I've cited a scholarly source and deleted the "notability" tag. Michael Hardy (talk) 17:08, 10 June 2012 (UTC)

Probabilistic-Complexity Theory
After barely glancing at the new article titled Probabilistic-Complexity Theory, I'm already getting suspicious of it. Wikipedia-newbieisms are not a reason for suspicion of anything but Wikipedia-newbieism, but what is the state of mind of someone who writes a paragraph that starts like this?:
 * As of now, research is still being done on this theory, but[.....]

Michael Hardy (talk) 17:22, 10 June 2012 (UTC)


 * Sounds like OR, if not a flat-out hoax. JRSpriggs (talk) 17:27, 10 June 2012 (UTC)
 * Probabilistic complexity is a valid subject of study in computational complexity theory. What this article describes, though, appears to be pure crankery and original research of a type that fails WP:FRINGE. I've attempted a redirect to the same target as Probabilistic complexity but we'll see whether that lasts. —David Eppstein (talk) 17:29, 10 June 2012 (UTC)


 * This article also had a prime example of another good indicator that the "abort" button must be hit: "The human brain also interacts with this invisible field,..." Rschwieb (talk) 21:47, 10 June 2012 (UTC)

In the context in which I read the sentence, "As of now, research is still being done on this theory" seemed to mean that when research is no longer being done, it's perfect. As if the writer were unaware of the fact that fields in which research is being done are considered to be of greater interest than those in which it's not. Michael Hardy (talk) 02:03, 11 June 2012 (UTC)

Polynomiography
Can anyone confirm Polynomiography is a valid, notable topic? The question arises after discussions at Talk:Fractal art about claims that Kalantari is the inventor of fractals not Benoît Mandelbrot. Input by mathematically minded individuals on the topic would be appreciated. - Shiftchange (talk) 03:12, 11 June 2012 (UTC)

New article created on dual tensors
See here. I have enough understanding to start this article, and did so for reasons in the link, but still no expert (yet) so if anyone who can add extend its scope - please do. You have my many thanks. =) F = q(E+v×B) ⇄ ∑ici 15:35, 10 June 2012 (UTC)


 * The excitement did not last long... it seems to be the same as the Hodge dual... so it may be deleted/merged already! =( The main article on the Hodge dual seems so much less followable (NOT saying that its badly written, techincal details are definitley neccersary), that I still wanted to create the new one... F = q(E+v×B) ⇄ ∑ici 15:51, 10 June 2012 (UTC)


 * For the record this is now a redirect to Hodge dual. F = q(E+v×B) ⇄ ∑ici 12:29, 13 June 2012 (UTC)

Modified langle and rangle templates for inline angular brackets
These templates are currently in the database as unused: for $⟨$ see p.6 no 5579 and for $⟩$ see p.9 no 8935. Recently after reworking them (and wasting a silly amount of time messing around with aligning things, which shouldn't have happened), I added them to $⟨$&#124;$⟩$.

Aesthetically they look ok (sort of), but the concern is they may cause spacing irritations, due to the glyphs in the template (but these are the closest ones matching angular brackets).

What do others think? Any objections to usage? WikiProject Physics has been notified. F = q(E+v×B) ⇄ ∑ici 12:27, 13 June 2012 (UTC)


 * According to the unicode standard, these aren't the right symbols for angle brackets. These are &amp;#x3008; and &amp;#x3009; which are Chinese punctuation symbols.  Again, according to the standard, you should use &amp;#x27E8; and &amp;#x27E9;.  However, be warned that these don't display in many browsers.  As a result, it's probably better to avoid using inline angle brackets entirely or, if you do use them, then just to use  mode.   Sławomir Biały  (talk) 13:20, 13 June 2012 (UTC)


 * One of the benefits of templates is that workarounds can be implemented and documented, and fixed once browsers become more capable. In that sense I think that the use of the incorrect unicode symbols would be admissible in a template, even though they should never be permitted directly inserted into an article.  I think total avoidance of the an inline representation due to lack of support is worse than a template-based workaround.  — Quondum☏ 14:28, 13 June 2012 (UTC)


 * Thanks - all points are fair eneogh, I did anticipate the suggested resort to . The principle motivation was for inline bra-ket notation which would look so much neater in html than LaTeX. For now the templates will not be used (much), at least modified to the proper angular brackets. On the contrary - they are in use for the Bracket article... F = q(E+v×B) ⇄ ∑ici 15:15, 13 June 2012 (UTC)


 * But - the chinese characters are also not supported by all browsers, so some other people will only see a box with $${}^{30\atop 08}...{}^{30\atop 09}$$ in it.--LutzL (talk) 15:23, 13 June 2012 (UTC)


 * The chinese characters are now irrelevent as they have been replaced. F = q(E+v×B) ⇄ ∑ici 15:25, 13 June 2012 (UTC)

"Parity of zero" should be the gold standard for math articles
Parity of zero explains why zero is even in an easy-to-read format that I just don't see in other articles, namely Riemann hypothesis. 68.173.113.106 (talk) 21:08, 28 May 2012 (UTC)
 * So you think our articles should go on for pages and pages about trivialities rather than even attempting to explain anything complicated. That's useful to hear (really!) but I suspect not everyone would agree. —David Eppstein (talk) 22:34, 28 May 2012 (UTC)
 * And the Degrees of evenness section should be launched directly into the sun.Naraht (talk) 02:15, 29 May 2012 (UTC)
 * Why? (Fair warning, I wrote it, so I may be a little defensive here.) Melchoir (talk) 03:37, 16 June 2012 (UTC)
 * I don't think that the article is a useful model for this project. Its contents are not really about mathematics but rather math education; the math is trivial and the pedagogy complex. CRGreathouse (t | c) 04:03, 29 May 2012 (UTC)
 * There's inherent difficulties in the Riemann hypothesis that are absent in Parity of zero. One would really need to compare articles of about comparable difficulty I think. That was like comparing quantum mechanics to Newton's laws of motion. Dmcq (talk) 08:45, 29 May 2012 (UTC)


 * Completely agree. The main contributors to parity of zero have done an excellent job, but it is not too hard to write simply about simple subjects. It is much harder to write simply about complex subjects. Gandalf61 (talk) 08:58, 29 May 2012 (UTC)
 * I see. Maybe we could start a campaign to improve the readability of certain math articles, starting with moderate-readability articles, then working our way up to the really confusing ones. The main reason why I never read them is because they're that confuzzling. 68.173.113.106 (talk) 00:31, 9 June 2012 (UTC)
 * Well, you know, the subject itself is confusing. Good writing can certainly help (or maybe better stated, bad writing can hurt), but there is no way to make advanced mathematics understandable without some serious effort on the reader's part.  Still, absolutely, writing them better is a good thing. --Trovatore (talk) 01:39, 9 June 2012 (UTC)

Golden Section
The featured article has become subject to an (almost) edit war and imho some at partially questionable edits. Hence some 3rd opinions and watchful eyes are needed and appreciated.--Kmhkmh (talk) 22:05, 13 June 2012 (UTC)


 * Do you mean Golden ratio? Also, I can't make sense of your first sentence -- perhaps you left out some words? --Joel B. Lewis (talk) 22:53, 13 June 2012 (UTC)
 * Sorry I end to skip words when typing quickly. I hope it is clear now and yes golden ratio and golden section are 2 words for the same thing more or less.--Kmhkmh (talk) 23:04, 13 June 2012 (UTC)
 * The truth behind is: he is also massivly involved in the german "Goldener Schnitt" article rewriting/fighting which currently happens and in german it is called "golden section". And I withdraw because of the chaos (and opinion pressing about new article design) there. Ask him, why he suddenly must spring in action here, triggering this wasteful issue. ;)  Regards Achim1999 (talk) 23:12, 13 June 2012 (UTC)
 * I'd like to add, "chaos" that you helped to create by questionable and unsourced edits and I'd like to avoid a a repetition of that in en.wp.--Kmhkmh (talk) 09:08, 14 June 2012 (UTC)
 * I like to add the wording "chaos" was coined not by me, but by a 3rd! And it was not for my contributions, but for the overall situation which currently exists! There are even a guy who must press others to NOT vote! :-( Achim1999 (talk) 10:47, 14 June 2012 (UTC)
 * Perhaps you two could both stick to discussions of content instead of bringing a flame war here? Thanks. --Joel B. Lewis (talk) 12:21, 14 June 2012 (UTC)
 * THere's hardly a flamerwar (yet). I answered exactly once to your question and once to Achim's comment.--Kmhkmh (talk) 12:28, 14 June 2012 (UTC)

Diophantine approximation
While we are at it, Diophantine approximation may also need a watchful eye. Achim has added a lot of interesting content, but it could do with some copy editing.—Emil J. 12:59, 14 June 2012 (UTC)
 * I have started to fix the grammatical errors and opaque wording in Achim's rewrite of Diophantine approximation, and improve its style. I am not checking its mathematical content, just clearing away some of the undergrowth. Maybe someone can follow on behind me and verify the contents ? The sparseness of references in the early parts of the article is somewhat concerning. Gandalf61 (talk) 12:39, 15 June 2012 (UTC)
 * I have commented Achim1999's edits in the talk page. In summary I prefer the old version, although it was a stub. D.Lazard (talk) 14:29, 15 June 2012 (UTC)

Brubeck, a database of topological information
What do we think of http://www.jdabbs.com/brubeck/? The author is currently asking for feedback here: http://www.reddit.com/r/math/comments/v3y40/introducing_brubeck_an_open_searchable_database/

As a dedicated database, it supports capabilities that a general-purpose wiki like Wikipedia doesn't, including a kind of automated theorem proving. I'm thinking that our articles should link to matching Brubeck entries in the External links section. For example, Knaster–Kuratowski fan should link to http://www.jdabbs.com/brubeck/spaces/cantors-teepee/. But before I create a template in Category:Mathematics source templates and start adding it to articles, I wanted to ask: does anyone object? Melchoir (talk) 03:25, 16 June 2012 (UTC)

Template:Infobox conic section
I have come across Infobox conic section, and thought perhaps you folks might like it. The infobox is currently not used on any articles. If you don't want it, it can probably be deleted. — This, that, and the other (talk) 10:53, 16 June 2012 (UTC)

References in mathematics articles
I noticed there are very few references to literature in mathematics articles. Is this because mathematics can be easily checked for correctness without consulting literature? When should I consider adding references when adding new content? Lennartack (talk) 15:23, 16 June 2012 (UTC)


 * Anything dealing with the history, discovery, people, and current research of the specific concept should be cited, and perhaps also applications. Mind  matrix  20:46, 16 June 2012 (UTC)


 * Let's be honest &mdash; it's because we're lazy. The paucity of references should be viewed as something to fix, not something to copy.  (On the other hand, I don't think we need to get manic about inline cites &mdash; a single general-reference citation for an exposition lasting a paragraph or two is probably sufficient IMHO, provided that everything in it does in fact appear in the cited work.) --Trovatore (talk) 20:56, 16 June 2012 (UTC)


 * I think if we can aim to get one citation per section that would be good. The problem I've come across a bit too often is people sticking in something they have worked out themselves. I'm a bit easy on that sort of thing if there seems a good reason, but having a citation with a range of page numbers would help keep peoples minds on the idea of summarizing what's there instead of doing their own thing. Dmcq (talk) 21:27, 16 June 2012 (UTC)


 * In my experience, it helps in keeping track of what appears in which general reference to repeat the general reference (using named refs) every paragraph that it is used (usually at the end). This is especially useful if several general references are used in a section. This is especially useful for future editors trying to improve the exposition, since they do not have to repeat the earlier work of figuring our what is treated where.TR 21:55, 16 June 2012 (UTC)

Suggested FA drive topic: Otto E. Neugebauer

 * Don't know if you folks do FA drives, but I ran across a bio of Otto E. Neugebauer on the Internet, and have claimed him as a hero.– Ling.Nut (talk) 09:11, 17 June 2012 (UTC)
 * Good luck with that — biographies tend to be easier than technical articles for getting though FA, and having a goal like this makes it easier to find improvements to make. But that one needs some effort to get into shape — for one thing, it doesn't even have a section describing his scholarly contributions and their impact. —David Eppstein (talk) 16:53, 17 June 2012 (UTC)
 * ...and it kinda has a faint copyvio-ish odor as well, though I haven't scrutinized it carefully. i don't actually have time to work on it, right now.. posted this hoping others might see it as a worthy task. But... a few months from now, I will probably have time. We'll see. Tks! – Ling.Nut (talk) 02:33, 18 June 2012 (UTC)

... but not too "precise"
I looked at the article Fermat's little theorem and saw an example of a pet peeve of mine: In the "generalizations" section is the formula

\forall a\in\mathbb{Z} : \quad a^m \equiv a^n \pmod{p} $$.

A lot of people who know what is intended by "divisible" have never been exposed to logical $$\forall\;$$ or set theory $$\in\;$$ notation, much less have any idea what $$\mathbb{Z}\;$$ is supposed to mean. It is, IMO, much better to say "for any integer a ...." or even "for any integer a (positive, negative, or zero) ..."

Virginia-American (talk) 12:33, 18 June 2012 (UTC)


 * Yes, though this example would be bad form in basically any mathematics context. I've changed it.  (Actually, it looks like someone more obsessive than I could make a whole bunch of the non-logic articles more readable simply by going through and replacing every instance of \forall with English words.) --Joel B. Lewis (talk) 12:59, 18 June 2012 (UTC)


 * The WP:MOSMATH explicitly discourages using quantifier notation in mathematics articles.  Sławomir Biały  (talk) 14:49, 18 June 2012 (UTC)
 * Well I think that notation is fine if the entry level for the topic is university mathematics. That's definitely not true though for things like Fermats' little theorem! Dmcq (talk) 14:58, 18 June 2012 (UTC)
 * I don't think there is ever a situation where the writing is improved by using this notation. You never see it in research level mathematics, and almost never in university level mathematics writing, either graduate or undergraduate.  Sławomir Biały  (talk) 15:52, 18 June 2012 (UTC)
 * I think replacing the formula by text is a good idea here. BUT "any" should not be used as a quantifier in this context; it is too ambiguous. Use "every" instead. —David Eppstein (talk) 16:06, 18 June 2012 (UTC)
 * Yes, absolutely, neither "\forall" nor "any" should be used if they can be avoided. (And indeed the FlT article now reads "... for every ....")  --Joel B. Lewis (talk) 16:37, 18 June 2012 (UTC)

Have you access to 'Prime curios' book?
If you have access to the book Prime Curios!: The Dictionary of Prime Number Trivia based on the prime curios website could you check it actually includes the coincidences mentioned in Talk:Mathematical coincidence please in the diff putting in 999779999159200499899 and some business about changing from bases 2 and 3 to base 10. Thanks. Dmcq (talk) 16:15, 18 June 2012 (UTC)

Zinbiel algebra
Some doubt has been cast over the validity of the redirect Zinbiel algebra. Views from experts would be welcome. South Jutland County (talk) 21:30, 18 June 2012 (UTC)


 * What does the first sentence actually mean, and where can one find a discussion of the doubt that is being cast? (Incidentally, to save other users who, like me, don't see it immediately: "Zinbiel" = "co-Leibniz" = Leibniz written backwards. --Joel B. Lewis (talk) 21:56, 18 June 2012 (UTC)
 * Probably here : Talk:Operad theory. Anne Bauval (talk) 22:15, 18 June 2012 (UTC)
 * Thanks. This is not my area of mathematics, but MathSciNet has 19 publications in which the title or review include the word "Zinbiel", by a variety of authors in several languages, dating to 2002.  It looks completely legitimate to me. --Joel B. Lewis (talk) 23:17, 18 June 2012 (UTC)
 * Note that both and  (who created the article) are almost certainly sockpuppet accounts of the community-banned user Echigo mole/A.K.Nole. Please see Sockpuppet investigations/Echigo mole. Mathsci (talk) 06:49, 19 June 2012 (UTC)

Mathematical language must be precise
I suspect that I will need help in a project I am about to undertake. Several articles use the term "evenly divisible" to mean "divisible" which is okay in a non-technical article but not okay in mathematics (it would be like calling 1 a prime number for instance). What bothers me isn't that editors would use this word but that they react with hostility when I attempt to change it - some people feel like they "own the article".

The first resistance I met was in the Y2K article:. One of them suggested that I use "exactly divisible" which is not preferred but I am prepared to compromise this way. I also got reverted on Fermat's Little Theorem. This article relates to number theory so I will not compromise here. Since I am talking to other mathematicians (I hope), maybe some of you could weigh in on the edit wars I post here. Connor Behan (talk) 03:47, 18 June 2012 (UTC)


 * The phrase "edit wars" should ring warning bells. You've posted two links to pages where you have started an edit war.  It's not something to be proud of.
 * In most contexts, "evenly divisible" means the same as "divisible". The choice of one or the other is just a matter of taste.  Personally I prefer "divisible" for mathematics articles such as Fermat's little theorem, but see no reason to delete "evenly" from non-technical pages such as Year 2000 problem.  That's only my personal opinion; I doubt that there will be a strong consensus either way.  I hope that any further discussion of the topic will remain civil.  In particular, public declarations that you refuse to compromise won't go down well on this site.  Jowa fan (talk) 05:05, 18 June 2012 (UTC)


 * We agree on what terminology should be used in mathematics articles :). It seems like we don't agree on what it means to start an edit war - I cited two sources for why my edit made the page better... the people who reverted the change (which even to a non-mathematician should be inconsequential) did not.
 * Compromise was too strong a word; here's what I meant. A part that worries me is that people seemed to genuinely believe that the standard definition of divisibility allowed 3 to be divisible by 2. I am willing to be civil and take the time to calmly explain why I think they are wrong. But I would not admit that they are right anymore than I would admit that a person saying 1 + 1 = 3 is right. Connor Behan (talk) 06:20, 18 June 2012 (UTC)
 * There should be something in articles for people who aren't familiar with the stuff but could cope with part of it straightforwardly. The articles are not just compendiums of knowledge, there is a relationship to the people who want to find the stuff. If knowledge is not accessible except to those who already know it then there is zero information in them. As to exactly divisible in an article aimed at a pretty low level that is good. They have spent time at school being drilled into figuring out what seven divided by three is. There is no point paring the language down to the bare essentials and leaving a beautiful struucture that only a mathematician will appreciate. Dmcq (talk) 08:09, 18 June 2012 (UTC)
 * Exactly divisible is probably better than evenly divisible, because the latter could conceivably be read as implying that the quotient is an even number. --Trovatore (talk) 08:14, 18 June 2012 (UTC)
 * Good point, more words means more ways to get the wrong meaning ;-) Divisible with no qualification can often be better. I reacted badly to the title 'Mathematical language must be precise' which implied unreadable articles to me. Dmcq (talk) 08:43, 18 June 2012 (UTC)

IMHO, a good way to avoid any ambiguity could be to replace "be divisible by" by "be a multiple of". Personally, I find that "year multiple of 100" sounds better than "year divisible by 100", together with avoiding any ambiguity. D.Lazard (talk) 09:30, 18 June 2012 (UTC)

"Multiple of" has the same problem as "divisible"; a non-mathematician might think it could be a non-integer multiple. This could be a particular problem in calendar-related articles, because there are a lot of cranks running around in that subject area who are pushing some version of calendar reform, or pushing some calendar on religious grounds. Such cranks like to seize on ambiguities, both by making arguments within Wikipedia, and basing arguments in other fora on Wikipedia articles. Jc3s5h (talk) 12:08, 18 June 2012 (UTC)

I think D. Lazard's suggestion to use (integer) multiple is good. Another possiblity is a footnote that says *here, and generally in number theory, "divisible" means "divisible without a remainder".

I don't have a source in front of me, but IIRC Richard Feynmann said (paraphrasing) "of course, 5 is divisible by 2." If someone is unfamilar with number theory and its conventions, restricting numbers to be integers may take a bit of getting used to.

In the original post, Connor Behan said ... Several articles use the term "evenly divisible" to mean "divisible" which is okay in a non-technical article but not okay in mathematics (it would be like calling 1 a prime number for instance). I disagree. Calling 1 prime is unambiguously wrong (even though Gauss did so sometimes). Saying "exactly" or "evenly divisible", or "divisible without a remainder", or "an (integer) multiple" of is at worst a bit wordy, and may be clearer to Wikipedia's intended audience. Saying "exactly divisible" the first time or two in an article, and then quietly dropping the abverb, seems clearest to me.

Virginia-American (talk) 12:12, 18 June 2012 (UTC)


 * I disagree that "saying 'exactly divisible' the first time or two in an article, and then quietly dropping the abverb, seems clearest". This approach works well in general writing: "Finnias Tiberius Flubberbuster III of Green Meadow, Wyoming...Mr Flubberbuster...." But in formulas or when writing rules or other legalistic text, any variation in wording often implies a difference in meaning. A reader who has just finished reading several articles, in Wikipedia and elsewhere, about the differences between the Gregorian, Revised Julian, and Julian calendar is apt to be thinking in a mode characteristic of legal scholars or computer programmers, and immediately assume that if the words "divisible" and "evenly divisible" occur in the same document, they must have different meanings. Jc3s5h (talk) 16:36, 18 June 2012 (UTC)

I don't think "exactly divisible" is an improvement over "evenly divisible". A person who hasn't been trained to think that "divisible" applies the quotient of two integers is an integer may think "exactly divisible" means the result is a rational number as opposed to an irrational number.


 * Is there any evidence whatsoever that any speaker of English has been confused by either of the terms "evenly divisible" or "exactly divisible"? These are long-standing parts of standard English usage; "evenly divisible" has had a wiktionary page for 7 years.  Language is inherently somewhat vague, but this is the least-convincing example of this problem I've ever seen brought up on Wikipedia.  As long as no one demands that we being using "is an aliquot part of", though, I'll be okay.  --Joel B. Lewis (talk) 16:54, 18 June 2012 (UTC)


 * I've never seen the phrase "exactly divisible" before. In the contexts where it's being suggested for use, I already know what it's supposed to mean. I don't know what I would make of it in an unfamiliar context. Jc3s5h (talk) 17:08, 18 June 2012 (UTC)


 * Maybe I'll repeat myself, but, IMO, "divisible" should be avoided when it may be easily replaced by "multiple". A mathematical reason is that multiplication is defined prior to division, and it is always better, when reasonable, to use the most basic definitions. But the main reason is that "divisible" may be ambiguous inside mathematics (divisibility inside the integers vs inside the rationals) as well as outside mathematics. Here is an example, which is not far from Y2K article:

Every year is (exactly, evenly) divisible by four into four quarters, but year 2001 is not divisible by four.
 * D.Lazard (talk) 17:18, 18 June 2012 (UTC)


 * I suggest that you-all just use the word "divisible" and attach a footnote the first time it is used in an article, saying "In number theory, divisible means with an integer quotient and no remainder.". JRSpriggs (talk) 17:54, 18 June 2012 (UTC)
 * Footnotes are generally a very bad idea for this sort of thing. As a general comment, this entire issue seems to be trying to find a solution for a non-problem.  It is generally clear from the context what "divisible" means.  If not, then the editor should try to make it clearer using his or her best judgement.  There's simply no need as I see it to mandate any particular one size fits all solution.  Sławomir Biały  (talk) 18:13, 18 June 2012 (UTC)
 * Could you elaborate on why footnotes are a bad idea? I thought the footnote idea sounded pretty good until I read your comment. After all parity (mathematics) and number do a similar thing but in parentheses. Connor Behan (talk) 20:48, 18 June 2012 (UTC)
 * Footnotes in Wikipedia are generally reserved for providing references. Mandating a solution that conflicts with this basic use is a bad idea.  Add to that the fact that footnotes encourage unclear writing, and more difficult reading.  Sławomir Biały  (talk) 21:50, 18 June 2012 (UTC)
 * Evidence that "evenly divisible" can be misinterpreted is, , , , , and  which took me a few minutes to find on Google. Connor Behan (talk) 20:19, 18 June 2012 (UTC)
 * Meanwhile, the same five minutes spent would have led you to believe that it's also completely unreasonable to use "is divisible by", since this seems to cause endless confusion: [1 ] [2 ] [3 ] [4 ] [5 ]etc. I particularly like [6 ], in which it is explained that "Divisible in math terms means capable of being evenly divided, without remainder."  Meanwhile, the same test proves that "multiple" is also unusable: [7 ] [8 ] [9 ].  (Actually this exercise leads me to believe that "integer multiple" is the best way to go -- multiple does seem to cause fewer problems than any version with "divisible".)  Language has a little bit of ambiguity in it, always; replacing "evenly divisible" with "divisible" removes none of the ambiguity at all.  --Joel B. Lewis (talk) 21:03, 18 June 2012 (UTC)
 * Your evidence for "divisible" and "evenly divisible" being equally ambiguous is not very convincing. In the links you posted, people are simply asking what "divisible" means, possibly because it's a word they've never seen before - like "ecclesiastical". In the links I posted, people demonstrate proficiency in English and mathematics and still seek clarification on the word "evenly divisible" because they think it is ambiguous on mathematical grounds. However, I agree that "integer multiple" is better than either of them. Connor Behan (talk) 21:29, 18 June 2012 (UTC)
 * In any event, none of these links either way seem to be to Wikipedia discussions, so I don't think they have much weight in this matter.  Sławomir Biały  (talk) 13:59, 19 June 2012 (UTC)

Input from editors who describe themselves as able to contribute to Wikipedia with an intermediate level of proficiency in English, like D.Lazard, is quite helpful. I hope there will be comments from editors who are native speakers of a few different varieties of English, and who attended elementary schools during different decades. Most of us learned such basic words in elementary schools, but those schools have a nasty habit of introducing new terminology to new generations. (I never heard of cursive writing while I was in school, even though I learned to do it. Now the converse is becoming true; they're taught the word "cursive" but not how to do it.)

As for the example "Every year is (exactly, evenly) divisible by four into four quarters, but year 2001 is not divisible by four", neither Julian nor Gregorian calendar years, whether common or leap, can be divided into four quarters each of which contains the same number of whole days. So I don't understand the purpose of the example. Jc3s5h (talk) 18:46, 18 June 2012 (UTC)


 * "Evenly divisible" is standard English for divisible with no remainder, supported by a wide variety of sources: dictionaries, textbooks, encyclopedias, and general usage. There is nothing imprecise about it. The adverb "evenly" does not refer to multiples of two in this usage--indeed it's the other way around: "even," as in an even number, means the number can be evenly divided in half.  It is common in mathematical writing to just say "divisible" but this is an elliptical expression for "divisible with zero remainder" or just "evenly divisible."  In ordinary english "divisible means "able to be divided." Implying "with no remainder" makes sense to mathematicians because any two non-zero numbers are "able to be divided" in fields. That's not so obvious to laypeople, so using the qualifier "even' is appropriate in articles likely to be read by them. Our guideline Make technical articles understandable says to "write one level down" and "avoid overly technical language."  That seems appropriate guidance here.--agr (talk) 19:06, 18 June 2012 (UTC)
 * I think I'm taking from all this that saying abc is a multiple of 4 is better than saying abc is /evenly/exactly// divisible by 4. Dmcq (talk) 20:51, 18 June 2012 (UTC)
 * Surely you need to say "is an integer multiple of 4" in order to actually remove the ambiguity? --Joel B. Lewis (talk) 21:03, 18 June 2012 (UTC)


 * But is it appropriate guidance for an article about mathematics? You seem to be saying that a word cannot be imprecise for a specialized field if it is common English. There are many examples against this; "brontosaurus", "generally", "decelerate", "accuracy / precision" and "countable" to name a few. Another argument is that sticking to one phrase or the other would make Wikipedia more consistent. Even before I started changing articles, a search for "divisible" turned up 1100 articles while a search for "evenly divisible" turned up 90 articles. Connor Behan (talk) 20:48, 18 June 2012 (UTC)


 * I'm not quite sure what Connor Behan is getting at, but a word may be used in a specialized way if any reader with a hope of reading the article would understand that the specialized meaning applied. For example, an advanced physics article could use the word "force" without explicitly stating it is the vector that results from multiplying the scalar mass by the vector acceleration. There would be no need to mention that the meaning "a group of soldiers" does not apply. But some of the articles that have been edited, such as calendar articles, are not primarily math articles.


 * I agree with others who endorse "integer multiple", but wikilink integer because I've taught some high school and middle school, and guarantee that some of these students are unfamiliar with the word "integer". Jc3s5h (talk) 21:15, 18 June 2012 (UTC) corrected 22:30 UTC.


 * There are words and phrases in ordinary English that are ambiguous in a technical context. "Evenly divisible" isn't one of them.  It has only one meaning, divisible with no remainder, and is widley understood by lay people and specialists alike. "Integer multiple,"  on the other hand, is technical jargon, never used in ordinary speech.  The mere fact that you suggest wikilinking "integer" makes my point. Every published explanation  of "leap year" I have found uses the term "evenly divisible."  Sources are king here. We should not be replacing a commonly understood, unambiguous term with jargon just to solve a problem that does not exist in the first place.--agr (talk) 13:08, 19 June 2012 (UTC)


 * Here is one counter example of a person, that had never heard the phrase "evenly divisible" before it turned up here. "Integer multiple" is a perfectly fine common English phrase.TR 15:20, 19 June 2012 (UTC)


 * The fact that you haven't heard the phrase "evenly divisible" is not a disproof of the (true) statement that it is widely understood. Any of the terms under discussion is understandable with 2 minutes on google; I agree with agr that "integer multiple" will be a less familiar phrase to most people than "evenly divisible".  --Joel B. Lewis (talk) 15:53, 19 June 2012 (UTC)


 * Can we at least agree, agr, that integer multiple is preferred in a mathematics article? I don't have time to track down published sources but I just looked at the first 10 results of a google search for "leap year" "divisible". "Evenly divisible" shows up 4 times, "divisible" shows up 5 times and "exactly divisible" shows up once. Connor Behan (talk) 20:35, 19 June 2012 (UTC)


 * In a mathematics article, I would have thought "divisible" was fine, unless there was some specific reason for thinking it was not fine.  Sławomir Biały  (talk) 22:31, 19 June 2012 (UTC)


 * For those of you who still think "evenly divisible" is fine, I did a Google search for "oddly divisible" and got 5 pages of hits. This is not a lot but I would have expected zero hits if "evenly divisible" were universally understood. While I find "integer multiple" to be a suitable alternative, I suspect that these are the same people who think that 7 is divisible by 3. Maybe they wouldn't think this if Wikipedia pages used terminology that did not support this conclusion. We have an opportunity to educate people here. — Preceding unsigned comment added by Connor Behan (talk • contribs) 07:07, 21 June 2012 (UTC)


 * It's not accidental that you're the only person to have used the adverb "universally" so far -- none of "divisible", "evenly divisible", or "integer multiple" will be universally understood. The (true) claim is that "evenly divisible" is a common English phrase, and so in widely or commonly understood.  --Joel B. Lewis (talk) 12:19, 21 June 2012 (UTC)

Organizing (or "permuting"??) the List of permutation topics
I've started to organize the List of permutation topics into sections.

So far,
 * Topics not yet classified into sections are at the beginning;
 * A topic may appear in more than one section;
 * But a topic not yet classified into one or more sections should appear only once (discuss!);
 * Which section topics appear, and in what order (ha!!) they appear, and which should be sub-sections within main sections, are all debatable topics;
 * There's a lot more work to do!!

Michael Hardy (talk) 21:55, 18 June 2012 (UTC)


 * ...and now it's an organized list: everything is in a section or a subsection. Next step: the rest of you will figure out what could have been done better, and implement those ideas. Michael Hardy (talk) 20:02, 19 June 2012 (UTC)

Here's how the table of contents looks so far:
 * Contents
 * 1 Particular kinds of permutations
 * 2 Combinatorics of permutations
 * 3 Permutation groups and other algebraic structures
 * 3.1 Groups
 * 3.2 Other algebraic structures
 * 4 Mathematics applicable to physical sciences
 * 5 Number theory
 * 6 Algorithms and information processing
 * 6.1 Cryptography
 * 7 Probability, stochastic processes, and statistics
 * 7.1 Random permutations
 * 8 Music
 * 9 Games
 * 9 Games

126 items are currently in the list, by my quick count. Michael Hardy (talk) 20:07, 19 June 2012 (UTC)


 * Yay! Leonxlin (talk) 15:27, 21 June 2012 (UTC)

Urban myth about π?
I remember hearing that somewhere in the number that a whole bunch of 8s show up either together or in a pattern. If this is not a myth would it be worth adding to the Chronology of computation of π page?--Canoe1967 (talk) 19:14, 21 June 2012 (UTC)
 * No, because it has little to do with the computation of pi. Appropriate places are the final paragraph of Pi, or Feynman point, which already covers a sequence of six 8s, starting at position 222,299. --Tagishsimon (talk) 19:32, 21 June 2012 (UTC)
 * I think it was an an episode of Northern Exposure. I don't know if the writers made it up or actually did research on it. They may have made it up, as the plot had a couple that were trying to break the record. I do remember it as 8's though, unlike the 6s and 9s mentioned in the Feynman point article. I will resolve this section for now, and thank you for your help.--Canoe1967 (talk) 19:48, 21 June 2012 (UTC)

Bell's theorem (again)
Some more eyes on the current goings-on at Bell's theorem would be appreciated. An editor there is insistent on rewriting the nutshell version of the theorem in the lead to one that is, in my mind, much less clear than what used to be there. An attempt has been made to engage the editor on the discussion page, but it has failed to attract sufficient interest. The editor in question is (apparently) convinced that, since there are two editors on the discussion page defending the old (consensus) revision, and one editor (himself) defending the new edit, that gives him the mandate to implement his edit. I've reverted him several times already, with edit summaries indicating WP:CONSENSUS and WP:BRD, as well as menitioning these on the discussion page. Sławomir Biały (talk) 21:26, 26 June 2012 (UTC)


 * I reverted to your version and added a ref which supports the consensus version, also a few others in the "unreferenced" tagged sections. Hope this helps. F = q(E+v×B) ⇄ ∑ici 23:17, 26 June 2012 (UTC)

Category for discussion
There is a discussion for the category: Abstraction that could do with your input. Brad7777 (talk) 16:10, 27 June 2012 (UTC)

Ornstein–Uhlenbeck process
Our Ornstein–Uhlenbeck process article currently begins like this:
 * In mathematics, the Ornstein–Uhlenbeck process (named after Leonard Ornstein and George Eugene Uhlenbeck), is a stochastic process that, roughly speaking, describes the velocity of a massive Brownian particle under the influence of friction.
 * In mathematics, the Ornstein–Uhlenbeck process (named after Leonard Ornstein and George Eugene Uhlenbeck), is a stochastic process that, roughly speaking, describes the velocity of a massive Brownian particle under the influence of friction.

Does "friction" make sense? The Ornstein–Uhlenbeck process is supposed to tend to return to its mean. Friction doesn't do that; it only retards motion. Michael Hardy (talk) 21:14, 27 June 2012 (UTC)
 * Not really, it appears to be more like a Restoring force. It would also make more sense in my opinion to replace "friction coefficient" with "spring coefficient" but it depends on what can be referenced. Brad7777 (talk) 21:29, 27 June 2012 (UTC)

Tensor calculus as a disambig page?
People may think of "tensor calculus" as the content of tensors in curvilinear coordinates, but this is a redirect to the main article on tensors. I would prefer to redirect to tensors in curvilinear coordinates, but including both in a disambiguation page would also be ok (maybe better?). Opinions? F = q(E+v×B) ⇄ ∑ici 10:19, 28 June 2012 (UTC)

List of partition topics
I've made the List of partition topics into a somewhat more organized article than it was. More work could be done. Possibly the section on set partitions could be further subdivided. Michael Hardy (talk) 16:52, 29 June 2012 (UTC)