Wikipedia talk:WikiProject Mathematics/Archive/2012/Feb

Use of "we"

I see that many of our math-related articles use the word "we", some of them quite often (i.e. "we find that...", "we can use [blank] to prove that...", if we take...", ect. Generally speaking, this is an unencyclopedic method of phrasing, and I usually don't to hesitste to change it in the rare cases that I find it elsewhere on Wikipedia. But as it seems to be so ubiquitous in math articles, I figured I had better check here before making multiple changes. Joefromrandb (talk) 00:12, 31 January 2012 (UTC)

Yes, these uses should be changed. CRGreathouse (t | c) 00:39, 31 January 2012 (UTC)

The WP:MOSMATH discourages the use of "we" but does not forbid it. At the same time "we" is very common and appropriate in professional mathematics, so it will appear in our articles by inertia and habit. IMO there's nothing wrong in general with rephrasing sentences to avoid "we" as long as adequate care is taken to rephrase the sentences in a reasonable way. — Carl (CBM · talk) 00:40, 31 January 2012 (UTC)

"We" should generally be avoided. Even in professional mathematics, it is abused. However, I say "generally" because every so often something comes along that resists any attempt to state clearly without it. Sławomir Biały (talk) 01:25, 31 January 2012 (UTC)

As MOS:FIRSTPERSON states, this form of "we" may be acceptable but rephrasing to avoid it is generally better (and in my experience not usually difficult or awkward). —David Eppstein (talk) 01:35, 31 January 2012 (UTC)

Thanks for the responses, all. I'm sure there will be occasions where "we" is quasi-necessary. In any case, I only intend to change it in instances where its removal is simple and doesn't require the intervention of a math expert, which I certainly am not. (Although I am fascinated by the things I'm learning in some of these articles!) Joefromrandb (talk) 01:40, 31 January 2012 (UTC)

The use of "we" is probably easier for the reader than rewriting, if the rewriting is into the passive voice. -- 202.124.75.209 (talk) 10:16, 31 January 2012 (UTC)

I think 'we' can be a bit annoying sometimes as in 'we can see' when a person can't and will have a lot of work seeing. I'll quote a bit from Mathematical jokes I like about this. "A mathematics professor is giving a lecture to his students and writing equations on a blackboard. He says, "At this point, it is obvious that this equation can be derived from that one." He pauses, then turns his back on the class and spends an hour filling the entire blackboard with more work. Finally he turns and announces triumphantly, "Yes, I was correct; it is obvious!" Dmcq (talk) 10:21, 31 January 2012 (UTC)

While the actual usage of the "royal we" in science and philosophy is perfectly fine, I suppose it is an important question of whether or not it should be allowed in the wiki format. The most awkward/annoying trope to me is the use of "one" as in "one sees that", "following one's instinct leads one to conclude that..." etc... Rschwieb (talk) 17:40, 31 January 2012 (UTC)

I agree. The word "one" just substitutes one bad pronoun for another. Sławomir Biały (talk) 20:04, 31 January 2012 (UTC)

What's wrong with "It follows that" or "it can be seen that" and so on? Otherwise, I suppose "we" is okay, as long as it's not used in the context "... and we're done". --Matt Westwood 20:02, 31 January 2012 (UTC)

To some extent we is a way of avoiding the passive voice. That's fine in journals. In an encyclopedia, I think passive is better than we, as a general rule. I agree with Sławek that a hard ban is probably undesirable. --Trovatore (talk) 21:16, 31 January 2012 (UTC)

Sentences containing the phrases "note that", "it follows that", "it can be seen that" etc are almost always made clearer and tighter without losing any meaning by deleting the phrase. —David Eppstein (talk) 22:19, 31 January 2012 (UTC)

That's true. The less trivial uses would be along the lines of we employ the same technique to..., which can be mechanically rephrased as the same technique is employed... (there's NOTHING inherently wrong with passive, people! It's fine!) or perhaps better in this case the same technique yields.... --Trovatore (talk) 22:27, 31 January 2012 (UTC)

The last example (the same technique yields...) is a nice example where not even the passive voice is needed. I'd suggest that a good guideline is that whenever "we", passive voice, and unnecessary helper phrases ("note that...", "we see that..." etc.) occur, an editor should seek a natural, encyclopedic rephrasing, and should feel free to make a change if the rephrasing is no clumsier but has substantially the same meaning. Note the criterion: clumsiness (or even wordiness). — Quondum^☏✎ 04:39, 1 February 2012 (UTC)

That seems reasonable a priori — my only concern is that too many editors are already too squeamish about the passive voice, for no particularly good reason. It's true that sometimes active voice is a little peppier, but some people turn it into a shibboleth, and in any case we don't necessarily need pep in encyclopedic math articles. So I don't necessarily want to encourage that. --Trovatore (talk) 04:48, 1 February 2012 (UTC)

Good point. Passive voice is more common in technical writing than in general prose, and for good reason. I too prefer it to dummy subject role placeholders e.g. "we", "it", "one". — Quondum^☏✎ 07:45, 1 February 2012 (UTC)

Algebraic structure

Algebraic structure is an abomination. Is there a good tag for this sort of situation? Rschwieb (talk) 15:10, 31 January 2012 (UTC)

I don't think we have an {{abomination}} tag, but the Expert-subject tag might be what you are looking for. If you add {{expert-subject|mathematics}} to an article then the article name is automatically added to the relevant sub-list at Wikipedia:Pages needing attention/Mathematics and also appears on Wikipedia:WikiProject Mathematics/Current activity. Gandalf61 (talk) 15:46, 31 January 2012 (UTC)

I suggest {{Multiple issues}} with, at least, the items "expert", "technical" and "wikify". "Technical", because it is difficult to read the page without knowing universal algebra. Need to "Wikify" is clear, even if it can only be done by an expert. Another reason for which an "expert" is needed is that the difference between "algebraic structure" and "non algebraic structure" is not made clear. In my opinion the difference is that an algebraic structure is defined by a formula of first order logic, that is the axioms may involve quantifiers only on elements and not on subsets. Thus ordered field is an algebraic structure, but R is not, as its definition involves an axiom with a quantifier on subsets. D.Lazard (talk) 16:44, 31 January 2012 (UTC)

The m.i. tag has been added (not by me). I also bumped the class from B down to Start.--RDBury (talk) 18:41, 31 January 2012 (UTC)

It's a classic Wikipedia mathematics article: largely correct, but written in such a way as to remove all danger of actually informing the reader of anything. The only thing that could make it better is more passive voice.</sarcasm> Seriously, though, it needs a rewrite, and a good discussion of one main example. -- 202.124.72.242 (talk) 11:13, 1 February 2012 (UTC)

Right now, it's organized into "axioms all identities" "not all axioms identities" and an "examples" section, which brings the repetition to a head. I can't appreciate this scheme at all. This article definitely should be accessable to laypeople, so we need to find a better framework. Three tasks I recommend:

1) The intro right now is not terrible, but it should at least be looked at, and the following (longer) section should contain a solid description of what makes an algebraic object an algebraic object (ala D.Lazard's comments above)

2) Next section could be full of examples, wlinks and blurbs, using the scheme of "no operations" "one operation" "two operations" "composite systems" and "even more structures".

3) The category theory section does not do either category theory or universal algebra justice, so we need an expert to sum up how they are related to the article title.

I'll begin work on #2, but #1 and #3 are best explained by someone other than me :) And I'm now realizing this would be a good time to transfer my comments to the talk page itself. I hope to see you all there. Rschwieb (talk) 14:06, 1 February 2012 (UTC)

UPDATE: Quondum alerted me to the existence of Outline_of_algebraic_structures, which largely duplicates the atrocities of Algebraic structure. My feeling is that Algebraic structure should aim to be a readable introduction to the topic, and the outline (which I imagine is limited in its usefulness) can remain as is. Any problematic issues about duplicate articles that I'm overlooking? Rschwieb (talk) 16:34, 1 February 2012 (UTC)

First, I'm having trouble imagining where you'd draw the line between 'Algebraic structure' and Algebra. 'Algebra' should already be a readable introduction to the topic and I'm not sure what 'Algebraic structure' would have in it that shouldn't be in 'Algebra'. Second, 'Outline of algebraic structures' would seem to fall under the jurisdiction of Wikipedia:WikiProject Outlines, the aims of which I tend to agree with but since certain of its proponents have antagonized members of this project in the past, don't expect too much enthusiasm here for articles with names which start with "Outline of ...".--RDBury (talk) 17:37, 1 February 2012 (UTC)

Comment about the line to be drawn between 'Algebraic structure' and Algebra: Algebra has several subtopics, the only one which interest us here is "abstract algebra", which is the study of specific algebraic structures (like groups) and is not concerned with a definition of what is an algebraic structure. On the other hand, universal algebra is the study of algebraic structures as mathematical objects. This leaves the place to a general definition of what is (and what is not) an algebraic structure, which should be the object of Algebraic structure. Note that a general definition is not easy, as 'totally ordered fields' and 'graded algebras' are clearly algebraic structures which are not immediate to define as such in the universal algebra framework. D.Lazard (talk) 18:21, 1 February 2012 (UTC)

Comparing "algebra" to "algebraic structure" is like comparing "language" to "nouns". The article should contain a description of what is meant, and several examples organized in a basic way. Right now, I find the organization of structures to be bizarre, even though it might be correct from a universal algebra standpoint. Any chance you will try your hand at the first few paragraphs of the article, Dr. Lazard? Rschwieb (talk) 18:37, 1 February 2012 (UTC)

Proofs related to the Digamma function is on AfD

See Wikipedia:Articles for deletion/Proofs related to the Digamma function. Sławomir Biały (talk) 12:18, 1 February 2012 (UTC)

You should probably notify User:HenningThielemann and anyone else who has contributed significantly to the article. —Mark Dominus (talk) 16:46, 1 February 2012 (UTC)

Never mind, I did it. —Mark Dominus (talk) 18:11, 1 February 2012 (UTC)

Dirichlet integer translation from french

Can somebody translate fr:Entier_de_Dirichlet from french into english please? Brad7777 (talk) 14:15, 1 February 2012 (UTC)

As far as I realized, it is a quadratic integer ring for d = 5. I made once some use of this ring during mediations and programming related to Penrose tilings. Will you be satisfied if I add a section to aforementioned article and make Dirichlet integer a redirect instead of a stub? Incnis Mrsi (talk) 15:15, 1 February 2012 (UTC)

I'd like to point out that the footnote in the first sentence says the following: "While the mathematical content of this article is a usual part of the field of number theory, the term "Dirichlet integer" is not in common usage. The set of these integers is usually denoted O_Q[√5] and they are often not given any name.". I, for one, have never heard this term and the only source for it given in the (quite detailed) French article is a blog. There's discussion on the talk page of the French article and on their Math WikiProject concerning the problems with this title. So, if we are to translate this, I think we should first come up with a better name. RobHar (talk) 15:59, 1 February 2012 (UTC)

I have just read this French page. I have not the time to translate it myself, but I like the page and I support the idea of the translation. Some more comments:

• Firstly, although Dirichlet integers could be an example in Quadratic integer, I do not support Incnis Mrsi's suggestion: the example would be around 10 times longer than the remaining of the page!
• Secondly: The French page consists in explaining, on a specific important example, most of the theory of quadratic integers. This example is especially important, as it underlies the properties of the golden ratio and the proof of Fermat's last theorem for n=5. The article is easy to understand and shows very well to which problems the number theorists of XIXth century were faced to prove Fermat's last theorem and what were the solutions. It is thus very useful for a non experimented user to understand the notion of quadratic integer. In other word, it is a counter example of the assertion of the sarcastic IP user in #algebraic structure.
• On the other hand, the title is wp:original research, and although there is no original research in the content, the page may be viewed as an original synthesis (but not in the sense of wp:original synthesis, as it does not advances any position). In any case, I support the translation per WP:IAR.
• For the title, my above comment suggests Quadratic integer (example) or Quadratic integer (detailed example)

D.Lazard (talk) 16:53, 1 February 2012 (UTC)

Actually, only a small part of fr:Entier de Dirichlet is dedicated to D = 5. There is much algebra applicable to other quadratic fields IMHO, but I do not attempt to translate the things not clear enough to me. Incnis Mrsi (talk) 17:40, 3 February 2012 (UTC)

There is a very long discussion about it here : fr:Projet:Mathématiques/Le_Thé/Archives_4#Nom_Dirichlet.

You may read theses sources (in English! :-) ):

K. Ireland M. Rosen A Classical Introduction to Modern Number Theory p 13

P. Ribenboim Fermat's Last Theorem for Amateurs Springer 2000 p 49-56

H. M. Stark An Introduction to Number Theory MIT Press 1978 and [1]

French wikipedians decided thas this article is quite borderline, but on the right side. It's an introduction to quadratic integers, but the title is a problem: Q(√5) was proposed, but rejected. --El Caro (talk) 17:10, 1 February 2012 (UTC)

Here's a (somewhat tongue-in-cheek, but maybe real) suggestion for a title: The ring of quadratic integers of discriminant five. This is what the article would be about and it avoids using mathematical notation (which was the opposition to titles such "Q(√5)" that were suggested on French wiki). RobHar (talk) 18:08, 1 February 2012 (UTC)

I'm not really seeing the problem with 'Dirichlet integer'. We already have articles on Gaussian integer and Eisenstein integer and 'Dirichlet integer', even if not the most common name, would be better than O_Q[√5]. I can't resist adding to the OP, learn to read mathematical French! It's much easier than learning regular French since there are a limited number of grammatical constructions and practically every other word is a cognate.--RDBury (talk) 15:34, 2 February 2012 (UTC)

"Gaussian integer" and "Eisenstein integer" are extremely common terms for these objects. Are you saying that if I write a blog post and call the ring of integers of the 7th cyclotomic field the "Lamé integers", then we can create an article here called that? RobHar (talk) 16:13, 2 February 2012 (UTC)

Yes, that's exactly what I'm saying. Actually I missed the part in the above discussion that the name is based on a single blog post, so I though there was at least one reliable source for the name even if it wasn't the most common one in use. So there was an error on my part but I don't see the need to make a sarcastic comment about it.--RDBury (talk) 06:43, 3 February 2012 (UTC)

That wasn't a sarcastic comment, that was an actual question. And since you answered yes, it was apparently a relevant question to ask. I do however completely disagree that we should be proliferating random designations of objects and there must be a guideline that supports my position. RobHar (talk) 14:35, 3 February 2012 (UTC)

Actually I was being facetious when I answered yes; I thought not supporting random names for things was implicit. Sorry for the misunderstanding; it sometimes causes confusion when text communication does not convey the intended tone of voice.--RDBury (talk) 15:54, 3 February 2012 (UTC)

Incidentally and off topic, since this this discussion is still warm while I desperately click on interwikis trying to find in any language an article about the space of continuous functions with compact support, it is amazing how being named after a mathematician helps to get an article in Wikipedia : just look at the list of examples in Function space#Functional analysis. There are 18 examples, none has been wikified with a red link, but only 6 have an article. By a happy coincidence, these are the 5 named after a person (and additionnally one with a short name, that is Lp space) ! Quite a number of fundamental articles are lacking, in my opinion : there is hardly a deep logic in having a separate article about Schwartz space but relegating the space of smooth functions with compact support (this is not even a redirect !) as a paragraph in the article about distributions. French Tourist (talk) 17:00, 5 February 2012 (UTC)

Meanwhile, I expanded the article. Please, check for possible mistakes. Incnis Mrsi (talk) 17:40, 3 February 2012 (UTC)

Integral value transformation

Integral value transformation is quite a badly written article, to say the least. Is it worth doing something with? Michael Hardy (talk) 02:39, 3 February 2012 (UTC)

I'd say it's worth deleting. A quick Google search for the title gives a bunch of badly written papers, all by the same small set of authors, which to me seem to fall into the category of pseudo-science. (Given any two sequences, it's possible to concoct a function sending one to the other. This usually isn't meaningful). I haven't found any secondary sources or anything else that helps the topic satisfy WP:GNG. Jowa fan (talk) 05:59, 3 February 2012 (UTC)

It's been deleted as copyvio of http://arxiv.org/ftp/arxiv/papers/1201/1201.4329.pdf. PamD 15:51, 3 February 2012 (UTC)

Additional opinions requested on Definite bilinear form

Debate at Talk:Definite bilinear form#Definite bilinear forms: symmetric only?. The question is whether the definition of definiteness is restricted to symmetric bilinear forms. Curiously, many but not all authors appear to restrict the definition to the symmetric case, although the restriction appears to be unnecessary and cumbersome. Also, the Properties seciton of the article needs checking and expansion (a few minutes by someone familar with the topic, particularly relating to eigenvalues and related properties). — Quondum^☏✎ 10:09, 3 February 2012 (UTC)

Mathworld's entry seems to support Quondum's position (that there is no real reason to restrict the definition.) Rschwieb (talk) 16:38, 3 February 2012 (UTC)

Smooth completion

AfD for Smooth completion may be found here. Tkuvho (talk) 19:44, 4 February 2012 (UTC)

Article moves and redirect bypasses by Jheald

[2] despite [3]. Suggestions? Incnis Mrsi (talk) 18:37, 5 February 2012 (UTC)

I noted what you wrote, but you were wrong. If an article gets renamed, it is only sensible to rename the "See also" sections and the {{main}} links that point to it.

The previous article title -- Rotation representation (mathematics) -- was rubbish. The new title Rotation formalisms in three dimensions may not be perfect, but it gives a much better idea of what the article's about. Jheald (talk) 18:47, 5 February 2012 (UTC) And if you're going to raise my edits for wider discussion, it's courteous to notify me of the fact. Jheald (talk) 18:47, 5 February 2012 (UTC)

I think his change is probably in good faith, however there probably should be some discussion before the page rename. If you bothered asking for the reasoning it would be helpful to provide a link to that discussion too. A link to your declaration of an edit's uselessness alone is not very helpful. It also doesn't substantiate uncooperativeness, so a link to that would be good too. Rschwieb (talk) 19:07, 5 February 2012 (UTC)

How amusing. I referred to WP:NOTBROKEN, an official Wikipedia guideline, and Jheald's edits are build on a personal taste − but it's me who was wrong. The title of Rotation representation (mathematics), an extensively linked article, was convenient to Wikipedia's editors for many years − but, according to Jheald, it is "rubbish". And he changed it, twice in a hour, without consulting anybody. This is an established article, not a kind of godforsaken stub. Incnis Mrsi (talk) 19:11, 5 February 2012 (UTC)

The old namewas indeed bad. "Representation" has a very specific meaning in the mathematics of symmetry operations such as rotations, a meaning that the old title did not refer to. Avoiding that word in this context is a good idea. So although I agree with Jheald that the new name may not be perfect (it's a bit long and clunky) it's a distinct improvement over the old. —David Eppstein (talk) 19:29, 5 February 2012 (UTC)

FWIW there's now a topic open at Talk:Rotation formalisms in three dimensions#Title if anyone has any good ideas. Jheald (talk) 19:38, 5 February 2012 (UTC)

More links to digi-area.com

Another user (see Wikipedia talk:WikiProject Mathematics/Archive/2011/Sep#Digiarea links) has added a bunch more links to digi-area.com; the most recent one was added to Polar coordinate system. The purpose of the site/product is provide people with pre-made formulas that can be used in TeX or Mathematica. I think this falls under WP:ELNO and I'm going to undo the changes, assuming there are no valid objections, but I was wondering if requesting some help from XLinkBot would be appropriate at this point.--RDBury (talk) 12:08, 6 February 2012 (UTC)

I had a look and the site seemed to provide no additional material about the topic so yes I agree with the removal. It does also just seem to be there as an advertisement. Dmcq (talk) 12:21, 6 February 2012 (UTC)

The topic has no copyable formulas in the formats (MathML, TeX, Mathematica input, Maple input). So, this is really additional material about the topic. If user interested in the topic, then he/she may want to have the copyable formulas. — Preceding unsigned comment added by SandraShklyaeva (talk • contribs) 12:36, 6 February 2012 (UTC)

The DG Library is free and unique resource of copyable formulas for differential geometry objects and its applications. So, the link has practical advantage for the user. I think that free and useful resource can not be an advertisement anyway. — Preceding unsigned comment added by SandraShklyaeva (talk • contribs) 12:43, 6 February 2012 (UTC)

I hope you have good luck with the DG Library site, but I agree that these links are not a good fit for our articles on Wikipedia. It is not hard to simply type a formula, and I can't see why someone would want to search for a website just so they can copy one. Moreover, the formula on the website may not be the exact formula that is desired, and the actual pages being linked to seem to have little content and no explanations [4]. Thus I do not see a strong benefit to including links to these formulas in our articles. — Carl (CBM · talk) 12:55, 6 February 2012 (UTC)

I agree with the removal, per Carl's reasoning. Sławomir Biały (talk) 12:56, 6 February 2012 (UTC)

Formulas of differential geometry objects not always simple and it is not easy to write formulas by hand. For example: Inverse Cassinian Cylindrical. It is just a waste of time. Moreover, most people do not make calculations in differential geometry by hand, because the calculation is very massive. People use different CAS's, so it will be useful to get already prepared formulas for theirs work. — Preceding unsigned comment added by SandraShklyaeva (talk • contribs) 13:21, 6 February 2012 (UTC)

More massive category changes

Brad7777 (talk · contribs · deleted contribs · logs · filter log · block user · block log) has returned, making thousands of changes to categorization of mathematics articles without any discussion. I thought we had a discussion here in which the overall tone was that Brad should stop what he is doing since many of his notions were somewhat controversial. At the time, I checked through the hundred or so mathematics category edits, and reverted the ones that didn't make any sense. But now he's using hotcat, and has done over a thousand such edits. He seems to be single-handedly attempting to redo all of the categories for mathematics articles based on his own personal opinion of what belongs in which category. This is disruptive and a waste of community resources to check all of this damage. What should be done about this? Sławomir Biały (talk) 01:24, 5 February 2012 (UTC)

He should stop, undo all his changes, and find something else to do with his time. There's no shortage of things to do to improve the encyclopaedia, starting e.g. here.--JohnBlackburne^words_deeds 01:47, 5 February 2012 (UTC)

I would support a topic ban on any changes to mathematical categories or to the categories of mathematics articles for this user. Many of his changes make sense, but many more are misguided or badly informed, and politely asking him to behave has had little or no effect. I think I already suggested this the last time around, but I think Wikipedia:Requests for comment/User conduct might be the appropriate next step. —David Eppstein (talk) 02:23, 5 February 2012 (UTC)

Let me know when the petition comes around so I can sign in all caps. Rschwieb (talk) 02:33, 5 February 2012 (UTC)

You must have really strong opinions against my edits, which one\s in particular do you think are non-constructive? Brad7777 (talk) 21:35, 5 February 2012 (UTC)

To my humble opinion, it would be much better to start with specific issues. It is hard to disagree that the categorization has place for improvement. So changes are welcome, though perhaps more discussion would be helpful too.

this and this (compare the timing) are a counterexample to David's statement. Sasha (talk) 03:46, 5 February 2012 (UTC)

ANY kind of large-scale changes made against consensus are disruptive. I would support a permanent ban. -- 202.124.74.138 (talk) 10:20, 5 February 2012 (UTC)

I hadn't noticed that. I had seen the removal of the cycle so origami was under paper folding but not vice versa and I had been wondering what to do about it because it was just causing trouble when trying to find things. I think I'll just go and reinstate the cycle and leave the various bits of the mathematics of origami in the paper folding category except for the top article mathematics of paper folding. Dmcq (talk) 12:41, 5 February 2012 (UTC)

I've got round the problem by putting some text at the top of the origami category referring to the paper folding category for mathematical aspects of origami. Dmcq (talk) 13:33, 5 February 2012 (UTC)

Nice one Brad7777 (talk) 21:31, 5 February 2012 (UTC)

One of the problems with this user seems to be a slight communication impairment. Not providing any rationale for his edits and either denying there is a problem when issues are raised at his talk page or acknowledging them but doing nothing with them. A possible remedy would be to have him post a description of the changes he is going to make on this talk page and link to that description from each of his edit summaries (he would have to stop using HotCat as this tool does not always allow you to write an edit summary). —Ruud 13:10, 5 February 2012 (UTC)

HotCat has two modes. In single change mode you cannot make your own edit summary. But in batch mode (+⁺) the user gets to usual page edit interface and can add his/her own changes, to a page itself as well as to the edit summary (where HotCat propose its format), even if only 1 change was made to categories. Incnis Mrsi (talk) 14:41, 5 February 2012 (UTC)

I assumed the edit summaries Hotcat gave were sufficient. I did not realize there was somewhere saying it wasnt. I will improve on this Brad7777 (talk) 21:27, 5 February 2012 (UTC)

Colleagues,

there is a long discussion here and also on Brad7777's talk page, but so far very little of it is constructive. I found three specific issues raised (origami, subharmonic functions, and manifolds), all the rest was between unconstructive and personal attacks.

It is a truism that every change is potentially against consensus. The earlier we start discussing content (in this case, the structure of the categories), the earlier the consensus that was mentioned so often could appear.

Sasha (talk) 14:36, 5 February 2012 (UTC)

One specific change I object to is the fact that Category:Projective geometry no longer contains either Pascal's theorem, or Desargues' theorem, or Pappus' theorem, or Brianchon's theorem. These are tucked away in a "theorems in projective geometry" category, but that makes it very inconvenient to someone who is not already intimately familiar with Brad7777's tucking away philosophy. Tkuvho (talk) 17:12, 5 February 2012 (UTC)

I would say it helps diffuse both Category:Projective geometry and category Category:Theorems in geometry (both with ~100 articles in them without this category). It may be slightly different to how the category was before, but it isn't difficult to find them and it would remain that way as more pages are added to Category:Projective geometry in the future. Perhaps the examples you have given should be in both Category:Projective geometry and Category:Theorems in projective geometry, but then who decides on which are the most important? Brad7777 (talk) 18:33, 5 February 2012 (UTC)

"....but so far very little of it is constructive". Let's summarise ... multiple users have begged Brad7777 to stop these wholesale changes to categories according to his whim ... 2 users seem to think that it is OK that he should continue (Sasha and Brad7777 ). And let's not forget that categories are meant to be useful to users of Wikipedia, most of whom won't be telepathic enough to follow the peculiar structure that bhas now been set up. Melcombe (talk) 20:41, 5 February 2012 (UTC)

What do you find peculiar about the edits I have made Melcombe? I agree that "categories are meant to be useful to users of Wikipedia" so which of my edits do you think have gone against that? Brad7777 (talk) 21:23, 5 February 2012 (UTC)

The problem is you are making so many so quickly without explanation that it's impossible for others to keep up. But checking through changes today what is the point of this unexplained edit? (the third one I checked).--JohnBlackburne^words_deeds 21:43, 5 February 2012 (UTC)

I am opposed to this intentional de-alphabetization of categories. It is good to de-alphabetize a single main topic for each category (often the one with the same name as the category) but beyond that it just makes things messy for no good reason. —David Eppstein (talk) 21:46, 5 February 2012 (UTC)

I add a space to articles with the same name. The stars on the categories of topological combinatorics, are because this page is noteworthy in the history of these categories. (I think its worth doing as they are also overcrowded). Looking again, I think Category:topology should be removed completely. Im not sure what you mean when you say "it's impossible for others to keep up"? Brad7777 (talk) 22:00, 5 February 2012 (UTC)

The proper way to highlight eponymous articles is with a space, not an asterisk. It's especially confusing to use both - why are some above the star and some below and in Category:topology? But the main problem is it should not have been moved – categories are not meant for sorting articles by how 'noteworthy' you think they are. It's not clear anyone else does, given that the article is still a stub after three years. If you really think it is noteworthy then improve the article. As for keeping up when you're changing categories it's often necessary to look at the category you've moved the page from and to to understand the change; it takes far longer than normal to understand what the change does, especially as you do not explain your edits in edit summaries and are making changes much more rapidly than most editors.--JohnBlackburne^words_deeds 22:19, 5 February 2012 (UTC)

I have seen it in many other categories, and do think its worth doing to seperate the main article from others of importance, but I'll avoid doing it. (It is one way to get them noticed for improvement). Ill add more detail to my edit summaries, is there somewhere that mentions what is suficient? Brad7777 (talk) 22:37, 5 February 2012 (UTC)

Was that the third one you checked with the intention of finding a mistake you think i would have made? Brad7777 (talk) 22:04, 5 February 2012 (UTC)

Break

I would like to ask specifically, that Brad please stop adding categories to redirect pages like paracompactness, compactness (topology), and probably more. This is just one reason I think Brad should stop doing any more category edits. It is going to take hours if not days to clean up his mess. Sławomir Biały (talk) 15:37, 6 February 2012 (UTC)

Only one more Connectedness (topology), and I have stopped, I created a discussion about it below. (I could undo those particular edits in under 3minutes). Are you assuming I have made a mess, or do you have any examples? Brad7777 (talk) 16:38, 6 February 2012 (UTC)

You should refrain from this or any further category edits. I am willing to consider the possibility that you are right about all this, but please consider the fact that a number of editors here feel that you have indeed made a mess. Tkuvho (talk) 16:46, 6 February 2012 (UTC)

It doesn't matter if they have a "feeling" I have made a mess. Wikipedia is not a soapbox, it is supposed to be an encyclopedia written from a neutral point of view (so my view must also be accounted for), free so that anybody can edit, free of personal attacks and free of worry about making mistakes. It would be nice to see some justification of all this mess I have created in terms of the edits I have done. I understand the point of the sceptical criticism (I use constructively) but what is with all the pessimism and totalitarian rules? All my edits have been in good faith. So for those reasons I will continue editing. Brad7777 (talk) 17:48, 6 February 2012 (UTC)

Similarly all of this criticism has been in good faith. You ask in this comment to see some justifications of the claim that you are making a mess, but the "mess" you are making is transpiring a bit too quickly to give you a thoughtful in depth justification. People are trying to say: "Something is telling me there might be a problem with these edits, but maybe there isn't. In the meantime, could you just chill for a bit so that we can look over the edits more carefully and figure out if there is or is not a problem." Your answer is: "Nah, I'm just going to keep going." So, people's reaction has been to simply bring up random examples that have disturbed them. This is not surprising. And know that if you continue and people take it a step further, your ban will also be done in good faith. RobHar (talk) 18:31, 6 February 2012 (UTC)

Yes, please do continue editing. But not categories. This encyclopaedia is run by consensus and there is a clear consensus you should leave categories alone. You have been given many examples of the problems you are causing, both here and on your talk page. No-one is going to review all of your category edits as there are too many of them and it takes too long. But those that have been reviewed show a continued pattern of problems, with the lack of care, the lack of good rationale and the broad disregard of standards and practices they exhibit. So take a break from categories and find something else to work on. There is no shortage of things to do that will actually improve the encyclopaedia.--JohnBlackburne^words_deeds 18:39, 6 February 2012 (UTC)

I concur: please stop editing categories Brad, in particular, unsorting articles within their categories. This is wasting effort and not improving the encyclopedia. Geometry guy 23:20, 6 February 2012 (UTC)

I'm not going to unsort any articles within their categories Brad7777 (talk) 14:41, 7 February 2012 (UTC)

Ditto. Rschwieb (talk) 14:03, 7 February 2012 (UTC)

Given this, are you going to undo the unsorting (which you have made to date) of articles within categories, or rely upon others to clean up? Geometry guy 01:03, 8 February 2012 (UTC)

I have cleaned up Brad7777 (talk) 19:09, 8 February 2012 (UTC)

"Picture perfect"

User:Baroc has been adding photographs of mathematicians to our biographies (e.g. Colin McLarty and Robert Phelps), and deserves our thanks!

 Kiefer.Wolfowitz 14:27, 8 February 2012 (UTC)

Request for comments on Euler's Formula Proofs

I am currently having an argument about whether a "by calculus" proof of Euler's formula should appear in the article of the same subject. I'd like some additional opinions on the subject, and so if you're interested I'd appreciate it if you could go to the talk page there and comment. Thanks. Holmansf (talk) 23:59, 8 February 2012 (UTC)

Mikhail Gromov

The page Mikhail Gromov went through several transformations and is currently redirected to his full name including the little-used middle name. The problem seems to be that there is an aviator of the same first and last name. I think a case can be made in favor of keeping the page at "Mikhail Gromov" with a hat sending the reader to the aviator. Tkuvho (talk) 12:29, 25 January 2012 (UTC)

Could someone comment whether it is reasonable to move Mikhail Leonidovich Gromov to Mikhail Gromov assorted with a hat concerning the aviator? Tkuvho (talk) 13:55, 9 February 2012 (UTC)

Category:Topology

This category currently has 214 articles in it, any suggestions for diffusing it? Brad7777 (talk) 22:23, 5 February 2012 (UTC)

NO. Ozob (talk) 22:33, 5 February 2012 (UTC)

I have a suggestion, what about moving the relevant lemmas into Category:theorems in topology? Brad7777 (talk) 22:40, 5 February 2012 (UTC)

Also a suggestion regarding Category:Topological spaces (see relevant section below) Brad7777 (talk) 13:47, 6 February 2012 (UTC)

Fiber bundle

Currently, the article fiber bundle is in the following categories:

• Category:Fiber bundles
• Category:Differential topology
• Category:Algebraic topology
• Homotopy theory

Whilst the category Category:Fiber bundles is in:

• Category:Topology
• Category:Differential geometry

First, does Category:Fiber bundles need to be a subcat of Category:Topology? Should it be made subcat of Category:Algebraic topology and Category:Homotopy theory instead, or aswell? In which case, secondly, does the article Fiber bundle need to be in any other category except Category:Fiber bundles? Any other comments? Brad7777 (talk) 22:55, 5 February 2012 (UTC)

Topological space

Currently this article is in the categories Category:Topological spaces and Category:General topology, whilst Category:Topological spaces is a subcat of Category:General topology. The topological space should be removed from Category:General topology, because this is overcategorization is it not? I also suggest Category:Topological spaces should be a subcat of Category:Topology aswell, as this could help defuse the category Category:Topology, any objections? Brad7777 (talk) 23:05, 5 February 2012 (UTC)

The overriding reason for categorization is as an aid in finding things, not a separate project to produce a Linnaean tree of knowledge. the business about overcategorization and cycles are guidelines to avoid decreasing the usefulness of categories by overfilling them with details. However if there is a major topic which is relevant it can be included if it doesn't imply dragging in a lot of other things. Also a cycle is fine if some people think the tree should go one way and other think it should go another. They are good guidelines but if something would look wrong to you if you followed them then don't do it. Dmcq (talk) 12:39, 6 February 2012 (UTC)

To me, it would look right having Category:Topological spaces as a subcat of Category:Topology. I would also expect all the articles which are directly in Category:Topology which are on topological spaces to be categorized in there instead. This is because I think the value of Category:Topology is in it being a content category. Brad7777 (talk) 12:57, 6 February 2012 (UTC)

Although I always objected to overcategorization (you even can see my diagram File:Categorization to 2 axes.svg about intersecting category hierarchies), a particular case of topological space is important enough to be included both to Category:Topology and Category:General topology, as a fundamental notion. There are several other articles which have to be (re)moved from "Topology" to subcategories. Incnis Mrsi (talk) 17:15, 6 February 2012 (UTC)

Category:Theorems in geometric topology

Opinions on the creation of this category? Category:Theorems in topology contains 49 articles. Category:Geometric topology contains 123 articles. Category:Theorems in geometric topology would possibly hold 13 articles and is likely to grow. Geometric topology already could do with diffusing, and is also likely to grow in the future. So i think this category will help. Articles for consideration:Grushko theorem, Rokhlin's theorem, Annulus theorem, Side-approximation theorem, Sphere theorem (3-manifolds), Bing's recognition theorem, Double suspension theorem, Blaschke selection theorem, Moise's theorem, Loop theorem, Gordon–Luecke theorem, Cyclic surgery theorem, Fary–Milnor theorem Brad7777 (talk) 00:25, 6 February 2012 (UTC)

What's wrong with leaving Category:Geometric topology as it is? Sławomir Biały (talk) 15:29, 6 February 2012 (UTC)

100+ articles which is likely to grow, hence it would be a good idea to create a few categories to help prevent it becoming over populated. Any objections to the creation of the Category:Theorems in geometrical topology? Brad7777 (talk) 16:52, 6 February 2012 (UTC)

I imagine that when a clearly orthogonal categorization scheme emerges, it is reasonable to follow it even if the number of articles doesn't seem to entirely justfy it. In this instance, "Theorems in [some category]" seems to be an orthogonal categorization scheme (i.e. it makes sense for any mathematical field), so if there are more than a few articles in the category that would be classified as a theorem, it would be reasonable to create the subcategory of theorems. — Quondum^☏✎ 17:50, 6 February 2012 (UTC)

Manifold and Classification of manifolds

Are these two articles overcategorized? They only need to be in one category: Category:Manifolds surely? Brad7777 (talk) 00:39, 6 February 2012 (UTC)

Manifolds are one of the most fundamental objects of study in topology, differential geometry, and especially geometric topology. I definitely don't think this is overcategorization. Our categorization system should satisfy the "least surprise" principle: that if a user expects to see an article in a category, then it should be there. This is clearly such a case. Sławomir Biały (talk) 15:28, 6 February 2012 (UTC)

That is why I do not think they would be surprised that Category:Manifolds currently is a sub cat of the same categories as manifold, in which they could quite easily find it. Hence I think its overcategorization. Articles should be placed in the most specific categories,(in this case one with the same name). I would think they are not needed in all the parent categories aswell. Brad7777 (talk) 16:47, 6 February 2012 (UTC)

On your user page, you have "Categorisation is not a transitive relation" yet many of your edits are in exact opposition to this as is your above statement. I think that there are times that it makes sense to have an article in both a category and one of its subcategories. For example, while it makes sense to have Fundamental theorem of algebra in the category "theorems in algebra", it also makes sense to list it in "algebra" (or perhaps "abstract algebra") since it is the "fundamental theorem" of that subject! Your edit removed it from "abstract algebra" AND "theorems in algebra" and placed it in "theorems in complex analysis", which seems like a twice-wrong re-categorization! RobHar (talk) 17:21, 6 February 2012 (UTC)

Er... Reading the article suggests (to my untrained ear) that the theorem was named before "algebra" came to mean abstract algebra. It seems a better name would have been Fundamental theorem of complex analysis, as it deals with exactly that, and does not have general applicability across all algebras. — Quondum^☏✎ 18:00, 6 February 2012 (UTC)

I don't really know how to start replying to this. A major topic in "abstract algebra" (if not the whole point of it) is studying solutions of polynomial equations, so I'd say that the first theorem that said that every polynomial (over Q or R) has a root in C is a pretty fundamental theorem in the subject. It showed for the first time that there exist algebraically closed fields. It's generalized to Kronecker's theorem which is pretty fundamental. I would not say that it "deals with" complex analysis. A common proof uses complex analysis and in fact many other theorems that are more suitably called the Fundamental theorem of that subject. For example, Cauchy's integral theorem is surely a much more suitable candidate for this name. There's so much more to say, but I'll stop here. RobHar (talk) 18:23, 6 February 2012 (UTC)

Is that not algebraic geometry? I think my rationale was more along the lines that there wasnt a category Category:Theorems in complex geometry at the time, that was the next best thing. It is problematic though Brad7777 (talk) 18:39, 6 February 2012 (UTC)

There is, a problem in the categorization of manifolds, but surely not a problem of overcategorization. Analytic manifold, analytic variety, complex manifold are close and strongly related notions. One may add complex variety which redirects to algebraic variety, when analytic variety would be better suited. I have not found any category more specific than Category: Mathematics which contains all these pages. D.Lazard (talk) 17:52, 6 February 2012 (UTC)

Would they somehow fit into Category:Mathematical structures? You should really be able to find them through Category:Mathematical concepts. Brad7777 (talk) 22:31, 6 February 2012 (UTC)

Category:Properties of topological spaces

At the moment this category seems to be being abused. Many of the articles are on "topological spaces with properties". Strictly, this is like placing articles on triangles in a category called "properties of triangles" while there is a category called "triangles". What are your thoughts on categorizing redirected pages to this category instead where possible. For example, Connectedness (topology), categorized into Category:Properties of topological spaces, instead of Connected space being categorized into there? This would be a more proper use of the categories. It would require that the redirects are more specific where possible, but would reveal which articles do not have a section on the property they have when they could do with one (especially because of this category). I would also suggest that articles which don't have a relevant redirect to them are left in there, although these tend to be mainly stub articles. Comments? Brad7777 (talk) 13:45, 6 February 2012 (UTC)

I don't see the abuse you talk about. "Connected space" is defined as "topological space with the property of being connected". One could argue that the article should be moved from Connected space to Connectedness (topology), but frankly, I don't see the benefit in that. And whether the article is named Connected space or Connectedness (topology), it certainly should be categorized into Category:Properties of topological spaces. — Tobias Bergemann (talk) 14:11, 6 February 2012 (UTC)

You are saying a "topological space with the property of X" belongs to Category:Properties of topological spaces, but you cannot see the logic in having the section on X (being the property of a topological space) in this category? I don't see why this wouldn't a better substitute? I guess one of the points im raising is that a redirect from for example Connectedness (topology) to the connected space is not useful when there is not a clear section on what you have just been redirected from, (given that this could have came from any page). When there is a clear section, it allows articles in categories like Category:Properties of topological spaces or Category:Structures on manifolds to be more relevant. It also allows articles like compact space to be categorized in Category:topological spaces instead of Category:Properties of topological spaces, promoting the proper use of categories. (It is a topological space, not a property of a topological space). The issue about the article being moved to the more specific category in these types of categories perhaps needs its own discussion. Brad7777 (talk) 14:36, 6 February 2012 (UTC)

I think "compact space" is a fine article for the properties category, because it is our article on compactness of topological spaces. For example compactness redirects there. In general our article on property XXX will be called "XXX space" instead of "Property XXX of a topological space" but describing "compact space" as "is a topological space, not a property of a topological space" seems to be confused. — Carl (CBM · talk) 14:57, 6 February 2012 (UTC)

Are you saying compactness and compact space are both properties of topological spaces? Yes I am confused Brad7777 (talk) 15:11, 6 February 2012 (UTC)

I see, you are treating wikipedia as some kind of quantum system? The property having both a wave and particle like form? Brad7777 (talk) 15:17, 6 February 2012 (UTC)

This is more of an English usage thing. "Compactness" is the property possessed by "compact topological spaces". There is not some particular space which is the "compact space", which is what it implies to put the "Topological spaces" category on that article. Instead a compact space is a space which is compact, i.e. one which exhibits compactness. Our article begins, "In mathematics, specifically general topology and metric topology, a compact space is an abstract mathematical space whose topology has the compactness property, ...". — Carl (CBM · talk) 16:05, 6 February 2012 (UTC)

What Carl is saying is spot on. RobHar (talk) 17:21, 6 February 2012 (UTC)

It may help to compare e.g. Arens–Fort space, which is a particular topological space, with paracompact space, which is about the property of paracompactness. I would put the former in the "Topological spaces" category and the latter in the "Topological properties" category. — Carl (CBM · talk) 17:45, 6 February 2012 (UTC)

I see what you saying, but I guess this is where the vagueness of the name Category:Topological spaces plays, because to me this category should contain all topological spaces, (A Compact space is a certain type of topological space) whilst Category:Properties of topological spaces suggest articles on or about the properties of topological spaces. The article Compact space does mention a property, but it could be improved by having a unique section on compactness as a property of topological spaces. (In this case the redirect to that section only needs to be included in this catgeory). I think in the case of paracompact space, paracompactness is better suited for Category:Properties of topological spaces with paracompact space in Category:Topological spaces. I would also add a tag to Arens-Fort space saying "paracompact spaces". Brad7777 (talk) 18:25, 6 February 2012 (UTC)

It's useful to have a category that describes individual, specific topological spaces. Category:Topological spaces is that category. And whatever that category is named, compact space does not belong to it because many different spaces are compact. What you are advocating would eliminate any meaningful distinction between Category:Topological spaces and Category:Topology, because everything in topology is in some sense about topological spaces. This seems destructive to me. Far too many of your edits seem motivated by a sense of ideological purity of the Wikipedia category system and/or a shallow syntactic analysis of article and category names rather than out of any actual understanding of the mathematics the categories are trying to describe, and this is a case in point. —David Eppstein (talk) 18:29, 6 February 2012 (UTC)

What you are describing seems better suited for an article, more specifically a type of list. See WP:DEFINING. I also think many general users of wikipedia would use syntactic analysis to find articles and categories they require so do think it is worth taking into account. Brad7777 (talk) 18:57, 6 February 2012 (UTC)

As I understand it:

• Category:Topological spaces is for specific spaces, ones that would have a definite article in front, such as the long line.
• * Category:Properties of topological spaces is for properties that an arbitrary space may or may not have. This includes articles that are eponymous with a property, e.g. paracompact space for paracompactness. A sign that an article belongs here instead of the former category is that the indefinite article is used, e.g. a paracompact space.

If there are no large objections, I will go about fixing the category tree to reflect this. — Carl (CBM · talk) 18:47, 6 February 2012 (UTC)

The idea of the category Category:Topological spaces as you want would be better suited for a list, see WP:DEFINING. Brad7777 (talk) 19:08, 6 February 2012 (UTC)

How is "it is a specific topological space" (in opposition to "it is a class of topological spaces" or "it is a number" or "it is a theorem" or whatever) not a defining characteristic of a mathematical structure? This is exactly what I mean about forgoing mathematical sense in favor of ideological purity. —David Eppstein (talk) 20:03, 6 February 2012 (UTC)

Are you saying we need a category Category:Specific topological spaces? Brad7777 (talk) 21:45, 6 February 2012 (UTC)

I'm saying that we have that category, it is Category:Topological spaces. — Carl (CBM · talk) 21:46, 6 February 2012 (UTC)

Category:Topological spaces doesnt define the articles it contains. It defines alot more. Brad7777 (talk) 21:51, 6 February 2012 (UTC)

The text at Category:Topological spaces says "This is a list of important or interesting topological spaces." which matches what I am saying. For example locally compact space is not a topological space, it is a type of topological space, which is why it should not be in a category whose title is "Topological spaces". — Carl (CBM · talk)

Are you suggesting that we need a category Category:Types of topological spaces? Brad7777 (talk) 22:23, 6 February 2012 (UTC)

I ask because Wikipedia is here to present facts Brad7777 (talk) 15:17, 7 February 2012 (UTC)

I have no idea how "presenting facts" is relevant to anything. I explained above what the two categories mean, and I see no need to rename them. Perhaps you could be more clear and direct in explaining exactly what you mean, because I am unable to tell what you are trying to say. — Carl (CBM · talk) 15:30, 7 February 2012 (UTC)

We already have that category its called Category:Properties of topological spaces.TR 15:32, 7 February 2012 (UTC)

All topological spaces have properties. Topological property explains what a topological property is. You are saying Category:Topological spaces should only include spaces of interest (subjective?) and not for example paracompact space which is a type of topological space. ( ~ like an equilateral triangle is a type of triangle and found in Category:Triangles.) You are saying paracompact space should go in Category:Properties of topological spaces even though it is not a property. It is a type of topological space with a certain property, just like every other topological space including the more specific ones you talk of whose property can be defined as a combination of properties. Yet in the case of the page about a specific property of a topological space, paracompactness, (which redirects to the relevant section in paracompact space,) for some reason you do not it think should be categorized into Category:Properties of topological spaces because it does not fit your personal ideal? That is not objective categorization at all. Brad7777 (talk) 17:53, 7 February 2012 (UTC)

We are saying that properties of topological spaces such as paracompactness should be categorized differently than individual topological spaces such as the Hawaiian earring. Is that so difficult to understand? I'm feeling WP:IDIDNTHEARTHAT is very relevant here. —David Eppstein (talk) 18:14, 7 February 2012 (UTC)

My rejection of the concept is not due to difficulty understanding or ignoring any points of view, I do not disagree that paracompactness and Hawaiian earring should be in different categories? I disagree with the view that both paracompactness and paracompact space should be, when one is more specificied for the category. I also think by WP:DEFINING your concept of a collection of individual spaces is better suited for a list, and disagree with it for the same reason that you wouldn't have Category:Shapes dedicated to articles on unique, interesting, individual (or any other similar words) type shapes. Brad7777 (talk) 21:08, 7 February 2012 (UTC)

We do have such a category: Category:Geometric shapes. In any case, lists do not replace categories, they complement them. This is why we also have List of geometric shapes. — Carl (CBM · talk) 23:18, 7 February 2012 (UTC)

Are you saying Category:Geometric shapes is similar to how you are describing Category:Topological spaces? Actually I think many of those shapes aren't referred to as "the", infact the shapes left are purely due to the "sieve" of subcategories. I guess this all comes down to a question along the lines of: Is a "circular shape" a shape or a type of shape? Brad7777 (talk) 18:56, 8 February 2012 (UTC)

RFC on topological properties

Could those who agree with fixing the categories to match my comment of 18:47, 6 February 2012 please leave some sort of positive comment so I can gauge consensus? — Carl (CBM · talk) 23:18, 7 February 2012 (UTC)

• Support. Ozob (talk) 11:20, 9 February 2012 (UTC)
• Support. Tobias Bergemann (talk) 13:47, 9 February 2012 (UTC)

Paracompact space

The article paracompact space currently begins with the following sentence:

In mathematics, a paracompact space is a topological space with the property of paracompactness.

Not only is this a meaningless sentence, the link paracompactness redirects back to the same article! This seems to be due to a significant edit by Brad7777. I will work on fixing the article, but more eyes on it (and other edits by Brad7777) would be helpful. — Carl (CBM · talk) 20:37, 7 February 2012 (UTC)

If you think there is a problem with my edit, you could let me know on my talkpage, or simply edit it, explaining your reasoning in the summary. (You could edit the grammar so that it says "which has the") WP:SOAP Brad7777 (talk) 21:21, 7 February 2012 (UTC)

At the time paracompactness redirected to a specific section, which is no longer needed. I apologize for the utter ridiculousness of it. Brad7777 (talk) 21:24, 7 February 2012 (UTC)

Categorizing redirects

The links Cofinite topology and Finite complement topology currently redirect to Cofiniteness#Cofinite topology, and I would like to add these redirects to Category:Topological spaces. However, given the discussion above concerning Category:Topological spaces and Category:Properties of topological spaces I thought I should ask before doing anything that might be seen as pouring oil into the fire. The article Cofiniteness itself is already in Category:General topology.

(There is an editing guideline at Wikipedia:Categorizing redirects concerning the categorization of redirects, and I think categorizing a redirect to a subsection of a larger article is covered by the section Subtopic categorization.)

— Tobias Bergemann (talk) 14:10, 9 February 2012 (UTC)

Ignoring the issue of redirects for the moment, I think there are three particular types of articles to look at:

1. Articles on particular topological spaces, for example the long line or the topologist's sine curve.
2. Articles about particular topologies, which could be put on different sets. For example, the discrete topology, the indiscrete topology, the Lawson topology
3. Articles about properties of a topological space. Examples include paracompactness, first countability, etc. The difference between this and #2 is that I cannot say "take a set and put the first countable topology on it" but I can say "take a set and put the discrete topology on it".

I think that these three types of articles generally belong in different categories. I'm not certain which those should be, or if the existing categories should be renamed. — Carl (CBM · talk) 15:17, 9 February 2012 (UTC)

I think cycle index needs expert attention

The article on cycle index confuses or elides the distinction between groups generally and permutation groups. Since cycle indices are properties of permutation groups, not of abstract groups, this renders it confusing, and possibly incorrect. I have put a more detailed complaint on the talk page. I hope someone more skilled in algebraic terminology can clean it up. —Mark Dominus (talk) 16:32, 10 February 2012 (UTC)

Looks like every group under scrutiny is a subgroup of the symmetries. If I were you I'd make a note in the intro to that effect, or tweak the major occurences that you found where "group" was unclearly used. Rschwieb (talk) 18:38, 10 February 2012 (UTC)

I have not check the details, but it seems that "group" is never used alone, always as "group of permutations". Thus there is no ambiguity, as "group of permutations" means "finite group acting on a finite set". Thus, in your example on the talk page, the two groups are isomorphic as groups, but are different as groups of permutations. Maybe it could be useful to recall in the lead that a group of permutations of degree n is a finite group acting on a set of n elements and that two isomorphic groups acting on two sets of different orders are not isomorphic as groups of permutations. D.Lazard (talk) 18:56, 10 February 2012 (UTC)

Is a function a rule or an association?

It depends on whether we want to enlighten or to obfuscate (see Talk:Function (mathematics)). Tkuvho (talk) 13:44, 12 February 2012 (UTC)

Fractal fraction

The mathematics article fractal fraction is up for deletion. Please comment at Wikipedia:Articles for deletion/Fractal fraction. — Arthur Rubin (talk) 17:57, 12 February 2012 (UTC)

Horocycle merged to horosphere

The article horocycle was recently merged to horosphere. I've undone this merger, but was quickly reverted. I'd appreciate outside input at Talk:Horosphere. Sławomir Biały (talk) 13:44, 13 February 2012 (UTC)

Surely one is just the one-dimensional specialisation of the other; or, alternatively, the other is a longstanding multidimensional generalisation of the first. Doesn't it make sense to treat both together? -- if not with horocycle under horosphere, then with horosphere under horocycle? Jheald (talk) 14:31, 13 February 2012 (UTC)

I am not so sure. Thus, the remark that the geometry of the horosphere is euclidean is not really significant for horocycles. The statement that a horocycle has geodesic curvature 1 cannot be made for horospheres, etc. Tkuvho (talk) 14:41, 13 February 2012 (UTC)

We have separate articles on circles and spheres. Surely this is the same distinction? —David Eppstein (talk) 16:12, 13 February 2012 (UTC)

Except that here the article seems to deal with general horo-n-spheres, so the distinction is perhaps different. We have n-sphere and circle, so I'm not saying there shouldn't be a separate article if enough material exists on it to justify this (though there is very little at the moment). — Quondum^☏✎ 17:22, 13 February 2012 (UTC)

There probably should be separate articles but seeing as how both are stubs and on related subjects it's not that surprising that an attempt was made to merge them. Our article on hypercycles is longer but apparently in need of more work, and I couldn't find anything on their higher dimensional analogs.--RDBury (talk) 21:01, 13 February 2012 (UTC)

I just found this discussion here. Circles, horocycles and hypercycles (generalized circles) are the 2D variants of generalized spheres (spheres, horospheres or hyperspheres) in Hyperbolic geometry (balls and disks are just the usual interiors). Actual descriptions vary by model and whether 2 or 3d but arise via the intersection of H^n with an affine plane (or an r-sphere as the intersection with an affine r+1 plane)88.82.206.110 (talk) 14:38, 18 February 2012 (UTC)Selfstudier (talk) 14:39, 18 February 2012 (UTC)

Is Correspondence (mathematics) a useful page?

I've just stumbled across the page Correspondence (mathematics). As well as being completely unsourced, it strikes me as a collection of things that really don't belong together—each definition could better be placed on the page for the appropriate topic. Also, the first definition contradicts the definition given at relation (mathematics). Links such as those from the first sentence of function (mathematics) to correspondence (mathematics) only serve to muddy the waters further. Does anyone see this page as worth keeping? Jowa fan (talk) 23:23, 13 February 2012 (UTC)

Maybe a bit slimmed down as a {{mathdab}}. But other articles should be linking to the articles listed at Correspondence (mathematics) rather than linking to Correspondence (mathematics) itself. —David Eppstein (talk) 23:35, 13 February 2012 (UTC)

BTW there is something like mathdab at ru:Отображение (значения) (Russian: Отображение = map). Other interlanguage links apparently correspond to map (mathematics) or are redirected, so the "article" is apparently a PoV fork. Incnis Mrsi (talk) 09:01, 14 February 2012 (UTC)

I see no contradiction between the first definition and the definition at binary relation that it refers to. It would be better I think to distribute the meanings and make it a proper disambiguation page I think, so yes the page would be slimmed down a bit. I see no evidence of any POV and don't know where that idea came from and the other interlanguage links do not support what is said as far a I can see. I wouldn't depend on how things are translated for very much anyway though I do like sometimes to look at other languages to get some ideas. Dmcq (talk) 09:23, 14 February 2012 (UTC)

The page Correspondence (mathematics) says correspondence is an alternative term for a relation between two sets, whereas binary relation says A correspondence: a binary relation that is both left-total and surjective. Jowa fan (talk) 11:32, 14 February 2012 (UTC)

I think the page should not be trimmed down. The many incarnations of correspondences all have something in common: "a point gets mapped to many points". A good article would make this clear. I have added two references. Jakob.scholbach (talk) 12:37, 14 February 2012 (UTC)

I wonder where the binary relation page got that definition of correspondence from. In page 1331 of Encyclopedic dictionary of Mathematics the definition of a correspondence is just any relation plus the two sets with no restriction about being left and right total. Dmcq (talk) 13:18, 14 February 2012 (UTC)

A recent change to function (mathematics) now defines a function as a correspondence. The discussion above is clear enough indication that the term is ambiguous, confusing, and unhelpful. The far better term "rule" is strongly supported by three editors but has met resistance on what seems like pedantic, if not bourbakist, grounds. Further input would be appreciated. Tkuvho (talk) 08:57, 15 February 2012 (UTC)

Well it would be if we can get a citation for the definition of correspondence in the article about binary relation. There's a citation in the article showing its use in function is perfectly correct and the dictionary entry I pointed to supports that as well. Dmcq (talk) 09:07, 15 February 2012 (UTC)

Tkuvho - the term "rule" will, for most people, imply a finite and deterministic rule or algorithm. As I expect you know, not every function can be defined by a finite rule, otherwise every function would be a computable function. The existance of incomputable functions is so fundamental that glossing over it in the article's lead would be a gross over-simplification. For me, the current opening sentence "In mathematics, a function is a correspondence that associates each input with exactly one output" strikes the right balance between accuracy, brevity and clarity. Gandalf61 (talk) 09:38, 15 February 2012 (UTC)

I responded at Talk:Function_(mathematics)#summary_of_correspondence_vs_rule. Tkuvho (talk) 07:48, 16 February 2012 (UTC)

In my opinion the debate follows that, in mathematics, "correspondence" has frequently its usual, non formal, English meaning, as in article function. But it may also have a technical meaning, subject to a formal definition, as in relation (mathematics). Thus I propose to modify the beginning of correspondence (mathematics) as

In mathematics and mathematical economics, correspondence may be used informally with its usual English meaning. It may also have a technical meaning subject to a formal definition.

• In the theory of relations, a correspondence is a relation between two sets, such that every element of each set is related to at least one element of the other.

(For the item, I have kept the definition of Relation (mathematics), but the item must be changed when the definition in Relation (mathematics) will change. D.Lazard (talk) 11:16, 15 February 2012 (UTC)

Have you a citation for that? I've put a citation needed into binary relation because as described above I found a dictionary giving something quite different - and which in fact works very well in the lead of function. I found no definition like the one in that article. Dmcq (talk) 19:15, 15 February 2012 (UTC)

No, I have no citation, but like you I am not sure that this definition is not OR. It is the reason of my comment in parentheses. My feeling is that this first item could be suppressed, the non formal meaning being sufficient for the definition of a function. D.Lazard (talk) 21:26, 15 February 2012 (UTC)

Proposed changes to mathematical categories

Good Olfactory (talk · contribs) has proposed renaming Category:Triangulation to Category:Triangulation (geometry). Discuss at Wikipedia:Categories for discussion/Log/2012 February 14. The same discussion page also contains a proposal to delete Category:Polyhedra rest category and merge it into its parent category. And there are also quite a few renames of mathematical categories proposed at Wikipedia:Categories for discussion/Speedy, e.g. Category:Logical symbols to Category:Logic symbols, Category:Tiling to Category:Tessellation, etc. —David Eppstein (talk) 22:50, 14 February 2012 (UTC)

Charles Wells (mathematician) at AfD

Charles Wells (mathematician) is up for deletion.  --Lambiam 02:44, 16 February 2012 (UTC)

External links at Tangram

There is a small dispute as to whether certain links should be included in the External links section. Additional opinions at Talk:Tangram#EL links removed will be appreciated.--RDBury (talk) 04:51, 17 February 2012 (UTC)

covering set

I always thought that covering set was another term for cover (topology). I was surprised that the covering set article is purely about a number-theoretic meaning. Now I'm not sure whether to add an xref. Can someone take a look? Thanks. 67.117.145.9 (talk) 04:03, 18 February 2012 (UTC)

It may also be confused with covering space. I have added a disambiguation hatnote in covering set. D.Lazard (talk) 08:16, 18 February 2012 (UTC)

Ayme's theorem

WP:OR? Michael Hardy (talk) 03:18, 19 February 2012 (UTC)

Yes. I'd be very skeptical of anything claimed to be a significant new result in Euclidean plane geometry, new and significant being pretty much mutually exclusive at this point in the history of the subject.--RDBury (talk) 05:13, 19 February 2012 (UTC).

Notability and secondary sources (lack thereof) could disqualify this for WP, regardless of "significance". Is there not some WP-related project for this kind of non-encyclopedic result where it does not have to adhere to quite the same criteria as for Wikipedia? It feels though there should be some middle ground between Youtube and Wikipedia. — Quondum^☏✎ 05:59, 19 February 2012 (UTC)

PlanetMath? Though in this case checking against the known centers in the Encyclopedia of Triangle Centers and, if unknown, adding it there looks appropriate. —David Eppstein (talk) 07:33, 19 February 2012 (UTC)

To RDBury. This result is certainly not significant. It is a special case of a general theorem which is certainly well known, even if I have never seen it explicitly written.

Theorem: Let ABC be a triangle. Let Sa, Sb, Sc (Ayme's notation) be three points constructed from the triangle. If these points are permuted by every permutation of A, B, C which leaves fixed the other choices implied by the construction, then the three lines ASa, BSb, and CSc are concurrent.

Proof: The matrix of the coefficients of the barycentric equations of the lines is antisymmetric, and thus has a null determinant.

It is thus easy to construct billions of similar theorems. D.Lazard (talk) 13:47, 19 February 2012 (UTC)

Ayme can post it up on ProofWiki himself, if he likes, and it will then probably (eventually) be categorised as an example of the aforementioned theorem on the coefficents of barycentric equations. But for once I'm in agreement: this is not significant enough for Wikipedia. --Matt Westwood 14:29, 19 February 2012 (UTC)

Conditional statement – a solution needed, not a smoldering edit war

At WP: Articles for deletion/Conditional statement (logic) I proposed to make a conceptdab article, but there was not any movement in this direction. Later, I asked help at WikiProject Logic, to be ignored. Now, at Conditional statement (logic) (edit | talk | history | links | watch | logs) users Artur Rubin and History2007 try to redirect this to material conditional, which I consider as inappropriate. On the other hand, Hanlon1755 (talk · contribs) pushes his own ideas about what is logical condition. Please, help to put the end to redirects' jumble and make a valid disambiguation of the term "conditional" in logic, programming and linguistics. Preferably, as a WP:CONCEPTDAB article. Incnis Mrsi (talk) 13:21, 14 February 2012 (UTC)

The dab page you refer to exists at Conditional statement. -- 202.124.72.200 (talk) 10:19, 15 February 2012 (UTC)

I could, although reluctantly, remember one (static) IP address, but it is not polite to prompt Wikipedia users to waste time for whois and reverse DNS queries and comparisons of persistently changing IPs. Please, register yourself; this is the last time I reply to an IP posting from this ISP. Incnis Mrsi (talk) 18:18, 15 February 2012 (UTC)

---

The war progressed for another 5 days. Now I self-proclaimed a mediation at Talk:Conditional statement (logic)#Conditions for acceptable solution and ask the WikiProject for support. Please, provide an explicit output. Don't give just a silent agreement, because warriors can disrespect my self-imposed conditions. Please, express some will to end the edit war even if the cause and exact conditions seems not so important. Incnis Mrsi (talk) 09:02, 20 February 2012 (UTC)

manifold destiny

There is a discussion at Talk:Manifold Destiny#Birman of Joan Birman's comments concerning Yau. My personal opinion is that the comment is not only incorrect but borders on slanderous, and should not be included. Tkuvho (talk) 07:59, 20 February 2012 (UTC)

An editor thinks it's censhorship here. Please comment. Tkuvho (talk) 12:38, 22 February 2012 (UTC)

Euler Archive

I was trying to track down a reference for the article on Euler's criterion when I found this: http://www.math.dartmouth.edu/~euler/

Is there a special convention or template for citing it?

Virginia-American (talk) 21:51, 21 February 2012 (UTC)

I don't think there is so just use the cite-web template or use cite-book with the url.--RDBury (talk) 23:22, 22 February 2012 (UTC)

Category move proposals

Wikipedia:Categories_for_discussion/Log/2012_February_15

There are four proposals to move categories in the logic department. I think some people who have actually done some study on the subject should take a look. Please do drop in. Greg Bard (talk) 02:19, 22 February 2012 (UTC)

Actually I agree with Greg Bard on not renaming these but haven't any real stake in the matter. I'd probably rename logical syntax to logic syntax rather than using parenthesis and logic symbol instead of logical symbol makes me think of drag and dropping a symbol in designing a circuit. Dmcq (talk) 13:03, 22 February 2012 (UTC)

Interviews about categories

When I saw this Wikipedia:Village pump (miscellaneous)#University research project on categories seeks interviewees I immediately thought of this project.Can't for the life of me say why ;-) Dmcq (talk) 17:57, 22 February 2012 (UTC)

Some extra eyes on matrix (mathematics)

A known problematic editor has set his sights on matrix (mathematics). I have no intention of further engaging with this particular editor. It would be helpful if some project members could keep an eye.TR 07:34, 21 February 2012 (UTC)

Upon being extended an invitation to edit cooperatively to address the concerns we raised, he gave up. This suggests the user was not interested in anything short of the reinstatement of the deleted text. The same tactic might shorten future skirmishes with the same user. Rschwieb (talk) 14:09, 24 February 2012 (UTC)

Merge help

Please discuss and do the merge at Talk:Arithmetic complexity of the discrete Fourier transform. I don't understand this math at all and can't do it myself. D O N D E groovily Talk to me 04:29, 22 February 2012 (UTC)

Solved by redirecting to Arithmetic_complexity_of_the_discrete_Fourier_transform#Bounds_on_complexity_and_operation_counts where one may find the relevant content of this page. The remainder of the page consisted in awful formulas lacking of any explanation, which have not their place in Wikipedia. D.Lazard (talk) 16:03, 24 February 2012 (UTC)

EoM again

I saw that there was an old thread about the Encyclopedia of Mathematics and its new wiki form at http://www.encyclopediaofmath.org. Of the points raised, I'm much the most concerned about the broken links, at present. Do we have a plan of action for fixing them? And, if we can decide about how that could be sorted out, where are we on MathJax or indeed any long-term solution for formulae? Charles Matthews (talk) 16:33, 22 February 2012 (UTC)

On the first issue, afaik there is no concerted effort but I hope people are fixing the broken links when they find them. There are probably more articles where there should be a link to EoM but there is none, broken or not. It seems like one of those tasks that seem like a good idea in principle but are too tedious to garner volunteers to actually get them done.--RDBury (talk) 23:38, 22 February 2012 (UTC)

From experience, this is rather boring and time-consuming. I have already suggested the following patch: a script that looks for eom links with id of the form ?/*, and replaces the id with the title field (space -> underscore). Of course, this can be only semi-automatic (although theoretically the script can also ping the page to check that it exists). Script experts, is this a feasible task? Sasha (talk) 02:01, 23 February 2012 (UTC)

Someone please do this! Sławomir Biały (talk) 13:11, 23 February 2012 (UTC)

Didn't we have a template for EoM?--Kmhkmh (talk) 14:25, 24 February 2012 (UTC)

the issue is as follows. EoM (later renamed springer, and later, SpringerEOM) is a template for EOM. However, the encyclopaedia changed its format a few months ago. Therefore the old links no longer work. The template itself has been fixed; what we are discussing is a way to fix the links (more precisely, change the "id" field from the format A/123456 to the new format Abc_equation). Sasha (talk) 15:26, 24 February 2012 (UTC)

There are 746 transclusions of the template {{SpringerEOM}} to fix. Bulk edit like this are probably done by a semi-automatic tool like WP:AWB.--Salix (talk): 16:42, 24 February 2012 (UTC)

how complicated is it? Does AWB have a ping option? Sasha (talk) 17:02, 24 February 2012 (UTC)

It fairly simple. You need to run it from windows and you start it by giving a list of files you want to edit, its smart enough to find out all the pages which transclude {{SpringerEOM}}. It then goes through the pages 1 by 1 and it can do some substitutions and allow you to adjust the edit. You need to OK each edit. You can go through many pages quickly about 4 a minute.--Salix (talk): 17:49, 24 February 2012 (UTC)

The news from the External link finder is actually not that bad. Just now there were 368 hits: but I took out those not from actual articles, and the number came down to 178. And some of those are multiple uses of the same link. So this could get done, I suggest. Charles Matthews (talk) 22:02, 24 February 2012 (UTC)

(this probably has to do mainly with my stupidity, but) I had trouble using the AWB regexp (and I did not find anything similar to a ping feature). If someone volunteers to post a working AWB script here, I am ready to share the load of running it. Sasha (talk) 22:14, 24 February 2012 (UTC)

You might not be registered to use it, see the AWB page for detail of registration.--Salix (talk): 14:31, 27 February 2012 (UTC)

I've made a simple converter[[5]] which can take the citation from the bottom of the springer page and produces the complete template with parameter for our reference. --Salix (talk): 14:31, 27 February 2012 (UTC)

thanks! (actually, I am AWB-registered, the problem was indeed with my stupidity). Sasha (talk) 15:58, 27 February 2012 (UTC)

Where did "labelled enumeration theorem" go?

The page symbolic combinatorics contains several redlinks to labelled enumeration theorem. It looks like the latter page existed in 2009, since it has been copied at http://citizendia.org/Labelled_enumeration_theorem, but I can't find a deletion discussion for it. Does anyone know what happened here? Jowa fan (talk) 03:51, 23 February 2012 (UTC)

The deletion log of labelled enumeration theorem says "Expired PROD, concern was: this is unsourced junk". PROD's don't have deletion discussions. Follow the link to see how they work. As an administrator I can see the deleted page history. It was prodded with "this is unsourced junk" in 2010 by User:Zahlentheorie who had created the article in 2006. PrimeHunter (talk) 04:04, 23 February 2012 (UTC)

From a brief look at the citizendia version it appears to be a variation on the Polya enumeration theorem. But is it an known theorem with a made up name, original research, or just junk? In retrospect an AfD might have been useful to determine which.--RDBury (talk) 23:15, 23 February 2012 (UTC)

I restored the article so that everyone can look at the content. I recommend adding additional references if the article is kept, to demonstrate that the topic passes the inclusion/notability criteria. This is just a pro forma undeletion, I have no opinion about whether the article should be deleted again. — Carl (CBM · talk) 16:43, 24 February 2012 (UTC)

Just browsing around and following some links, I just noticed that Proofs involving the totient function was PROD-ded in July 2010 ("concern was: wikipedia is not a directory of proofs, but rather of theorems"), while under its old title Totient function/Proofs it was AfD-ded in 2007 : Wikipedia:Articles for deletion/Totient function/Proofs and the result was Keep. Maybe some events I did not notice took place between 2007 and 2010, but might it not be a similar dubious Prod-ding ? French Tourist (talk) 09:45, 25 February 2012 (UTC)

A few minutes later, I notice the strange Wikipedia_talk:WikiProject_Mathematics/Archive_51#Strangest_edit_war_I.27ve_ever_seen. Might it be related with this PROD-ding ? French Tourist (talk) 10:03, 25 February 2012 (UTC)

There is a no double jeopardy for PRODs, see Wikipedia:Proposed deletion#Nominating under 'Before nomination'. So technically the PROD was improper, not that I'd request that it be restored.--RDBury (talk) 15:35, 25 February 2012 (UTC)

Proofs by Dooooot

I don't think any of these "proofs" should be given, for the following reasons:

1. Almost all of the rules for which he provides a "proof" are considered primitive rules in some system
2. The selection of rules used seems arbitrary, and needs a source
3. The proofs do not fall under WP:CALC, so they need sources.

— Arthur Rubin (talk) 03:42, 25 February 2012 (UTC)

You didn't specify which proofs, but I assume one of them is the one given in Hypothetical syllogism. In that case at least I agree and I'd question whether is it encyclopedic as well, generally if the proof is easy enough to assign as an exercise then we don't need to have it here. Another issue is that proofs should be in prose, not a table of symbols. Also, turquoise? This might be raised at the logic project as well.--RDBury (talk) 08:06, 25 February 2012 (UTC)

There's other wikis that go in for that sort of stuff. Proofs here should be either short and unobtrusive or have some element of notability in the literature. I don't think Wikipedia should become a repository for every proof in Mizar for example, they should refer to a source for this sort of thing. Dmcq (talk) 09:42, 25 February 2012 (UTC)

More to the point, you can't provide a proof of particularly this sort of PropLog theorem without first stating exactly which axioms you are working from. In order for the HS proof to be of any worth at all, at least one ought to allow Modus Ponendo Ponens as an axiom (or previously proved). Instead a great pile of other theorems (Transposition, Constructive Dilemma, etc.) are used instead, making this ridiculously overcomplicated. Besides, it uses LEM which unnecessarily removes it from the domain of constructivist proofs. So this proof is IMO seriously unworthy of WP. If all the rest of this user's proofs are like that, then I concur. --Matt Westwood 07:56, 26 February 2012 (UTC)

Oh, and even more to the point, the proofs are circular. To prove absorbtion, conjunction is used. To prove conjunction, absorption is used. As proofs go, these are complete and utter piffle.

Aha, I just see someone's already made that point below. --Matt Westwood 08:00, 26 February 2012 (UTC)

(ec) I was referring to the ones he seems so proud of at User:Dooooot#Proofs I've Written, although there may be others. WikiBooks and WikiVersity (if it's still open) seem better venues. — Arthur Rubin (talk) 09:56, 25 February 2012 (UTC)

Yes they seem reasonable places for someone who wants to go in for this sort of thing. Dmcq (talk) 10:16, 25 February 2012 (UTC)

More to the point, my guess is that the "proofs" are formally invalid, because they confuse levels of the system, normally kept separate by using distinct symbols, e.g. ⊢ versus →. If the "proofs" were valid, we'd call them "theorems of inference". — Quondum^☏✎ 10:39, 25 February 2012 (UTC)

I notice a certain circularity: Modus ponens is used to "prove" Disjunctive syllogism and vice versa. — Quondum^☏✎ 11:18, 25 February 2012 (UTC)

I don't think we should have "proofs" of these rules. I would not object to a truth table in some cases, though. Sławomir Biały (talk) 14:23, 25 February 2012 (UTC)

It does seem a bit funny to prove the inference rule modus ponens. Dmcq (talk) 14:29, 25 February 2012 (UTC)

Such "proof" as Hypothetical syllogism#Proof unlikely is useful, but is misleading in its use of negation and equivalences valid in classical logic only. If you did not get yet why is it incorrect, I resort to the analogy with algebra. Consider an identity $2x^{2}+2(x+1)^{2}=(2x+1)^{2}+1$ and a proof deriving it from $(a+b)^{2}+(a-b)^{2}=2a^{2}+2b^{2}$:

$2x^{2}+2(x+1)^{2}=2((x+{\frac {1}{2}}-{\frac {1}{2}})^{2}+(x+{\frac {1}{2}}+{\frac {1}{2}})^{2})=4((x+{\frac {1}{2}})^{2}+{\frac {1}{4}})=(2(x+{\frac {1}{2}}))^{2}+1=(2x+1)^{2}+1$

Yes, a proof is valid for real, complex and rational numbers, but it is invalid for any field of characteristic 2 (there is no such number as ½) and it is inapplicable to unital rings (because there is no division at all), although the identity still holds. The "universally correct" proof should be:

$2x^{2}+2(x+1)^{2}=4x^{2}+4x+2=(4x^{2}+4x+1)+1=(2x+1)^{2}+1$

I am convinced that a proof may be useful only if it is valid in the most strict theory where a statement in question is a theorem. Incnis Mrsi (talk) 16:54, 25 February 2012 (UTC)

I think a lot of what you're saying is covered in point 2 in the original post. In general it's one of the pitfalls of doing proofs in an encyclopedia rather than than a text book that you don't get to formally establish which axioms are being used and which theorems are "known" and can be used without raising questions of circularity. In many cases you can make reasonable assumptions as to what should be considered common knowledge for the purposes of a proof, but for symbolic logic there are many equivalent formulations of the axioms and rules of inference and having a proof without knowing which formulation is being used doesn't make much sense. In fact in most of these cases the proposition may just as easily be taken as a axiom so giving a proof is unnecessary. I like the idea above of using truth tables as justification rather than formal proofs, they should be enough to convince casual readers, who probably compose a large segment of our readers anyway. Truth tables would be especially useful in cases where the result may be counterintuitive, $\neg p\to (p\to q)$ for example.--RDBury (talk) 04:53, 26 February 2012 (UTC)

If one still did not get the point, I repeat: the problem with some concrete formula, which Wikipedia attempts to present as a theorem (logical one, algebraic or else), is not only in an arbitrary selection of rules (Arthur Rubin) or even axioms. The problem is that Wikipedia, unlike a textbook, must obey WP:NPOV, which means that a description of P→Q, Q→R ⊧ P→R from classical PoV without mentioning other propositional calculi contradicts to the Wikipedia policy. On the other hand, I do not see a grave heresy in proofs of axioms and unordered graphs of proofs. I know what is circulus vitiosus, but if the article on the "axiom" C′ says A, B, C ⊢ C′ and the one about C says A, B, C′ ⊢ C, this does not mean a logical flaw, but only equivalence of {A, B, C} and {A, B, C′}. Incnis Mrsi (talk) 07:57, 26 February 2012 (UTC)

The proofs should be allowed, with qualifying language. Any given proof isn't "the" proof but rather "a" proof. I do understand Rubin's points though. Even the transformation rules template gives a particular set of rules. However, that isn't intended to represent any particular system, but rather gives common rules used in various systems. At some point I think this kind of information (i.e. Dooot) is expected in a comprehensive encyclopedia article on particular rules of inference. Greg Bard (talk) 19:25, 26 February 2012 (UTC)

I think they need to be cited or deleted. If there really is some sort of subtle problem introduced by a logic aficianado, it would be fuel for confusion. Secondly, has anyone figured out why there are two "proofs" here? To all appearances the second seems like a less efficient duplicate of the first. Rschwieb (talk) 20:53, 27 February 2012 (UTC)

Projective range

I came up on the page Projective range. It lacks of a formal definition that I can understand. Should it be expanded or deleted? D.Lazard (talk) 22:47, 26 February 2012 (UTC)

This is standard classical terminology in projective geometry. Several collections of specially related objects are referred to as pencils (a pencil of lines through a point in a plane, a pencil of hyperplanes through a codimension 2 space, a pencil of conics, etc.). In all these cases the dual concept to a pencil is called a range. The page in question is certainly not well written and lacks clarity, but I would say that it needs to be expanded rather than deleted. I don't see myself doing that for at least a couple of weeks. An alternative might be a merge into Duality (projective geometry), where the originator of Projective range has placed an out of context sentence containing a link to the new page. Bill Cherowitzo (talk) 06:06, 27 February 2012 (UTC)

My understanding is that the generic term is "projective form" which would include projective pencils, projective sheaves, etc. So I'd suggest changing the name covering all of these in the article.--RDBury (talk) 07:15, 27 February 2012 (UTC)

Proposing stubs: Zero algebra, Trivial algebra, Flexible algebra

The following "trivial" or "uninteresting" cases seem to have encyclopedic value at least inasmuch as they provide clarity for someone seeking to understand their status. Unlike a field with one element, they appear to be uncontrovertial:

• Zero algebra is used to mean an algebra over a field (or ring) in which the product is given by the map a × b ↦ 0. These are usually uninteresting, but appear to be mentioned in some sources. I imagine it sees use in the classification of algebras.
• Trivial algebra is an algebra over a set of one element (see nLab, mentioned in Quasivariety). It is a category covering several cases such as singleton set, trivial group and trivial ring.
• Trivial algebra over a field (or ring) is an obvious example of a trivial algebra, on par with trivial group and trivial ring. It would seem appropriate for completeness, but I've not seen reference to this specifically.

I've come across another term in a few places and papers, enough to warrant a stub:

• Flexible algebra, defined as an algebra with the property (ab)a = a(ba) for all a and b. (See Planetmath.)

Any opinions on the creation of these stubs? — Quondum^☏✎ 07:21, 27 February 2012 (UTC)

In general I'd oppose creating a stub unless there is reasonable expectation that the article can be expanded beyond that or it would awkward to put the material in another article. For example for zero algebra I's suggest adding it as section of Algebra over a field, then creating a redirect to that section. It would be reasonable to include the zero algebra there anyway as an example. The fact that articles for similar objects should not carry any weight here, see WP:OTHERSTUFF.--RDBury (talk) 09:42, 27 February 2012 (UTC)

Some comments about "zero algebra": There are two notions of zero algebra. The non unital one that you consider, which is, in fact, another name for "module", and the unital one which is the direct sum of the basis ring and a module, with null product for two elements of the module. This is not an "uninteresting" notion, at it allows frequently to extend straightforwardly to modules and submodules some notions which are primarily defined for rings and ideals. For example, this allows, not only to extend the theory of Gröbner bases to modules and submodules, but also to use for submodules any implementation of a Gröbner basis algorithm for ideals. Thus the question is what is the right place for "zero algebra", in module (mathematics) or in algebra (ring theory) or in both. D.Lazard (talk) 10:38, 27 February 2012 (UTC)

Thanks for the input. I have followed RDBury's guideline and avoided stubs (and not even created redirects), but inserted sections for zero algebra in Algebra over a field#Kinds of algebras and examples and a point on flexible algebras in Algebra over a field#Non-associative algebras. I am having difficulty reconciling an algebra with an identically zero product with a module, so I'm leaving that as beyond my present understanding. The rest I've left alone. — Quondum^☏✎ 15:24, 27 February 2012 (UTC)

I came too late for "zero algebra", but put in my 5коп for "trivial algebra". In Wikipedia, it may be referred as a "trivial algebra", although such link lies on the edge of WP:EGG. Zero-dimensional space just has no dimensions at all. Any possible linear structure is not relevant, because may be either trivial or not existent. Incnis Mrsi (talk) 15:50, 27 February 2012 (UTC)

Got wrong, not yet and probably not such. I expected an article about 0d linear space, but it is about a topological one. Something to be disambiguated and fixed. Incnis Mrsi (talk) 15:57, 27 February 2012 (UTC)

Now all is in order, trivial algebra is linkable. By the way, I discovered and fixed a severe mistake. One user thought that "trivial module" is something like "zero algebra" from this topic, which is (according to MathWorld) not true. All three 0-dimensional algebraic entities are now in one article. Incnis Mrsi (talk) 16:47, 27 February 2012 (UTC)

It's probably not so much a severe mistake as it is a difference in convention. A google search immediately returns several instances of "trivial module" meaning any module for which mr=0 for any choice of elements m in the module, r in the ring. Both the concept you put in and this one are "trivial" in some sense so it is natural different people use them different ways. I think we should modify it a bit to reflect this, as is done with zero/trivial ring. It's a little arbitrary to declare one sense correct, here. It only perpetuates the confusion of usage. Rschwieb (talk) 18:06, 27 February 2012 (UTC)

So, I can propose to rename it to zero space to wipe an ambiguity out ultimately. This name has an advantage to omit mentioning of a ground object (either a ring or a field). Happily, I have a technical possibility to kick the current redirect off. Certainly, if there was no objections here to this move. Incnis Mrsi (talk) 18:35, 27 February 2012 (UTC)

I think renaming should depend on which usage dominates. If the trivial product version mr=0 usage is in the minority, I would suggest keeping the name as is, but mention this as an alternative interpretation of the term within the article. Technically, a zero vector space is still over a base ring/field, and thus does not really get rid of mentioning which. One could just as easily omit this mention in the case of a trivial algebra/module. — Quondum^☏✎ 18:54, 27 February 2012 (UTC)

Yes, I agree, it should be based on which usage is predominant among workers in the field. Not being one of them, I'm not sure which one that would be. But I want to urge very strongly that the decision not be based on MathWorld. MW has some uses, but a reliable source for nomenclature it is not. --Trovatore (talk) 00:17, 28 February 2012 (UTC)

Okay, I see how the unital zero algebra works. I generally don't know what is meant by "direct sum", since its meanings can be so different. This would imply that dual numbers constitute a unital zero algebra over the reals. Thanks for the assistance. — Quondum^☏✎ 17:46, 27 February 2012 (UTC)

Exactly, the dual numbers are the unital zero algebra build up from a real vector space of dimension one. I'll add this example in algebra over a field. D.Lazard (talk) 19:00, 27 February 2012 (UTC)

Jean-Claude Sikorav

Jean-Claude Sikorav is a new article by Tkuvho, which will probably soon be listed on AfD. Comments/improvements are welcome. Sasha (talk) 19:52, 27 February 2012 (UTC)

It has just been the topic of a somehow frantic (and sometimes badly informed) deletion review on :fr (the result was "Keep"). The article had been created there by a group of two juvenile students of École Normale Supérieure de Lyon, where JCS teaches, and I am not yet sure whether they were serious or if they were playing a funny joke with Wikipedia. You can have a look at the (quite unhealthy) debate at fr:Discussion:Jean-Claude Sikorav/Suppression. French Tourist (talk) 21:17, 27 February 2012 (UTC)

I agree that, unless there is some clearer sign that the article passes WP:PROF, it is likely to be a subject of a deletion discussion, particularly because it was already deleted once under CSD and undeleted by me. My undeletion was only to give more time to add content. I think the current content of the article does not make for a clear case that the notability guidelines are satisfied. — Carl (CBM · talk) 22:18, 27 February 2012 (UTC)

I think the citations in Google scholar and the award are enough that he would probably pass an AfD. (I'm not convinced that calling out the citation count explicitly within the article is a good idea, though.) —David Eppstein (talk) 23:33, 27 February 2012 (UTC)

Category:Theorems in number theory

Are there any suggestions of subcategories for this category in order to improve the usefulness of this category? At the moment there is around 80 articles in it which may be daunting to somebody looking through the theorems of number theory or maybe not. At the moment there are a few subcats; a couple which are more specific branches of number theory and another relating to the prime numbers, but perhaps there are more that could be added for ease of the user. Perhaps related - where does number theory and algebraic geometry intersect? Brad7777 (talk) 00:45, 28 February 2012 (UTC)

I would suggest "theorems in additive number theory", "theorems in the geometry of numbers", and "theorems on discrepancy" (or perhaps "theorems on equidistribution", a subcat of "theorems in analytic nt") -- if we can populate them in a reasonable way. Also, many of the theorems now in "theorems in number theory" can be moved to either algebraic or analytic n.t. (e.g. Mordell-Weil -> algebraic n.t., Turan-Kubilius -> analytic n.t., ...) Sasha (talk) 05:29, 28 February 2012 (UTC)

Maths rating template name

There is a suggestion at Template talk:Maths rating to rename the template. — Carl (CBM · talk) 11:56, 28 February 2012 (UTC)

Administrator requested

Wikipedia:Sockpuppet investigations/119.154.67.223 notes disruptive editing by three neighboring IPs.

Blocks for disruptive editing are warranted, regardless of the SPI issue.  Kiefer.Wolfowitz 12:12, 28 February 2012 (UTC)

Make that FOUR neighboring IPs.

Please help relieve poor Melcombe from vandal fighting against this Lahore-based terminator/Energizer Bunny from hell.  Kiefer.Wolfowitz 12:18, 28 February 2012 (UTC)

There seems to be about 8 users from this Lahore prefix, perhaps one of whom is not a disruptive editor.

Please protect the pages mathematician, statistics, etc. from IP editors.  Kiefer.Wolfowitz 12:21, 28 February 2012 (UTC)

It looks like the changes are being reverted OK at the moment, and there is some presumption against protection as long as reverts are effective. But, if the problem grows particularly large or particularly long-lived, contact me and I can protect the pages. — Carl (CBM · talk) 14:25, 28 February 2012 (UTC)

{{Maths rating}}

template:Maths rating is under discussion, please see template talk:Maths rating

70.24.251.71 (talk) 05:35, 29 February 2012 (UTC)