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{{WikiProject Mathematics archive list}}

===Wikibook proposal===

Since the purpose of the article originally started by StuRat was in part didactic, how about farming it out as a wikibook?  There is still the historical question of the relation of Boole's algebra to the different entity called Boolean algebra to be sorted out, and yet another new article housed at BL might be the best place to do this.  The new article can then comment on the non-mathematical aspects of cultural usage that originalyy prompted StuRat to write his text, and the genuinely encyclopediac contribution of the BL article can still be accomodated in the BA article. --- [[User:Chalst|Charles Stewart]] 18:57, 1 November 2005 (UTC)

:I have no objection to there being a WikiBook on either, or both, the current [[Boolean logic]] content and the current [[Boolean algebra]] content.  However, if this is to be used as a justification for deleting either article, in whole or in part, from WikiPedia, I am strongly opposed to that.  [[User:StuRat|StuRat]] 19:07, 1 November 2005 (UTC)

::The new article would not be based on your article, but it would be non-PhD-level and it would document what non-algebraists get out of the mathematics.  I don't think that a compelling case for en.wikipedia to host an introduction to BAs for people who don't want to learn algebra has ever been made, if that is the deletion that my proposal makes that you object to. --- [[User:Chalst|Charles Stewart]] 19:11, 1 November 2005 (UTC)

:::The basics of set theory are taught well before algebra in school.  For example, an episode of the [http://pbskids.org/ PBS kids] (ages 7-11) math show [http://pbskids.org/cyberchase/ Cyberchase] contained an introduction to set theory including Venn diagrams.  Any assumption that elementary set theory, and the Boolean logic operations based on it, requires advanced algebra, is therefore faulty. [[User:StuRat|StuRat]] 19:40, 1 November 2005 (UTC)

::I don't see the relevance of your remark to mine. --- [[User:Chalst|Charles Stewart]] 20:17, 1 November 2005 (UTC)

:::I was responding to the statement "I don't think that a compelling case for en.wikipedia to host an introduction to BAs for people who don't want to learn algebra has ever been made...", which seems to be saying that a knowledge of algebra should be required to understand the introduction sections.  My point is that the introductory level material can be made without the use of algebra, and that such material can be added later. [[User:StuRat|StuRat]] 20:55, 1 November 2005 (UTC)

::I made no such claim.  WP articles on topics of broad interest should be accessible, even if the article should contain material that is not generally accessible.  Wikibooks is the place for tutorials, see [[WP:NOT]], point 8 of '''Wikipedia is not an indiscriminate collection of information''', which is what "an introduction to BAs for people who don't want to learn algebra" would be.  What is at stake in hosting such an introduction here rather than there?  I see no point of principle at play here besides the one about following policy.  --- [[User:Chalst|Charles Stewart]] 15:38, 2 November 2005 (UTC)

:::Your statement that "WP articles '''on topics of broad interest''' should be accessible..." seems to imply that you don't think that we should have the goal of making '''all''' articles accessible.  I disagree, and think that all articles should be made accessible to the broadest audience possible. Removing info from Wikipedia makes it considerable less likely to be found and thus less accessible. [[User:StuRat|StuRat]] 15:56, 2 November 2005 (UTC)

::I believe that there are articles for which it is not very important to spend much time thinking about the general reader, but instead most effort should be directed at the specialist.  As you are aware, I've been citing [[analytic continuation]] as an example of this for some time.  --- [[User:Chalst|Charles Stewart]] 19:12, 2 November 2005 (UTC)

I don't think suggesting a wikibook is helpful. What is in wikibooks and what is here is in no way related.--[[User:MarSch|MarSch]] 18:31, 2 November 2005 (UTC)

:Are you disputing the policy?  Are you aware that both WP and Wikibooks are both hosted by and reflect the values of the Wikimedia Foundation? --- [[User:Chalst|Charles Stewart]] 19:12, 2 November 2005 (UTC)

::I believe [[User:MarSch|MarSch]] means the same thing as me, that while adding a WikiBook on any topic is a worthy goal, to use that as a justification for deleting material from WikiPedia, if that is your intent, is not at all helpful. [[User:StuRat|StuRat]] 20:00, 2 November 2005 (UTC)

== Issues with the real numbers ==

See [[Talk:Mathematical analysis#Mathematical.2FReal Analysis]]. A fellow is having problems with the modern defintion of real numbers (among other things). He/she says "infinitesimals exist". My reply would be that the real numbers are defined by axioms, and it follows from those axioms that there are no infinitesimals. It would be good however to have more in-depth comments than that on that talk page.  [[User:Oleg Alexandrov|Oleg Alexandrov]] ([[User talk:Oleg Alexandrov|talk]]) 11:22, 29 October 2005 (UTC)
:I would take the reals to be defined in terms of other things rather than axiomatized, but the answer comes out the same: "this is what we're talking about; talk about whatever you like, but don't call it the reals". At a cursory glance it looks like you're arguing with a crank over there. The best way to do that is not to; since he seems to have given up, I'd just let it go. --[[User:Trovatore|Trovatore]] 19:49, 1 November 2005 (UTC)

::Infinitessimals exist, John Conway does a marvelous and fun construction in "On Numbers and Games". Although they exist in between real numbers, they're not exactly "numbers" themselves, though. I've always wondered if its possible to do some sort of calculus with them, e.g. treat them as some sort of fiber bundle or something over the reals, and get something other than trivial results.  No idea.  [[User:Linas|linas]] 16:04, 3 November 2005 (UTC)

:::WHat about [[non-standard analysis]]? --[[User:MarSch|MarSch]] 16:57, 3 November 2005 (UTC)
:::and [[Non-standard calculus]]? --[[User:MarSch|MarSch]] 17:06, 3 November 2005 (UTC)
::::J.H. Conway's surreals and NSA's hyperreals are both interesting structures (or classes of structures in the case of the hyperreals; there are nonisomorphic structures that fit the description). But they aren't the reals. Considerations involving them may tell us things ''about'' the reals, but they aren't the reals. Sorry to use baby talk; I imagine that both of you ''know'' these things--I'm just listing the points that can't be fudged when presenting the material to naive readers, or when having a discussion with a crank (if the latter is adjudged necessary). --[[User:Trovatore|Trovatore]] 17:10, 3 November 2005 (UTC)

::::: The infinitesimals are not real, and they are not imaginary either. Gosh, what's left then? [[User:Oleg Alexandrov|Oleg Alexandrov]] ([[User talk:Oleg Alexandrov|talk]]) 17:45, 3 November 2005 (UTC)

:::::: My professor in introductory calculus would occasionally refer to indeterminate forms, infinities, and infinitesimals as "Christmas trees". Actually quite a good way to stop you from carelessly using them as regular numbers. [[User:Fredrik|Fredrik]] | [[User talk:Fredrik|talk]] 18:01, 3 November 2005 (UTC)

:::: It's worth amplifying on [[non-standard analysis]], though I think the original discussion was at a much lower level of sophistication. Suppose we lay out a system of axioms for the reals, then look around for possible models that satisfy those axioms. A standard model includes just what we expect and no more. A non-standard model — which supports the same set of theorems — can exist and have extra goodies like infinities and infinitesimals. To put the extra goodies to work requires careful distinctions. Another tactic is to use [[topos]] theory and the different logics that allows. In this way we get a somewhat different version of infinitesimals such as those discussed in smooth infinitesimal analysis [http://publish.uwo.ca/~jbell/invitation%20to%20SIA.pdf] (PDF). A limited number of mathematicians enjoy these foundational games; many more seem to take the attitude "go away, we're trying to get work done here". But then, I remember hearing some insist that category theory was a waste of time, on the one hand; and I've seen topos logic [http://publish.uwo.ca/~jbell/catlogprime.pdf] (PDF) [http://historical.library.cornell.edu/cgi-bin/cul.math/docviewer?did=Gold010&seq=3&frames=0&view=50] [http://www.cwru.edu/artsci/math/wells/pub/ttt.html] put to serious work in the semantics of programming languages, on the other hand. I feel it's a delicate topic, because while I'm in the camp that enjoys foundational explorations, I'm painfully aware that most of the people who raise questions on Wikipedia about infinities and infinitesimals are clueless cranks. Too often the cranks are able to get some leverage because of loose writing, acceptable for informal mathematical discussion but not careful enough to stave off false interpretations. It's a difficult discipline, should one choose to accept it. For thousands of years mathematics progressed with stronger intuition than foundation, and I suspect that even though we're taught we ''should'' respect foundations today, many still just pay lip service. And for good reason: if we have to dot every "i" and cross every "t" any time we speak, we'll be tongue-tied. --[[User:KSmrq|KSmrq]]<sup>[[User talk:KSmrq|T]]</sup> 20:31, 3 November 2005 (UTC)

== Parameterize ==

During the travails of my spellbot, I got the following comment:

:It turns out that both "parameterize" and "parametrize" (the bot's spelling) are very common; M-W lists both. I learned the first version somewhere back in the mists of time and only found out just now of this variant. I was actually surprised to see that in many of my books also use the second version, and I never noticed... (incidentally the bot also corrected a "parameterise" to "parametrise", too. Yay for bots that also know British spelling :-) [[User:Choni|Choni]] 13:06, 29 October 2005 (UTC)

Makes me really wonder, is it indeed correct/widespread to use "parameterize" (one extra "e") as synonymous with "parametrize"? I never encountered the former, even though it would make sense as it all comes from "parameter". Thanks. [[User:Oleg Alexandrov|Oleg Alexandrov]] ([[User talk:Oleg Alexandrov|talk]]) 13:15, 29 October 2005 (UTC)

:I am only familiar with the former version.  It seems more natural, being closer to the root word, as well. [[User:StuRat|StuRat]] 23:55, 31 October 2005 (UTC)

: [http://www.bartleby.com/61/16/P0061650.html American Heritage] seems happy with both, nodding slightly towards including the "e". That agrees with my practice when writing or proofreading: either is fine. It might be nice if an article was at least self-consistent, but frankly I doubt many readers would notice. In contrast, "parametric" does not allow an extra "e". --[[User:KSmrq|KSmrq]]<sup>[[User talk:KSmrq|T]]</sup> 00:11, 1 November 2005 (UTC)

:: Of the four permutations, the only one that looks really wrong to me is "parametrise". I think british and american speakers actually ''pronounce'' the word slightly differently. (I'm an Australian speaker.) Reminds me of aluminium vs aluminum. [[User:Dmharvey|Dmharvey]] [[Image:User_dmharvey_sig.png]] [[User talk:Dmharvey|Talk]] 00:14, 1 November 2005 (UTC)

:::I think aluminium is what is used in most languages. Therefore I prefer to use it also in English. --[[User:MarSch|MarSch]] 12:45, 1 November 2005 (UTC)

:::The situation is a bit different, because in the case of Aluminium, there is actually an international standard that specifies the official name as "Aluminium", and not "Aluminum".  See for example [http://www.iupac.org/reports/periodic_table/IUPAC_Periodic_Table-4Feb05.pdf IUPAC Periodic Table of the Elements], which says: '“Aluminum” and “cesium” are commonly used alternative spellings for “aluminium” and “caesium.”'.   As an American, I find this annoying, but that's the way it goes. -- [[User:Dominus|Dominus]] 15:49, 1 November 2005 (UTC)

::::Hey that's good :) Now we only need to get rid of [[potassium]] and call it [[Kalium]] instead.--[[User:MarSch|MarSch]] 17:07, 1 November 2005 (UTC)

:::::Sure, but then we need to find a way to extract it from [[kale]], instead of [[potash]]. 17:58, 1 November 2005 (UTC)

::::Americans don't get annoyed; we effect regime change. I can say that now that I'm in Canada. Then again the Canadians might not know I'm joking. --[[User:Trovatore|Trovatore]] 20:28, 1 November 2005 (UTC)

:::::Yea, you might get kicked "oot". [[User:StuRat|StuRat]] 20:46, 1 November 2005 (UTC)

::::::Let's get back on task, eh? For what it's worth, I've met people (including myself) who insist it should be spelled "parametrize" (or "parametrise" if you live across the pond). I'm not sure how often I've run into the latter, though. - [[User:Gauge|Gauge]] 03:45, 10 November 2005 (UTC)

==Hilbert problems==

The [[Hilbert problems]] page is seeing some development, which is only right and proper. It is also raising numerous issues, in respect of what a 'solved' problem is. This is an opportunity, to do better than other Web treatments (few of the historians really have all the background to write with authority on all 23). The words 'worms', 'can' and 'of' come to mind.

I wonder whether the laudable effort to get a table summary of it all on the page hasn't had its day. It is hard to write enough in a table entry, since some of the problems have several 'ply' in them. I also think that where <nowiki>[[Hilbert's n-th problem]]</nowiki> is now a redirect, we really need to have the buffer of a separate page. For example, [[Hilbert's fifth problem]] used to redirect to [[Lie group]], but it seems clearer not to have arguments about what a Lie group is, and what the Fifth Problem was, on the ''same'' page.

Please come and help. This page missed Featured Article status over the summer, but has already been much expanded. [[User:Charles Matthews|Charles Matthews]] 09:49, 3 November 2005 (UTC)

== Help wanted at [[rotation]] ==

See [[talk:rotation#Request for comment]]. [[User:Oleg Alexandrov|Oleg Alexandrov]] ([[User talk:Oleg Alexandrov|talk]]) 00:58, 6 November 2005 (UTC)

== proofs of quadratic reciprocity ==

If anyone's feeling energetic, I started an article on [[Proofs of quadratic reciprocity]]. Sadly, it was a bigger job than I foresaw, and I've had enough for now. It needs several things done to it; see [[Talk:Proofs of quadratic reciprocity]] for my opinion on this. Thanks! I should go back to writing blahtex and existing in the real world now... [[User:Dmharvey|Dmharvey]] [[Image:User_dmharvey_sig.png]] [[User talk:Dmharvey|Talk]] 03:11, 6 November 2005 (UTC)

:I've intervened to link to [[Gaussian period]] to use indirection on the quadratic field. IMO this can be an interesting page, but mainly to send the reader to other parts of the site. [[User:Charles Matthews|Charles Matthews]] 11:17, 6 November 2005 (UTC)

==[[:Category:Professors]]==

[[Wikipedia:Categories for deletion/Log/2005 October 30]] - the classification of academics needs a big clean-up. Please come and vote. [[User:Charles Matthews|Charles Matthews]] 11:56, 6 November 2005 (UTC)
== Articles listed at AFD ==
* {{On AFD|Dragan conjecture}}
Unfortunately, the automation makes it difficult to manually add articles such as this to the current activity list. [[User:Uncle G|Uncle G]] 00:53, 10 November 2005 (UTC)
** ''Done'' (by placing <nowiki>{{math-stub}}</nowiki> in the article).  It should be picked up, eventually. [[User:Arthur Rubin|Arthur Rubin]] [[User_talk:Arthur_Rubin|(talk)]] 01:14, 10 November 2005 (UTC)
== [[Exclusive nor]] ==
See the talk page.  Has anyone else heard of this, outside of MathWorld? [[User:Arthur Rubin|Arthur Rubin]] [[User_talk:Arthur_Rubin|(talk)]] 01:14, 10 November 2005 (UTC)

:It would seem more logical to me to call this thing NXOR, per the suggestion at the talk page. XOR is probably a more familiar operation than NOR, and it is much easier to figure out what NXOR means: XOR goes 1 only on different inputs, so NXOR must go 1 only on the equal inputs. With XNOR one would probably have to draw a truth table. I checked that it is also equivalent to XAND, but people probably aren't used to working with XAND (I wasn't until I thought about it a bit). - [[User:Gauge|Gauge]] 04:23, 10 November 2005 (UTC)

::If it is true only on the same inputs (both true or both false), wouldn't the simplest and most logical name be SAME ? [[User:StuRat|StuRat]] 11:46, 10 November 2005 (UTC)

:::I don't think we should use the name that seems simplest, but rather the name accepted in the mathematical community.  Anyway, my TI calculator says XNOR, not NXOR. -[[User:Lethe|Lethe]] | [[User talk:Lethe|Talk]] 14:31, 10 November 2005 (UTC)

::::There are also far more Google hits for "logical SAME" than either "logical XNOR" or "logical NXOR", see the article's talk page for details.  I would say that this is evidence it is more accepted by the mathematical community.  Note that while "SAME" is a normal English phrase, "logical SAME" is not. [[User:StuRat|StuRat]] 14:39, 10 November 2005 (UTC)

:::::Many of the google hits for "logical SAME" seem to be consecutive sentences the first of which ends in logical, while the second starts with same.  some seem to be grammatical errors for "logically same".  I see very few google hits for "logical SAME" which indicate that it is used as an operator in logic or CS.  I think your hit count is unreasonably high, given that you're searching two very common english words.  On the other hand, when you google xnor, every single hit is about the logical/CS operator.  Could you perhaps provide a textbook (or something more authoritative than google) that uses SAME for this operator, because I'm of the opinion that it's always called XNOR. -[[User:Lethe|Lethe]] | [[User talk:Lethe|Talk]] 16:09, 10 November 2005 (UTC)

::::::I will look for some.  Meanwhile, can we keep the discussion on the article's talk page ?  Having it in two places seems quite unnecessary. [[User:StuRat|StuRat]] 17:01, 10 November 2005 (UTC)

:I have a design that comprises 18 such gates open in another window as I write this.  '''xnor''' is what such a gate is called in [[Verilog]]. [[User:Uncle G|Uncle G]] 15:03, 10 November 2005 (UTC)

== [[Function Iteration]] -- possible OR ==

The new article [[Function Iteration]] has the general smell of being original research. It doesn't look wrong, it just looks home-grown.  Anyone care to do something about that? AfD maybe? [[User:Linas|linas]] 01:26, 11 November 2005 (UTC)

:AfD seems like a good idea. [[User:Fredrik|Fredrik]] | [[User talk:Fredrik|talk]] 01:32, 11 November 2005 (UTC)
:: I would agree with that. [[User:Oleg Alexandrov|Oleg Alexandrov]] ([[User talk:Oleg Alexandrov|talk]]) 02:00, 11 November 2005 (UTC)
:Seems borderline to me. I think the math project has quite a lot of stuff that people figure out themselves by routine methods, on the theory that it must be written up ''somewhere'', and I think it would be counterproductive to get too rigid about OR when it comes to that sort of thing. But yes, this is probably over the line; it's a bad sign that the author signed his work. Maybe just redirect to [[Attractor]]? --[[User:Trovatore|Trovatore]] 02:49, 11 November 2005 (UTC)

:Isn't there some template that would say something like "this may be OR/POV, but nobody is quite sure, it can be true, citations are needed"? It would be more apropriate than deletion in some cases. It's the second instance of this I came across lately. [[User:Samohyl Jan|Samohyl Jan]] 07:28, 11 November 2005 (UTC)

::Needs citations to show it's already published. Otherwise to AfD as original research. [[User:Charles Matthews|Charles Matthews]] 08:44, 11 November 2005 (UTC)

:::The last section of [[Function iteration]] names Paul Bird as its author. A [http://en.wikipedia.org/w/index.php?title=Scalar_Gravity&oldid=27558141 previous version] of the article [[Scalar Gravity]] also mentioned named. Scalar Gravity is probably original research; see the discussion on [[Wikipedia:Articles for deletion/Scalar Gravity]]. That enough evidence for me to suspend my assumption of good faith, so I replaced the whole article with a redirect to [[function composition]]. In fact, since time immemorial ([http://en.wikipedia.org/w/index.php?title=Function_composition&diff=745216&oldid=53807 diff]) the latter article includes the sentence 
::::"In some cases, an expression for ''f'' in ''g''(''x'')&nbsp;=&nbsp;''f'' <sup>''r''</sup>(''x'') can be derived from the rule for ''g'' given non-integer values of ''r''.  This is called [[fractional iteration]]." 
:::It is a pity though as it is an interesting subject, but original research has no place in Wikipedia. -- [[User:Jitse Niesen|Jitse Niesen]] ([[User talk:Jitse Niesen|talk]]) 13:23, 11 November 2005 (UTC)

== more on "article too technical" ==

see [[Wikipedia:Village pump (policy)/Archive O#Frustration with make technical articles accessible policy]]

[[User:Dmharvey|Dmharvey]] [[Image:User_dmharvey_sig.png]] [[User talk:Dmharvey|Talk]] 18:55, 11 November 2005 (UTC)

== a list or a category of categories ==

I want there to be either a list of categories or a [[Wikipedia:categories|category]] of [[category theory|categories]] here.  The more I think about it, the more I think it should be a list, not a category.  One reason is that some categories probably don't deserve their own articles.  Another is that it might be neat if we could put the categories in a table and like list their properties (cartesian closed, concrete, abelian, monoidal, etc).  But then again, I've never liked (wp organizational) categories.  Anyway, I started a [[User:Lethe/list of categories|list]], which is basically just me adding a whole bunch of categories to the short list that was already at [[category (mathematics)]], in my user space because I wasn't sure if it should be an article.  Have a look? -[[User:Lethe|Lethe]] | [[User talk:Lethe|Talk]] 06:10, 12 November 2005 (UTC)
::You mean like the category of small categories? (couldn't resist...) - [[User:Gauge|Gauge]] 05:39, 13 November 2005 (UTC)
: Having a list of categories (as in [[category theory]]) would be nice. However, I find the table at the link you mention intimidating. I have no idea of categories, that is just an esthetic observation; maybe the table is useful. Anyway, if you decide to make such a list, it is good to add it to the [[List of lists of mathematical topics]] and also categorize it in [[:Category:Mathematical lists]]. [[User:Oleg Alexandrov|Oleg Alexandrov]] ([[User talk:Oleg Alexandrov|talk]]) 17:23, 12 November 2005 (UTC)
::: If a programming metaphor will help, think of [[category (mathematics)|categories]] as an [[object-oriented]] approach to mathematics. (Hidden humor intended.) The idea is to approach structures through maps. For example, look not just at [[vector space]]s, but also at [[linear transformation]]s, the maps that preserve the structure. Look not just at [[group]]s, but also at group [[homomorphism]]s. In fact, category theory has found that the structures themselves (called objects) are less important that the maps (called arrows). We can give an arrow definition of "[[product (category theory)|product]]", say, that applies identically to any kind of category. (Example: an individual [[poset]] is automatically a category, with an arrow ''A''→''B'' meaning ''A''&le;''B''; its products are greatest lower bounds.) By the same reasoning, we study category-to-category maps (called [[functor]]s), such as the forgetful functor that maps a vector space to the additive group of its vectors. We also consider functor-to-functor maps (natural transformations). By adding additional axioms we isolate categories (called [[topos|topoi]]) that can replace [[set]]s as a foundation for all of mathematics. A <b>''table''</b> of categories (hint: good name) has the potential to organize diverse topics in a way that reveals common patterns. Category thinking has already had a broad and subtle influence on mathematics. (Warning: POV ahead!) In much the same way as lesser beings see groups and vector spaces everywhere, higher beings see categories. ;-) --[[User:KSmrq|KSmrq]]<sup>[[User talk:KSmrq|T]]</sup> 13:31, 13 November 2005 (UTC)
::I think both a list ''and'' a category are appropriate. However the category name needs some thought, because it seems unavoidable that it will use the word "category" in two quite distinct senses in one short phrase. For example [[:Category:Mathematical categories]] isn't good, because it looks like it should be a collection of all subcats of [[:Category:Mathematics]].  The only things I can think of that are clear sound a little like jokes (e.g. [[:Category:Category-theoretic categories]]. Actually maybe that one's not bad; once you get over the sound of it, it pretty much covers what needs to be covered. --[[User:Trovatore|Trovatore]] 17:29, 12 November 2005 (UTC)
:::As regards the list, please note that there is already a [[List of category theory topics]], and it includes a section that has some of the function of Lethe's new list. The lists should be coordinated in some way: The new list could be merged into the old one; the now-redundant part of the old one could be removed, with a link to the new one;  or minimally, there could just be dab-style notices at the top of both. The name [[List of categories]] suffers from the same linguistic problem mentioned in my last intervention. Could be [[List of category-theoretic categories]]. --[[User:Trovatore|Trovatore]] 17:47, 12 November 2005 (UTC)
:::::I took your suggestion on the name of a category.  I went ahead and created the category.  I probably will move the list into article space at some point as well. -[[User:Lethe|Lethe]] | [[User talk:Lethe|Talk]] 18:21, 13 November 2005 (UTC)
::::::Cool. I've made it a subcat of [[:Category:Category theory]], and removed that now-redundant category from the articles in both. --[[User:Trovatore|Trovatore]] 19:17, 13 November 2005 (UTC)
:::::::What's a pipe category? -[[User:Lethe|Lethe]] | [[User talk:Lethe|Talk]] 00:34, 14 November 2005 (UTC)
::::::::(Think think think.) Sorry, no clever answer for such a promising straight line. When my edit summary says "pipe cat" it means that I pipe the category to a different name. Otherwise the whole category would be under the letter "C". It doesn't affect how the article name is displayed in the category listing, just how it's alphabetized. --[[User:Trovatore|Trovatore]] 00:38, 14 November 2005 (UTC)
::::I did notice the list of categories under the 'C' heading of [[:Category:Category theory]].  I didn't see that other list.  Thanks. -[[User:Lethe|Lethe]] | [[User talk:Lethe|Talk]] 17:59, 12 November 2005 (UTC)
I really like my table, but I'm afraid it's way too wide for most people's monitors... -[[User:Lethe|Lethe]] | [[User talk:Lethe|Talk]] 20:43, 12 November 2005 (UTC)

==Vector (spatial)==
It looks like [[vector (spatial)]] has been used in some contexts where [[coordinate vector]] or [[vector space|vector]] would have been more appropriate. I started to go through and fix things until I realized there must be at least a few hundred pages to check that link to [[vector (spatial)]]. My understanding is that spatial vectors (per their article) only refer to vectors in dimensions at most 3. This would make such links to [[vector (spatial)]] inappropriate when considering vectors in higher (or arbitrary) dimensions. How should we proceed to address this problem? - [[User:Gauge|Gauge]] 07:14, 13 November 2005 (UTC)

A related note: I suggest that for clarity we rename [[Vector (spatial)]] to [[Vectors in three dimensions]].--[[User:Patrick|Patrick]] 11:00, 13 November 2005 (UTC)

:That does sound reasonable, assuming the point of the article is to contain the most basic facts and intuitions. [[User:Charles Matthews|Charles Matthews]] 11:16, 13 November 2005 (UTC)

:: I think what Gauge mentions is the result of a disambiguation of [[vector]] gone wrong. Somebody was using a bot several days ago to do that disambig, and I guess that person did not do the homework well. 

:: I for one like [[vector (spatial)]] more than [[vectors in three dimensions]]. The former is clear enough to non-math folks, and the latter looks needlessly complicated. [[User:Oleg Alexandrov|Oleg Alexandrov]] ([[User talk:Oleg Alexandrov|talk]]) 17:37, 13 November 2005 (UTC)

:::Considering that ''vector space'' is the generalized kind, it is somewhat odd to use "spatial" to distinguish from it.--[[User:Patrick|Patrick]] 23:04, 13 November 2005 (UTC)

:I also disagree.  The proposed name feeds into the misconception that a 3-vector as used in physics and engineering is only special in that it has three components.  It is not.  The distinguishing feature of spatial vectors is not that they are three dimensional, but that they transform as the spatial coordinates do under rotations.  They would be equally distinct in this sense if space had two dimensions, or four. [[User:Stevenj|&mdash;Steven G. Johnson]] 19:18, 13 November 2005 (UTC)
::(''copied from [[talk:vector (spatial)]] by'' [[User:Oleg Alexandrov|Oleg Alexandrov]] ([[User talk:Oleg Alexandrov|talk]]) 23:09, 13 November 2005 (UTC))

::The proposal was based on the line that was at the top: "This article treats vectors in 3-dimensional real space." If the article is going to focus on this distinguishing feature that is fine. Note that the article is inconsistent in whether it is about 3D or also about other spaces with this feature.--[[User:Patrick|Patrick]] 09:07, 14 November 2005 (UTC)

::For a better understanding of "a vector is an object with properties which do not depend on the coordinate system used to describe it" it may even be helpful to start with the 1D case.--[[User:Patrick|Patrick]] 09:22, 14 November 2005 (UTC)

:::I agree that the article's introduction needs revision; it's clearly been the victim of "edit-creep".  I think the 1d case is actually more abstract, however.  (Note that, in 1d, vectors and scalars are still distinct under coordinate inversions.)  [[User:Stevenj|&mdash;Steven G. Johnson]] 16:55, 14 November 2005 (UTC)
 
I'm not even sure I like the existence of this article in the first place.  Is there really so much to be said about vectors in '''R'''<sup>3</sup> that wouldn't fit in an examples section of [[vector space]] that these vectors need their own article?  Remember that we're an encyclopedia, not a textbook. -[[User:Lethe|Lethe]] | [[User talk:Lethe|Talk]] 00:28, 14 November 2005 (UTC)

: Vector spaces are way too abstract for most people, while the [[vector (spatial)]] article is looking at things from the physics perspective. And as Steven Johnson is saying above, physical vectors have nice interpretations in respect to coordinate changes. I would not support merging [[vector (spatial)]] into [[vector space]] which is about the math structure. [[User:Oleg Alexandrov|Oleg Alexandrov]] ([[User talk:Oleg Alexandrov|talk]]) 06:40, 14 November 2005 (UTC)
:::Well I don't feel very strongly about this, so I'm not actually proposing a merger, but just let me say that I don't think that every topic that can be discussed on different levels of abstraction should get one separate article per abstraction.  So just because vector spaces can be discussed either abstractly or concretely, doesn't mean that we should have a concrete vector article and an abstract vector article.  But I note that there are a lot of similar dummy articles already in place, so I guess people want them.  whatever. -[[User:Lethe|Lethe]] | [[User talk:Lethe|Talk]] 17:14, 14 November 2005 (UTC)

::It's not just an interpretation, it's a ''definition'' &mdash; physical, spatial (axial) vectors have additional defining properties beyond those of an abstract vector space.  (This is, unfortunately, something that is not often emphasized in undergraduate courses, where students sometimes get they impression that they are just any old element of '''R'''<sup>3</sup>.  Nor is it usually mentioned in higher-level math courses; that's why I would prefer to begin the article with "in [[physics]]" rather than "in [[mathematics]].")  [[User:Stevenj|&mdash;Steven G. Johnson]] 16:55, 14 November 2005 (UTC)

== Wikisource wants to delete all source and data ==
Wikisource is currently contemplating deleting all mathematical and astronomical tables (including expansions of transcendental numbers, tables of logarithms, ephemerides, and so forth) and all source code.  See [[Wikisource:Wikisource talk:What Wikisource includes|Wikisource talk:What Wikisource includes]] for the discussion of this. [[User:Uncle G|Uncle G]] 15:49, 13 November 2005 (UTC)
*I'm afraid a couple of lists have been deleted already. To be sure, I feel the best solution would be to simply move these pages back to Wikipedia. If it doesn't belong on any wiki, it should at least be moved to a place where it can be monitored by people who care about it. On a larger scale, it would be useful to have more namespaces available for non-article content, for example Data:, Proof:, Example:, ... - [[User:Fredrik|Fredrik]] | [[User talk:Fredrik|talk]] 15:58, 13 November 2005 (UTC)
**People who care should go to Wikisource and ''contribute to the discussion''. [[User:Uncle G|Uncle G]] 21:59, 13 November 2005 (UTC)
***I don't see a good place to enter, and it appears a decision has been made anyhow. [[User:Fredrik|Fredrik]] | [[User talk:Fredrik|talk]] 19:25, 14 November 2005 (UTC)

== unitary versus unital ==
I got confused the other day when I saw [[unitary]] in the context of a C*-algebra.  Eventually I figured out that it means "having multiplicative identity", and I changed it to [[unital]].  I now see that some authors do use unitary in this sense (Hungerford), though it isn't mentioned in our page on unitary.  I'm going to add a mention there, but I kind of also want to change all instances I come across to unital, which is less ambiguous.  How do you feel about the word unitary to mean having identity in an algebra, or over a ring with identity for a module?  -[[User:Lethe|Lethe]] | [[User talk:Lethe|Talk]] 16:01, 13 November 2005 (UTC)

:I prefer "unital". I've never heard "unitary" being used to describe these things, and C*-algebras make a good case for avoiding confusion and keeping the terminology consistent. - [[User:Gauge|Gauge]] 20:16, 13 November 2005 (UTC)

== Spelling vandal ==

One person uses multiple account to change the spelling of math articles one way or another. I reverted whatever I saw so far (that does classify as vandalism I would say, as that person was warned half a day before to not do that). I guess we need to take a close look at the recent changes to math articles from the [[list of mathematical topics]] to watch for more. Note that the person in question makes sure that the user page and talk page are blue, I guess to mislead people. [[User:Oleg Alexandrov|Oleg Alexandrov]] ([[User talk:Oleg Alexandrov|talk]]) 07:03, 14 November 2005 (UTC)
:Could you point us to some examples? I've noticed that from time to time I have to revert someone who changes "provably" to "probably" or "provable" to "probable", but I've never been ''quite'' sure whether that person is a vandal, or just doesn't understand either the meaning of the English words or the subject matter. --[[User:Trovatore|Trovatore]] 07:19, 14 November 2005 (UTC)

::Oleg is probably refering to [[User:Spellchecker]], who is changing spelling from American to British English ([http://en.wikipedia.org/w/index.php?title=Mathematics&diff=28186830&oldid=28183844 example]). <small>I could live with that, British English being obviously superior, but this user is making the unforgivable mistake of using the widespread but terribly wrong -ise variant. :)</small> Today, similar accounts have appeared, like [[User:Imperiul]] ([http://en.wikipedia.org/w/index.php?title=Gradient_descent&diff=prev&oldid=28269387 example]). Whoever it is, they must feel very strongly about it, making a new account just to change a single letter. -- [[User:Jitse Niesen|Jitse Niesen]] ([[User talk:Jitse Niesen|talk]]) 11:28, 14 November 2005 (UTC)

::: What examples? Yesterday I single-handedly (mouse-buttonly) repelled an entire attack of spelling clones, I expected to be awash in glory when I wake up in the morning, and instead you are asking for examples? [[User:Oleg Alexandrov|Oleg Alexandrov]] ([[User talk:Oleg Alexandrov|talk]]) 19:13, 14 November 2005 (UTC)

Is it really a problem? Sure, changing "provably" to "probably" is probably (provably?) uncool, but if someone wants to waste their time changing "sanitise" to "sanitize" or the other way, I say let 'em waste their time. It's better than real vandalism. Don't we have better things to do? (On the other hand, I would of course object to such spelling changes on articles like [[George Bush]] or [[Vegemite]]). [[User:Dmharvey|Dmharvey]] [[Image:User_dmharvey_sig.png]] [[User talk:Dmharvey|Talk]] 13:06, 14 November 2005 (UTC)

:Well, there's a ''policy'' about this whole issue. Short version: If it's about a topic specific to one country/culture, use the appropriate version of English, otherwise use the one the article started with. I don't think we can allow such policies to be circumvented just because it seems like more trouble than it's worth. The matter should be explained to this user, and if he continues, there should be consequences. --[[User:Trovatore|Trovatore]] 16:29, 14 November 2005 (UTC)

::I follow the maxim "don't ascribe anything to malice which can be ascribed to ignorance".  I've seen cases where less common words were replaced by more common words which seem to fit in the sentence, and I assume those editors honestly thought they had found a typo.  When I revert back, I'm careful to describe the meaning of the word, so they are educated and don't try to "fix" it again.  It's a shame we can't somehow mark words with a "this is not a typo" flag, to prevent this mistake in the first place.  This reminds me of a problem IBM had in their user manuals...they contained blank pages at the end of chapters, but then people would call and complain that vital pages of their manual were blank, so they ended up printing "This page left intentionally blank" on those pages.  Ironically, printing that on them meant they were no longer blank, LOL. [[User:StuRat|StuRat]] 04:07, 22 November 2005 (UTC)

::: That was repeated change of spelling after being repeatedly warned, and creating a lot of accounts to do that, presumably to hide his/her tracks. I would not say that person is evil, but you surely can't assume good faith here. [[User:Oleg Alexandrov|Oleg Alexandrov]] ([[User talk:Oleg Alexandrov|talk]]) 04:54, 22 November 2005 (UTC)

::::I certainly don't mean to say that it's always an innocent mistake, just that it sometimes is. [[User:StuRat|StuRat]] 05:04, 22 November 2005 (UTC)

== spare hacking time anyone? ==

Hi y'all,

There's been an idea floating around for a while now that would of interest to all frequent mathematics article editors. I can't remember who originally thought of it. I'm wondering if there's anyone out there with time + skill + motivation to actually make it happen.

Wouldn't it be lovely if we could write our equations with $ or $$ signs instead of bulky <nowiki><math></nowiki> tags, just like in TeX. Every now and then this gets proposed as a change to the wikisource markup, but I tell you, it ain't gonna happen that way, because it's just too big a change. I think the main objection is that it would weird out too many non-math people out if they got funny TeX errors every time they tried to use ordinary $ signs. Fair enough.

But there's another way to do this which might satisfy everybody. What we need is some kind of javascript thing which automatically and transparently translates between $ and <nowiki> <math></nowiki> tags on the way in and out of the edit box (and presumably translates $ signs in the wikisource to something sensible like "\$"). This proposal would have no effect whatsoever on the database or the mediawiki software; it would stay recorded as <nowiki><math></nowiki> in the database. From what I understand, we have available some mechanism for personalised javascript (e.g. via monobook.js), which presumably could override the default behaviour when you load a page for editing or save an edited page. Then all that would be required is that a user copies the script to their own monobook.js, and they would be able to work with $ signs -- no thought required. Anyone who isn't interested doesn't have to use it.

Now, I'm pretty clueless when it comes to javascript, and I don't know how monobook.js works, and I don't have time to research it now. I've been led to believe, through some conversations I had a while back, that such a thing was technically feasible. Does anyone have any comments on feasibility? Does anyone here know enough to sit down and write the thing? Am I making any sense at all? [[User:Dmharvey|Dmharvey]] [[Image:User_dmharvey_sig.png]] [[User talk:Dmharvey|Talk]] 01:34, 16 November 2005 (UTC)

: See [[User:ABCD/monobook.js]] for how to create javascript functions, how to do automatic search and replace, and how to create a tab (in addtion to the existing "article", discussion", "edit", "watch", "move" tabs) and bind your function to that tab, so that when you click on it it gets executed. I found ABCD's code very well structured and easy to understand. You just need to carefully remove the parts you don't need (after you understand how the pieces fit together), and tweak one of his functions into doing what you want. Javascript is very similar to C, which I think you know. You could try to get started, and I could try to help if you get stuck. [[User:Oleg Alexandrov|Oleg Alexandrov]] ([[User talk:Oleg Alexandrov|talk]]) 01:56, 16 November 2005 (UTC)

:: You're right, I probably ''could'' work it out myself -- I just don't have much time right now. I'm canvassing for someone else to give it a try if they feel so inclined. [[User:Dmharvey|Dmharvey]] [[Image:User_dmharvey_sig.png]] [[User talk:Dmharvey|Talk]] 02:07, 16 November 2005 (UTC)

::: Let's assume you are properly devoting most of your time to completing [[m:blahtex|blahtex]], not some meaningless "doctorate". [http://www.math.harvard.edu/~dmharvey/index.php] Someone who is writing a translator from LaTeX to MathML is hardly in a position to complain about bulky tags. ;-)
:::: A little of both right now. Be patient. I do intend to finish blahtex first. :-) [[User:Dmharvey|Dmharvey]] [[Image:User_dmharvey_sig.png]] [[User talk:Dmharvey|Talk]] 12:29, 17 November 2005 (UTC)
::: The TeX delimiters can cause trouble, both in translating and in using. There's a good reason for LaTeX (and XML) balanced notation, an opener that can be distinguished from a closer. (Admittedly "\[" and "\]", and even "\(" and "\)", can also be annoying and an awkward fit to wiki notation.) The problem is, without balance you have to mind the nesting, which means parsing, not just string replacement; and you have to be prepared for bad (unbalanced) input. An accidentally omitted closing "$" is common, and wreaks havoc. Frankly, if wiki syntax supported "e^{x}" for superscripts (e<sup>x</sup>) and "a_{k}" for subscripts (a<sub>k</sub>), it would be less painful to use &lt;math&gt; tags for the rest. --[[User:KSmrq|KSmrq]]<sup>[[User talk:KSmrq|T]]</sup> 10:08, 17 November 2005 (UTC)
:::: Using $ is no worse than <nowiki>''</nowiki> for emphasising text; that wreaks havoc on me occasionally, but it's pretty easy to deduce what's going wrong. And you're right: it's not just string replacement. Makes the project just a little more interesting. Wanna try? [[User:Dmharvey|Dmharvey]] [[Image:User_dmharvey_sig.png]] [[User talk:Dmharvey|Talk]] 12:29, 17 November 2005 (UTC)
:::: And you probably need to look out for <nowiki><nowiki></nowiki> tags too :-0 [[User:Dmharvey|Dmharvey]] [[Image:User_dmharvey_sig.png]] [[User talk:Dmharvey|Talk]] 12:30, 17 November 2005 (UTC)

I don't see any advantage whatsoever in using $ and $$ instead of "bulky" <nowiki><math></nowiki> tags. The only thing I used to hate about <nowiki><math></nowiki> is that they are a pain to type, but right about the edit box you have the buttonbar with the math tags in. Click on that, and if you hit any keystroke that silly text "Insert formula here" will disappear, and you are ready to go.

: It's a matter of personal preference. I find the math tags also get in the way of readibility for me. If you disagree, you don't have to use it! (And certainly you don't have to write it!) [[User:Dmharvey|Dmharvey]] [[Image:User_dmharvey_sig.png]] [[User talk:Dmharvey|Talk]] 21:31, 17 November 2005 (UTC)

Another thing. I don't think it is a good idea to write a Wikipedia article as if it is a LaTeX document. This may result in too many inline PNG formulas. And no, MathML is not just behind the hill, coming any day or two. :) [[User:Oleg Alexandrov|Oleg Alexandrov]] ([[User talk:Oleg Alexandrov|talk]]) 16:48, 17 November 2005 (UTC)

: No, not in a day or two, but I think six months is eminently realistic to see MathML being trialled on Wikipedia -- quite possibly much less. I'm guessing we'll have a good solid test wiki running by February, but don't quote me on this :-). Anyway, I think the question of $ signs is mostly independent of the rendering method. My long distant goal is that "wikified math" (e.g. '''Q'''(&zeta;<sub>''n''</sub>)) -- even single symbols like ''x'' -- should eventually become completely deprecated in favour of inline TeX. But perhaps this a discussion for another day :-) [[User:Dmharvey|Dmharvey]] [[Image:User_dmharvey_sig.png]] [[User talk:Dmharvey|Talk]] 21:31, 17 November 2005 (UTC)

:: From the time it gets its "first trial", to the time it is ''the default'', I won't give less than two years. Now, if you expect that there will come a time when anybody will be promted to install mathplayer to see a math article on Wikipedia, that time will probably be never, or at least five more years. That is to say, HTML math is here to stay, that's how I see it. [[User:Oleg Alexandrov|Oleg Alexandrov]] ([[User talk:Oleg Alexandrov|talk]])

::: I think you are being unduly pessimistic. When there's a will, there's a way. (Gosh, I've only been living in the US for two years, and look how hopelessly optimistic I've become!) Anyway, I hope that when we start lobbying the wikimedia server people to incorporate our code, that you will support us. Or at the very least, wish us the best of luck. [[User:Dmharvey|Dmharvey]] [[Image:User_dmharvey_sig.png]] [[User talk:Dmharvey|Talk]] 01:58, 18 November 2005 (UTC)

==calling all topologists==
Expert fact-checking and other assistance requested at [[Inductive dimension]]. --[[User:Trovatore|Trovatore]] 07:25, 16 November 2005 (UTC)
=="Dimension" category up for renaming==
Someone has proposed [http://en.wikipedia.org/wiki/Wikipedia:Categories_for_deletion/Log/2005_November_16#Category:Dimension_to_Category:Dimensions here] that [[:Category:Dimension]] be renamed to [[:Category:Dimensions]]. Personally I disagree (though I'm open to argument). Please contribute (whether you agree with me or not). One possibility is that overly disparate concepts are being muddled together in this category. --[[User:Trovatore|Trovatore]] 19:00, 16 November 2005 (UTC)

:Not to start a big fight (and [[dimensional analysis]] cdould easily be made a subcategory), I'd say the [[Buckingham Pi theorem]] shows what that has to do with dimension ([[rank of an abelian group]], whatever). [[User:Charles Matthews|Charles Matthews]] 09:54, 17 November 2005 (UTC)

== [[List of well known mathematical formulas]] ==

Well known to whom? This seems a little silly. [[User:Dmharvey|Dmharvey]] [[Image:User_dmharvey_sig.png]] [[User talk:Dmharvey|Talk]] 03:18, 19 November 2005 (UTC)
:I agree. I put it on AfD. --[[User:Trovatore|Trovatore]] 03:52, 19 November 2005 (UTC)

== Examples? ==
Hi, I'm not sure if this is the right place to put this, but I was wondering if there were any policies concerning examples on math pages? I dunno, but it seems that it might be useful if pages had some example problems (like if the [[Green's theorem]] page had an sample problem to find the area of a planar region, or whatever)... Thanks :-)--[[User:Sciyoshi|yoshi]] 00:59, 22 November 2005 (UTC)
:Examples are absolutely encouraged. Most people are just too lazy to provide them. I would say, though, that there's an appropriate level of detail to present in an example. It shouldn't be worked out like a homework assignment; just enough detail should be given to get the reader started on working it out. That's my own take; we'll see if others agree with me. --[[User:Trovatore|Trovatore]] 01:04, 22 November 2005 (UTC)
:Oh, amend the above to "most people, including me, are usually too lazy...." I didn't mean that to come across as a criticism of the other editors in the project. --[[User:Trovatore|Trovatore]] 01:07, 22 November 2005 (UTC)
::haha :-) I think it would be nice to have some completely worked out problems (like sample homework problems)... but I guess I should just contribute some and see what others think. sorry kinda new to wiki stuff :-) --[[User:Sciyoshi|yoshi]] 01:14, 22 November 2005 (UTC)

:Examples? Yes, please. An encyclopedia is probably not the right place to challenge a reader to "work it out". Use good judgment; examples may be stated without proof, or a proof may be included if it is short and instructive. Equally important, and omitted more often still, are counterexamples ("near misses"). For Green's theorem, say, a figure-8 curve might be used to show what can go wrong. Also, a good picture is worth ten thousand equations (for some topics and some readers). --[[User:KSmrq|KSmrq]]<sup>[[User talk:KSmrq|T]]</sup> 01:50, 22 November 2005 (UTC)
::I agree that it's not a place to "challenge a reader", but I think it's even less a place to present detailed solutions to exercises. Examples are great, but let's keep them reasonably brief. Nonexamples (cases where the method doesn't work, in this instance) are also useful, as you say. --[[User:Trovatore|Trovatore]] 01:57, 22 November 2005 (UTC)
::: Anybody writing an article without examples sins against the [[math style manual]] and his own soul. :) [[User:Oleg Alexandrov|Oleg Alexandrov]] ([[User talk:Oleg Alexandrov|talk]]) 02:07, 22 November 2005 (UTC)
YES ABSOLUTELY DO EXAMPLES. I would err more than most to the side of providing examples. (If I have the time, that is.) As long as they don't distract from the main discussion. [[User:Dmharvey|Dmharvey]] 02:33, 22 November 2005 (UTC)

:I agree, examples are a capital idea !  I think the more thorough the better, as long as they aren't redundant with other examples.  Many readers who can't follow a purely theoretical discussion can easily follow it with a few examples.  For those who don't need the examples, they are easy to skip, especially if they are properly demarcated in their own sections.  Closely related to examples are applications - how this bit of math can be used to benefit mankind. [[User:StuRat|StuRat]] 03:49, 22 November 2005 (UTC)

==Hessian matrix usage==

Please consider posting an example of obtaining and using a Hessian matrix to find the maxima of a likelihood function such as a multinomial function.  Alternatively, please consider posting a reference or two where such information can be found.  Thank you. {{[[User:Mark W. Miller|Mark W. Miller]] 20:25, 23 November 2005 (UTC)}}

Thanks also to the individual who alerted me to how to sign my notes.  -- [[User:Mark W. Miller|Mark W. Miller]] 20:37, 23 November 2005 (UTC)

:Well, you need the definition of [[Hessian matrix]], and you need at a maximum to check it's [[negative-definite]]. [[User:Charles Matthews|Charles Matthews]] 08:15, 24 November 2005 (UTC)

::Thanks.  I'd already read the article.  I was hoping an example would be added there, or for a reference or two that contained an example.  My note was originally made in the Examples section, but was moved to its own section by someone else. -- [[User:Mark W. Miller|Mark W. Miller]] 19:11, 24 November 2005 (UTC)

: The simplest examples would likely come from [[quadratic programming]], minimization of a multivariate quadratic function with linear constraints. Ignore the constraints. The [[objective function]] can be written ''f''('''x''')&nbsp;= ½ '''x'''<sup>T</sup><b>G</b>'''x''' + '''c'''<sup>T</sup>'''x''', where '''G''' is the Hessian. Because '''G''' is a real symmetric matrix, it can always be diagonalized, with the signs revealing the essence of the situation.

::{| cellspacing="8"
! Hessian matrix || diagonal form || signature || kind of extremum
|-
| <math>\begin{bmatrix}2&1\\1&2\end{bmatrix}</math>
| <math>\begin{bmatrix}3&0\\0&1\end{bmatrix}</math>
| positive definite
| minimum
|-
| <math>\begin{bmatrix}-2&1\\1&-2\end{bmatrix}</math>
| <math>\begin{bmatrix}-3&0\\0&-1\end{bmatrix}</math>
| negative definite
| maximum
|-
| <math>\begin{bmatrix}1&2\\2&1\end{bmatrix}</math>
| <math>\begin{bmatrix}3&0\\0&-1\end{bmatrix}</math>
| indefinite
| saddle point
|}

: It's easy enough to render a picture for each of these. Or consider the algebra, say of the indefinite example. In the diagonalized variables, ''f''(''p'',''q'')&nbsp;= ½ (3 ''p''<sup>2</sup> − ''q''<sup>2</sup>). Clearly as ''p'' goes to positive or negative infinity ''f'' increases, while as ''q'' does the same ''f'' decreases. The square terms dominate any contribution from linear terms, thus '''c'''<sup>T</sup>'''x''' cannot affect the kind of extremum, but only its position. A constant term would only globally offset the value of ''f'', nothing more, so it is omitted.

: In the absence of constraints it is trivial to find the unique extremum of a quadratic objective. For more general functions, this would only be a ''local'' description, and finding a global extremum becomes difficult or impossible, as the function values can rise and fall unpredictably on a large scale. Nevertheless, this quadratic local description using the Hessian is often the best guidance we have in searching for a true extremum.

: Is this the kind of thing you were looking for? Hope it helps. --[[User:KSmrq|KSmrq]]<sup>[[User talk:KSmrq|T]]</sup> 20:03, 24 November 2005 (UTC)

::Thanks.  I think it is.  I need to study it more, but I think it is. -- [[User:Mark W. Miller|Mark W. Miller]] 08:14, 26 November 2005 (UTC)


:::  I have now looked into Hessian Matrices and optimization a little, particularly with the Newton-Raphson Method and am starting to understand it a little.  I've also looked into diagonalizing matrices which I think means creating a matrix of eigenvalues.  I used a computer to obtain the eigenvalues of the three Hessian matrices above.  I'm wondering if the middle one is: 

::: <math>\begin{bmatrix}-1&0\\0&-3\end{bmatrix}</math>.

::: Maybe the order doesn't matter.  I still need to obtain the eigenvalues by hand.  Anyway, thanks for the help.  I've learned quite a bit this Thanksgiving holiday.  -- [[User:Mark W. Miller|Mark W. Miller]] 10:44, 27 November 2005 (UTC)

::::[[Matrix diagonalization]] (not our most readable article, I'm afraid) indeed results in a matrix with the eigenvalues of the original matrix on the diagonal and the order does not matter, so it seems you understood it correctly. -- [[User:Jitse Niesen|Jitse Niesen]] ([[User talk:Jitse Niesen|talk]]) 13:17, 27 November 2005 (UTC)

== [[Wikipedia:Peer review/Logic/archive1]] ==

Your participation is appreciated... --- [[User:Chalst|Charles Stewart]] 20:10, 23 November 2005 (UTC)

== math reference desk ==

The [[Wikipedia:Reference desk]] was not too long ago split into subjects.  Currently, there is a [[Wikipedia:Reference desk/Science]] subsection which is where math questions should go.  It seems to me that math questions are a pretty small fraction of the posts there, and most go unanswered (unless they're high school math questions).  How would you feel about having a separate place for math questions?  I like to ask questions, and I like to answer questions, so I would like it. -[[User:Lethe|lethe]] [[User talk:Lethe|<sup>talk</sup>]] 20:25, 23 November 2005 (UTC)

: If such a page existed, I would have it on my watchlist. [[User:Dmharvey|Dmharvey]] 23:19, 23 November 2005 (UTC)

:I would too. --- [[User:Chalst|Charles Stewart]] 23:31, 23 November 2005 (UTC)

:Same here, I support the addition of such a page. [[User:StuRat|StuRat]] 00:32, 24 November 2005 (UTC)

:I support this, although I may not have any time to answer questions. - [[User:Gauge|Gauge]] 04:13, 18 December 2005 (UTC)

: I am not very old on the project, so I don't know the level of questions that are posted, but I'll be willing to answer any that I can, and I too might have questions. So I '''support''' this. [[User:deeptrivia|deeptrivia]] ([[User talk:deeptrivia|talk]]) 04:19, 18 December 2005 (UTC)

== Original research wiki ==

I've enjoyed editing WP so much that I've decided that it might be a good idea to organize my original-research thoughts, half-baked ideas, and full-fledged research results using a wiki, as opposed to trying to maintain a collection of half-finished LyX (TeX) documents (which is what I currently do, along with deep piles of paper).  I was about to install my own private copy of the mediawiki software on my server when it occurred to me that perhaps I should enquire here first...  Is there some public place where this could be done? I gather planetmath might be one-such, but I rather like the mediawiki interfaces.  I don't know if wikibooks allow original resarch; also, as I want to publish my personal notes, I want to exert considerable editorial control (i.e. deny write access by default, grant write access only to friends). 

The reason I find this interesting is the hyperlinking. Writing traditional, "flat", "linear" mathematics papers requires a review of basic concepts and notions early in the paper.  Using a wiki allows these steps to be skipped, in favor of links. It also allows hyperconnections between related concepts: as sometimes, the difficulty of writing a math paper is figuring out how to lay out the ideas in linear order. So I think that playing with a wiki for pure research and pseudo (self-)publication might be a worthwhile experiment.  But where shall I experiment?  [[User:Linas|linas]] 17:37, 25 November 2005 (UTC)

:[[Wikicities]] has an inactive mathematics wiki at http://math.wikicities.com. If that one is too general, I'm sure a pure research wiki could be set up at Wikicities if requested. Doesn't solve the problem of write access though. - [[User:Fredrik|Fredrik]] | [[User talk:Fredrik|t]][[Special:Contributions/Fredrik|c]] 18:02, 25 November 2005 (UTC)

== psychology ==

Hey everyone. I'm sure you've all seen talk pages featuring rather long-winded conversations like [[Talk:Mathematical_analysis]] (and archives), [[Talk:Proof_that_0.999..._equals_1]], [[Talk:Four_color_theorem/archive2]].... Typically an anon shows up and starts saying -- how to put this diplomatically? -- controversial things. Then the regulars here leap to the defence of rational thought. My question is: what motivates these people? What makes them tick? Why do they bother? Do they really think they're correct? Or are they just having fun? [[User:Dmharvey|Dmharvey]] 20:19, 25 November 2005 (UTC)


:Who are you referring to, the cranks or the regulars? In either case, the individual is motivated by an ah-ha moment, a sudden realization of a great truth that must be shared with the world. That ah-ha realization is presented in as simple terms as possible; the individual often lacks the formal background, and the intellectual stamina (and training) to triple-check their results (part of what one learns in school is not just collections of facts, but also the mental rigor to ask the right questions. Amateurs often lack the second bit.).  

:Also: Its a lot easier to argue than to double-check; its also easier to argue than to admit one's errors.  Sometimes, during the argument, one can hide/obscure one's errors, thus saving face.  One may also wait for the opposing side to make an even bigger blooper, which will distract attention, leaving the first side (although still wrong), relatively vindicated.  These very natural and inherent argumentation techniques work well when there is no clear-cut right and wrong.  

:Think of all the political arguments you've been in. Think of all the arguments you've had with e.g. a lover, where you clung to arguments you knew wer wrong or pushed an indefensible point.  Now realize that to the untrained, an argument about math is not really any different.  You, as a mathematician, do believe in absolute right and wrong; with no grey; but the other side does not have as clear a vision of right and wrong as you do.

:Physicists are notable in having training for dealing with grey areas: things that "feel right" but aren't provable or easily provable or easily formalizable. Some of the bitter battles in physics are high-end versions of the silly arguments you quote above. See e.g. the [[Hanbury-Brown and Twiss effect]]. [[User:Linas|linas]] 20:59, 25 November 2005 (UTC)

:As a culture, we often celebrate as heroes not those who were smarter or had deeper insights, but who rather were able to stay on track, and not fall into the pitfalls and distractions.  [[User:Linas|linas]] 21:05, 25 November 2005 (UTC)


:Maybe we can create a central page where me move such posts so these anonymous people can battle each other out? (Unless they team up.) - [[User:Fredrik|Fredrik]] | [[User talk:Fredrik|t]][[Special:Contributions/Fredrik|c]] 20:40, 25 November 2005 (UTC)

: There is no single motivation. I'll suggest a few common ones; but the bigger question is how best to respond.
:# Divine revelation, or the equivalent sense of individual insight.<br /> One of my most embarrassing memories is telling one of the top people in a field about such an idea I'd had, and being gently pointed at a major oversight. Unfortunately, some folks are so convinced they see truths to which others are blind, no amount of facts or reasoning will sway them.
:# Valid skepticism of sloppy arguments, leading to invalid dismissal of the assertions.<br /> This applies to some of the discussions I've seen at [[Talk:Proof_that_0.999..._equals_1]]. Scientists and mathematicians use a casual shorthand style of communicating amongst themselves, and they lack training in foundations. Consequently, they write things for a more general audience that can be misunderstood, then they fumble around not knowing how to fill the gaps.
:# Hyperactivity.<br /> Many Wikipedians are young and energetic, and type faster than they can think. Properly tamed, this can be a force for good. If it runs amok, this can cause widespread disruption. It is impossible for someone with a slower metabolism to keep up with manic edits, and Wikipedia's vandalism controls may not apply. Confined to talk pages, it's not so harmful; but it typically infects articles as well. One hint that this is happening is a look at the edit history; if it shows a long string of small edits at short intervals, chances are it's either hyperactivity or paranoia.
:# Need for attention.<br /> This common motive sometimes stands alone, but can be coupled with other motives. It doesn't matter if the attention is laudatory or derogatory, so long as there's lots of it. Long responses, however clear or correct, only feed the beast. Others jumping in to help likewise make things worse. One symptom of this motivation is use of insults, as seen at [[Talk:Proof_that_0.999..._equals_1]]. Consciously or unconsciously, these are intended to goad more response. Don't take the bait! Admins must quickly and firmly respond as [[User:Jitse Niesen|Jitse Niesen]] has done, saying such behavior is not tolerated; otherwise, it will escalate.
:# The elevator doesn't reach the top floor.<br /> The general public suspects most mathematicians are mentally ill; some really are. Notable examples include [[Theodore Kaczynski]] (the unabomber) and [[Theodore Streleski]] (who after 19 years as a mathematics graduate student at Stanford murdered an adviser). Intelligence does not imply rational behavior; fortunately irrational behavior is often easy to spot (but not always). Wikipedia probably acts as a magnet for some of these folks, and we can only hope that their efforts here divert them from more harmful activities in the physical world. If you can handle the other motives, you probably have most of the tools for this one as well.
: Speculating about motives can help suggest effective responses, but the usual rule here and elsewhere is to try to deal with the behavior itself, regardless of motives. As a rough analogy, rather than try to decide who is a terrorist and who is a freedom fighter, we would say "Blowing up innocent civilians is unacceptable behavior"; likewise, torture. --[[User:KSmrq|KSmrq]]<sup>[[User talk:KSmrq|T]]</sup> 23:05, 25 November 2005 (UTC)

Interesting thoughts guys. Thanks. [[User:Dmharvey|Dmharvey]] 01:06, 26 November 2005 (UTC)

: When I was a student (of applied mathematics), I knew a crazy guy like this. He seemed to be quite clever and interested (he impressed me, because he wrote some quite interesting computer simulations), but he didn't pass the first year (though I am not sure if he really dropped out). I think he had a problem that he was too focused to solving his own problems on his own and was uninterested in the contributions of others (mathematicians); for example, he was interested in [[tetration]] (like some guy here too), but when I told him to read something about algebra, he refused. [[User:Samohyl Jan|Samohyl Jan]] 12:48, 26 November 2005 (UTC)

==Category:Mathematical model on CfD==
[[User:CarlHewitt]] has created a new category, [[:Category:Mathematical model]], which he's been populating with theories, not models. I've put it on CfD. Opinions solicited (as always, whether they agree with mine or not). --[[User:Trovatore|Trovatore]] 00:42, 26 November 2005 (UTC)

: Ummm... perhaps he's just using the term "model" in a broader sense than that used in logic? [[User:Dmharvey|Dmharvey]] 00:56, 26 November 2005 (UTC)
::Possible in the abstract, but none of the articles with which he populated the category ([[Set theory]], [[Peano axioms]], [[Non-Euclidean geometry]]) fit any notion of model known to me, and the danger of confusion from calling them "models" is unacceptable in any case. --[[User:Trovatore|Trovatore]] 01:19, 26 November 2005 (UTC)
:::See the discussion at [[Wikipedia:Categories_for_deletion/Log/2005_November_26]].  Regards,--[[User:CarlHewitt|Carl Hewitt]] 18:25, 26 November 2005 (UTC)

: Hewitt is conflating at least two different meanings of "model". This category is of dubious use. More useful is the existing category of scientific model, which he's going around removing .--[[User:CSTAR|CSTAR]] 20:15, 26 November 2005 (UTC)

::It has been proposed to create category [[:Category:Mathematical model]] (to go with the existing article [[Mathematical model]]) as a subcategory of [[:Category:Scientific modeling]]. [[User:CSTAR|CSTAR]] opposes this proposal. Regards,--[[User:CarlHewitt|Carl Hewitt]] 20:32, 26 November 2005 (UTC)

== Google books ==

Today I discovered the thing called Google books. I had a question about harmonic functions, and I found excellent excerpts from books where this topic is covered. This tool would be very helpful for editors who are too lazy to use the library, and could also be used in checking the information and adding references to existing articles. [[User:Oleg Alexandrov|Oleg Alexandrov]] ([[User talk:Oleg Alexandrov|talk]])

: Is really great, except that you can only view three pages, so you still need to go to the library. &mdash;''[[User:R.Koot|R. Koot]]'' 01:02, 26 November 2005 (UTC)

:: Of course you need to go to the library if you want to read a lot. 

:: The big question is, how will this affect Wikipedia? How valuable is it to spend a good chuck of time writing an article if you are aware that the same information is already summarized in two pages in a book online which anybody can read? [[User:Oleg Alexandrov|Oleg Alexandrov]] ([[User talk:Oleg Alexandrov|talk]]) 01:31, 26 November 2005 (UTC)

::: I think the viewing constriction and search limitations are large enough to prevent this from being used as anything else than a very handy index to my library. I used it to find some books on the [[actor model]]. More importantly, an encyclopedia is something very different from a book. On Wikipedia you can look up something about a specific thing, person or theorem. When you read a book, you will often need/want to read the entier thing. Of course, then you've gained a lot more knowledge, but it would have taken you a lot longer. &mdash;''[[User:R.Koot|R. Koot]]'' 02:08, 26 November 2005 (UTC)

:::: I agree with R. Koot. For me it is much easier to rapidly digest information from Wikipedia than it is from Google Books. Additionally some books have pages missing from them (a feature Google provides for publishers). [[User:127|127]] 15:28, 30 November 2005 (UTC)

==Computability, recursion theory==
Background: Due to the influence of Soare, in recent years it has been fashionable to use the term "computability theory" for what used to be called [[recursion theory]]. Very recently on WP, [[:Category:Computability]] was renamed to [[:Category:Theory of computation]], where some of the articles are a good fit, but by no means all of them. Also the [[computability theory]] article underwent a substantial rewrite, focusing almost entirely on the aspects of interest to computer scientists rather than mathematical logicians.

This left a big void, as recursion theory or computability theory (as you prefer) is standardly considered one of the four branches of mathematical logic (the other three being [[set theory]], [[model theory]], and [[proof theory]]). So I created [[:Category:Recursion theory]] and a stub article at [[recursion theory]].

What needs to happen now:
#A decision needs to be reached about whether this split is really correct, and if so, what are the criteria. The rough criterion I used to divide articles between the categories was whether I thought the topic would be studied by people who think of themselves as mathematical logicians, or people who think of themselves as computer scientists. A very substantial overlap remains. If the categories were to be remerged, though, it certainly couldn't be under the name "Theory of computation". If the articles were remerged, the new article would have to spend less time talking about Turing degree '''0''', to get to some real topics in recursion theory faster.
#Assuming the articles remain split, [[recursion theory]] needs to be enormously expanded.
#I was conservative in ''removing'' [[:Category:Theory of computation]] from articles. Someone who knows about theory of computation should go through the articles in the intersection of the two cats and say "That's not theory of computation" on some articles.

See the discussion at [[Talk:Computability theory (computation)]]. --[[User:Trovatore|Trovatore]] 20:31, 26 November 2005 (UTC)

: I strongly believe these two categories should remain split. As this is important to both mathematicians and computer scientists their will always be one party who will get confused if we merged them. (E.g. computer scientist being not so very interested about thing with a Turing degree greater then 0, and mathematical logicians being not se very interested in thing with Turing degree 0. &mdash;''[[User:R.Koot|R. Koot]]'' 16:32, 27 November 2005 (UTC)

: A aplit here seems to make sense.  [[Computability theory]] should be the article called [[Computability theory (computation)]], with the reference at the top to recursion theory.  Though really the two are the same topic, its just that recursion theory more with nonphysical computational models.  Also, [[Computation]] should redirect to [[Computer]], and a new article perhaps using some of the content from [[Computation]] should be at [[Theory of Computation]], which would be a good overall starting point for the whole shebang.  [[Complexity theory]] is currently of pretty embarassing quality and needs to be rewritten.  I may do that at some point, though before I did I wanted to see how my [[Computability theory (computation)]] was recieved, and since I started that from a stub it seems less likely to be a problem.  --[[User:Readams|Readams]] 22:32, 28 November 2005 (UTC)

== something's up with tex rendering ==

Does this look a bit odd to anyone else?
<math>\iint</math>
[[User:Dmharvey|Dmharvey]] 01:37, 27 November 2005 (UTC)

: Yes, it's broken for me. The top right corner of the second integral sign is cut off. I've had a quick look through [[Help:Formula]] and caught no defects there, but caching could hide recent breakage. Here's an experiment:
::{| style="background:cyan"
|-
| <math>\int</math> || <math>\iint</math> || <math>\iiint</math> || <math>\oint</math>
|-
| <math>\int_{\!.}^{}</math> || <math>\iint_{\!.}</math> || <math>\iiint_{\!.}</math> || <math>\oint_{\!.}</math>
|-
| <math>\int_i^{}</math> || <math>\iint_i</math> || <math>\iiint_i</math> || <math>\oint_i</math>
|-
| <math>\int \omega</math> || <math>\iint \omega</math> || <math>\iiint \omega</math> || <math>\oint \omega</math>
|}
: There seems to be a pattern. --[[User:KSmrq|KSmrq]]<sup>[[User talk:KSmrq|T]]</sup> 02:46, 27 November 2005 (UTC)

== [[Carl Hewitt]], [[User:R.Koot|Rudy Koot]] and [[User:ems57fcva|Edward Schaefer]] ==

See [[Talk:Model (abstract)#Dispute]] and [[Wikipedia:Requests for arbitration#Carl Hewitt]]. &mdash;''[[User:R.Koot|R. Koot]]'' 16:38, 27 November 2005 (UTC)
:Also please see [[User_talk:CarlHewitt#Arbitration_with_Rudy_Koot_and_Edward_Schaefer]]--[[User:CarlHewitt|Carl Hewitt]] 18:52, 27 November 2005 (UTC)

:Isn't this kind of dispute an unavoidable consequence of the non existence of well identified editorial boards with reknown expertise in each domain? [[User:Taxipom|pom]] 00:52, 28 November 2005 (UTC)

::The dispute would not be avoided by editorial boards. Many of Carl Hewitt's additions were technically incorrect, as many here, who are domain experts, will attest.  Having a formal editorial board confirm that there are numerous, flagarant, technical problems with Carl Hewitt's edits would not diminish the controversy. (And that is the root of the problem). [[User:Linas|linas]] 04:05, 28 November 2005 (UTC)

:::Dear [[User:Linas|Linas Vepstas]],
:::Can you point out a single technically incorrect contribution that I have made in the area of Computer Science?
:::Regards,--[[User:CarlHewitt|Carl Hewitt]] 04:25, 28 November 2005 (UTC)

::::Carl, all of our arguments and collisions were over issues in the areas of gravitation/general relativity, quantum mechanics and, to a lesser extent, electronics. I don't beleive we ever discussed computer science issues. [[User:Linas|linas]] 22:05, 28 November 2005 (UTC)

:::::Linas, we have certainly had our collisions! See [[User_talk:CarlHewitt#Note_to_CSTAR]].
:::::However, it was sad to see [[User:CSTAR]] drop off the face of the Wikipedia.
:::::Regards, --[[User:CarlHewitt|Carl Hewitt]] 23:12, 28 November 2005 (UTC)

:::The role of an editorial board is not only expertise. Its role is fundamental in the refeering process: its arbitration is definitive and accepted by all parts ''a priori''. [[User:Taxipom|pom]] 11:03, 28 November 2005 (UTC)

==[[User:CSTAR]]==
I can't help noting that [[User:CSTAR]] has abandoned Wikipedia, or has gone into hiding, or is at least taking a [[wikivacation]]. It is hard for me not to conclude that this RfC and some of the personal attacks it engendered was the proverbial straw.  I enjoyed CSTAR's company, ad saw him as a good, highly qualified editor working in the general area of [[operator algebra]]s and (surprise) [[C*-algebra]]s.  Unfortunately, this meant that he was often involved in disputes fending off the latest cranky quantum mechanics edit, and I suspect this sapped a lot of his energy.  I am not happy about his departure, as he was a valuable and trusted editor. [[User:Linas|linas]] 22:05, 28 November 2005 (UTC)
:CSTAR was pretty much our only line of defense against the local variables agenda of Catherine Thompson.  Without him, we're lost.  What RfC are you referring to? -[[User:Lethe|lethe]] [[User talk:Lethe|<sup>talk</sup>]] 03:34, 29 November 2005 (UTC) ''Edit: Oh, you must be talking about the stuff in the post above this one.  I see. -[[User:Lethe|lethe]] [[User talk:Lethe|<sup>talk</sup>]] 03:43, 29 November 2005 (UTC)''
::I tried to follow a bunch of those links to see what happened, and I couldn't really follow the various threads.  Nor do I think I want to.  So I'll just say again that if crackpottism and rudeness soured CSTAR on this place, more's the pity.  -[[User:Lethe|lethe]] [[User talk:Lethe|<sup>talk</sup>]] 03:54, 29 November 2005 (UTC)

== [[Addition]] has been overrun by Sigmas! ==

Seriously, though, I think [[Addition]] needs a content shuffle. Please drop by [[Talk:Addition#Split.3F]]. [[User:Melchoir|Melchoir]] 06:00, 28 November 2005 (UTC)

:Okay, I've got a decent consensus over there, so you may return from the edges of your seats. If anyone wants to help clean up after me, go ahead and visit [[addition]] and [[summation]] this weekend. [[User:Melchoir|Melchoir]] 19:09, 29 November 2005 (UTC)

== math reference desk made ==

[[Wikipedia:Reference desk/Mathematics]].  No posts yet. -[[User:Lethe|lethe]] [[User talk:Lethe|<sup>talk</sup>]] 06:43, 29 November 2005 (UTC)

: Good move. [[User:Dmharvey|Dmharvey]] 12:52, 29 November 2005 (UTC)

== [[Dimitri Egorov]] or [[Dmitry Yegorov]]? ==

:''Copied from [[Portal:Russia/Russia-related Wikipedia notice board]] -- [[User:Jitse Niesen|Jitse Niesen]] ([[User talk:Jitse Niesen|talk]]) 13:44, 30 November 2005 (UTC)''

Ghirlandajo, I noticed you moved [[Dimitri Egorov]] to [[Dmitry Yegorov]]. I debated with myself for a while as to how exactly I should name the article, given that there are alternate spellings. Actually I was only considering the difference between Dimitri and Dmitri, but clearly his family name can be spelled differently too. In the end, I chose Dimitri Egorov because that's the spelling given on [http://genealogy.math.ndsu.nodak.edu/html/id.phtml?id=24109 The Mathematics Genealogy Project]. Since you're living in Russia, I obviously bow to your knowledge on this subject, but I'm wondering if there is a standard way of spelling Russian names such as this? Forgive my [[Canadian]] ignorance on the subject - I'm hoping to maybe add some more stubs of Russian mathematicians in the future, and it would be great if I knew how to do it properly to begin with. Cheers! --[[User:Peruvianllama|PeruvianLlama]]<sup><small>([[User talk:Peruvianllama|spit]])</small></sup> 20:24, 21 November 2005 (UTC)
:I want to thank you for the article you created. We already have [[Boris Yegorov]], [[Aleksandr Yegorov]], and now [[Dmitry Yegorov]]. I just thought it helpful to standartize the spelling of this surname. By the way, a disambiguation page would be helpful too. --[[User:Ghirlandajo|Ghirlandajo]] 21:35, 21 November 2005 (UTC)
::I actually had the same question. The spelling Egorov seems to be much more common. I think I understand where you're coming from: the surname seems to be written Егоров in the Cyrillic alphabet, and the Cyrillic Е at the start is typically transliterated with "Ye". However, I think the fact that Egorov is the common spelling (if that's true) takes priority. What do you think about this? -- [[User:Jitse Niesen|Jitse Niesen]] ([[User talk:Jitse Niesen|talk]]) 22:35, 22 November 2005 (UTC)

:::The spelling used should be the one under which his English-language papers (or translations to English) are most commonly published. Da? [[User:Linas|linas]] 00:38, 1 December 2005 (UTC)
:::: With "Da" meaning yes, in Russian (Egorov would approve :) [[User:Oleg Alexandrov|Oleg Alexandrov]] ([[User talk:Oleg Alexandrov|talk]]) 02:53, 1 December 2005 (UTC)
:::::Just a comment, [[Boris Eltsin]] is a redirect to [[Boris Yeltsin]]. Both Dmitriy and Dmitry are acceptable, I met people who spelled their names both ways, I am not so sure about Dimitri.([[User:Igny|Igny]] 03:37, 1 December 2005 (UTC))
::::::According to [[MathSciNet]], 72 papers have "Egorov" in the title (including a Math. Intelligencer article ''Dimitri&#301; Egorov: Mathematics and religion in Moscow,'' where the last letter of the given name is i-[[breve]]), 30 "Egoroff", and none "Yegorov" (Egorov/Yegorov himself died in 1931, so his papers are not in MathSciNet). Given this, I intend to move the page back. -- [[User:Jitse Niesen|Jitse Niesen]] ([[User talk:Jitse Niesen|talk]]) 13:49, 5 December 2005 (UTC)
:::::::Obviously the [[Special:Whatlinkshere/Dmitry_Yegorov]] will pick this up too, but I thought I'd explicitly point out that that disambig page [[Yegorov]] will need to be changed. In fact, generalizing this conversation to the surname in general (and not just that of Dimitri/Dmitri/Dmitry Yegorov/Egorov), perhaps the disambig page could use some working over. --[[User:Peruvianllama|PeruvianLlama]]<sup><small>([[User talk:Peruvianllama|spit]])</small></sup> 14:40, 5 December 2005 (UTC)

==Requesting mathematical relations for [[Intentionally blank page]]==
I was told this project is "the best WikiProject on Wikipedia", so I am hoping someone can help. I would like to equivalently represent the use of the phrase "The page is intentionally left blank" on blank pages. The phrase is a self-refuting meta-reference, in that it falsifies itself by its very existence on the page in question. I made this same request at [[Wikipedia:Reference_desk/Mathematics#Requesting_math_logic_statements|the reference desk]], but only got limited answers. One person suggested using [[Gödel number]]ing, while another said:

:"The "self-referential propositional calculus" of [[Yiannis N. Moschovakis]] is expressive enough to capture the liar. (Note that Gödel sentences do not capture the liar; they assert their own ''unprovability'', not ''falsehood''.) Moschovakis gives SRP a semantics using least-fixed-point recursion. The liar comes out neither true nor false using that semantics."

But I am at a loss as to how to proceed from here. I will be submitting this article to [[WP:FAC]] soon, and would really like to have a paragraph concerning specifically this. Thanks!  &mdash; <small>[[User:Brian0918|<b style="color:black;">BRIAN</b>]][[User_talk:Brian0918|<span style="color:gray;">0918</span>]] &bull; 2005-12-5 02:09</small>

:I'm afraid I don't know enough logic to answer your question. However, I can try to explain the above quote. Firstly, "self-referential propositional calculus" (whatever that may be) is something that probably very few people know about so think carefully whether including it in [[Intentionally blank page]] is useful. Secondly, "the liar" refers to the [[liar paradox]], which is not quite the same, as noted on [[Talk:Intentionally blank page]] (but if "self-referential propositional calculus" can express the liar paradox, it might also be able to express "this page is blank"; my best guess would be "''p'' = &epsilon;" where ''p'' refers to the proposition itself and &epsilon; is something like the [[sequence|null sequence]]). Thirdly, in my opinion the link with [[Gödel's incompleteness theorem|Gödel's second incompleteness theorem]] is rather weak and definitely not worth mentioning in the introduction, if at all. -- [[User:Jitse Niesen|Jitse Niesen]] ([[User talk:Jitse Niesen|talk]]) 13:20, 5 December 2005 (UTC)

== Categories ==

I saw that [[:Category:Differential equations]] is not in [[:Category:Equations]]. However, both categories are subcategories of [[:Category:Mathematics]], so if I'd place [[:Category:Differential equations]] in [[:Category:Equations]] then I'd violate the guideline of not including a category ''A'' in both another category ''B'' and an ancestor of ''B''. Any ideas on how to proceed? -- [[User:Jitse Niesen|Jitse Niesen]] ([[User talk:Jitse Niesen|talk]]) 10:35, 6 December 2005 (UTC)

: I think that rule is meant to be a guideline rather than a hard rule. A guideline which is useful most of the time but not all of the time. In this case I would say it is a good idea to have the equations in both categories.

: A related question. [[:Category:Equations]] is both in [[:Category:Mathematics]] and [[:Category:Algebra]]. I would argue that equations are fundamental enough that being in [[:Category:Mathematics]] should be enough. Or should [[:Category:Equations]] still be in [[:Category:Algebra]], together with  [[:Category:Identities]] and [[:Category:Polynomials]] which are also categorized there? [[User:Oleg Alexandrov|Oleg Alexandrov]] ([[User talk:Oleg Alexandrov|talk]]) 15:58, 6 December 2005 (UTC)

::It's a bit boring, but I agree with you that [[:Category:Equations]] should not be in [[:Category:Algebra]], also because it contains integral equations which I wouldn't classify as algebra. I fixed this. -- [[User:Jitse Niesen|Jitse Niesen]] ([[User talk:Jitse Niesen|talk]]) 17:36, 6 December 2005 (UTC)

== Re-creation of [[:Category:Mathematical model]] ==

I have proposed the re-creation of [[:Category:Mathematical model]].  Please discuss in [[Talk:Mathematical model]].   Thanks,--[[User:CarlHewitt|Carl Hewitt]] 19:16, 6 December 2005 (UTC)

== 0.999... ==

Hi everybody! If you're not already aware of the mess attached to the talk page of [[Proof that 0.999... equals 1]], consider yourself lucky. I'm here to solicit comments on my proposal to rewrite that page and confront all the popular misconceptions. Please see [[Talk:Proof that 0.999... equals 1#If I may speak to the article itself...]]. Thanks, [[User:Melchoir|Melchoir]] 21:25, 6 December 2005 (UTC)

:Hi, I think it is useless to post on that talk page, since in my opinion at least two of the anons (if not identical) are trolls, i.e. people who know better but choose to cause confusion. Things that went unremarked and that are the reason of my suspicion: 
:*there are no predecessors (next smallest elements) in the usual order on the rational or real numbers, and 
:*I think it is highly unlikely that anyone was taught real numbers at school. Decimal fractions were surely taught, and also periodic infinite digit sequences as representations of fractions. Infinite digit sequences in general may have been mentioned, but surely no operation was defined on them, and most surely there was no proof that e.g. the multiplication is associative.
:What may serve as argument: 
:*In contemporary mathematics, noone constructs real numbers by infinite numbers of digits. One of the articles cited tries, IMO, to highlight the difficulties of this approach. 
:*Real numbers are defined by the field axioms, the archimedian axiom and the order completeness (total order axiom?). Models of real numbers are constructed by Dedekind sections, classes of Cauchy sequences or nested intervalls. All models satisfy the axioms and are equivalent. 
:*Infinite digit sequences are (besides infinite continued fractions) one of the representations of real numbers, <math>m.d_1d_2d_3\dots</math> has the interpretation that each of the rationals <math>q_n:=m+\sum_{k=1}^n 10^{-k}d_k</math> is an approximation of the represented real number and that this real number lies inside the intervall <math>[q_n,q_n+10^{-n}]</math>. This gives a Cauchy sequence or a sequence of nested intervalls, so we end up in one of the models. 
:*For the digit sequence in question, those intervalls are <math>[1-10^{-n},1]</math>, so there is no sense in stating that 1 is outside or bigger than the numbers in those intervalls.
:--[[User:LutzL|LutzL]] 08:23, 9 December 2005 (UTC)
::I fully agree it is useless to continue loosing time with this. Don't you think there should be a special category for such useless time consumming futilities? [[User:Taxipom|pom]] 19:04, 9 December 2005 (UTC)
:::The page should never have been created - anyone knowledgeable could have predicted the result. There is no assumption here that a proof is 'encyclopedic', and the result is ''of course'' just a case of something on geometric progressions. To create a page precisely because people without a full background argue about such matters is to ask to have one's time wasted. Yes <nowiki>[[Category:Pages which were not such a good idea]]</nowiki>. [[User:Charles Matthews|Charles Matthews]] 11:58, 9 December 2005
::::Thank you, category added. (for about 1mn before having been reversed by someone...) [[User:Taxipom|pom]] 01:31, 10 December 2005 (UTC)
:This argument only draws attention because it expresses a peculiarity of positional notation systems. Therefore, I move that this matter be resolved by merging the article into [[positional notation]]. I have added the appropriate tag. [[User:Deco|Deco]] 02:12, 10 December 2005 (UTC)
:: I'll comment more on the article [[Talk:Proof that 0.999... equals 1|talk page]], but several remarks here are puzzling. Please be careful to distinguish between the [[Proof that 0.999... equals 1|article]] and its talk page. Yes, there is endless and sometimes ridiculous discussion on the talk page, but the overwhelming majority of the chatter has ''nothing'' to do with the actual contents of the article. Even the remark here about "just a case of … geometric progressions" ignores the proofs actually used, one of which is based on Dedekind cuts and another on Cauchy sequences. Nowhere ''in the article'' is the value of 0.999… defined as a limit of a geometric progression.
:: Frankly, given that the talk page is supposed to be about improving the article, I'm surprised one of the seasoned Wikipedians here has not intervened to put a stop to the nonsense. If it's a bad idea to have an article we ''know'' will attract controversy, we'd better get rid of [[abortion]] and [[Jesus Christ]] and [[socialism]] and … . (Mounting soapbox.) This ongoing misuse of the talk page ''could'' spill over into the article, despite the complete lack of reputable dispute about its topic. ''That'' is a weakness of Wikipedia, whatever the disposition of this article. --[[User:KSmrq|KSmrq]]<sup>[[User talk:KSmrq|T]]</sup> 03:44, 10 December 2005 (UTC)

FWIW, Don't under-estimate infinite-digit sequences. The [[z-transform]] of the sequence of digits in the ([[p-adic]]) expansion of a real number is a [[Cantor space]], and so, in this very certain sense, there are topologies of the real number line where 0.999... is inequivalent to 1.000... Its a subtle point, and it seems to have something to do with "why there are fractals", which are crawling with these kinds of topological inequivalences.  There are topologies that naively seem to be isomorphic to the real numbers, but on closer examination are not. The expansion in terms of digits is one of them. So maybe the article isn't very good, but the topic merits a deeper examination, since its a truism often taught in grade/high school, and has difficult subtleties associated with it. [[User:Linas|linas]] 07:22, 10 December 2005 (UTC)

:Oh, Linas, ny mistake - what the page needs is more of your stream-of-consciousness free association - that will really set them straight:). Of course, like 0/0 one can squeeze some good mathematics out of it. But common sense applies: Gresham's Law and Don't Feed the Troll. The analogy with contentious topics in religion or politics is no apt. There is not the slightest need to have a page with this exact title, and it could usefully be merged. [[User:Charles Matthews|Charles Matthews]] 14:37, 10 December 2005 (UTC)

== Arabic numerals RfC ==

Just a note that [[Arabic numerals]] has been listed at [[WP:RFC]] under mathematics regarding a heated dispute over numerous content changes. [[User:Peyna|Peyna]] 16:26, 11 December 2005 (UTC)

== [[User:CSTAR|CSTAR]] has left the building ==

For those who may not know, [[User:CSTAR|CSTAR]] (a well respected math and physics editor) [[User:CSTAR|has left Wikipedia, perhaps for good]], primarily because of the [[Wikipedia:Requests for arbitration/Carl Hewitt|Carl Hewitt affair]]. [[User:Paul August|Paul August]] [[User_talk:Paul August|&#9742;]] 20:39, 12 December 2005 (UTC)

:Let's hope his comeback tour is planned, though. [[User:Charles Matthews|Charles Matthews]] 20:42, 12 December 2005 (UTC)
::Yes let's. [[User:Paul August|Paul August]] [[User_talk:Paul August|&#9742;]] 21:01, 12 December 2005 (UTC)

:He told me he would think about returning in the New Year, but he indicated that it was very far from certain he wanted to return.  Carl Hewitt may have been the proximate cause of his departure, but he's had more than his fair share of unrewarding WP experiences.  If he does return, I wish him better luck with what follows. --- [[User:Chalst|Charles Stewart]] 21:40, 12 December 2005 (UTC)
:: It seems that [[User:R.Koot|R.Koot]] left for the same reason. I think both of them should have waited for the conclussion of the RfArb against Carl Hewitt, but I do understand how frustrating it should have been to deal with this person. [[User:Oleg Alexandrov|Oleg Alexandrov]] ([[User talk:Oleg Alexandrov|talk]]) 22:08, 12 December 2005 (UTC)


==WikiScience==

[http://meta.wikimedia.org/wiki/Proposals_for_new_projects#WikiScience WikiScience]

Everybody here please have a look at my MetaWiki proposition for the creation of ''wikiscience'', a technical wiki-based encyclopedia that will allow for ORIGINAL contributions from users plus the most up-to-date research from professionals (as well as being a math and science encyclopedia).  Wikipedia as it stands is far from this, as well as other sites such as "Mathworld".  Math and science is simply too technical and evolving of a subject to be thrown about with the rest of wikipedia articles.  Math and science, given its special nature of presentation and subject, needs to be part of the wikipedia whole, yet ''seperate'' and organized (I think we all agree).  I believe that the wikimedia foundation has the momentum and the user base to make this extroadinary contribution to the math and science community, but I need supporters before wikimedia makes this happen.

If you are interested in making this happen please visit the link and show your support.  Also, if you want more detail of my idea, or have any suggestions or criticisms please visit [http://meta.wikimedia.org/wiki/Wikiscience WikiScience Details]! Thanks!  --[[User:B21.12.52.123|B21.12.52.123]] 12:55, 13 December 2005 (UTC)

:I'm thinking along the lines of "arxiv.org", but with wikilinks and author-controlled pages. Among other things, it would put an end to l'Affaire Hewitt ici, and allow a flourish of edits there. As such, I strongly support and recommend further development. I also support because I want to experiment with keeping my personal research notes/diary in media-wiki style. [[User:Linas|linas]] 21:12, 13 December 2005 (UTC)
I'm against it.  I think it will divide the efforts of editors, with the most technically inclided editors eschewing wikipedia general.  I don't think there should be a limit on how technical articles in wikipedia get (Wikipedia wants to be the sum total of human knowledge).  To the critics who complain when they come to an article that's too technical, well, we can make each article as approachable as possible, but in many cases that will still be entirely incomprehensible to most people.  C'est la vie. -[[User:Lethe|lethe]] [[User talk:Lethe|<sup>talk</sup>]] 22:03, 13 December 2005 (UTC)

::  This is a good point.  Should non-technical, simple summeries of math and science concepts still be in wikipedia?  Or should all of math and science move to WikiScience?  I am leaning toward the first one, that is, wikipedia (like any other encyclopedia) should still have relatively simply worded and accessable concepts in math and science, but for more in-depth and up-to-date modern (and original research from users) research, plus more in depth on the "simple" concepts, wikiscience would be the home.  Does this divide contributers?  Not if the technicality of the articles on wikipedia is kept to a minimum (like other paperbased encyclopedias).  In fact, I would say that what is one wikipedia right now suffices for this pupose, so no extra work would need to be done in wikipedia.--[[User:B21.12.52.123|B21.12.52.123]] 22:47, 13 December 2005 (UTC)  

:: I would like to know more specifics on how you propose to decide who is allowed to edit a page. [[User:Dmharvey|Dmharvey]] 22:10, 13 December 2005 (UTC)

:::I'll post some ideas soon...--[[User:B21.12.52.123|B21.12.52.123]] 22:47, 13 December 2005 (UTC)

::::Bad idea, as far as I'm concerned. We have a perfectly adequate framework for mathematical exposition here (modulo the troubles with symbols). Integrating mathematics with history, geography and intellectual trends goes on here in a way sadly missing in most texts. Our mathematics here is a clear advance on both PlanetMath and MathWorld, and the main current difficulty seems mostly to get ''enough'' people working on bringing the coverage up to date. We have the ''quality'' of people tp do that, so it's a matter of time, really. [[User:Charles Matthews|Charles Matthews]] 22:51, 13 December 2005 (UTC)

:::::I am leery of anything that might result in duplication of effort. Wikiscience should not be an encyclopedia, since we already have that here. Since that is how it has been defined above, I am against it. - [[User:Gauge|Gauge]] 05:27, 18 December 2005 (UTC)

What do you mean by: "Math and science is simply to technical and evolving of a subject to be thrown about with the rest of wikipedia articles.  Math and science, given its special nature of presentation and subject, needs to be … ''separate'' …". Are you saying that the math and science content should be moved from Wikipedia to Wikiscience? [[User:Paul August|Paul August]] [[User_talk:Paul August|&#9742;]] 22:54, 13 December 2005 (UTC)

: All this Wikiscience business makes me weary. Serious posts by anonymous contributors also (make an account, buddy).

: As Lethe said, there should be no limit to how technical or complicated articles on Wikipedia can get. Yes, one should strive to make things approachable, but within limit of common sense. 

: Some people might indeed be happy contributing to a project like Wikiscience (Linas is an example). But talking about moving (not copying, but moving) technical content from Wikipedia to there is not serious. [[User:Oleg Alexandrov|Oleg Alexandrov]] ([[User talk:Oleg Alexandrov|talk]]) 00:53, 14 December 2005 (UTC)

::OK, here's the rub: if WikiScience is offered as a ''competitor'' to WP, then I agree with Charles and Oleg: heavy-duty, in-depth science articles belong on WP. Furthermore, the creation of wikiscience will not "cure" any purported problem about lack of depth in WP articles. On the other hand, if Wikiscience is offered as a companion to WP, that's different. The "companion" properties I'd like to see are (1) encouragement of publication of original research and (2) total control of articles by primary authors. I envision the ideal companion to be an "arxiv.org with wikilinks and social infrastructure". 

::Set up as a companion in this way, it won't dilute resources: for example, I still do original research, and my doing that should not be construed a "dilution".  Another example: WP editors who are in constant clashes may find life to be more acceptable over there, since they'll always get thier way. Would thier departure be much of a loss to WP? Probably not. 

::The one thing I want to do, that WP won't let me do, is for me to keep a set of pages of my original reaserch, that I totally control. While I can do this on external websites, its not ideal. On my personal website, I'm missing a collaborative environment and a place to discuss. At planetmath, I'm missing the mediawiki interfaces I've grown accustomed to here. And its not "integrated" with WP: cross-linking is hard, visual presentation is different. On arxiv.org, I've got publication, and a stable, long-term document repository; but I'm missing collaboration, etc. What I would very much like to see in the WikiScience proposal is a solution to these problems. [[User:Linas|linas]] 00:58, 14 December 2005 (UTC)

: Wikipedia does not yet have an adequate solution to becoming a reputable encyclopedia. That issue must be addressed across all articles, not just science and mathematics. Incorporation of original research is a separate question, though quality control mechanisms may overlap. A reader is looking for coverage, correctness, and clarity. (Can I find what I want, including recent work? Can I believe what I read? Can I understand it?) A writer is looking for exposure, helpful feedback, and a vetting process that is expert and fair. (Also, perhaps, scholarly credit and article stability.)
: The WikiScience proposal might provide a venue for original research, but it does not address the Wikipedia-wide issues, and it does not provide the vital details of how readers and writers are to be satisfied. Note that Wikipedia, with no technical changes, could choose to flag some articles as "advanced". --[[User:KSmrq|KSmrq]]<sup>[[User talk:KSmrq|T]]</sup> 02:56, 14 December 2005 (UTC)

--[[User:B21.12.52.123|B21.12.52.123]] 11:02, 14 December 2005 (UTC)===Wikipedia vs Wikiscience===

'''First off''', I am not an annonymous user.  I chose this name arbitrarily when I was just starting to contribute to wikipedia articles.  If this name bothers any of you I guess I can change to a "normal" name.  My name is Parker W. and I am an ex-math major from the University of Oklahoma.  I am a real person lol...later on if this gets more support I will start a mailing group so people can contact me personally.

'''Charles Matthews:''' Wikipedia as it stands is FAR from any serious math resource.  The trial of Michael Jackson is like 10 times longer and more complex than the article on E.  Given E is one of the most beautiful and important numbers in math, this is a travesty or at least an embarrasment to wikipedia's scope in math.

:Show me where else on the Web you can find a page like [[Enriques-Kodaira classification]]. [[User:Charles Matthews|Charles Matthews]] 09:43, 14 December 2005 (UTC)

::Great article, but this is simply out of place here.  No one will look at it here; this is akin to sticking this article in Encyclopedia Brittanica...its just awkward here.  Wouldnt you rather it be at a place it can be respected and used?  '''People DONT come here for serious math and science research/enrichment/collaborations and those of you who think so are in denial: you are wasting your time here with these advanced articles!'''  They need a proper HOME; such as wikiscience.--[[User:B21.12.52.123|B21.12.52.123]] 09:59, 14 December 2005 (UTC)

:That is nonsense, and annoying nonsense at that. [[User:Charles Matthews|Charles Matthews]] 10:06, 14 December 2005 (UTC) 
::Agreed.  It is nonsense.  As wikipedia grows in coverage, every math grad student in the world will know to come here.  This article will certainly see use.  Who cares how it compares to Michael Jackson? -[[User:Lethe|lethe]] [[User talk:Lethe|<sup>talk</sup>]] 10:16, 14 December 2005 (UTC)

::I looked at said article here just a couple of days ago. I am a PhD student, and I found it fascinating and useful. - [[User:Gauge|Gauge]] 05:48, 18 December 2005 (UTC)

:::The comparison with the MJ article was used by me as an example of the focus of the general user base of wikipedia.  Wikipedia, by its nature, is constantly ''regressing'' to the mean, that is, the interests of the "average" person.  This is completely fine in most cases when you need information on popular topics but is completely disabling to the promotion of advanced non-popular topics.  I did a little walkthrough of wikipedias science as math articles and about 20% of the time the article said "this article needs the attention of an expert".  Gee, thats a real affirmation of wikipedias strength in math and science; and this isnt in the beggining stages, this is after 4 YEARS of wikipedia.

:::Face it; it is a vicious cycle.  You are surrounded by people who don't care about any of this stuff and never will.  The articles (or lack therof) show it.  What we need is a different ''framework'' and community of more like-minded people, similar to PlanetMath, but much much better, parterned with wikipedia.  Don't throw your pearls amoung the swine!--[[User:B21.12.52.123|B21.12.52.123]] 11:00, 14 December 2005 (UTC)

:I agree with Charles; Wikipedia's mathematics coverage is one of its high points. -- [[User:The Anome|The Anome]] 10:10, 14 December 2005 (UTC)

::Of course you do.  Your POV is that of a mathlover (or I assume you wouldnt be here).--[[User:B21.12.52.123|B21.12.52.123]] 11:03, 14 December 2005 (UTC)

'''Paul August and Oleg:'''  As I said before ''"...that is, wikipedia (like any other encyclopedia) should still have relatively simply worded and accessable concepts in math and science, but for more in-depth and up-to-date modern (and original research from users) research, plus more in depth on the "simple" concepts, wikiscience would be the home.  Does this divide contributers?  Not if the technicality of the articles on wikipedia is kept to a minimum (like other paperbased encyclopedias).  In fact, I would say that what is one wikipedia right now suffices for this pupose, so no extra work would need to be done in wikipedia"''

That is, WikiScience is in my mind a ''companion'' to Wikipedia.  As any encyclopedia, Wikipedia will have entries on math and science, moving them or getting rid of all the math and science articles in wikipedia would be absurd.  However, for the lastest "peer-reviewed" (at least compared to wikipedia) research, both amateur and professional, for indepth technical articles suitable to those in the math and science fields, and for proper ''organization'' and stucture that is helpful to those seeking mathematical and scientific information, WikiScience will serve that function.

'''C'est la vie''' remarked that "wikipedia wants to be the sum total of human knowledge".  This is not correct.  Wikipedia, however revolutionary and huge it my be, is still an encyclopedia and has many guidelines as to what shouldn't be in the encyclopedia such as definitions of words, news stories and the like.  This is why wikitionary, wikinews were created, respectively.  The content matter of these sister projects is just to different to be mixed in with what is suppost to be an '''encyclopedia'''.
:First of all, my username is [[User:Lethe|Lethe]], not '''C<nowiki>'</nowiki>est la vie'''.  Second of all, Jimbo himself said:
:::"Imagine a world in which every single person on the planet is given free access to the sum of all human knowledge. That's what we're doing." -Jimmy Wales, July 2004
:Therefore, I believe all math knowledge that has been vetted by the publication process should be here.  Thus WikiScience will only be appropriate as a place for pet projects and crackpots.  Once something is published, it needs to be here, as soon as someone is ready and able to put it.  We are not bound to keep things down to high school knowledge here, and I think that suggestions to limit the amount or extent of knowledge to go here will be rabidly opposed. -[[User:Lethe|lethe]] [[User talk:Lethe|<sup>talk</sup>]] 10:20, 14 December 2005 (UTC)

:: Hey, folks, [[WP:BITE|don't bite]]. And [[User:B21.12.52.123|B21.12.52.123]], you might want to spend a little more time acquainting yourself with Wikipedia's culture, values, processes, and content before you try to reform it. (It's hard to get people to follow you if you're stepping on their toes.) --[[User:KSmrq|KSmrq]]<sup>[[User talk:KSmrq|T]]</sup> 11:43, 14 December 2005 (UTC)

As is with what I proposed to be put in wikiscience.  But just because ''wikinews'' and ''wiktionary'' were created, doesnt mean that all articles defining words and all articles reffering to current events were removed!  These articles in math and science which are "different" are what I call technical articles.

'''"Techical vs "non-technical" math and science articles '''


Technical articles and qualitatively and quantitively different from non-technical articles, as I shall dub them, which are currently in wikipedia.

The key difference is rigor.  Going back to my example of the Michael Jackson trial (no offence to MJ:)), a minor detail such as, Mr. Mesereau's shows were black at the trial would have no effect on the overall information of the article.  If that were in-fact, not true, than the article would not be compromised.  

With a techical article it WOULD be compromised if a small detail was wrong, unfounded, or erronious.  The ENTIRE article would be compromised in the eyes of any serious student/enthusiast or researcher.  This is why we have CRC handbooks, Mathematical encyclopedias, or resources such as the arxiv.  Now this does not mean that any of the articles in math and science here are "wrong" or "unfounded" or inadequate, it just means that they serve a different purpose from technical articals.  This is that of ''exposition''.  Technical articles are not generally expository (all though than can be), are more in-depth, and contain more "sensitive" topics (topics that the reader my require a corresponding source or cite, as well as a cite of proof).  One is not "better" than the other, they are just serving different needs.  Wikipedia currenty does not meet the latter's needs.

What is the crucial difference then that wikipedia can't facilitate?  This is that of ''critical review''.  Critical review is the lifeblood of technical articles.  I will wait and give my list of possible implementations of critical review just in case you guys want to respond to anything I said of have criticisms or concerns of what I just posted.

--[[User:B21.12.52.123|B21.12.52.123]] 05:04, 14 December 2005 (UTC)

'''IN SUMMERY:''' '''WikiScience is to Wikipedia as The CRC Handbook plus Mathword plus summeries of discoveries in the latest math and science journals, plus orginal contributions from users and professionals is to Encyclopedia Brittanica. '''  Neither one is "better" they are just different.  Wikipedia will still have math and science articles just as Brittanica does. 


:There might be a place for a wiki which allowed original research in mathematics. However in my opinion Wikipedia is currently the best single resource for mathematics. And I expect it to remain so for a long time to come. I can see no good reason to restrict Wikipedia to only a certain level of mathematical sophistication.  [[User:Paul August|Paul August]] [[User_talk:Paul August|&#9742;]] 05:11, 14 December 2005 (UTC)

:: Wikipedia is already restricted in mathematical sophistication...visit the article on E like I mentioned.  It is ''WikiScience'' that would be unrestricted.  You are not going to find a technical article on E even in the greatest paper based encyclopedias because thats not what they are there for, wikipedia is no different.--[[User:B21.12.52.123|B21.12.52.123]] 05:25, 14 December 2005 (UTC)

:::Time to up the sophistication level of the ''e'' article, then. -- [[User:The Anome|The Anome]] 10:12, 14 December 2005 (UTC)
Regardless of the current quality of math wikipedia, we aim to subsume EB, CRC Handbook (isn't that just a table of data?  That actually, we will not subsume), mathworld, EDM2, Soviet encyclopedia, and others.  -[[User:Lethe|lethe]] [[User talk:Lethe|<sup>talk</sup>]] 10:50, 14 December 2005 (UTC)

:"We" aim?  You and who else?  Are you implying that a small group of people could assimilate that much information into wikipedia?  Its going to take an army of nerds to do it.  That is the key.  We need to create an accomadating environment that attracts NERDS and specialists.  This environment would include proper peer-review that specialists desire, collaboration possibilities, original research inclusion, everything that a math and sci specialist or enthusiast WANTS and needs.  Well guess what?  That isnt wikipedia.  So whats happening?  A lone band of nerds (I use that term in the utmost respect) is trying to assimilate huge bodies of knowledge into a place that isnt meant for them.  We need a '''NERD ARMY''' my friend, and that army won't assemble at wikipedia.   

--[[User:B21.12.52.123|Hypergeometric2F1&#91;a,b,c,x]]] 11:29, 14 December 2005 (UTC)  

:We had this once.  It was called [[Nupedia]].  [[Larry Sanger]] has been lamenting its demise for years, and making calls to arms to restore an expert-based, limited-editing pedia for just as long.  It's not a terrible idea, but just so you know, it's been tried already, and people aren't to keen to give it another go here at wikipedia. -[[User:Lethe|lethe]] [[User talk:Lethe|<sup>talk</sup>]] 11:45, 14 December 2005 (UTC)

:: Looks like I missed this conversation overnight. I'd just like to say I sympathise with the points expressed by Charles, Lethe, Paul, etc, and not so sympathetic to B21.12.52.123. [[User:Dmharvey|Dmharvey]] 12:55, 14 December 2005 (UTC)
----

I have joined the Wikipedia:Project Mathematics and have introduced myself on the participants 
page.  I will keep campaigning for this idea, but in the meantime I will contribute what I can and see what happens.
--[[User:B21.12.52.123|B21.12.52.123]] 06:58, 14 December 2005 (UTC)

I have also created a new nickname to assuade confusion --[[User:B21.12.52.123|Hypergeometric2F1&#91;a,b,c,x]]] 11:18, 14 December 2005 (UTC)

::Welcome to the project B21/Hypergeometric. Yes it will take a lot of people and considerable time to create all the content we envision, but fortunately we have many qualified mathematics editors and all the time in the world. Are you familiar with all the content that [[Wikipedia:WikiProject Mathematics/Participants|this small "army of nerds"]] and others have already created (see [[List of mathematical topics]] and [[List of lists of mathematical topics]])?  I think your idea of joining the Mathematics Project to gain some experience in how Wikipedia works (or doesn't as the case may be) is a good one. You are correct in saying that original research, being non-encyclopedic, has no place on Wikipedia, and as I said above a separate wiki that allowed that might be a good idea. But for encyclopedic content I think it will be very hard to do better than Wikipedia. Again welcome. [[User:Paul August|Paul August]] [[User_talk:Paul August|&#9742;]] 15:07, 14 December 2005 (UTC)

===Debunking a claim===

Above, [[User:B21.12.52.123|Hypergeometric2F1&#91;a,b,c,x]]] wrote that 

:''I did a little walkthrough of wikipedias science as math articles and about 20% of the time the article said "this article needs the attention of an expert".''

Well, I counted all the mathematics and mathematician articles which have either a {{tl|attention}} or {{tl|cleanup}} or {{tl|expert}} template either in the article or on its talk page. I found 98 of those. [[Wikipedia:WikiProject Mathematics/Current activity|Jitse's tool]] states that there are 33 more at [[Wikipedia:Pages needing attention/Mathematics]] (and thre could be an overlap with the first 98). All in all, we get 131 pages needing attention of a total of 11000-11713 articles, which is 1.19%, a far cry from 20%. [[User:Oleg Alexandrov|Oleg Alexandrov]] ([[User talk:Oleg Alexandrov|talk]]) 22:14, 14 December 2005 (UTC)

:[[User:Ems57fcva|EDS]] told me that the "Nature" magazine is actually quite positive about Wikipedia: "Researchers should read Wikipedia cautiously and amend it enthusiastically." [http://www.nature.com/news/2005/051212/full/438890a.html]. -- [[User:Jitse Niesen|Jitse Niesen]] ([[User talk:Jitse Niesen|talk]]) 23:09, 14 December 2005 (UTC)

:: For the last time I am not ''dissing'' wikipedia, I like wikipedia I just think that as a pluralistic encyclopedia it will be constantly regressing toward the mean interests of the populace which excludes higher math.  Wikipedia lacks the sophistication, community, and peer-review that is required for serious content that can be relied upon by people in research communities.  

::Never the less, I am ending this argument for now, as I have just realized I am a big IDIOT for coming in here and saying that wikipedia lacks something to people that are still here working to better it after all this time.  Honestly, I want you guys to succeed and I will add various things to wikipedia myself (I'm currently practicing my LaTeX), however I don't think it will really take off.  In the meantime, I am thinking of ways to implement a math original research wiki so we'll see how that goes.--[[User:B21.12.52.123|Hypergeometric2F1&#91;a,b,c,x]]] 05:29, 15 December 2005 (UTC)
::: The point of this subsection is that you have been overblowing things out of proportion. Now, the math on wikipedia project took off a long time ago, and is actually sucessful. As far as your original research wiki, we shall see. Good luck practising LaTeX and the new research wiki. [[User:Oleg Alexandrov|Oleg Alexandrov]] ([[User talk:Oleg Alexandrov|talk]]) 16:51, 15 December 2005 (UTC)
::: You came in boldly wanting to make things better, and your attempt was awkward. Sounds like a typical new Wikipedian to me. Welcome. --[[User:KSmrq|KSmrq]]<sup>[[User talk:KSmrq|T]]</sup> 22:07, 15 December 2005 (UTC)

== Strange Reflections of Wikipedia ==
If you use Yahoo to find references to superlogarithm you will discover some interesting clones of Wikipedia pages. The term superlogarithm appeared on a past version of the [[tetration]] page, but now appears almost nowhere else on the net. Now the term superlogarithm appears on both the Free WebCam Tetration and Sex Pictures Logarithm pages of a rather unusual Wikipedia clone at newpenisenlargement.com. [[User:Daniel Geisler|Daniel Geisler]]

:Haven't you heard? newpenisenlargement.com is the number one mathematics resource on the net! - [[User:Gauge|Gauge]] 02:58, 23 December 2005 (UTC)

== Integer group names ==

I would dearly love to rewrite the following:
:: The finite group can be '''Z'''/2'''Z''', '''Z'''/2'''Z'''+'''Z'''/2'''Z''', '''Z'''/3'''Z''', '''Z'''/3'''Z'''+'''Z'''/3'''Z''', '''Z'''/4'''Z''', '''Z'''/4'''Z'''+'''Z'''/2'''Z''', or '''Z'''/6'''Z''', giving 7 families of such surfaces.
I find it almost unreadable, because of the insistence on quotient notation. I would prefer subscripts:
::The finite group can be '''Z'''<sub>2</sub>, '''Z'''<sub>2</sub>+'''Z'''<sub>2</sub>, '''Z'''<sub>3</sub>, '''Z'''<sub>3</sub>+'''Z'''<sub>3</sub>, '''Z'''<sub>4</sub>, '''Z'''<sub>4</sub>+'''Z'''<sub>2</sub>, or '''Z'''<sub>6</sub>, giving 7 families of such surfaces.
From my background, this is merely a matter of different conventions. Yet I get the feeling that some people feel uncomfortable with the subscript notation and habitually use quotient notation. What's up with that? --[[User:KSmrq|KSmrq]]<sup>[[User talk:KSmrq|T]]</sup> 11:54, 14 December 2005 (UTC)
:I think the subscript is preferred for [[p-adic numbers]], and the quotient notation is preferred for modular groups to avoid confusion.  I think it should be OK to use the subscript as long as you clarify that you are talking about the quotient groups. -[[User:Lethe|lethe]] [[User talk:Lethe|<sup>talk</sup>]] 12:05, 14 December 2005 (UTC)
::[[Wikipedia:WikiProject Mathematics/Conventions]] for where we are on this. [[User:Charles Matthews|Charles Matthews]] 12:42, 14 December 2005 (UTC)

Thanks for the replies. From my reading of the conventions talk page, it appears that '''Z'''<sub>''n''</sub> has three possible interpretations: (1) the additive group of integers modulo ''n'', (2) the ring of integers modulo ''n'', and (3) the ''p''-adic numbers with ''p''&nbsp;=&nbsp;''n''. I take it that for ''n'' prime, we would use a different notation if we mean the [[Galois field]]. Are there any other ambiguities I should be aware of? And do the interpretations differ more by area of mathematics, or area of the globe?

One reason I ask is because the article with the opaque quotient notation was talking about algebraic topology groups (no cohomology rings), where ''only'' interpretation (1) would make sense (so far as I know), yet quotients were used anyway. (Furthermore, the sentence itself tells us we're talking about groups.) So I'm trying to get a better understanding, not of just ''what'' people do, but ''why''.

I understand it can be hard to explain choices; for example, I know for me there are contexts in which I would always use ''C''<sub>''n''</sub>, and others in which I would never do so, but use '''Z'''<sub>''n''</sub> instead. Still, any further insights would be appreciated. --[[User:KSmrq|KSmrq]]<sup>[[User talk:KSmrq|T]]</sup> 02:02, 15 December 2005 (UTC)

:I don't know what article or context we're talking about, but in my experience, the cyclic group '''Z'''<sub>''n''</sub> is written multiplicatively while the cyclic group '''Z'''/''n'''''Z''' is written additively. So, it's a little strange to see "'''Z'''<sub>2</sub>+'''Z'''<sub>2</sub>". On the other hand, it's far easier to read, so I'd prefer it. [[User:Melchoir|Melchoir]] 04:38, 16 December 2005 (UTC)
:: Curious. Compare your expectations against our [[Wikipedia:WikiProject Mathematics/Conventions|conventions]]. (The original context is not so important, it merely provoked my question; but it was a page mentioned here in another thread, [[Enriques-Kodaira classification#Hyperelliptic_.28or_bielliptic.29_surfaces.|Enriques-Kodaira_classification]].) --[[User:KSmrq|KSmrq]]<sup>[[User talk:KSmrq|T]]</sup> 08:33, 16 December 2005 (UTC)
:::Huh. Well, I guess conventions wouldn't be any fun if we didn't have lots of them. [[User:Melchoir|Melchoir]] 08:57, 16 December 2005 (UTC)

== templates revisited ==

Today I happened across an old conversaion I had with Oleg a few months ago on [[Talk:Transcendental number]] about templates in the math project (the discussion also arrived here; see [[Wikipedia talk:WikiProject Mathematics/Archive10|archive]]).  We all pretty easily voted to delete them: [[Template:change]], [[Template:structure]], [[Template:space]], and [[Template:quantity]].  I'm a mild [[inclusionist]] and was a little nervous about so much deletion, but I was assuaged when I saw [[Template:Mathematics-footer]].  My main concern was lack of consistency across other technical subjects (confer [[Template:Natural sciences-footer]] and [[Template:Physics-footer]], for example), and this one addresses that fine.  Today, upon tripping on the old discussion, I noticed that while we do have this template, it's pretty much unused.

So how do we feel about these templates these days?  Are they useful as a navigational tool?  Is it worth having this one for the sake of consistency?  I'm somewhat inclined to add the footer to all the articles mentioned within.  Here it is, for reference. -[[User:Lethe|lethe]] [[User talk:Lethe|<sup>talk</sup>]] 16:12, 14 December 2005 (UTC)
{{Mathematics-footer}}

: Hey, whom are you calling a deletionist? :) [[User:Oleg Alexandrov|Oleg Alexandrov]] ([[User talk:Oleg Alexandrov|talk]]) 18:23, 14 December 2005 (UTC)

== Proposed renaming ==

There has been some discussion about renaming the pages linked to from the following template:
{{MathTopicTOC}}

The current proposal is as follows:

{| border=1 cellpadding=2 style="border: 1pt solid black; border-collapse: collapse; margin-left: 2em;"
|-
! Current name || Proposed name
|-
| [[List of mathematical topics]] || [[List of mathematics articles]]
|-
| [[List of mathematical topics (A)]] || [[List of mathematics articles (A)]]
|-
| [[List of mathematical topics (B)]] || [[List of mathematics articles (B)]]
|-
| ''etc.'' || 
|-
| [[List of lists of mathematical topics]] || [[List of mathematics lists]]
|}

Older discussion on this topic may be found at [[Talk:List of lists of mathematical topics#Renaming this page]].

Comments? Objections? If you agree, please state so. -- [[User:Fropuff|Fropuff]] 03:19, 15 December 2005 (UTC)

*For the record, I '''agree''' with this proposal. -- [[User:Fropuff|Fropuff]] 03:21, 15 December 2005 (UTC)
* '''Support'''. The [[List of mathematical topics (A)]] has no topics in it, all are articles. [[User:Oleg Alexandrov|Oleg Alexandrov]] ([[User talk:Oleg Alexandrov|talk]]) 03:27, 15 December 2005 (UTC)
* '''Support'''. The new names describe the content of the articles far better than the old names. <small>&mdash;''the preceding [[User:Tompw|Tompw]] 18:12, 16 December 2005 (UTC)''</small>
* '''Support'''. This all seems good. [[User:Paul August|Paul August]] [[User_talk:Paul August|&#9742;]] 22:45, 15 December 2005 (UTC)
* '''Sopport'''.  Lot of renaming this involves! --- [[User:Chalst|Charles Stewart]] 18:26, 16 December 2005 (UTC)
: Done. Now is the time to go edit your watchlist and remove from there all the redirects this move created. :) [[User:Oleg Alexandrov|Oleg Alexandrov]] ([[User talk:Oleg Alexandrov|talk]]) 03:36, 23 December 2005 (UTC)
::Thanks for doing the grunt work on this Oleg. I wasn't looking forward to it. -- [[User:Fropuff|Fropuff]] 04:49, 23 December 2005 (UTC)

== Organizing the math pages needing attention ==

See [[Wikipedia talk:Pages needing attention/Mathematics#Listing the pages needing attention]] for some discussion. [[User:Oleg Alexandrov|Oleg Alexandrov]] ([[User talk:Oleg Alexandrov|talk]]) 05:30, 15 December 2005 (UTC)

== External peer review by ''Nature'' ==

I turn your attention to [http://www.nature.com/news/2005/051212/full/438900a.html this article by ''Nature''] and [[Wikipedia:External_peer_review#Nature|Wikipedia's response]]. [[User:Karol Langner|Karol]] 06:04, 15 December 2005 (UTC)

I just wanted to say I enjoy this resource and find it useful.  I am not a mathematician or a statistician, although I use both a fair bit in my work.  I learned a great deal from this very forum over a few days just last month.  Wikipedia will only improve with time.  Comparing Wikipedia with Encyclopedia Britannica at this point hardly seems fair.  Wikipedia has been around for, what, 5 years.  Encyclopedia Britannica has been around “forever”.  If Wikipedia compares favorably with Encyclopedia Britannica already in at least some regards imagine what Wikipedia might be like 20 years from now.

I also think that technical articles are great.  Personally I would prefer that more of them have examples and references.  But this forum and the math help desk have been helpful to me in climbing the learning curve on technical issues.  Some things I’ve learned here I tried off-and-on unsuccessfully to learn elsewhere on the internet over the course of several years.

As for the reliability of Wikipedia, perfect reliability is, in a Popperian sense, perhaps an unattainable ideal in that all of science is constantly being revised.  Although, examples and references are one way for the reader to verify factual information and the state of the art as described in Wikipedia articles.  As such, examples and references act, to an extent, like peer review.

I guess my point is that people will find these articles, will use these articles, and will be glad you wrote them, regardless of how specific or technical those articles may be… …particularly if those articles contain examples and references and are aimed at people who don’t know as much as you do about the subject.  

I didn’t know the most appropriate place to put my comments so I stuck them here.  Sorry if these comments are out of place.
[[User:Mark W. Miller|Mark W. Miller]] 06:41, 20 December 2005 (UTC)

==Original research wiki==

I have created a discussion page for the implementation of a wiki, [http://meta.wikimedia.org/wiki/Talk:Wikipolis#Structure_of_Wikipolis Wikipolis], allowing for dynamic collaborations, original research, and some form of peer-review.  I invite you all to add your ideas!--[[User:B21.12.52.123|Hypergeometric2F1&#91;a,b,c,x]]] 10:01, 15 December 2005 (UTC)

==Somer pseudoprime==

[[Somer pseudoprime]] is a puzzling new page, and hard to verify through Google. [[User:Charles Matthews|Charles Matthews]] 22:11, 16 December 2005 (UTC)
: I've corrected a typo, and corrected the wikilinks, but ... '''ALL''' Google entries with [[Somer pseudoprime]] but without [[Wikipedia]] [http://www.google.com/search?hl=en&q=%22Somer+pseudoprime%22+-wikipedia&btnG=Google+Search] are copies of the wikipedia entries for [[25 (number)|25]] or [[49 (number)|49]]. [[User:Arthur Rubin|Arthur Rubin]] | [[User_talk:Arthur_Rubin|(talk)]] 23:48, 16 December 2005 (UTC)
::Someone should look at [[Somer-Lucas pseudoprime]] at the same time. Right now it's copyvio from MathWorld, but even if it weren't, it'd still be a bare definition without context. The MathWorld article at least has a reference,
:::Ribenboim, P. "Somer-Lucas Pseudoprimes." §2.X.D in The New Book of Prime Number Records, 3rd ed. New York: Springer-Verlag, pp. 131-132, 1996.
::If someone has the book, maybe it'll show cause why both articles shouldn't go to AfD. --[[User:Trovatore|Trovatore]] 21:16, 17 December 2005 (UTC)
:::For what it's worth, they are not mentioned in Ribenboim, The Little Book of Big Primes. This is the abridged version of The New Book of Prime Number Records, which we do not have in our library. -- [[User:Jitse Niesen|Jitse Niesen]] ([[User talk:Jitse Niesen|talk]]) 15:59, 19 December 2005 (UTC)

Since the [[On-Line Encyclopedia of Integer Sequences]] reference is only from 2003, I see no good reason to have this hanging around. [[User:Charles Matthews|Charles Matthews]] 16:17, 19 December 2005 (UTC)

:Jitse, Charles, please clarify: Are you talking about Somer, Somer-Lucas, or both? My gut says get rid of both, at least as they stand. --[[User:Trovatore|Trovatore]] 19:56, 19 December 2005 (UTC)
::Both. Furthermore, I would delete them if it were up to me. But I'm hesitant to cite nonnotability as a reason for deletion. -- [[User:Jitse Niesen|Jitse Niesen]] ([[User talk:Jitse Niesen|talk]]) 20:32, 19 December 2005 (UTC)
:::My take (although I'm relatively new as a Wikipedian).  [[Somer pseudoprime]] -- delete as neologism.  [[Somer-Lucas pseudoprime]] -- delete as copy-vio '''and''' nonsense, because of the ''d''. [[User:Arthur Rubin|Arthur Rubin]] | [[User_talk:Arthur_Rubin|(talk)]] 23:43, 19 December 2005 (UTC)

== Math pages needing attention ==

Somewhere above, in the discussion about wikiscience, a claim was made that around 20% of math articles need attention of an expert. Well, the number is just a fraction of that, for the moment 1.54%, meaning 169 articles, but that's still a big number. On Fropuff's suggestion, I wrote a script which will daily add to [[Wikipedia:Pages needing attention/Mathematics]] math pages having various attention templates, like {{tl|cleanup}}, {{tl|expert}} etc. So, I'd just like the community to be aware of that page (most of us are, I think), and visit it from time to time. :) [[User:Oleg Alexandrov|Oleg Alexandrov]] ([[User talk:Oleg Alexandrov|talk]]) 02:37, 17 December 2005 (UTC)

:More depressingly, about a quarter of the articles are tagged as stubs. -- [[User:Jitse Niesen|Jitse Niesen]] ([[User talk:Jitse Niesen|talk]]) 13:13, 17 December 2005 (UTC)
::  I don't see that as such a big problem. Would we better off if those stub articles did not exist at all (8000 long articles without the extra 3000 stubs)? Often times an article grows only gradually, and a stub may inspire somebody to expand it, without having to start from zero. Besides, many stubs are complete enough, one just should remove the stub tag. I am more depressed when I see really badly written articles, and/or with errors. So, [http://bible.cc/matthew/19-14.htm let the little ones come to me] :)  [[User:Oleg Alexandrov|Oleg Alexandrov]] ([[User talk:Oleg Alexandrov|talk]]) 18:07, 17 December 2005 (UTC)
:::I was thinking, if an article is a stub, and probably will never be anything more than a stub, does that mean it should probably just find a home as a section in another article?  I was thinking of my recent stub [[invariant basis number]].  That article might be comfortable as a section in [[dimension theorem for vector spaces]].   -[[User:Lethe|lethe]] [[User talk:Lethe|<sup>talk</sup>]] 21:03, 17 December 2005 (UTC)
::::I have no problem with "small" articles like this. If this is all that can be said about this, then we should just remove the stub tag. [[User:Paul August|Paul August]] [[User_talk:Paul August|&#9742;]] 21:31, 17 December 2005 (UTC)

:::: (replying to Lethe after an edit conflict.) That merging idea may work in specific cases, but I would not apply it as a general principle. Often times one may want to look up a specific term, and it may not make sense to read an entire article on a bigger concept to find that term. Also, you may create that section in the bigger article containing the stub, but nobody knows for how long that material will stick around before being edited out. 

:::: And I would not be totally opposed to a concept showing up both in its own stubby article and as a section in something bigger. In short, I would argue that one should use a lot of caution when eliminating stubs by merging, and if not sure, err on the side of leaving the stubs as they are. [[User:Oleg Alexandrov|Oleg Alexandrov]] ([[User talk:Oleg Alexandrov|talk]]) 21:38, 17 December 2005 (UTC)

:::::Yes I agree with all of what Oleg says. I think a lot of people think that, for the sake of efficiency, content should not be "duplicated". But while that might be best for a book say, it might not make so much sense for Wikipedia. Moreover I think it is a benefit to have several articles from different points of view (not in the sense of POV). That is, an article about "invariant basis number" can address that content in a different way than "dimension theorem for vector spaces" would. [[User:Paul August|Paul August]] [[User_talk:Paul August|&#9742;]] 21:55, 17 December 2005 (UTC)

Actually, we may need those stubs. My feeling is that we have plenty of graduate students and other useful people editing anonymously, who currently are not able to start articles. We should aim to add 'good stubs' on many topics. [[User:Charles Matthews|Charles Matthews]] 22:07, 17 December 2005 (UTC)

: My understanding is that the ban on anons creating new pages is an experiment. An important question to be answered is whether the imposition of creating an account substantially diminishes valuable contributions. I wonder how we would be able to decide the impact on new pages. You seem to be anticipating a visible loss; I'm inclined to think otherwise. We shall see. --[[User:KSmrq|KSmrq]]<sup>[[User talk:KSmrq|T]]</sup> 06:03, 18 December 2005 (UTC)

::Well, we don't know. We can't know whether the creator of [[Andreotti-Frankel theorem]] would have been happy to log in. There are issues in using institutional IT systems, and I certainly don't know what they might be. In any case my argument is not based on speculation on the possible harmful effects, which are hard to establish, but on the idea that the 'good stub', which in the past has been a big factor in developing WP, is still a good idea. What is more, as mathematicians, we should be the greatest appreciators here of the effects of exponential growth: if the red links in each article are still triggering a branching proportional to the size of the article base (say, in advanced parts of mathematics), then probably it is futile to worry too much about getting down the stubs as a proportion. That will only happen when we get closer to 'saturation' of the subject, so that the intellectual map 'closes up'. [[User:Charles Matthews|Charles Matthews]] 09:29, 18 December 2005 (UTC)

::: Your original wording ties stub need to anon creation ban. But as you elaborate, stubs can stimulate growth, regardless. As I understand the history of Wikipedia and its ilk, there has long been a tension between attracting quantity and assuring quality. Apparently, it's easy to guess wrong. I'm certainly curious to know the outcome. Anyway, I'm not currently nervous about having too many stubs; sometimes a stub tag just means the editor feels insecure about her expertise, which is better than overconfidence. --[[User:KSmrq|KSmrq]]<sup>[[User talk:KSmrq|T]]</sup> 10:54, 18 December 2005 (UTC)

::Actually, attracting mathematicians is a good idea, period. They tend to have other interests and a fact-based approach, and this makes them effective contributors to WP as a whole. [[User:Charles Matthews|Charles Matthews]] 11:13, 18 December 2005 (UTC)

::::Just to clarify, I did not mean to say that stubs are bad. My remark was in response to Oleg's, who said that 1.54% of the articles need attention of an expert. I wanted to say that it could be argued that stubs should be included in that number. Of course, a stub is better than no article, just like a messy article or one that is too technical is better than no article; it seems we all agree on that (on the other hand, an article riddled with errors is worse than no article, in my opinion). -- [[User:Jitse Niesen|Jitse Niesen]] ([[User talk:Jitse Niesen|talk]]) 13:40, 18 December 2005 (UTC)

:::::So I think a stub is ''usually'' better than no article, but I'd like to propose that an exception is when an entry from "requested articles" is fulfilled with an uninformative stub. My request would be, if you don't know something substantial about the topic, please leave it for someone who does. I recall a particular case where someone requested [[Joe Blow]] in the "mathematicians" section of requested articles, and someone else immediately wrote a stub that said simply "'''Joe Blow''' is a mathematician". My intuition is that this action substantially ''reduced'' the probability that we'd have an informative article about Blow in the near future, because it took him off the requested list. --[[User:Trovatore|Trovatore]] 19:53, 18 December 2005 (UTC)

::No one would call that a 'good stub'. [[User:Charles Matthews|Charles Matthews]] 22:50, 18 December 2005 (UTC)

::There is such a thing as [[Wikipedia:Requests for expansion]] which is supposed to complement [[Wikipedia:Requested articles]] and deal with precisely this, but it doesn't get as much press.  I can see that it has the potential to become wildly out of control like [[:Category:Stubs]], but perhaps we should encourage its use?  List it on [[Wikipedia:WikiProject Mathematics/Current activity|Jitse's wonderful current activity page]]?  —[[User:Blotwell|Blotwell]] 23:25, 20 December 2005 (UTC)

== Merry Christmas! ==

Merry Christmas, all! (... with the understanding that paganism is older than Christianity, either way, cheeriest of holidays!)  [[User:Linas|linas]] 02:41, 25 December 2005 (UTC)

: Yes, why not. [[User:Dmharvey|Dmharvey]] 03:13, 25 December 2005 (UTC)
:: Why not? Now that's a great answer! :) Let me try a proper response:

:: Ho-ho! Merry Christmas to you all! Wish you a Happy New Year, lots of edits, less wiki-stress, and that you also spend some healthy time outside this addictive place! And whatever else you wish for yourselves or others! [[User:Oleg Alexandrov|Oleg Alexandrov]] ([[User talk:Oleg Alexandrov|talk]]) 03:52, 25 December 2005 (UTC)

::: "lots of edits" and "spend some healthy time outside this addictive place" are mutually inconsistent. Unless the edits are very short. [[User:Dmharvey|Dmharvey]] 04:25, 25 December 2005 (UTC)

== A linear functional which is not continuous ==

I wrote the article [[A linear functional which is not continuous]] only to immediately discover on its [[Talk:A linear functional which is not continuous|talk page]] a suggestion to move it to [[Non-continuous linear functional]] (darn, everybody should be drunk and sleeping this post-Christmas morning, not checking the recent changes). What do people think (if it matters at all)? [[User:Oleg Alexandrov|Oleg Alexandrov]] ([[User talk:Oleg Alexandrov|talk]]) 17:36, 26 December 2005 (UTC)

:Isn't there a mechanism for providing both names for the article? Both seem fine... [[User:Randall Holmes|Randall Holmes]] 17:40, 26 December 2005 (UTC)

:By the way, I've been steadily editing through this period, and it has been <strong>awfully</strong> quiet :-)  Happy Hanukkah! [[User:Randall Holmes|Randall Holmes]] 17:41, 26 December 2005 (UTC)
:: Yeah, still quiet. :) Yes, there is a mechanism for providing both names, it is called a redirect, see [[Wikipedia:Redirect]]. So I guess the argument is about which is the primary meaning, for all that's worth. [[User:Oleg Alexandrov|Oleg Alexandrov]] ([[User talk:Oleg Alexandrov|talk]]) 02:31, 27 December 2005 (UTC)
I like the first name.  Compare with stuff like [[An infinitely differentiable function that is not analytic]].  Also, is "non-continuous" a word?  Shouldn't that be "discontinuous"? -[[User:Lethe|lethe]] [[User talk:Lethe|<sup>talk</sup>]] 03:02, 27 December 2005 (UTC)

: Personally, I don't like the idea of a name for an encyclopedic article beginning with "A". Also, I think the original proposed name is too long. I'd go for [[Non-continuous linear functional]]. But maybe it's just me. --[[User:Meni Rosenfeld|Meni Rosenfeld]] 12:49, 29 December 2005 (UTC)

:I agree with Meni; initial articles are okay if they are title of a book or work of art, but I don't think they belong in a general article.  Even if it has to do with showing existence.  Isn't there some other way to word it?  [[User:Gene Nygaard|Gene Nygaard]] 21:37, 30 December 2005 (UTC)

Hi there :) - the article was moved to [[A linear map which is not continuous]] - is that what people have decided on? Right now it looks like no consensus, but I thought I'd just give everyone a buzz... <small>[[User:RN|WhiteNight]] <sup>[[User talk:RN|<span style="color:#6BA800;">T</span>]] | [[Special:Emailuser/RN|<span style="color:#0033FF;">@</span>]] | [[Special:Contributions/RN|<span style="color:#FF0000;">C</span>]]</sup></small> 23:28, 30 December 2005 (UTC)

: How about [[linear map which is not continous]], dropping the leading "A" which makes people uneasy. The other option seems to be [[discontinous linear map]], based on above. [[User:Oleg Alexandrov|Oleg Alexandrov]] ([[User talk:Oleg Alexandrov|talk]]) 00:27, 31 December 2005 (UTC)

:: [[Discontinuous linear map]]/[[Discontinuous linear functional]] and [[Infinitely differentiable non-analytic function]] seem reasonable. We anyway don't expect people to search for and bump into these articles directly, and we are probably going to use these as examples to show that being a "linear map" doesn't imply being continuous, and smoothness doesn't imply analyticity, in main articles on linear maps and analytic functions, so I guess the title is not all that crucial. Bottomline: Unless we are missing on something important, the shorter the better. [[User:deeptrivia|deeptrivia]] ([[User talk:deeptrivia|talk]]) 00:44, 31 December 2005 (UTC)

I moved the article [[A linear functional which is not continuous]] to [[discontinuous linear map]] which seems to address all concerns on this page. I made a bunch of other alternative titles redirect to it. [[User:Oleg Alexandrov|Oleg Alexandrov]] ([[User talk:Oleg Alexandrov|talk]]) 19:57, 31 December 2005 (UTC)
: However, I find [[Infinitely differentiable non-analytic function]] a very clumsy name for [[An infinitely differentiable function that is not analytic]]. [[User:Oleg Alexandrov|Oleg Alexandrov]] ([[User talk:Oleg Alexandrov|talk]]) 19:57, 31 December 2005 (UTC)
::[[Non-analytic infinitely differentiable function]]? [[User:Pmanderson|Septentrionalis]] 06:29, 10 January 2006 (UTC)

== Anon's editing of Einstein ==

IP, 69.22.98.162 ([http://en.wikipedia.org/w/index.php?title=Special:Contributions&target=69.22.98.162 contributions]) has been making edits to [[Albert Einstein]], [[Henri Poincaré]] and [[David Hilbert]], essentially questioning the originality of Einstein's theory of [[special relativity]], giving as a source this: [http://www.xtxinc.com] (see [[Talk:Albert_Einstein#His Theory]] and [[Talk:Albert_Einstein#Nobel prise edit]]), all of which I think have been reverted (by me and others).  I don't really know much about the history of the development of relativity, (beyond what little I've read on Wikipedia), if anyone can shed any useful light on this, your help would be welcome. [[User:Paul August|Paul August]] [[User_talk:Paul August|&#9742;]] 23:01, 28 December 2005 (UTC)

:It is true that Poincaré had his own insights into Special Relativity and that Hilbert actually developed a theory of General Relativity about the same time Einstein did, but Einstein’s version was more complete. See [[History of general relativity]] and [http://nobelprize.org/physics/educational/relativity/history-1.html] for some background. I just read an article where it is argued that Einstein’s first wife, who was a physicist, should have been listed as a co-author of his work on Special Relativity or at least been acknowledged for her assistance. [[User:Daniel Geisler|Daniel Geisler]] 05:45, 28 January 2006 (UTC)

== Titles from another encyclopaedia ==
* {{On AFD|A001622}}
Now is your chance to answer the question: Should Wikipedia have redirects for OEIS titles? &#9786; [[User:Uncle G|Uncle G]] 01:58, 30 December 2005 (UTC)

==Domain of a partial function==
Currently there's an inconsistent usage among various articles that should probably be cleared up. [[Partial function]] claims that, given a partial function ''f'':''X''&rarr;''Y'', its domain is ''X''. I think the more standard usage is that the domain of ''f'' is the subset of ''X'' on which ''f'' is defined; this is the usage assumed in [[Recursively enumerable set]] and [[Uniformization (set theory)]]. I don't know a name for ''X'', though, given this convention. In any case we should standardize on one convention. My strong preference is for the second; I don't think I've seen the first convention used anywhere but WP. --[[User:Trovatore|Trovatore]] 19:32, 30 December 2005 (UTC)
:Well, I'm sure that the [[codomain]] always means ''Y'' and never ''f(X)'', which is the range.  It seems to me that the logical thing would therefore be to call ''X'' the domain and ''f<sup>-1</sup>(Y)'' the corange, so that a partial function is a function from its corange onto its range just as a module homomorphism is an isomorphism from its coimage to its image.  But I don't claim any knowledge of what's standard in this field.  —[[User:Blotwell|Blotwell]] 03:45, 31 December 2005 (UTC)

::Your suggestion has a pleasing symmetry but is definitely not standard. I am essentially certain that my convention ''is'' standard. What I don't know is a name for the ''X''; if anyone could tell me that, it would be easier to figure out how to fix [[Partial function]]. --[[User:Trovatore|Trovatore]] 05:04, 31 December 2005 (UTC)

:::Where I've learnt, we called ''Y'' the "range" and ''f(X)'' the "image", and for a partial function, we called ''X'' the "domain" and ''f<sup>-1</sup>(Y)'' the "preimage". While I would be happiest if that was the convention used in [[Wikipedia]], we could use your convention of ''Y''-codomain, ''f(X)''-range, while adopting ''X''-domain and ''f<sup>-1</sup>(Y)''-preimage (which I think is more standard than [[User:Blotwell|Blotwell]]'s corange. --[[User:Meni Rosenfeld|Meni Rosenfeld]] 14:20, 31 December 2005 (UTC)
::::The problem with "preimage" is it makes me want to ask, "preimage of what?". ("Image" has the same problem as a substitute for "range".) I strongly urge the adoption of "domain" to mean the set where ''f'' is defined (what Paul calls the "exact domain" below); I believe this is completely standard among recursion theorists, who are the people who most naturally come upon partial functions. What we need is a name for ''X'' (or I suppose we could just leave it unnamed if there's no standard name). --[[User:Trovatore|Trovatore]] 18:31, 31 December 2005 (UTC)

[http://www.ksl.stanford.edu/people/brauch/demo/frame-ontology/EXACT-DOMAIN.html This site] uses "domain" for ''X'' and "exact-domain" for  ''f<sup>-1</sup>(Y)''. When working In the category of sets and partial functions (often called '''PfN'''), ''X'' would be called the domain of ''f'' (at least as a morphism). [[User:Paul August|Paul August]] [[User_talk:Paul August|&#9742;]] 16:22, 31 December 2005 (UTC)
:So the [[morphism]] article mentions that an alternative name for the "domain" of a morphism is its "source" (clearly a better word when discussing abstract morphisms, which needn't be functions of any sort). Perhaps we could call ''X'' the "source" of the partial function, if that usage can be attested somewhere. That would free up "domain" for its more standard use. --[[User:Trovatore|Trovatore]] 18:37, 31 December 2005 (UTC)
:::I'm afraid "source" would be an unfortunate choice. In category theory, "domain" and  "codomain" is the standard terminology, since the term "source", would be in conflict with the fundamental categorical notion of "source" (dual "sink") as defined, for example, in: Adámek, Ji&#345;í, Herrlich, Horst, & Strecker, George E.; (1990). [http://katmat.math.uni-bremen.de/acc/acc.pdf ''Abstract and Concrete Categories''] (4.2MB PDF) (Chapter III: Sources and Sinks: 10.1, p. 169)  Perhaps we can we just retain ''X'' as the domain, but note however that in many contexts (e.g. recursion theory), the domain of a partial function ''f'' can mean instead: ''f<sup>-1</sup>(Y)''.  [[User:Paul August|Paul August]] [[User_talk:Paul August|&#9742;]] 20:51, 31 December 2005 (UTC)
::I once did a course called something like "Mathematical foundations of quantum mechanics" in which we discussed unbounded linear operators. You would have a linear map T : L^2 -> L^2 (for example the "differentation" operator), but even though it was written like that, it wasn't defined on all of L^2. The part of L^2 that it ''was'' defined on (which includes, for example, the smooth functions) was called the domain of T, denoted I think dom T. Unfortunately I can't find anything on wikipedia which backs up this usage, probably because I don't actually know anything about quantum mechanics or functional analysis. [[User:Dmharvey|Dmharvey]] 20:00, 31 December 2005 (UTC)
:::See the article [[Closed operator]], which treats this topic.  The convention I've seen is to call ''T'' in your example an operator '''on''' ''L''<sup>2</sup>, and use '''domain of ''T''''' to denote the subset of ''L''<sup>2</sup> on which ''T'' is actually defined. [[User:Brian Tvedt|Brian Tvedt]] 18:12, 1 January 2006 (UTC)

:For what it's worth, IMHO, ''X'' is not used outside of category theory and related morphism topics.  '''Domain''' is used for the range of ''f<sup>-1</sup>'' (seems better terminology than trying to say ''f<sup>-1</sup>(Y)'') in almost all other contexts. I'm not attempting to back this up with Wikipedia usage, just with common mathematical terminology. -- [[User:Arthur Rubin|Arthur Rubin]] | [[User_talk:Arthur_Rubin|(talk)]] 23:08, 31 December 2005 (UTC)
::Yeah, I agree with Arthur; we don't usually ''need'' a name for the ''X'' (it would just be convenient to have a name for it in the [[Partial function]] article). The set of values for which ''f'' is defined is a more useful concept, and more standardly called the domain of ''f'' (though the article should mention the other usage, which does seem to show up on a few websites). I'll make the appropriate edits if no one objects (could be a little while; I've got to get on a plane back to the Great White North very early tomorrow morning). --[[User:Trovatore|Trovatore]] 01:54, 1 January 2006 (UTC)

: My preference is that in any context where it is necessary to distinguish between ''X'' and the preimage of ''f'', use the category-theory terminology: call ''X'' the domain. To even speak of ''f'' as a ''partial'' function, it must be the case that the domain and preimage are different. Unfortunately, the mathematics community has never standardized terms across all fields, so issues like this will continue to appear. The category-theory usage was adopted because it works better in general; but if it is not a convention that is familiar and comfortable in a narrower context, best practice would be to alert readers to the conflict and to state clearly the convention to be used in the article in question.
: Incidentally, the Unicode character U+0290D, "&#x290d;", is better notation than "→" but requires a font like [[Code2000]] to display. --[[User:KSmrq|KSmrq]]<sup>[[User talk:KSmrq|T]]</sup> 07:04, 1 January 2006 (UTC)
::The problem with "preimage of ''f''" is that it isn't standard (standard terminology would be "the preimage of ''Y'' under ''f''", which is too long-winded). OTOH the terminology "the domain of ''f''" for the set of all points where ''f'' is defined is clearly the majority usage. --[[User:Trovatore|Trovatore]] 07:16, 1 January 2006 (UTC)
::: Again, these "standards" vary with context. I'm more familiar today with usage where the definition of a mapping ''includes'' its source and target, so that "the preimage of ''f''" is perfectly well-defined, as is "the preimage of ''S''⊂''Y'' under ''f''". Yet in my (distant) youth, the convention was exclusively that the domain of ''f'' was as you say. The conflict is real; we can't wish it away. Best practice remains clarity of definition and full disclosure of potential conflicts. --[[User:KSmrq|KSmrq]]<sup>[[User talk:KSmrq|T]]</sup> 08:58, 1 January 2006 (UTC)

OK, in accordance with the above discussion, I've edited [[Partial function]] and [[Domain (function)]] to indicate the existence of both usages. I've edited [[Recursively enumerable set]] and [[Uniformization (set theory)]] to specify which sense of the term is in use. But there are bunches more articles that link to [[Partial function]] and/or [[Domain (function)]]; I'm not likely to get around to checking them individually any time soon. --[[User:Trovatore|Trovatore]] 23:37, 4 January 2006 (UTC)

JA: Seems like "domain" is standard for the designated set, after all, what if it's just a  relation L c X x Y ?  And I think that "domain of definition" is used for the other thing by many folks in computing contexts, for example, Arbib et al.  [[User:Jon Awbrey|Jon Awbrey]] 07:40, 14 January 2006 (UTC)