View source for Wikipedia talk:WikiProject Mathematics/Archive/2010/Mar

{{WikiProject Mathematics archive list}}

== Unsourced mathematical biographies ==

There has been a [[Wikipedia talk:Deletion of unreferenced BLPs|lot of pressure lately to summarily delete all inadequately-sourced biographical articles]], and some of these articles are ones this project may wish to preserve. Please see [[Wikipedia:Pages needing attention/Mathematics]], especially the sections on [[Wikipedia:Pages needing attention/Mathematics#Articles lacking sources|unsourced articles]] and [[Wikipedia:Pages needing attention/Mathematics#Articles lacking reliable references|unreliably sourced articles]] and add appropriate sources to the biographical articles (and others, but the biographical ones are urgent). —[[User:David Eppstein|David Eppstein]] ([[User talk:David Eppstein|talk]]) 19:21, 21 January 2010 (UTC)

:Here is a list of all the math articles I could find that are in [[:Category:All unreferenced BLPs]]. Note that many of them will actually be referenced (external links count for this purpose). To coordinate work, simply remove names from the list below when you are done with them. I can always generate a new list later to see if any were missed. &mdash;&nbsp;Carl <small>([[User:CBM|CBM]]&nbsp;·&nbsp;[[User talk:CBM|talk]])</small> 19:44, 21 January 2010 (UTC)

:I'm a bit lost with [[WP:Arbitration/Requests/Case#BLP deletions|all these recent discussions]]; are people going to delete unreferenced BLP without warning, or is there going to be a [[WP:PROD]]-like process? — [[User:Miym|Miym]] ([[User talk:Miym|talk]]) 19:46, 21 January 2010 (UTC)

::For the moment, the safest assumption is that they might be deleted without warning; who know how things will turn out. In any case, checking the articles and correcting the templates is certainly a good idea. If someone does delete an article, and you would like it to be undeleted to fix it, just contact an admin (David Eppstein and I are both admins). &mdash;&nbsp;Carl <small>([[User:CBM|CBM]]&nbsp;·&nbsp;[[User talk:CBM|talk]])</small> 19:53, 21 January 2010 (UTC)

:::Thanks for the list Carl. I'm also an admin, other members of this project who are admins include: [[User:Charles Matthews|Charles Matthews]] and [[user: Oleg Alexandrov|Oleg Alexandrov]]. [[User:Paul August|Paul August]] [[User_talk:Paul August|&#9742;]] 20:39, 21 January 2010 (UTC)

:::: I would similarly be happy to undelete an article on request. [[User:CRGreathouse|CRGreathouse]]<small> ([[User talk:CRGreathouse|t]] | [[Special:Contributions/CRGreathouse|c]])</small> 20:41, 21 January 2010 (UTC)

:::: I'm also an admin, for the moment, and would happen to undelete an article on request.  (After checking for vandalism, of course.)  — [[User:Arthur Rubin|Arthur Rubin]]  [[User talk:Arthur Rubin|(talk)]] 20:54, 21 January 2010 (UTC)

:At least some of these could be fixed by turning the external links section into a references section.--[[User:RDBury|RDBury]] ([[User talk:RDBury|talk]]) 21:10, 21 January 2010 (UTC)

:Not to belittle or deemphasize the importance of history... but to be quite frank I dont think the history of mathematics or the biographies of mathematicians are of any consequence.  These articles - though important in their own right - should be maintained by the historians and not the mathematicians.  History is a distraction to those with an interest in math, and only adds superfluous content to already lengthy articles. I recommend starting a Mathematics History project, separate and distinct from the Mathematics project, to be a sub-categorization of both the Mathematics Project and the History project, operated and maintained in conjunction by each. --[[Special:Contributions/98.247.99.158|98.247.99.158]] ([[User talk:98.247.99.158|talk]]) 23:35, 14 February 2010 (UTC)
::On the contrary, the history of mathematics and the biographies of mathematicians are of considerable consequence, both in their own right, and in relation to mathematics. And while the contributions of historians would be very helpful and welcome in this area, so are the contributions of mathematicians. As far as "history [being] a distraction to those with an interest in math" &mdash; not for me and many others I know. And not only is the historical content in mathematics articles not "superfluous", it is in fact a requirement for a complete treatment of a subject. [[User:Paul August|Paul August]] [[User_talk:Paul August|&#9742;]] 18:46, 15 February 2010 (UTC)

By the way, there is a recently opened  RfC, in progress, on the unreferenced BLP controversy, [[Wikipedia:Requests for comment/Biographies of living people]].  Those with an interest in the issue might want to comment there. [[User:Nsk92|Nsk92]] ([[User talk:Nsk92|talk]]) 01:36, 22 January 2010 (UTC)

=== List ===

<s>[[Luigi Ambrosio]]</s> - [[Lennart Åqvist]] - [[Basilio de Bragança Pereira]] - <s>[[Christopher Daykin]]</s> - [[Ryszard Engelking]] -
[[Wally Feurzeig]] - [[Richard Fikes]] - <s>[[William Floyd (mathematician)]]</s> - <s>[[Bent Fuglede]]</s> - 
<s>[[Jean-François Le Gall]]</s> - 
<s>[[Peter Geach]]</s> - [[Jayanta Kumar Ghosh]] - [[Massimo Gobbino]] - [[Paul Gochet]] - <s>[[Valery Goppa]]</s> -  [[Lothar Göttsche]] - [[Alex Grossmann]] - [[Gu Chaohao]] - [[Otomar Hájek]] - 
[[Les Hatton]] - <s>[[Alexander Hurwitz]]</s> -
[[Eugenio Oñate Ibañez de Navarra]] - [[Ronald L. Iman]] - [[Robert Jueneman]] - [[Hartmut Jürgens]] -
[[David Klein (California State University Northridge)]] - [[Karl-Rudolf Koch]] - <s>[[Volodymyr Korolyuk]]</s> - [[Dan Krewski]] -
[[Phillip Longman]] -  [[Michael Makkai]] -  [[Stuart J. Murphy]] -
[[S. Jay Olshansky]] - [[Volker Oppitz (scientist)]] - [[Julian Peto]] -
[[Stanisław Radziszowski]] - [[Olivier Ramaré]] - [[Gregory G. Rose]] - [[Craig L. Russell (software architect)]] -
[[Mohammad Sharif (Afghanistan)]] - [[Tanush Shaska]] - <s>[[Larry E. Smith]]</s> - [[Emilio Spedicato]] - 
[[Matthew Stephens (statistician)]] - <s>[[Jacques Stern]]</s> - [[Martin Stokhof]] - <s>[[Arthur Swersey]]</s> -
[[Minoru Tanaka (mathematician)]] - <s>[[Lester G. Telser]]</s> - [[Reginald P. Tewarson]] -<s> [[Walter Thirring]] </s> -  [[Walter Trump]] - <s>[[Bryan Tse]] (prodded)</s> - [[Tathagat Avatar Tulsi]] -
<s>[[Douglas Wiens]]</s> - [[Mike Wissot]] - [[Peter Wludyka]] - [[Mario Wschebor]] - [[Miloš Zahradník]] - [[Christoph Zenger]]

This was obtained by [http://toolserver.org/~dschwen/intersection/index.php?linklist=&catlist=All+unreferenced+BLPs%0D%0AMathematicians&deep=7&do_intersection=Query category intersection]. [[User:Pohta ce-am pohtit|Pcap]] [[User_talk:Pohta ce-am pohtit|<small>ping</small>]] 04:34, 23 January 2010 (UTC)
: I merged and pared down both lists to include only the remaining articles that have neither been sourced nor deleted. —[[User:David Eppstein|David Eppstein]] ([[User talk:David Eppstein|talk]]) 03:51, 6 February 2010 (UTC)

::I added a few more. &mdash;&nbsp;Carl <small>([[User:CBM|CBM]]&nbsp;·&nbsp;[[User talk:CBM|talk]])</small> 12:09, 10 February 2010 (UTC)

=== Whack-a-mole? ===
Apparently there are several IP editors that just add back the {{tl|unreferencedBLP}} tag. I've noticed this on several articles. An example relevant here is [http://en.wikipedia.org/enwiki/w/index.php?title=Sourav_Chatterjee&action=historysubmit&diff=339439450&oldid=339343591]. [[User:Pohta ce-am pohtit|Pcap]] [[User_talk:Pohta ce-am pohtit|<small>ping</small>]] 05:02, 23 January 2010 (UTC)

:To be fair, [[Sourav Chatterjee]] was pretty clearly a vanity piece. I have hacked at it some. &mdash;&nbsp;Carl <small>([[User:CBM|CBM]]&nbsp;·&nbsp;[[User talk:CBM|talk]])</small> 05:27, 23 January 2010 (UTC)
:: AfD then? Is the award significant? [[User:Pohta ce-am pohtit|Pcap]] [[User_talk:Pohta ce-am pohtit|<small>ping</small>]] 05:31, 23 January 2010 (UTC)
:::I am not at all familiar with the person. There is the award in combination with the editorship, which is uncommon for someone 3 years out of grad school in pure math; I don't know about statistics. I think it would be a close call on AFD. &mdash;&nbsp;Carl <small>([[User:CBM|CBM]]&nbsp;·&nbsp;[[User talk:CBM|talk]])</small> 05:39, 23 January 2010 (UTC)

:::: Apparently, some of the puffery was added by [http://www.maxmind.com/app/locate_ip?ips=59.93.204.27 someone from India] [http://en.wikipedia.org/enwiki/w/index.php?title=Sourav_Chatterjee&diff=prev&oldid=338138772 fairly recently]. [[User:Pohta ce-am pohtit|Pcap]] [[User_talk:Pohta ce-am pohtit|<small>ping</small>]] 05:42, 23 January 2010 (UTC)

:::::Yeah; the article says Chatterjee is at Courant, so who knows. It could be him, a family member, a long-lost lover, or a random admirer. &mdash;&nbsp;Carl <small>([[User:CBM|CBM]]&nbsp;·&nbsp;[[User talk:CBM|talk]])</small> 05:44, 23 January 2010 (UTC)

:::::: By the way, some Kansas IP [http://en.wikipedia.org/enwiki/w/index.php?title=Sourav_Chatterjee&diff=prev&oldid=318295075 tried] to stub the article a couple of times, and the anti-vandal squad reverted. Obviously all this happened just because it lacked references :P [[User:Pohta ce-am pohtit|Pcap]] [[User_talk:Pohta ce-am pohtit|<small>ping</small>]] 05:51, 23 January 2010 (UTC)
:::::: For those not watching the article: [[Wikipedia:Articles for deletion/Sourav Chatterjee]]. [[User:Pohta ce-am pohtit|Pcap]] [[User_talk:Pohta ce-am pohtit|<small>ping</small>]] 06:14, 23 January 2010 (UTC)
::::::: I know him personally and some of his work. I'm pretty sure he didn't write this article. He might be exceptionally good, but it certainly seems too early to have an article on him. For instance, I know a lot of youngish probabilists who are more notable than him (say, based on citations of their first ten papers on Google Scholar, or on prizes) without wikipedia articles on them. But, with the current more realistic article, I don't think it matters much if it is deleted or not. --[[User:GaborPete|GaborPete]] ([[User talk:GaborPete|talk]]) 05:22, 27 January 2010 (UTC)
:::::::: I agree with Gabor. [[User:Tsirel|Boris Tsirelson]] ([[User talk:Tsirel|talk]]) 11:42, 27 January 2010 (UTC)

*There is a general discussion of BLPs at [[Wikipedia:Requests for comment/Biographies of living people]]. This is likely to affect many articles on minor professors of mathematics and textbook writers, so comments before this closes Thursday would be advisable. [[User:Pmanderson|Septentrionalis]] <small>[[User talk:Pmanderson|PMAnderson]]</small> 21:30, 26 January 2010 (UTC)

FYI: I asked Jimbo about his opinion about the article, after the AfD had closed. He [http://en.wikipedia.org/enwiki/w/index.php?title=User_talk:Jimbo_Wales&oldid=343011877#You_might_remember thinks] that having articles like that around is "probably a lot more trouble on average than they are worth". [[User:Pohta ce-am pohtit|Pcap]] [[User_talk:Pohta ce-am pohtit|<small>ping</small>]] 10:17, 10 February 2010 (UTC)

Note: I restored the above thread. Do we still need this? [[User:Paul August|Paul August]] [[User_talk:Paul August|&#9742;]] 20:09, 28 February 2010 (UTC)
:I don't know whether we still need this. Discussion and confusion seems to be ongoing at [[Wikipedia:Requests for comment/Biographies of living people]] but may eventually lead to a process whereby unreferenced BLPs are deleted after some waiting period. I think the clear-cut cases from the math list have mostly already been dealt with, but we can save some trouble now by finishing off the list; if it's just the ones listed above it doesn't seem like too much to handle. —[[User:David Eppstein|David Eppstein]] ([[User talk:David Eppstein|talk]]) 20:21, 28 February 2010 (UTC)

== Regressive discrete Fourier series ==

[[Regressive discrete Fourier series]] was until moments ago a complete orphan; now it's linked to from the [[list of Fourier analysis topics]].  I added [[:Category:Fourier analysis]], so the bots should add it to the [[list of mathematics articles]] and then to our current activities page.  In the mean time, do what you can with it. [[User:Michael Hardy|Michael Hardy]] ([[User talk:Michael Hardy|talk]]) 19:30, 27 February 2010 (UTC)

== Resources box ==

I added a few items. Enjoy, but if not, undo.--[[User:RDBury|RDBury]] ([[User talk:RDBury|talk]]) 19:44, 28 February 2010 (UTC)

: I surmise that you're referring to this:&nbsp;[[Wikipedia:WikiProject Mathematics/Nav]]. [[User:Michael Hardy|Michael Hardy]] ([[User talk:Michael Hardy|talk]]) 20:20, 28 February 2010 (UTC)
== Gravitational potential ==

A third set of eyes would be appreciated at [[Gravitational potential]].  I draw the line at [http://en.wikipedia.org/enwiki/w/index.php?title=Talk:Gravitational_potential&diff=346801141&oldid=346797183 personal attacks] like this. [[User:Sławomir Biały|<span style="text-shadow:grey 0.3em 0.3em 0.1em; class=texhtml">Sławomir Biały</span>]] ([[User talk:Sławomir Biały|talk]]) 02:22, 28 February 2010 (UTC)

:Please help.  The editor is now insistent on edit warring to include extremely dubious content in the article, and remove my best effort at a compromise. [[User:Sławomir Biały|<span style="text-shadow:grey 0.3em 0.3em 0.1em; class=texhtml">Sławomir Biały</span>]] ([[User talk:Sławomir Biały|talk]]) 01:33, 2 March 2010 (UTC)

::I second this plea. I've tried to help a bit, but clearly something more is required. [[User:RobHar|RobHar]] ([[User talk:RobHar|talk]]) 02:55, 2 March 2010 (UTC)

== Elliptic curve primality testing ==

I've done enough cleanup on [[elliptic curve primality testing]] for one night.  Various conventions of [[WP:MOS]] and [[WP:MOSMATH]] still need to get applied here.
: 
But also: the article is an orphan: lots of other articles should link to it and do not. [[User:Michael Hardy|Michael Hardy]] ([[User talk:Michael Hardy|talk]]) 04:16, 1 March 2010 (UTC)

: From a cursory look, it's a canonical example of textbook exposition. For example, the end of the lead that spills into the first section ("We will now state a proposition &hellip;") made me cringe. Has anyone checked whether this text has been lifted wholesale from a book? [[User:Arcfrk|Arcfrk]] ([[User talk:Arcfrk|talk]]) 17:30, 1 March 2010 (UTC)
::That may simply be bad style, but the paper credited was [http://www.iai.uni-bonn.de/~adrian/ecpp/p316-goldwasser.pdf Goldwasser, Shafi, Kilian, Joe, "Almost All Primes Can Be Quickly Certified"]. I haven't followed the link, but if it really dates primality testing from Gauss, it is unusually inept even for mathematicians' history of mathematics. I suspect that, at least, is home-grown folly.  [[User:Pmanderson|Septentrionalis]] <small>[[User talk:Pmanderson|PMAnderson]]</small> 23:30, 1 March 2010 (UTC)
:::It doesn't. "Fermat, Euler, Legendre, and Gauss", after a mention of Eratosthenes. Our editor is unable to convey the sense of his source, so I doubt he is plagiarizing. [[User:Pmanderson|Septentrionalis]] <small>[[User talk:Pmanderson|PMAnderson]]</small> 23:32, 1 March 2010 (UTC)

== Reciprocal property ==

Is the article titled [[reciprocal property]] worth anything? [[User:Michael Hardy|Michael Hardy]] ([[User talk:Michael Hardy|talk]]) 04:32, 1 March 2010 (UTC)
:The reference given is totally inappropriate but I searched Google books and saw it being used in several places as a phrase with more than the obvious meaning. In particular the [[Penny Cyclopedia]] has "A reciprocal property is one which each of two things has with reference to the other; thus if A and B be what are called conjugate diameters of a conic section, the tangent at either extremity of A is parallel to B, and that at either extremity of B is parallel to A. Hence these lines are reciprocally connected with each other, and are therefore called conjugate; for the word conjugate, which denotes joined, generally means joined by a reciprocal property." Not sure that the article can be extended beyond a DICDEF or whether the terms has any modern currency. It seems to not be a strictly math term so maybe this isn't the place to ask.--[[User:RDBury|RDBury]] ([[User talk:RDBury|talk]]) 05:54, 1 March 2010 (UTC)
::Is it attested in the past century? Obscure and archaic terminology probably belongs on Wiktionary, with a redirect to  the modern term, which should link to Wiktionary. In this case, that would be [[reflexive relation]]. [[User:Pmanderson|Septentrionalis]] <small>[[User talk:Pmanderson|PMAnderson]]</small> 16:30, 1 March 2010 (UTC)
:::It's not the same as a reflexive relation, the example given in PC shows that. The problem is the term seems to be used in a number of unrelated subject; I saw something about viscous fluid flow, the RSA algorithm, the properties of antennas, and others, all using it in a different way but rarely actually defining it or at least not where you can see in the book preview. If you want to do the research to turn this into an workable article then I'm not going to say it's impossible. On the other hand I didn't see any evidence that the article as created isn't just an extrapolation of a phrase used on a speculative science calendar store website. This is why Wikipedia has a rule about adding material that's not properly referenced, it takes longer to fix it than it does to add it, even if you end up deleting it.--[[User:RDBury|RDBury]] ([[User talk:RDBury|talk]]) 18:38, 1 March 2010 (UTC)
::::My apologies, you are of course correct; this is an 1-to-1 [[Symmetric relation]]: A is related to B iff B is related to A. [[User:Pmanderson|Septentrionalis]] <small>[[User talk:Pmanderson|PMAnderson]]</small> 23:20, 1 March 2010 (UTC)

== Perfect Cube Confusion ==

Hello, I am wondering whether 0 is a perfect cube or not? '''<span style="font-family:Georgia;">[[User:Math Champion|<span style="color:green;">Math</span>]] [[User talk:Math Champion|<span style="color:teal;">Champion</span>]] | [[User:Math Champion/Guestbook|<span style="color:blue;">sign!</span>]]</span>''' 04:07, 2 March 2010 (UTC)
:Yes, it is; it's the cube of the integer 0.  In the future, please ask this sort of question at [[Wikipedia:Reference desk/Mathematics]]. --[[User:Trovatore|Trovatore]] ([[User talk:Trovatore|talk]]) 04:25, 2 March 2010 (UTC)
== Covariance (categories) ==

What do we think of the article titled [[Covariance (categories)]]? [[User:Michael Hardy|Michael Hardy]] ([[User talk:Michael Hardy|talk]]) 19:49, 26 February 2010 (UTC)

:Being somewhat of a dilettante when it comes to category theory, it is difficult for me to get any meaning out of the article. Also I get no hits whatsoever for the phrase "quantitative category theory" in either Google, Google books, or Google scholar. [[User:Sławomir Biały|<span style="text-shadow:grey 0.3em 0.3em 0.1em; class=texhtml">Sławomir Biały</span>]] ([[User talk:Sławomir Biały|talk]]) 20:59, 26 February 2010 (UTC)
::It appears to be integrating over a "real or complex" category; I may also be a dilettante, but I've never heard of either, and the idea of integrating over a large category makes my head hurt. [[User:Pmanderson|Septentrionalis]] <small>[[User talk:Pmanderson|PMAnderson]]</small> 00:06, 27 February 2010 (UTC)
:::The claim that "Cov(''F'',&nbsp;''G'') is [[Negative and non-negative numbers|negative]] [[iff]] exactly one of ''F'' and ''G'' is contravariant" is especially mysterious to me, since, if the preceding definition makes any sense at all, it (a) requires ''F'' and ''G'' to be covariant and (b) defines Cov to be always positive. [[User talk:Algebraist|Algebraist]] 00:15, 27 February 2010 (UTC)
::::I'd like to put money down on this article being completely made up. [[User:RobHar|RobHar]] ([[User talk:RobHar|talk]]) 00:28, 27 February 2010 (UTC)
:::::The user seems to be a subtle vandal. [http://en.wikipedia.org/enwiki/w/index.php?title=Factorial&diff=next&oldid=302555505], [http://en.wikipedia.org/enwiki/w/index.php?title=Factorial&diff=next&oldid=221955653], and he was also responsible for the now-deleted [[mitimorphism]] (which, IIRC, provoked a discussion much like the present one.) [[User:Ozob|Ozob]] ([[User talk:Ozob|talk]]) 04:10, 27 February 2010 (UTC)
::::::Just prod it as gibberish and put a warning on the user's talk page. In fact I think I'll just go ahead and do that now. It doesn't even make sense as having substituted different words for something else. [[User:Dmcq|Dmcq]] ([[User talk:Dmcq|talk]]) 09:43, 27 February 2010 (UTC)
::::::And if you want proof it is rubbish how about integrating the absolute value of something and getting a negative number? [[User:Dmcq|Dmcq]] ([[User talk:Dmcq|talk]]) 10:05, 27 February 2010 (UTC)

Nonsense, but rather well-written and clever nonsense, not like most attempts. [[User:Michael Hardy|Michael Hardy]] ([[User talk:Michael Hardy|talk]]) 16:27, 27 February 2010 (UTC)

Not sure how to mark this in the prod template, but IMHO it would be better to redirect the article to [[Functor#Covariance and contravariance]] than to delete it.—[[User:EmilJ|Emil]]&nbsp;[[User talk:EmilJ|J.]] 15:37, 1 March 2010 (UTC)
:I suppose you could just change the page to a redirect rather than wait for the prod to expire. [[User:Dmcq|Dmcq]] ([[User talk:Dmcq|talk]]) 16:21, 1 March 2010 (UTC)
::OK, since nobody objected I've done just that.—[[User:EmilJ|Emil]]&nbsp;[[User talk:EmilJ|J.]] 11:12, 2 March 2010 (UTC)

== A trigonometric identity for a circulant matrix ==

[[A trigonometric identity for a circulant matrix]] seems to be the work of a competent mathematician unaware of Wikipedia's policy against original research and the one against identifying the author by name within the article.  It's on AfD. [[User:Michael Hardy|Michael Hardy]] ([[User talk:Michael Hardy|talk]]) 04:27, 2 March 2010 (UTC)

: Userified: [[User:Daviddaved/A trigonometric identity for a circulant matrix]]. [[User:CRGreathouse|CRGreathouse]]<small> ([[User talk:CRGreathouse|t]] | [[Special:Contributions/CRGreathouse|c]])</small> 06:12, 2 March 2010 (UTC)

::I just had a look at that and I must admit I'm a bit surprised if nobody has done something like that before. It looks an interesting formula but if it isn't in a reliable source that's that I guess. [[User:Dmcq|Dmcq]] ([[User talk:Dmcq|talk]]) 15:33, 2 March 2010 (UTC)
:::If you set ''x'' = ''y''<sup>2</sup> and factor, it ought to resolve into a fairly predictable statement about symmetric polynomials of  the roots of unity; which may be why no reliable source has bothered. [[User:Pmanderson|Septentrionalis]] <small>[[User talk:Pmanderson|PMAnderson]]</small> 20:06, 2 March 2010 (UTC)
::::It doesn't resolve into anything straightforward to me. It does involve symmetric polynomials of the real part of the roots of unity which should resolve into something reasonable and here is shown to do so but I haven't seen it worked out before. [[User:Dmcq|Dmcq]] ([[User talk:Dmcq|talk]]) 23:46, 2 March 2010 (UTC)

== Hyperbolic geometry ==

The section [[Hyperbolic geometry#Homogeneous structure|Homogeneous structure]] was recently added to the [[hyperbolic geometry]] article. Apart from not including sources, and not being particularly clear, the question I wanted to ask is: in what sense is a geometric space "isomorphic" to some group? Does this mean the symmetry group of the space is isomorphic to the group ? There are other wikipedia aricles that also say such and such a space is isomorphic to such and such a group without first defining a group on the space. [[User:Charvest|Charvest]] ([[User talk:Charvest|talk]]) 14:53, 2 March 2010 (UTC)

:It says the space is isomorphic to the quotient of two groups, I don't think it should be taken to mean the quotient ''group'' of two groups. Given any homogeneous space, it's symmetry group G will be transitive, so the space can be identified with G/G<sub>1</sub> where G<sub>1</sub> is the subgroup of G that fixes a point. Here the quotient just means the collection of cosets and is not itself a group in general. That being said, the section seems to assume a familiarity with Minkowski space that I, for one, don't have.--[[User:RDBury|RDBury]] ([[User talk:RDBury|talk]]) 16:36, 2 March 2010 (UTC)

::Not a quotient group! Thanks. I'll continue this at the reference desk. [[User:Charvest|Charvest]] ([[User talk:Charvest|talk]]) 22:46, 2 March 2010 (UTC)

== A general question regarding sources and citation ==

I was wondering what I can do in the following situation: I am reading an article and there is a statement I cannot prove myself nor do I know any source as where to find a proof for the statement. What is the best way to request a source or reference for the statement? Is it ok to do so even? I think that every statement made in an article should be either clear to the reader with a certain mathematical eduaction or should be referenced. [[User:Quiet photon|Quiet photon]] ([[User talk:Quiet photon|talk]]) 15:08, 2 March 2010 (UTC)

:You can add the template {{tl|fact}} to the article just after the claim, and leave a brief query on the talk page. If that doesn't give a response in a reasonable amount of time, try asking here for people to look at it. But in general it's best to start by just asking on the talk page of the article; the people who have the article on their watchlist may be in a better position to give you an answer. &mdash;&nbsp;Carl <small>([[User:CBM|CBM]]&nbsp;·&nbsp;[[User talk:CBM|talk]])</small> 15:19, 2 March 2010 (UTC)

:(e/c) First, look down to the "References" section. Chances are that it gives a book covering the topic or a similar general source which includes the statement, it's just that the article is missing detailed inline refs. Failing that, you can request a citation by adding a {{tlx|cn}} template after the statement. However, bear in mind that if it is not a high-traffic article, it may easily take months until someone adds a source (or deletes the claim). If you really need a proof ''now'', you may be better off by asking at the [[WP:RD/MA|Math Reference Desk]].—[[User:EmilJ|Emil]]&nbsp;[[User talk:EmilJ|J.]] 15:27, 2 March 2010 (UTC)

::Thank you for your answers! So just to check if I understand correctly, it is neither the goal of the Mathematics Portal to reference every statement made in an article nor to provide the proofs themselves? Or is it just that at the moment other things, such as writing missing articles or improving the overall quality are more important? Please forgive my tenacity, I really want to contribute, but I feel that I have to understand the goals and conceptions of the Mathematics Portal first. [[User:Quiet photon|Quiet photon]] ([[User talk:Quiet photon|talk]]) 15:44, 2 March 2010 (UTC)
:::In theory, all statements on WP are supposed to be referenced, but many articles are far from this goal. On the other hand, we are not supposed to provide proofs (unless the particular proof has itself encyclopedic merit).—[[User:EmilJ|Emil]]&nbsp;[[User talk:EmilJ|J.]] 15:49, 2 March 2010 (UTC)

:::The goal is to provide enough referencing to (1) provide resources for the reader to look into the material in greater depth and (2) give specific inline references for things that need them. Those things are usually obvious: direct quotes, statements of opinion, and controversial or surprising statements should ideally have inline references. For general articles that could be rewritten from a single textbook, we don't usually try to put inline citations on every fact, but we do try to reference a couple good textbooks where someone could learn about the facts in the article and more.

:::It is ''not'' our goal to include proofs of every fact. This is in line with the idea that Wikipedia is an encyclopedia, not a textbook. If one compares other sources like the CRC Concise Encyclopedia of Mathematics or the Stanford Encyclopedia of Philosophy, they also do not try to prove every fact they mention. 

:::The best advice for getting started is: pick an area you know about, pick an article that needs work, and expand it. Keep what you add in line with what can be found in the literature about the area, and add references to anything that a careful referee would ask you to reference in  a research paper. 

:::&mdash;&nbsp;Carl <small>([[User:CBM|CBM]]&nbsp;·&nbsp;[[User talk:CBM|talk]])</small> 16:52, 2 March 2010 (UTC)

::::Very helpful, thank you. I have seen only one proof so far in the Wikipedia, and I did some searching and I found it again: [[Conservative force]] under mathematical description. At the time I was learning about that I was very greatful for it. I think it is a great way implement proofs if needed and I, if I ever get to edit or write an article will use it when I see need for a proof, if that's ok? [[User:Quiet photon|Quiet photon]] ([[User talk:Quiet photon|talk]]) 17:36, 2 March 2010 (UTC)

::::(e/c)The goal of references is to establish verifiability, resources for readers to get more information should come under the heading of Further Reading or External Links. Verifiability through reliable external sources is one of the pillars of Wikipedia and any material that may be questioned should have a citation.--[[User:RDBury|RDBury]] ([[User talk:RDBury|talk]]) 17:42, 2 March 2010 (UTC)

:::::References are both for verifiability and to help the reader explore the topic; these are complementary goals, not conflicting ones. Many of our articles use "general references", because much of their material is unlikely to be "questioned", and if it is we can easily point it out in the literature. It's important to remember that "verifiable" means "in principle, this material can be found in the literature". It is perfectly possible for material to be verifiable even though an inline citation is not provided.  This is why I said, "keep what you add in line with what can be found in the literature about the area". &mdash;&nbsp;Carl <small>([[User:CBM|CBM]]&nbsp;·&nbsp;[[User talk:CBM|talk]])</small> 19:10, 2 March 2010 (UTC)
:::::.+1--[[User:Kmhkmh|Kmhkmh]] ([[User talk:Kmhkmh|talk]]) 22:44, 2 March 2010 (UTC)
One might also try: (1) asking the person who put the statement there in the first place; and (2) asking at Wikipedia's mathematics reference desk. [[User:Michael Hardy|Michael Hardy]] ([[User talk:Michael Hardy|talk]]) 21:40, 2 March 2010 (UTC)

: I would mention as no-one else seems to the [[Wikipedia:Scientific citation guidelines|Scientific citation guidelines]], the gist of which is that science is not BLP. While a biography (or history, or geography) article consists of facts all of which should be individually verifiable it's often unnecessary for science, where a lot of the theory on a page is common, uncontroversial knowledge. Better to provide a two or three good general references which cover the whole subject well. This does not stop editors questioning dubious statements or providing references for them, but maybe explains why good maths articles in particular have few citations per paragraph than e.g. good biographies.--<small>[[User:JohnBlackburne|JohnBlackburne]]</small><sup>[[User_talk:JohnBlackburne|words]]</sup><sub style="margin-left:-2.0ex;">[[Special:Contributions/JohnBlackburne|deeds]]</sub> 22:27, 2 March 2010 (UTC)
::It seems to me that what you're saying is consistent with the Scientific citation guidelines. It already says the scientific subjects don't need a footnote for each statement, especially when that would disrupt the flow of the article, so I'm not sure what in the guidelines you're saying don't need to follow. I object to long articles covering a variety of subtopics where there is not way of telling which section comes from which source, if any. [[Newton's method]] is like this, there are lots of references but some of them are general numerical analysis texts and there is no way of knowing without going through all the references which are intended to support which facts. This is a bit of a shame because the article itself is well written enough to qualify for GA status (imo), but with the referencing style as it I doubt it would get past even a preliminary review.--[[User:RDBury|RDBury]] ([[User talk:RDBury|talk]]) 05:10, 3 March 2010 (UTC)

@Quiet photon: If you want to provide access to proofs to the readers of a math article, you can do so by providing references to literature/journal articles containing them (also online copies of them). In addition you could provide link to some website or a wikibook containing the proof in the external links section.--[[User:Kmhkmh|Kmhkmh]] ([[User talk:Kmhkmh|talk]]) 22:41, 2 March 2010 (UTC)

== AN/I  thread ==

A thread related to the article [[Zeno's paradoxes]] has been opened at [[Wikipedia:Administrators' noticeboard/Incidents#User:Steaphen]]. [[User:Nsk92|Nsk92]] ([[User talk:Nsk92|talk]]) 23:51, 2 March 2010 (UTC)
: I moved to [[WP:AN]] where topic bans are usually discussed. [[User:Pohta ce-am pohtit|Pcap]] [[User_talk:Pohta ce-am pohtit|<small>ping</small>]] 01:57, 3 March 2010 (UTC)
== Featured picture candidates part 2 ==

Of the two recent nominations for featured picture, [[:File:Pythagoras-2a.gif]] was promoted and is now a featured picture. [[:File:Penrose Tiling (Rhombi).svg]] did was not promoted even though there were no oppose votes. Thanks to [[User:Noodle snacks]] for making the nominations. There is a new nomination [[:File:Desargues theorem.svg]] with discussion at [[Wikipedia:Featured picture candidates/File:Desargues theorem.svg]]. 

These featured picture discussions don't appear in either [[Wikipedia:WikiProject Mathematics/Current activity]] or in [[Wikipedia:WikiProject Mathematics/Article alerts]], nor do the featured pictures appear in [[Wikipedia:WikiProject Mathematics/Recognized content]]. One issue seems to be that the 'maths rating' template does not include a file class so pictures related to WPM use the outdated 'maths banner' template instead.--[[User:RDBury|RDBury]] ([[User talk:RDBury|talk]]) 02:42, 5 March 2010 (UTC)

== Spaced en-dashes ==

Remember a few months ago when someone tried to rename [[Seifert–van Kampen theorem]] to "Seifert – van Kampen theorem" because the Manual of Style said that was the right thing to do, despite the fact that no math publications spell it that way? There's now an RFC going on about this issue (and about en-dashes used to separate multiple items in similar contexts): please see [[Wikipedia talk:Manual of Style#RfC: Disjunctive en dashes should be unspaced]], and leave your opinion there if you have one. —[[User:David Eppstein|David Eppstein]] ([[User talk:David Eppstein|talk]]) 04:30, 6 March 2010 (UTC)
== Coxeter-Dynkin diagrams: PNG or SVG ==

&lt; removing my own entry here; belongs in [[Talk:Coxeter–Dynkin diagram]] &gt; —[[User:Tamfang|Tamfang]] ([[User talk:Tamfang|talk]]) 20:01, 7 March 2010 (UTC)

== Pros and cons of notations for sine and cosine series ==

Opinions of mathematicians (and others) are welcomed at [[Talk:Trigonometric_functions#Pros_and_cons_of_notations_for_series]]. [[User:Michael Hardy|Michael Hardy]] ([[User talk:Michael Hardy|talk]]) 05:31, 8 March 2010 (UTC)
== Proposed move of [[Satisfiability and validity]] ==

FYI [[http://en.wikipedia.org/wiki/Talk:Satisfiability_and_validity#Requested_move]] [[Special:Contributions/65.46.253.42|65.46.253.42]] ([[User talk:65.46.253.42|talk]]) 21:28, 8 March 2010 (UTC)

== Proposed move of [[Continuous function (topology)]] ==

Should the page be moved to [[Continuous map]]?  Comment at talkpage. [[User:Tkuvho|Tkuvho]] ([[User talk:Tkuvho|talk]]) 12:26, 10 March 2010 (UTC)

:The discussion thread seems to be [[Talk:Continuous_function_(topology)#Requested_move|here]]. &mdash;&nbsp;Carl <small>([[User:CBM|CBM]]&nbsp;·&nbsp;[[User talk:CBM|talk]])</small> 12:41, 10 March 2010 (UTC)

== Proposed merger of Real part and Imaginary part ==

I'm considering merging [[Real part]] and [[Imaginary part]] into a new article [[Real and imaginary parts]]; would anyone object to that? ―&nbsp;<i style="background: white; color: blue; font-weight:600; font-family: monospace">[[User:A. di M.|A.]]_di_M.</i> (formerly Army1987) 15:54, 10 March 2010 (UTC)

: Be [[WP:BOLD]]!  Sounds good to me. [[User:CRGreathouse|CRGreathouse]]<small> ([[User talk:CRGreathouse|t]] | [[Special:Contributions/CRGreathouse|c]])</small> 03:07, 11 March 2010 (UTC)

== Proposed deletion of "Research Students Conference Probability and Statistics" ==

I don't really have particularly strong feelings one way or the other about this proposed deletion, but the comments in the deletion discussion so far seem like examples of the reasons why I sometimes feel as if people who spend all their time hanging around the AfD pages are not respectable: [[Wikipedia:Articles_for_deletion/Research_Students_Conference_Probability_and_Statistics#Research_Students_Conference_Probability_and_Statistics]]. [[User:Michael Hardy|Michael Hardy]] ([[User talk:Michael Hardy|talk]]) 06:41, 11 March 2010 (UTC)
== "Skew shape", "skew diagram"? ==

The article titled [[Young's lattice]] refers to the "skew shape" ''p''/''q'', at the point where it's giving the [[M&ouml;bius function]] of the lattice.  It is unclear what that term means.  In [[Young_tableau#Skew_tableaux]] we find the term again, but it's not clear how the reader of [[Young's lattice]] would find his way there.  It says "if the skew shape is a disjoint union of squares", but I wonder what in this context could possibly ''not'' be a disjoint union of squares.
: 
So can someone clarify, within the article? [[User:Michael Hardy|Michael Hardy]] ([[User talk:Michael Hardy|talk]]) 19:37, 7 March 2010 (UTC)
:I was just wondering that myself. I also don't know what it means. —[[User:David Eppstein|David Eppstein]] ([[User talk:David Eppstein|talk]]) 19:48, 7 March 2010 (UTC)

:::Perhaps they mean that the difference is a "disconnected union" rather than "disjoint union"? [[User:JRSpriggs|JRSpriggs]] ([[User talk:JRSpriggs|talk]]) 20:48, 7 March 2010 (UTC)

It may be a case of "too much of a good thing" (by an expert). A clear enough definition appears in the first line, but it is then obscured by too many caveats and qualifiers. I did a bit of detective work. [http://en.wikipedia.org/enwiki/w/index.php?title=Young_tableau&oldid=185190811 Here] is an old revision where skew diagrams are defined the way I first wrote it, and [http://en.wikipedia.org/enwiki/w/index.php?title=Young_tableau&diff=prev&oldid=194863012 here] is Marc's expansion that's closer to the present form. As for the course of action, a picture would help a lot, and I don't think it's worthwhile to accent attention on the ambiguity of the notation ("skew diagram" vs "skew shape") too much. [[User:Arcfrk|Arcfrk]] ([[User talk:Arcfrk|talk]]) 05:16, 8 March 2010 (UTC)
: Oh: You mean in the first line of a section of the article titled [[Young tableau]], not the first line of anything in the other article that is what I was asking about. [[User:Michael Hardy|Michael Hardy]] ([[User talk:Michael Hardy|talk]]) 05:34, 8 March 2010 (UTC)

::There are two confusions going on. For the terminology, a "skew shape" is a pair of partitions (comparable in Young's lattice), while a "skew diagram" is a set of squares that can be obtained as set theoretic difference of their diagrams. The map from skew shapes to skew diagrams is not injective, which is why one must take care to distinguish, and not say (or define) skew diagram when a skew shape is meant (it is like confusing "fraction" and "rational number" when talking about "the denominator of a rational number"). The [[Young diagram]] article is excessively explicit about this, to which I plead guilty; blame frustration about the fact that more than half of the authors (even the best) get this wrong. But in this case the real confusion was using the term "disjoint" where "disconnected" should have been used (a set of squares being considered connected if they are joined via common edges, not just corners). So the proper thing to say that the [[M&ouml;bius function]] taken at a skew shape is nonzero if and only if all squares of the corresponding skew diagram are disconnected. I've made such a change. [[User:Marc van Leeuwen|Marc van Leeuwen]] ([[User talk:Marc van Leeuwen|talk]]) 14:16, 13 March 2010 (UTC)

== Featured picture candidates part 3 ==

An alternate version of the Desargues theorem diagram [[:File:Desargues theorem alt.svg]] was promoted to featured picture. However, with all the changes that happened in the process the lines are slightly misaligned at the point c so some repair would be helpful. Meanwhile there is a new nomination, see [[Wikipedia:Featured picture candidates/File:BIsAPseudovector.svg]].--[[User:RDBury|RDBury]] ([[User talk:RDBury|talk]]) 05:18, 12 March 2010 (UTC)
== Proposed merger of Mathematical constant and Constant (mathematics) ==

[[User:IRP|IRP]] has proposed a merger of [[Mathematical constant]] and [[Constant (mathematics)]]. Discussion is [[Talk:Constant (mathematics)|here]]. [[User:Gandalf61|Gandalf61]] ([[User talk:Gandalf61|talk]]) 11:04, 14 March 2010 (UTC)

== Help with [[History of Logic]]? ==

The article [[History of logic]] has been nominated for a featured article [[Wikipedia:Featured article candidates/History of logic/archive1|here]]. The nominating editor has asked me for help concerning the post-WWII period, asking if forcing was the only significant result, and if "reverse mathematics" ought to be mentioned (see: [[User talk:Paul August#Logic after WW2]]). Any assistant anyone could give would be appreciated. Thanks, [[User:Paul August|Paul August]] [[User_talk:Paul August|&#9742;]] 15:21, 14 March 2010 (UTC)

== Crooked egg curve ==

Could those who know algebraic geometry comment at [[Wikipedia:Articles for deletion/Crooked egg curve]]? [[User:Michael Hardy|Michael Hardy]] ([[User talk:Michael Hardy|talk]]) 03:26, 15 March 2010 (UTC)
== article assessments: issues with "field" and progress report ==

I posted a few months ago about plans to work on the article assessments. Here is a progress report on wha's been accomplished, some issues I noticed when I was doing it. &mdash;&nbsp;Carl <small>([[User:CBM|CBM]]&nbsp;·&nbsp;[[User talk:CBM|talk]])</small> 13:17, 12 March 2010 (UTC)

=== Status updates ===

; Filling in assessments : There were about 1,400 articles that had a maths rating tag with incomplete information (at least one of the quality, priority, and field parameters was not filled in). I went through and assessed these. Many of them were stubs, which were easy. Very few of the unassessed ones were long articles where seriously reading the article was necessary. Right now, we have about 7,100 articles with talk page assessments, and about 23,000 on the [[list of mathematics articles]]. We seem to gain 2-3 talk page assessments per day, on average. 

; New WP 1.0 bot : In January, the new WP 1.0 bot was turned on. It uses the same templates as the old one, but now the information is stored in a database on the toolserver where it can be searched dynamically. Eventually, this system is going to replace the VeblenBot system to make per-project tables for the math project. 

; New log page format : The new WP 1.0 bot keeps its log pages in a more useful format. The log is at [[Wikipedia:Version 1.0 Editorial Team/Mathematics articles by quality log]] 

; Tools : I have several tools for article assessments listed on [[User:CBM]].

=== Issue: assigning fields to articles ===

Right now, each article with a maths rating template is assigned to exactly one of these fields:
:general, basics, analysis, algebra, geometry, applied, probability and statistics, number theory, discrete, foundations, mathematical physics, topology, history, mathematicians 
There are a few problems I noticed when I was assessing articles:
* Algebraic geometry is particularly difficult to fit into this scheme, and I think its articles are split between algebra and geometry. Riemannian geometry, Lie theory, dynamical systems, and category theory are also difficult to fit into the system. 
* Some articles fit into more than one field. For example, [[C*-algebra]] would fit into both mathematical physics and analysis, and [[Cohomology]] would fit into both topology and algebra
* The geometry category includes both pure geometry and a large number of articles on polyhedra, polytopes, and similar objects. Splitting the polyhedra into their own field would probably make it easier to keep tack of them separately. I think this is one of our less well-known resources: we have an enormous library of articles on different polyhedra.

It's certainly worth making it possible to put more than one field on an article. But I think that revisiting the selection of fields would be worthwhile. 

One nice thing about our current system is that it is not too fine. I think that the MSC rating system is too fine four our needs. But one possibility for us would be to start with the [http://msc2010.org/mscwiki/index.php?title=MSC2010 MSC 2010 system] (just the 2-digit codes) and then combine those into groups to form our fields. For example, we could make a list of the MSC codes corresponding to "topology", and then say that our "topology" field corresponds to the topics listed under those MSC codes. If a topic would be normally be filed under more than one MSC code, then we can assign it to more than one of our "fields" as appropriate.   How do other people feel about that? &mdash;&nbsp;Carl <small>([[User:CBM|CBM]]&nbsp;·&nbsp;[[User talk:CBM|talk]])</small> 13:17, 12 March 2010 (UTC)

:I think the "applied" category should definitely be replaced with more specific ones such as "optimization", "game theory", "numerical analysis" and "information theory". And there should be one for "dynamical systems" and one for "computation". [[User:Bethnim|Bethnim]] ([[User talk:Bethnim|talk]]) 16:46, 12 March 2010 (UTC)
:Separate categories for "algebraic geometry", "differential geometry" and "category theory" would also be reasonable. [[User:Bethnim|Bethnim]] ([[User talk:Bethnim|talk]]) 16:56, 12 March 2010 (UTC)
::We have to be careful not to make them too fine, though, or the fields become just a replacement for the categories already on the articles. The idea behind the fields to to give a relatively coarse splitting. 

::The benefit of matching things with MSC fields is to make it easier to tell what articles go in each field. For example, when you say "computation", I don't know if you mean numerical analysis or recursion theory. Similarly, I would not be able to guess what you mean by "optimization". &mdash;&nbsp;Carl <small>([[User:CBM|CBM]]&nbsp;·&nbsp;[[User talk:CBM|talk]])</small> 19:08, 12 March 2010 (UTC)

::: I also think that the fields, whatever they are chosen to be, should remain course-grained. [[User:CRGreathouse|CRGreathouse]]<small> ([[User talk:CRGreathouse|t]] | [[Special:Contributions/CRGreathouse|c]])</small> 21:08, 12 March 2010 (UTC)

::::Me too. I like the idea of being able to assign multiple fields to the same article. [[User:RobHar|RobHar]] ([[User talk:RobHar|talk]]) 05:00, 13 March 2010 (UTC)

I mentioned this above, but if there changes being made anyway, is there any chance of getting file class added so we don't have to mess around with a separate template for images? There has been a lot of activity for featured pictures lately and while I don't mind posting notification manually it would be nice if it was handled by the normal machinery. There are a few other non-rating classes that other projects use as well such as list.--[[User:RDBury|RDBury]] ([[User talk:RDBury|talk]]) 14:41, 13 March 2010 (UTC)

:The current template already supports FL-Class and List-Class; VeblenBot just needed to be told to look at them, which I did just now. The WP 1.0 bot tables have had them for a while ([[User:WP 1.0 bot/Tables/Project/Mathematics  |here]]). The bot that does the current activity page needs to be updated to look for FP discussions; maybe a [[List of mathematics images]] could be created to facilitate that. 

:The issue with the math rating template and images is that it needs to be set up so that the images are automatically rated as NA-priority. If we are already going to be revamping the field system, this can be done at the same time. &mdash;&nbsp;Carl <small>([[User:CBM|CBM]]&nbsp;·&nbsp;[[User talk:CBM|talk]])</small> 16:00, 13 March 2010 (UTC)

I went through the list of top-level [http://www.ams.org/mathscinet/msc/msc2010.html MSC fields] and tried to fit them into a small number of fields that we could use to classify articles. Here is the resulting list. I've left out 00-XX General, since it doesn't fit anywhere. I've put several MSC fields into several WP fields; sometimes this is because a single MSC field doesn't fit well anywhere (such as K-theory) and other times it's because the MSC fields are too broad (e.g., 01-XX History and biography). Keep in mind that I'm way out of my depth here, as I've never read even a single paper in most of these fields. Some of my choices will be completely wrong, so I invite corrections.

{| class="wikitable"
|-
! Field
! MSC numbers
|-
| History
|
* 01-XX History and biography
|-
| Biography
|
* 01-XX History and biography
|-
| Foundations
|
* 03-XX Mathematical logic and foundations
* 18-XX Category theory; homological algebra
|-
| Discrete mathematics
|
* 05-XX Combinatorics
* 39-XX Difference and functional equations
* 52-XX Convex and discrete geometry
* 68-XX Computer science
|-
| Algebra
|
* 06-XX Order, lattices, ordered algebraic structures
* 08-XX General algebraic systems
* 12-XX Field theory and polynomials
* 13-XX Commutative algebra
* 14-XX Algebraic geometry
* 15-XX Linear and multilinear algebra; matrix theory
* 16-XX Associative rings and algebras
* 17-XX Nonassociative rings and algebras
* 18-XX Category theory; homological algebra
* 19-XX $K$-theory
* 20-XX Group theory and generalizations
|-
| Number theory
|
* 11-XX Number theory
|-
| Geometry and topology
|
* 14-XX Algebraic geometry
* 19-XX $K$-theory
* 51-XX Geometry
* 52-XX Convex and discrete geometry
* 53-XX Differential geometry
* 54-XX General topology
* 55-XX Algebraic topology
* 57-XX Manifolds and cell complexes
* 58-XX Global analysis, analysis on manifolds
|-
| Analysis
|
* 19-XX $K$-theory
* 22-XX Topological groups, Lie groups
* 26-XX Real functions
* 28-XX Measure and integration
* 30-XX Functions of a complex variable
* 31-XX Potential theory
* 32-XX Several complex variables and analytic spaces
* 33-XX Special functions
* 34-XX Ordinary differential equations
* 35-XX Partial differential equations
* 37-XX Dynamical systems and ergodic theory
* 39-XX Difference and functional equations
* 40-XX Sequences, series, summability
* 42-XX Harmonic analysis on Euclidean spaces
* 43-XX Abstract harmonic analysis
* 44-XX Integral transforms, operational calculus
* 45-XX Integral equations
* 46-XX Functional analysis
* 47-XX Operator theory
* 49-XX Calculus of variations and optimal control; optimization
* 58-XX Global analysis, analysis on manifolds
|-
| Mathematical physics
|
* 37-XX Dynamical systems and ergodic theory
* 70-XX Mechanics of particles and systems
* 74-XX Mechanics of deformable solids
* 76-XX Fluid mechanics
* 78-XX Optics, electromagnetic theory
* 80-XX Classical thermodynamics, heat transfer
* 81-XX Quantum theory
* 82-XX Statistical mechanics, structure of matter
* 83-XX Relativity and gravitational theory
* 85-XX Astronomy and astrophysics
* 86-XX Geophysics
|-
| Applied mathematics
|
* 41-XX Approximations and expansions
* 65-XX Numerical analysis
* 90-XX Operations research, mathematical programming
* 91-XX Game theory, economics, social and behavioral sciences
* 92-XX Biology and other natural sciences
* 93-XX Systems theory; control
* 94-XX Information and communication, circuits
|-
| Probability and statistics
| 
* 37-XX Dynamical systems and ergodic theory
* 60-XX Probability theory and stochastic processes
* 62-XX Statistics
|-
| Education
|
* 97-XX Mathematics education
|}

[[User:Ozob|Ozob]] ([[User talk:Ozob|talk]]) 17:27, 13 March 2010 (UTC)

:: Judging by our current categories as well as the MSC listings, I'd say we shouldn't split out history.  (We only have 68 articles in it, while the others average ~600.) Would Education be roughly the same as our current Basics, along with articles about mathematical pedagogy? If not, I don't think there would be enough to break that out on its own. I'm not sure that 33-XX Special functions belongs in applied math, but I'm not sure where else it would go.
:: [[User:CRGreathouse|CRGreathouse]]<small> ([[User talk:CRGreathouse|t]] | [[Special:Contributions/CRGreathouse|c]])</small> 18:56, 13 March 2010 (UTC)

:::I don't think we have enough "education" articles to make them worth a section; I would put them "general". Somehow, math education is not well represented on Wikipedia.

:::For "history", I think the issue is that the current restriction of only one field means that most articles with historical aspects are listed under some other field. For example, I would think that an article on Gauss or Euler would count as both history and biography, but they would just be under biography right now. Similarly [[Euclidean geometry]] is under geometry right now. I don't know at what point things become historical, but if something involves Euclid I think it clearly is. &mdash;&nbsp;Carl <small>([[User:CBM|CBM]]&nbsp;·&nbsp;[[User talk:CBM|talk]])</small> 19:07, 13 March 2010 (UTC)

Keep in mind that the MSC mainly covers research mathematics, but our encyclopedia articles are broader, also covering e.g. school textbook mathematics. So even if we wanted to go to a finer-grained system such as the MSC, the MSC itself would probably be inadequate: for instance, where does elementary arithmetic fit? Maybe 11-XX, maybe 97-XX, but neither is really a good fit. —[[User:David Eppstein|David Eppstein]] ([[User talk:David Eppstein|talk]]) 20:15, 13 March 2010 (UTC)

:I didn't include a "general" section because it's not relevant to the MSC; but I think it's really a good idea. I think we should have a "general" section which encompasses the current "basics" and "general" fields as well as all our education articles. Once we've corrected our embarrassing deficit of education articles, we can create a field for them.

:Regarding 33-XX Special functions, I was conflicted over that, but I didn't know what the right solution would be. One possible solution is to list it under every field, because there are special functions everywhere. I also considered making it its own field, since sometimes the same special function will turn up in seemingly unrelated contexts. I feel like putting it under applied math is kind of like giving up, because you know it's no good, but other people do it, so you know you'll get away with it... [[User:Ozob|Ozob]] ([[User talk:Ozob|talk]]) 20:59, 13 March 2010 (UTC)

::I agree that we need a "general" section as a catchall. For example, we have articles on journals, professional societies, and mathematics competitions. And television shows, I believe. 

::I don't object to the current "basics" section, although it would be nice to expand it once we can have more than one field per article. For example, right now [[Pentagon]] is in geometry, but it would be nice to have that sort of thing listed in "basics" as well. &mdash;&nbsp;Carl <small>([[User:CBM|CBM]]&nbsp;·&nbsp;[[User talk:CBM|talk]])</small> 21:15, 13 March 2010 (UTC)

::: Where would the article [[Differential analyser]] appear in the above classification? It is computer science but it isn't discrete mathematics. [[User:Bethnim|Bethnim]] ([[User talk:Bethnim|talk]]) 22:20, 13 March 2010 (UTC)
:::I think Computer science should be in the applied section. Combinatorics should be a standalone category, and there shouldn't be a discrete section at all. [[User:Bethnim|Bethnim]] ([[User talk:Bethnim|talk]]) 22:33, 13 March 2010 (UTC)
:::Difference and functional equations is fine being in the analysis section. [[User:Bethnim|Bethnim]] ([[User talk:Bethnim|talk]]) 22:35, 13 March 2010 (UTC)

::::I don't think [[differential analyser]] is a mathematics article at all. It belongs to the history of computing.
::::Why do you think there shouldn't be a discrete mathematics section? [[User:Ozob|Ozob]] ([[User talk:Ozob|talk]]) 22:51, 13 March 2010 (UTC)
:::::For one thing, although computer science is mostly about discrete computation, articles such as [[computable analysis]] and on continuous computation paradigms(http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.97.1895&rep=rep1&type=pdf) , are not discrete mathematics. Solutions to Difference and functional equations can be continuous functions. So the only real category left is combinatorics and even that isn't just about discrete mathematics ([[analytic combinatorics]], [[infinitary combinatorics]]). [[User:Bethnim|Bethnim]] ([[User talk:Bethnim|talk]]) 23:01, 13 March 2010 (UTC)
:::::And many discrete concepts such as ''Discrete Calculus of Variations'' are direct analogs of notions in analysis and so should logically be categorized as ''analysis'' rather than discrete. Basically I don't think discreteness is a valid criteria for categorizing things. [[User:Bethnim|Bethnim]] ([[User talk:Bethnim|talk]]) 23:19, 13 March 2010 (UTC)

::::::Hmm. Where would you put [[graph theory]], [[matroid]], and [[coding theory]]? [[User:Ozob|Ozob]] ([[User talk:Ozob|talk]]) 00:37, 14 March 2010 (UTC)
:::::::With coarse-grain I'd put graph theory and matroid theory in a combinatorics category, and put coding theory into applied. With finer-grain I'd put coding theory in Information theory and graph theory would have its own section. [[User:Bethnim|Bethnim]] ([[User talk:Bethnim|talk]]) 03:19, 14 March 2010 (UTC)

:One thing that springs to mind with the above list is that it seems to be tuned for research so it would be hard to categorize basic freshman calculus subjects. Where, for example, would [[Derivative]], [[Catenary]], and [[Ratio]] go?--[[User:RDBury|RDBury]] ([[User talk:RDBury|talk]]) 00:08, 14 March 2010 (UTC)

::Derivative would go under analysis, catenary under geometry, and ratio under general. (There isn't a general section in the list above, but consensus seems to be that we need one.) [[User:Ozob|Ozob]] ([[User talk:Ozob|talk]]) 00:21, 14 March 2010 (UTC)
:::Analysis is one of our categories, it's not in the MSC. Perhaps Catenary would go under Special functions since cosh, or under differential geometry since it's defined by curvature. My point is that these more general knowledge articles are going to be ambiguous at best. In any case, it would be a good idea to do a test classification of a couple of dozen articles before deciding on anything rather than trying to decide based purely on intuition.--[[User:RDBury|RDBury]] ([[User talk:RDBury|talk]]) 11:56, 14 March 2010 (UTC)
::::Ah, I thought you were asking a different question. I'm not particularly concerned about stuffing elementary articles into the MSC, because they won't fit; as we've already noted here, the MSC is intended for research. My intent was to use the MSC as a guide to classifying more advanced topics. But I don't feel like it really worked; I came up with roughly the classifications we have now, and I'm not really satisfied with them. I was struck with insight when I looked at the IMU list mentioned below: The IMU list has an entire section for Lie theory! In the MSC classification, Lie algebras are in 17Bxx, making them completely separate from Lie groups, which are in 22Exx. But you can't lump together all of 17-XX with 22-XX: For instance, finite dimensional algebras go in 17, topological groups go in 22, and the two subjects have hardly anything to do with each other (that I know of). So I feel like the MSC really doesn't capture this very well, and consequently no scheme based off of it will capture it either. [[User:Ozob|Ozob]] ([[User talk:Ozob|talk]]) 22:17, 15 March 2010 (UTC)

I've taken the liberty of slightly tweaking Ozob's list above. In particular, I moved special functions to analysis as any special function I know of is related to some differential equation/integral/series (though, of course, any specific special function may be in many other fields). But in looking through the list, it's clear that the top-level MSC is both too fine and too coarse. I do think it gives a good understanding of which fields we need though, but I don't think it succeeds in allowing for a clear way to classify any given article. [[User:RobHar|RobHar]] ([[User talk:RobHar|talk]]) 02:56, 14 March 2010 (UTC)

My main concern about Ozob's list is that it still has algebraic geometry under geometry. Is the idea to simply put both "algebra" and "geometry" fields on those articles?  &mdash;&nbsp;Carl <small>([[User:CBM|CBM]]&nbsp;·&nbsp;[[User talk:CBM|talk]])</small> 11:28, 15 March 2010 (UTC)

:An alternative to the MSC list is the IMU list: http://www.mathunion.org/activities/icm/icm-2010-program-structure/  where Algebraic geometry, Lie theory and Dynamical systems each get their own sections. Although under the IMU scheme, recursion theory is part of foundations, and category theory is part of algebra, and Control theory and optimization art lumped together (but excluding combinatorial optimization). [[User:Bethnim|Bethnim]] ([[User talk:Bethnim|talk]]) 15:55, 15 March 2010 (UTC)

::I like that system a lot better, actually. We would need to tweak it a little, but I think it would be relatively easy to understand which section an article belongs in, unlike the current system. &mdash;&nbsp;Carl <small>([[User:CBM|CBM]]&nbsp;·&nbsp;[[User talk:CBM|talk]])</small> 18:27, 15 March 2010 (UTC)

:::I like this system better, too. I should comment that I did really intend to lump all kinds of geometry and topology together: I feel like hardly anyone in algebraic geometry seems to take differential geometry seriously enough, and yes, I did feel like the articles that had both geometric and algebraic content could be put under both. But the IMU system is better, I think; In practice, commutative algebra and algebraic and complex geometry are yoked together very tightly, but their connection with differential geometry is pretty slim. [[User:Ozob|Ozob]] ([[User talk:Ozob|talk]]) 22:23, 15 March 2010 (UTC)

== Optimization algorithm ==

[[Optimization algorithm]] is currently a redirect and until less than an hour ago, didn't even exist as a redirect.  I found that quite surprising.
: 
Should there be such an article? [[User:Michael Hardy|Michael Hardy]] ([[User talk:Michael Hardy|talk]]) 04:26, 15 March 2010 (UTC)

:However, [[Optimization (mathematics)]] exists. What else should it be? [[User:Tsirel|Boris Tsirelson]] ([[User talk:Tsirel|talk]]) 10:09, 15 March 2010 (UTC)
== Gauss interpolation formula ==

I am going now to create an article about equidistant interpolation but have a trouble with Gauss interpolation formula. Can anyone please verify this formula:[http://eom.springer.de/g/g043440.htm]. I have tried but unsuccessfully.--[[User:MathFacts|MathFacts]] ([[User talk:MathFacts|talk]]) 10:17, 15 March 2010 (UTC)

:I thought that we had an article on [[difference equations]], but it just links to [[recurrence relation]] which does not do the subject justice.
:There are some errors on the Springer page to which you linked, and the notation is not clear. If I were you I would look for a better source. [[User:JRSpriggs|JRSpriggs]] ([[User talk:JRSpriggs|talk]]) 08:13, 16 March 2010 (UTC)
::You might want to check whether the technique you are looking for is not already covered by [[interpolation]]. [[User:JRSpriggs|JRSpriggs]] ([[User talk:JRSpriggs|talk]]) 08:36, 16 March 2010 (UTC)

== Square (algebra) ==

[[Square (algebra)]] is such a simple subject that it doesn't need attention from mathematicians. (?)
: 
So one might be tempted to think.
: 
I found it a horrible mess.  I did some cleanup.  At one point it asserted that the '''"general term"''' of the series
: <math> 1^2 + 2^2 + 3^2 + \cdots + n^2 \, </math>
is
: <math> \frac{n(n+1)(2n+1)}{6}. </math>
: 
Someone out there is challenged by the task of understanding what "general&nbsp;term" means.  Should that be who writes this article?
: 
Which topics should be included is a question that needs to be considered by someone who has some competence.  The present choice of topics is a bit weird, to say the least. [[User:Michael Hardy|Michael Hardy]] ([[User talk:Michael Hardy|talk]]) 18:42, 16 March 2010 (UTC)

: [[Square number]] is also in questionable shape, if not as bad as [[square (algebra)]]. [[User:Michael Hardy|Michael Hardy]] ([[User talk:Michael Hardy|talk]]) 18:59, 16 March 2010 (UTC)
:My feeling is that [[Square (algebra)]], at least in its present form, reads too much like a chapter from a middle school algebra textbook and is too elementary in scope for an encyclopedia article. I would not be opposed to prodding of AfD-ing it. [[User:Nsk92|Nsk92]] ([[User talk:Nsk92|talk]]) 20:22, 16 March 2010 (UTC)

::At the risk of being called overly critical (again), there are many subjects like this; too elementary for many mathies to take an interest so that leaves the field open for people to fill up the article with things they sort of remember from high school. One that I tried to clean up recently was [[Ratio]] but I only did about half of it. Badly written and uninformative aren't criteria for deletion though, unless a complete rewrite is in order.--[[User:RDBury|RDBury]] ([[User talk:RDBury|talk]]) 21:08, 16 March 2010 (UTC)
== Proposed deletion of [[Zenzizenzizenzic]] ==

Discussion at [[Wikipedia:Articles for deletion/Zenzizenzizenzic (2nd nomination)]]. [[User:Gandalf61|Gandalf61]] ([[User talk:Gandalf61|talk]]) 11:29, 19 March 2010 (UTC)

== Professor of mathematics ==

[[Professor of mathematics]] is a red link.  Two articles link to it.  Should we redirect it?  Or create an article?  Or delete the links?  Or let our posterity decide six months from now? [[User:Michael Hardy|Michael Hardy]] ([[User talk:Michael Hardy|talk]]) 22:26, 19 March 2010 (UTC)
:De-link them.  It's a phrase of ordinary English, understandable from its component words; shouldn't have an article. --[[User:Trovatore|Trovatore]] ([[User talk:Trovatore|talk]]) 22:28, 19 March 2010 (UTC)

OK, I've done that.  Now a question of no immediate practical import occurs to me.  Is there any way to tell which articles ''formerly'' linked to a particular title? [[User:Michael Hardy|Michael Hardy]] ([[User talk:Michael Hardy|talk]]) 02:38, 20 March 2010 (UTC)
:No practical way that I know of.  (In principle, of course, you could enumerate the history of every article in the encyclopedia.)  This is the rationale, I think, for why you're not supposed to empty categories that you've proposed for deletion.  --[[User:Trovatore|Trovatore]] ([[User talk:Trovatore|talk]]) 04:35, 20 March 2010 (UTC)

== Featured picture candidates part 4 ==

[[User:Noodle snacks]] didn't do a nomination this week so I decided to try one. See [[Wikipedia:Featured picture candidates/File:Helicatenoid.gif]]. If you have some knowledge of differential geometry it would be helpful to check the caption; I tried to describe a local isometry in layman's terms, but maybe it could be done better.--[[User:RDBury|RDBury]] ([[User talk:RDBury|talk]]) 06:50, 20 March 2010 (UTC)
== Footer templates ==

I made some changes to the [[Template:Applied-footer|Applied Mathematics template]] a month or so ago. I proposed similar expansion and organization of the [[Template talk:Mathematics-footer|Pure Mathematics template]]. (Following the earlier discussion (on the mathematics template's talk page), I suggest that somebody develop a "Basic mathematics" template. Thanks[[User:Kiefer.Wolfowitz|Kiefer.Wolfowitz]] ([[User talk:Kiefer.Wolfowitz|talk]]) 17:50, 18 March 2010 (UTC)

===Industrial and applied mathematics===
I boldly changed the title to reflect the established usage of SIAM, British, and European organizations, and reflecting the problem that "applied mathematics" is often narrowly understood in terms of the grand British tradition of using analytic methods on problems in the physical sciences, etc. [[User:Kiefer.Wolfowitz|Kiefer.Wolfowitz]] ([[User talk:Kiefer.Wolfowitz|talk]]) 21:00, 18 March 2010 (UTC)

=== Theoretical Computer Science ===
This is probably the best venue for this discussion.
There was recently a discussion on the [[Talk:P versus NP problem#Theoretical computer science is branch of applied mathematics|talk page]] for the "[[P versus NP problem]]" article.  There appears to be a consensus that [[Theoretical Computer Science]] is not in [[Applied Mathematics]].  With this in mind, I propose that the [[Template talk:Applied-footer|Applied Mathematics footer]] be modified. I would be [[WP:BOLD|bold]] and just make the change, but several articles would likely need to be modified to fully effectuate the change. And it might also be affected by the discussion Kiefer started above. <b><span style="color:green;">Jwesley</span>[[User_talk:Jwesley78|<sub>78</sub>]]</b> 18:11, 18 March 2010 (UTC)
:Certainly, there is no such consensus. As the voice that opposes your visison of things perhaps the most, I would like to point out that there is agreement that there is overlap between these disciplines. While it may be agreed that statement that TCS is branch of applied mathematics does not reflect the situation, it has also been pointed out that on applied mathematics template was listed as branch of applied mathematics (apparently by a previous consensus opposite to one which is claimed), and it has also been pointed out that many theoretical computer scientists work at applied mathematics departments at places like MIT rather than in CS departments. To disregard all this and say that there is a "concensus" while there is ongoing controversy is awful misrepresentation of facts.[[User:Dlakavi|Dlakavi]] ([[User talk:Dlakavi|talk]]) 12:56, 19 March 2010 (UTC)
: Sounds good to me. [[User:CRGreathouse|CRGreathouse]]<small> ([[User talk:CRGreathouse|t]] | [[Special:Contributions/CRGreathouse|c]])</small> 18:14, 18 March 2010 (UTC)
:: Your "consensus" needs clarification, because many mentioned that theoretical CS is often housed in math departments, particularly in applied mathematics divisions, notably at MIT. There was consensus that Theoretical CS is not part of traditional British "applied mathematics", but that is hardly relevant to ''contemporary'' applied mathematics as defined by reliable sources, especially [[Society for Industrial and Applied Mathematics|SIAM]] and the [[International Mathematics Union]]
::*{{cite book | last = Engquist | first = Björn (ed.) |authorlink = Björn Engquist |coauthors= [[Wilfried Schmid]] (ed.) | title = Mathematics Unlimited: 2001 and Beyond | publisher = Springer | location = Berlin | year = 2001 | isbn = 9783540669135 |page= 1225 }}
::whose current President is [[Lovasz]]. 

::SIAM publishes 
::*''SIAM Journal on [[Discrete mathematics|Discrete]] and [[Algebra|Algebraic Mathematics]]''
::*''SIAM Journal on [[Computing]]''
::*''SIAM Journal on [[Optimization]]''
::all of which are covered by the CS reviewing journal; all of these journals have significant overlap in editorial boards, author, references, with the leading CS journals. This argument could be strengthened by looking at the [[Institute for Scientific Information|ISI]] list of journals in CS theory, but I assume you recognize that theoretical CS has a substantial overlap with applied mathematics. (IMHO, this overlap is much larger than the overlap with [[mathematical statistics]].) 
::SIAM cosponsors many of the main ''prizes in theoretical computer science'' (or at least prizes that prominently feature theoretical computer scientists): [[Mathematical_Programming_Society#George_B._Dantzig_Prize|George Dantzig prize]], the [[Fulkerson Prize]], etc.

:: The [[Theoretical computer science]] article plants the CS flag on [[Theoretical_computer_science#Scope|many mathematical theories]]: [[Category theory]], [[Graph theory]], [[number theory]], [[mathematical logic]], etc.! (Why avoid the connection to  mathematics now?)

::I believe that the previous editors are rightly concerned that Theoretical CS has much less overlap with the grand '''British''' tradish of '''"applied mathematics",''' with analytic methods (and some heuristics) applied to problems of physical science---But what about the extensive literature on formal power series and automata theory? Thanks [[User:Kiefer.Wolfowitz|Kiefer.Wolfowitz]] ([[User talk:Kiefer.Wolfowitz|talk]]) 19:09, 18 March 2010 (UTC)

:::*The journals you list are not really journals in "Theoretical Computer Science". JoDaAM is close enough, but this argument is still not very strong. SIAM, like the ACM (Association for Computing Machinery), might be broader than its name would imply. <b><span style="color:green;">Jwesley</span>[[User_talk:Jwesley78|<sub>78</sub>]]</b> 20:10, 18 March 2010 (UTC)

* (I also made this comment [[Talk:P versus NP problem#SIAM and .22applied.22|here]].) So there's no confusion, the question is not to what extent are TCS and Math related; they obviously are. In some ways, Computer Science (as a whole) is an "applied" branch off of Mathematics. The question here is specifically whether "Theoretical Computer Science" should be lumped into the category of "Applied Mathematics". TCS is the least "applied" of any field in CS. Many topics in TCS have no direct application. Since TCS is often not-in-any-way "applied", placing TCS within AM might be worse than placing another more applied field of CS (e.g., Artificial Intelligence) into AM. <b><span style="color:green;">Jwesley</span>[[User_talk:Jwesley78|<sub>78</sub>]]</b> 20:04, 18 March 2010 (UTC)

: I made this comment there as well: :: 
: Can we try to change the name of the template so that it is somewhat coherent and lists the topics of mathematical research that have strong ties to (empirical) science, engineering, and other concerns? <!-- (The old template was a dull antique. I tried to modernize it.) --> I would suggest "Applicable Mathematics" or "Mathematics for Applications". Would either name be better and acceptable? [[User:Kiefer.Wolfowitz|Kiefer.Wolfowitz]] ([[User talk:Kiefer.Wolfowitz|talk]]) 20:12, 18 March 2010 (UTC) I changed the title to the established '''''"Industrial and Applied Mathematics",''''' (as noted above) because the others are less established and objectionable.  [[User:Kiefer.Wolfowitz|Kiefer.Wolfowitz]] ([[User talk:Kiefer.Wolfowitz|talk]]) 21:02, 18 March 2010 (UTC)

===Computational mathematics===
Following the discussion, I removed "[[Theoretical computer science]]" and replaced it with "[[Computational mathematics]]", there being no short way to write "mathematics associated with theoretical computer science". Does this deal with the problem? (It may be useful to change the name of the footer to "industrial and applied mathematics", which is established at least).[[User:Kiefer.Wolfowitz|Kiefer.Wolfowitz]] ([[User talk:Kiefer.Wolfowitz|talk]]) 20:36, 18 March 2010 (UTC)
: I like this change.  Some of the subtopics should be reassigned or removed; It's definitely a move in the right direction. Thanks, <b><span style="color:green;">Jwesley</span>[[User_talk:Jwesley78|<sub>78</sub>]]</b> 20:42, 18 March 2010 (UTC)
::I object to the name "computational mathematics". Nobody calls it this; it's called "theoretical computer science". It is not Wikipedia's purpose to innovate. Calling this discipline anything other than "theoretical computer science" will only confuse people. Until we can sort this out, I've reverted. [[User:Ozob|Ozob]] ([[User talk:Ozob|talk]]) 00:41, 19 March 2010 (UTC)

::While I have no extremly strong objection to the change, it is misleading. Michael Sipser is theoretical computer scientist and is in the applied mathematics department at MIT. Many people who are important in theoretical computer science have degree from applied mathematics departments (Peter Shor is both a graduate of MIT applied math PhD program, and a professor there, and yet he is the leading person in quantum computation theory; even more traditional parts of TCS have such people alot). It is no more fair to say that this is part of mathematics as it is part of computer science. These are interdisciplinary areas, and being listed in more than one place is not inaccurate. Daniel Spielman is at applied mathematics department at Yale, has finished applied mathematics PhD at MIT and has been at MIT applied math department, and is one of the persons in Theoretical CS at yale (http://theory.cs.yale.edu/)... I am sure many more examples can be found. [[User:Dlakavi|Dlakavi]] ([[User talk:Dlakavi|talk]]) 13:07, 19 March 2010 (UTC)
:::That's a silly argument. Departments have names that often result from tradition or accidents of university-specific history and politics. Go through the winners of the [[Gödel Prize]] and you'll find plenty of confusion. Avi Wigderson is at the School of Mathematics (IAS, Princeton). But he was in the computer science department at the Weizmann institute. Babai has a Ph.D. in math, works in a CS department, organizes the Budapest Semesters in Mathematics. Saks heads the Mathematics Graduate Program at Rutgers while Szegedy, also at Rutgers, is in the CS department. Razborov who was at Steklov (math) is currently in Chicago (cs). The thing is, the name of a department is not a great indicator. When my department switched its name from Computer Science Department to Software Engineering Department, I did not become more of an engineer. And my students now get degrees with a different name but they take the same courses, do the same research. (But the name change did allow us to hire three new profs) [[User:Pichpich|Pichpich]] ([[User talk:Pichpich|talk]]) 23:41, 19 March 2010 (UTC)
::::It is not silly at all. If a math department employs a theoretical computer scientist, then, by definition, they believe that he is doing math. Or at least that what he is doing is awfully close to math, close enough that they think he fits in. We all agree&mdash;you gave examples yourself&mdash;that there are theoretical computer scientists in mathematics departments. (I know some.) Therefore some people believe that theoretical computer science is a branch of math, so the name is not inappropriate. Wikipedia does not introduce new or reshape old terminology; it follows the sources. If reliable sources say that theoretical computer science is a branch of math, who are we to argue? [[User:Ozob|Ozob]] ([[User talk:Ozob|talk]]) 03:40, 21 March 2010 (UTC)
::::: The original question was whether TCS is "applied" mathematics.  We've strayed from the original question, asking instead whether TCS should be called "Mathematics" (of course it should).  In my perspective, the very fact that the field is called "''Theoretical'' Computer Science" should be enough to conclude that it's not "applied" in nature. <b><span style="color:green;">Jwesley</span>[[User_talk:Jwesley78|<sub>78</sub>]]</b> 03:59, 21 March 2010 (UTC)

=== What is "Applied Math"? ===
Re: {{Applied-footer}}
There are many subjects listed in the [[Template talk:Applied-footer|"Applied Math" footer]] that do not belong.  Apparently there's a disagreement about which attributes distinguish "applied" from "pure" mathematics. This might be a good place to discuss it. <b><span style="color:green;">Jwesley</span>[[User_talk:Jwesley78|<sub>78</sub>]]</b> 21:06, 18 March 2010 (UTC)

: Can we agree that the present template does reflect the IMU book's discussion of mathematics (pursued closely with empirical science and applications) and the applications featured by recent Fields medalists? (It does not try to represent the curriculum in Glascow for example.) [[User:Kiefer.Wolfowitz|Kiefer.Wolfowitz]] ([[User talk:Kiefer.Wolfowitz|talk]]) 21:41, 18 March 2010 (UTC)

::Look, there's a difference between these nav templates and explicit claims in an article about what is a branch of what.  I don't really ''like'' nav templates and wouldn't mind if they were just deleted, but if we have to have them, it's not unreasonable to suppose that someone looking for ways to apply math would be interested in some CS-related links.  That's not the same thing as making the frankly weird claim that P?=NP is a question of applied math. --[[User:Trovatore|Trovatore]] ([[User talk:Trovatore|talk]]) 21:52, 18 March 2010 (UTC)

:::Nobody put the P?=NP question on the template. BTW, Smale and the Clay Foundation think that P=NP? is a central question of mathematics (after von Neumann's time), and Smale's judgement has been relied on by mathematicians for many decades; c.f. [[Vladimir I. Arnol'd]] acknowledgment in the ''Notices of the AMS'' article listed on the [[V. I. Arnold]] page.
::::No, but this discussion didn't arise because of the template; it arose out of an edit war on the P?=NP page.
::::I don't have any problem saying P?=NP is a question of mathematics.  I don't think it's a question of ''applied'' mathematics.  It strikes me as very far towards the theoretical end.  Note that a proof (in either direction, although we all know that P!=NP so there's really only one candidate) would not necessarily have any applications at all to real-world problems. --[[User:Trovatore|Trovatore]] ([[User talk:Trovatore|talk]]) 22:37, 18 March 2010 (UTC)
:::::I am somewhat puzzled; would you please explain a bit, why a proof of P=NP (yes, if in this direction) would not apply to real word? [[User:Tsirel|Boris Tsirelson]] ([[User talk:Tsirel|talk]]) 07:07, 19 March 2010 (UTC)
::::::All it would (necessarily) do is tell you that there ''is'' a polynomial-time algorithm for (name your favorite NP-but-not-obviously P problem).  It wouldn't necessarily tell you what that algo is.  Even if it ''did'', the bound might be ''n''<sup>1000000</sup> or something, which for practical purposes might as well be the Ackermann function. --[[User:Trovatore|Trovatore]] ([[User talk:Trovatore|talk]]) 08:20, 19 March 2010 (UTC)
:::::::I see, thanks. [[User:Tsirel|Boris Tsirelson]] ([[User talk:Tsirel|talk]]) 11:46, 19 March 2010 (UTC)
: There is no consensus on the definition of applied mathematics or the existence of applied mathematics; see [[Vladimir I. Arnol'd]] acknowledgment in the ''Notices of the AMS'' article listed on the [[V. I. Arnold]] page. [[User:Kiefer.Wolfowitz|Kiefer.Wolfowitz]] ([[User talk:Kiefer.Wolfowitz|talk]]) 22:54, 18 March 2010 (UTC)
::No, of course there's not a consensus on the definition, and there's never going to be.  That's not a problem.  Putting a claim that a particular question is part of applied math, when actually very few workers in the field think of it that way, ''is'' a problem.  --[[User:Trovatore|Trovatore]] ([[User talk:Trovatore|talk]]) 22:56, 18 March 2010 (UTC)
:::Some of the more notable people interested in the question (P!=NP) - like Daniel Spielman of Yale - are actually at applied math departments. If a prize is offered by the major institution that wants to "disseminate mathematical knowledge" to the question, why is then wrong to say that it is an applied mathematics question too. Mathematicians (pure and applied), people form CS departments, logicians etc all pertain to this fundamental question. [[User:Dlakavi|Dlakavi]] ([[User talk:Dlakavi|talk]]) 13:32, 19 March 2010 (UTC) 
:::Which ones do people have a problem with? Of course any such split will be very fuzzy but I see no problem with classifying P≠NP as applied even if it probably will require some rather abstract logic for its solution if people don't just give up and accept it as an axiom. The distinction just makes it easier to find things. It's like the amount of information needed to describe a picture. The top is sky and the bottom is ground to start with. That doesn't mean a bird in the sky is blue or made of air. [[User:Dmcq|Dmcq]] ([[User talk:Dmcq|talk]]) 12:16, 19 March 2010 (UTC)

===Theoretical computer science: The Myths of a Discrete-Continuous Divide and a Pure-Applied Divide===

If ''applied'' means ''analysis'' then ''Theoretical computer science'' does overlap with applied. Not that the talking about pure/applied makes much sense. The applied math template should be merged with the main math footer template.

''Theoretical computer science'' considers both discrete and continuous computational processes, and both discrete and continuous input/output: 

*Continuous computability theory:
**[[Computable analysis]]
**[[Algorithmic complexity theory]]

*Continuous complexity theory:
**Complexity theory of continuous time computation using dynamical systems or other continuous models of continuous computation.
**[http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.33.4678&rep=rep1&type=pdf Complexity theory of numerical analysis] (various approaches including [[Information-based complexity]], [[algebraic complexity theory]])
Including P!=NP over R

*[http://scholar.google.com/scholar?q=%22analog+coding%22+OR+%22analogue+coding Analog coding theory]

*[http://scholar.google.com/scholar?q=%22analog+encryption%22+OR+%22analogue+encryption "analog encryption" OR "analogue encryption"]

*[[analog vlsi]]

*[http://scholar.google.com/scholar?q=%22analog%20Automata%22%20OR%20%22continuous%20Automata "analog Automata" OR "continuous Automata"]

Many concepts in analysis have discrete versions giving rise to discrete analysis. See [[discrete mathematics]] for examples. So analysis shouldn't be contrasted with discrete. Analysis isn't just about limits or continuity, it is a collection of concepts and methods about functions and function spaces, be they discrete or continuous.

Other topics often categorized as part of discrete mathematics:

*Graph theory
**[http://scholar.google.com/scholar?q=%22continuous+graphs%22+OR+%22continuous+graph%22+vertices continuous graphs]
**[http://scholar.google.com/scholar?q=%22Analysis%20on%20graphs Analysis on graphs]

*Lattices: [http://scholar.google.com/scholar?q=%22continuous+lattices continuous lattices]

*Operations research: [http://scholar.google.com/scholar?q=%22operations+research%22+%22continuous+processes continuous processes in operations research]

*Game theory: [[Differential game]]

*Logic: [http://scholar.google.com/scholar?q=%22continuous%20logic "continuous logic"] (fuzzy logic)

What is the most pure mathematics subject ? The queen of mathematics, number theory.

What is the most applied ? Mathematical physics.

Here are the Google results for [http://scholar.google.com/scholar?q=%22Number%20theory%20and%20physics "Number theory and physics"]

Number theory isn't concerned solely discrete objects: Transcendental numbers, Diophantine approximation, p-adic analysis, function fields

There is no pure. There is no applied. And ''discrete mathematics'' as a distinct branch of mathematics is a nonsense.

[[User:Bethnim|Bethnim]] ([[User talk:Bethnim|talk]]) 13:04, 19 March 2010 (UTC)

== [[Mathematical finance]] versus "[[Financial mathematics]]" ==

Some editors use the "[[financial mathematics]]" rather than the standard term "[[mathematical finance]]". This seems as imperialistic as the use of "[http://www.maa.org/devlin/devlin_06_02.html Bayesian mathematics]" (sic.) to refer to [[Bayesian statistics]] (imho)! [[User:Kiefer.Wolfowitz|Kiefer.Wolfowitz]] ([[User talk:Kiefer.Wolfowitz|talk]]) 19:10, 20 March 2010 (UTC)

== Animation at Tesseract ==

Another editor might be able to cast a fresh eye at [[Talk:Tesseract#New_Animations]] where [[User:Jgmoxness]] wishes to insert a new animation into the article but I'm objecting. [[User:Dmcq|Dmcq]] ([[User talk:Dmcq|talk]]) 21:35, 20 March 2010 (UTC)
== Mathematics template (footer): ==

Here is the current template (footer):
{{Mathematics-footer}}

Would the following navigational-box template be an improvement, and useful for further discussion?
{{Navbox
|name       = Mathematics
|titlestyle = 
|title      = Topics in [[Mathematics]]
|state=expanded
|groupstyle = 
|group1=[[Elementary mathematics|Basics]]
|list1=[[Arithmetic]] - [[Algebra]] - [[Euclidean geometry]] - [[Descriptive statistics]] - [[Probability]] - [[Statistics]] - [[Trigonometry]] - [[Calculus]] - [[Logic]] 
|group2=[[Foundations of mathematics|Foundations]]
|list2= [[Mathematical Logic]] - [[Set theory]] - [[Category theory]] - [[Automata theory|Automata]] & [[Formal language]]s
|group3= [[Abstract algebra|Algebra]]<br /> & [[Combinatorics]] 
|list3=  [[Combinatorics]] - [[Ordered set]]s & [[Lattice theory|Lattices]]- [[Universal algebra]] -  [[Group theory|Group]]s - [[Ring theory|Ring]]s - [[Field theory|Field]]s - [[Module theory|Modules]] - 
[[Associative algebras|Associative]] - [[Lie theory|Lie]] - [[Linear algebra|Linear]] & [[Multilinear algebra|Multilinear]] - [[Representation theory|Representation]]s - [[Commutative algebra]] & [[Algebraic geometry]]
|group4=[[Number theory]] 
|list4=[[Algebraic number theory]] - [[Analytic number theory]]
|group5=[[Geometry]] 
|list5= [[Elliptic geometry|Elliptic]] & [[Hyperbolic geometry]] - [[Incidence geometry]] - [[Projective geometry]] - [[Discrete geometry|Discrete]] & [[Convex geometry]] • [[Differential geometry]] • [[Integral geometry]] 
|group6=[[Topology]]
|list6=[[General topology|Point-set topology]] - [[Algebraic topology]] - [[Differential topology]] 
|group7=[[Analysis]] 
|list7= [[Measure theory|Measure]] & [[Integral|Integration]] - [[Complex analysis]] - [[Fourier analysis|Fourier]] & [[Harmonic analysis]] - [[Functional analysis]] - [[Operator theory]] - <br />
[[Approximation theory]] - [[Numerical analysis]] - [[Differential equations]] - [[Dynamical systems]] - [[Control theory]] - [[Calculus of variations|Variational calculus]] 
|group8=[[Probability theory]]
|list8= [[Probability distribution|Distributions]] of [[random variable]]s - [[Stochastic process]]  - [[Stochastic analysis]] - [[Functional integration|Path integral]]  - [[Malliavin calculus|Stochastic variational calculus]]
|group9= [[Mathematical sciences]] <!-- [[Decision science]]s --> 
|list9= [[Statistical theory]] - [[Operations research]] - [[Optimization (mathematics)|Optimization]] -  [[Game theory]] •[[Mathematical economics]] - [[Mathematical finance]] 
| below = '''[[:Category:Mathematics|Category]]''' {{·}} [[Portal:Mathematics|Mathematics portal]] {{·}} [[Topic outline of mathematics|Outline]] {{·}} [[List of mathematics topics|Topics]]
}}<noinclude>
Thanks! [[User:Kiefer.Wolfowitz|Kiefer.Wolfowitz]] ([[User talk:Kiefer.Wolfowitz|talk]]) 20:05, 20 March 2010 (UTC)

:To begin with, I think it's strange to lump algebra and combinatorics together (and put number theory in there), yet have a separate "algebras" section. I also find it strange to have two sections called analysis. [[User:RobHar|RobHar]] ([[User talk:RobHar|talk]]) 21:01, 20 March 2010 (UTC)

::True, true. I created larger groups of algebra and analysis, and then put number theory as its own category. [[User:Kiefer.Wolfowitz|Kiefer.Wolfowitz]] ([[User talk:Kiefer.Wolfowitz|talk]]) 22:02, 20 March 2010 (UTC)
:::What is the point of this discussion?  There is a clear and settled consensus against this sort of template on mathematics articles. --[[User:Trovatore|Trovatore]] ([[User talk:Trovatore|talk]]) 22:38, 20 March 2010 (UTC)

:::: Your precise reference to this "clear and settled consensus" would help me and perhaps some  other editors (involved in this week's extensive discussion). This template exists and is used in articles, so it is worth discussing.

: I don't see the need for anything like that in maths articles, as generally relevant links are or should be in the article. E.g. when covering a maths topic well it inevitably mentions related topics that it depends on, that depend on it, or that are related in some other way, and mention them in context so it is clear how they relate. It's missing a lot of basic topics which would only make it bigger [[Number]], [[Complex Number]], [[Vector]], [[Matrix]], [[Tensor]], [[Function (mathematics)|Function]], [[Dimension]], [[Plane (geometry)|Plane]], as well as important mathematical topics from [[mathematical physics]].
: It's different from a template like [[:Template:Neil Gaiman]] where one of those articles generally refers to few, maybe only one (the author), of the others, and the number of articles is limited (in this case to his works that have articles). Maths is much bigger and much more interrelated, so much trickier to summarise in a navigation box. Better to make sure articles are properly categorised and include a prominent link to [[Mathematics]] which sort of does the same job.--<small>[[User:JohnBlackburne|JohnBlackburne]]</small><sup>[[User_talk:JohnBlackburne|words]]</sup><sub style="margin-left:-2.0ex;">[[Special:Contributions/JohnBlackburne|deeds]]</sub> 00:36, 21 March 2010 (UTC)

We also have [[Portal:Mathematics]] with a section "Topics in mathematics" that looks quite good on first sight. It might be good if the presentation there could be harmonised with the template, so that people find it easier to switch from one to the other. [[User:Hans Adler|Hans]] [[User talk:Hans Adler|Adler]] 00:56, 21 March 2010 (UTC)

::IMO most of these navigation templates are more trouble than they're worth and should be used as sparingly as possible. Changing a modestly sized one into a half page is a step in the wrong direction.--[[User:RDBury|RDBury]] ([[User talk:RDBury|talk]]) 10:02, 21 March 2010 (UTC)

== Multiplicative navigation over natural numbers ==

Please, [[Template talk:Infobox number#Multiplicative navigation|discuss this proposal]]. [[User:Incnis Mrsi|Incnis Mrsi]] ([[User talk:Incnis Mrsi|talk]]) 21:30, 21 March 2010 (UTC)
== Article assessment proposal ==

I'd like to go ahead and make a proposal regarding changes discussed above to the [[Wikipedia:WikiProject_Mathematics/Wikipedia_1.0/Assessment|article assessment]] categories and such.

===1. Change list of "fields"===
The current list is:
* [[Wikipedia:WikiProject_Mathematics/Wikipedia_1.0/General|general]]
* [[Wikipedia:WikiProject_Mathematics/Wikipedia_1.0/Basics|basics]]
* [[Wikipedia:WikiProject_Mathematics/Wikipedia_1.0/Algebra|algebra]]
* [[Wikipedia:WikiProject_Mathematics/Wikipedia_1.0/Analysis|analysis]]
* [[Wikipedia:WikiProject_Mathematics/Wikipedia_1.0/Applied mathematics|applied]] (includes numerical analysis)
* [[Wikipedia:WikiProject_Mathematics/Wikipedia_1.0/Discrete mathematics|discrete]]
* [[Wikipedia:WikiProject_Mathematics/Wikipedia_1.0/Foundations, logic, and set theory|foundations]] (includes logic and set theory)
* [[Wikipedia:WikiProject_Mathematics/Wikipedia_1.0/Geometry|geometry]]
* [[Wikipedia:WikiProject_Mathematics/Wikipedia_1.0/Mathematical physics|mathematical physics]]
* [[Wikipedia:WikiProject_Mathematics/Wikipedia_1.0/Number theory|number theory]]
* [[Wikipedia:WikiProject_Mathematics/Wikipedia_1.0/Probability and statistics|probability and statistics]]
* [[Wikipedia:WikiProject_Mathematics/Wikipedia_1.0/Topology|topology]]
* [[Wikipedia:WikiProject_Mathematics/Wikipedia_1.0/Mathematicians|mathematicians]]

'''I would like to propose the following list''':
*General (taking in the current "basics" field)
*History & biography
*Algebra
*Algebraic geometry
*Analysis
*Applied mathematics
*Combinatorics (taking some of the content of the current "Discrete" field)
*Foundations, logic, & set theory
*Geometry
*Mathematical physics
*Number theory
*Probability & statistics
*Theoretical computer science (taking some of the content of the current "Discrete" field)
*Topology

In words:
*I think we can consolidate the "basics" field into the "General" field and have the latter be about "general mathematics" and "things generally about the field/study of mathematics".
*Rename "mathematicians" and consolidate it with articles on the history to form "History & biography"
*Add "Algebraic geometry" to deal with algebraic geometry and complex geometry and the such
*Remove "Discrete mathematics" and "replace" with "Combinatorics": I've always consider discrete mathematics to be, at worst: the name of a course taught in math departments to computer science majors involving some basic abstract algebra, some graph theory, some combinatorics, and some elementary number theory; and at best: a convenient word to throw around if you have diverse interests in finite things. I put "replace" in quotes as some of the content would need to be moved in "Theoretical computer science"
*Add "Theoretical computer science"

Thoughts? [[User:RobHar|RobHar]] ([[User talk:RobHar|talk]]) 23:40, 19 March 2010 (UTC)
:I'm guessing you'd also want to include some of the content of "discrete" in geometry? But given some of your recent edits in which you claimed that a major subarea of discrete geometry was not even mathematics at all, I'm not sure. Does graph theory count as combinatorics or topology, in your view (it could reasonably be either)? Is category theory algebra, or something else? —[[User:David Eppstein|David Eppstein]] ([[User talk:David Eppstein|talk]]) 00:20, 20 March 2010 (UTC)

::I had a feeling that my recent mistake would come up here. See my talk page for some comments on that (I might say I don't see how my recent mistake affects my proposal here at all). My second proposal is to allow placing things in several fields which deals with some of your questions. More specifically though, part of my suggestions are related to the discussion above, where a few people seemed to like the [http://www.mathunion.org/activities/icm/icm-2010-program-structure/ IMU list] which has no discrete math category (it places "discrete geometry" in geometry, if that's what your first question is about, though I think most discrete geometry in wiki is already placed in the geometry field). Re graph theory: is it currently a problem whether graph theory is "discrete math" or "topology"? There are certainly topological methods in graph theory. Re category theory: I'm not proposing anything on that subject. It is currently listed in the "Foundations" description and if you look around a lot of category theory articles are listed in that field. I've always felt uncomfortable with that as there are many categorical things that I consider more appropriately as algebra (though some of it is clearly more foundational in nature). I would say that I don't believe anything in my proposal changes the way category theory is treated. Are you trying to say that you think something should be done specifically to deal with it? [[User:RobHar|RobHar]] ([[User talk:RobHar|talk]]) 01:04, 20 March 2010 (UTC)
:::By the way, since I suspect this didn't come through very clearly: mostly I like the IMU list and mostly I think your proposed changes are good. I was quibbling a little with the rationale, but not really with the changes themselves. And I was wondering about some edge cases, but there will always be edge cases. —[[User:David Eppstein|David Eppstein]] ([[User talk:David Eppstein|talk]]) 04:58, 20 March 2010 (UTC)
:To the 3 changes you proposed:
:*Merge '''basics''' and '''general''' -- sounds good. They're both not too populated compared to some of the other categories, so merging wouldn't create an overly large category.
:*Merge '''mathematicians''' with '''history''' -- also sounds good. Again, history has very few articles, so merging sounds good to me.
:*Add '''algebraic geometry''' -- no comments.
:*Split '''discrete''' into '''combinatorics''' and '''TCS'''; recategorize other things -- This sounds good too. Things that are in currently in discrete but have very little to do with combinatorics/TCS should be recategorized. For example [[Discrete Fourier transform]] should not be categorized as ''discrete'' just because it has that word in the title. 
:This, of course, doesn't address the point about using fields from the IMU for categorization, but it looks like a step in the right direction. --[[User:RobinK|Robin]] ([[User talk:RobinK|talk]]) 03:55, 20 March 2010 (UTC)

It was suggested above to think about using the fields from the IMU (see [http://www.mathunion.org/activities/icm/icm-2010-program-structure/]). At the least, I'd like to think about how to group the fields there to arrive at our list. Unfortunately, I have been traveling, so I will not be able to write more about this until tomorrow sometime. &mdash;&nbsp;Carl <small>([[User:CBM|CBM]]&nbsp;·&nbsp;[[User talk:CBM|talk]])</small> 02:46, 20 March 2010 (UTC)

: I strongly support using the IMU list as a template. The absence of designated fields for algebraic geometry, Lie theory, and dynamical systems is a fundamental weakness of the current wiki classification scheme: articles in these subjects are scattered through several fields such as algebra, geometry, analysis, and applied mathematics, often without a compelling reason; the IMU list certainly takes care of that issue as well. [[User:Arcfrk|Arcfrk]] ([[User talk:Arcfrk|talk]]) 05:36, 20 March 2010 (UTC)
::The IMU is nearly the same as the proposed list and it has some additions that wouldn't hurt. The main differences are:
::# While we just have Applied mathematics the IMU has Numerical analysis and scientific computing, Control theory and optimization, and Mathematics in science and technology. 
::# While we just have Analysis the IMU also has Functional analysis and applications, Dynamical systems and ordinary differential equations, and Partial differential equations. 
::# We have General while the IMU has Mathematics education and popularization of mathematics. While much of the General topics might go into Math. Ed., we do have articles that are specific to Math. Ed. so I'm not sure it would be wise to try to merge them.
::# The IMU has Lie theory and generalizations. We have this under Algebra but perhaps this has enough crossover with analysis and topology that should be split off. 
::One thing that should be kept in mind is what purpose this classification serves. We already have have multiple other ways for people to find articles they're interested in (categories, OoK, etc.). So unless there is a positive benefit to come out of this that outweighs the work that will go into categorizing the articles, we should just drop the subject parameter and save ourselves the effort. I personally think the benefit is in directing effort; e.g. I like to work on geometry articles and it's handy to have a ready made list of geometry articles that are stub or start class. On that basis the categories should be based on areas of expertise and/or preference. Given that, it's not a good idea to make the classification too fine; if the people who want to edit articles on ODEs are also going to want to edit articles on PDEs then separating just adds work with no benefit. The IMU adds five or six more subjects; I have no objection to adding them as long as it can be argued that they help people find articles that need work.--[[User:RDBury|RDBury]] ([[User talk:RDBury|talk]]) 08:14, 20 March 2010 (UTC)
::One thing I've felt is missing is 'recreational'. They tend to be stuck under general but I think a distinct 'field' would be good even if it isn't a field as such. [[User:Dmcq|Dmcq]] ([[User talk:Dmcq|talk]]) 10:49, 20 March 2010 (UTC)
:::I guess I can comment on what thoughts I had that got me from our current list and the IMU list to the list I proposed. In our current list, I found that I could never place algebraic geometry properly: many concepts aren't really geometry, but they're what one would call a geometric notion in the subject, rather than an algebraic notion (like some sort of "global" algebraic behaviour analogous to a geometric concept for example). I think this holds for complex analytic geometry as well (and the more recent rigid analytic geometry in the nonarchimedean world), so as the IMU does, I would suggest placing that in the "algebraic geometry" field (which could be renamed to include "complex" in the title). I also felt that, for the most part, functional analysis fits into "analysis", as do ODEs and PDEs. Of course, some articles in these latter subjects fit well into "mathematical physics", and the numerical methods would fit into "applied", but I'm pretty sure mathematically speaking, functional analysis, ODEs and PDEs fall inside the field of analysis. I felt dynamical systems (from a mathematical point of view) fit into "analysis" or possibly "probability". My understanding of the use of the term applied mathematics within mathematics is that it refers to a specific field that includes numerical analysis, computational aspects, and such, so that it would contain control theory and optimization. Though I'm not sure how everything that fits under "Mathematics in science and technology" would fit in. Perhaps it could be lumped in with applied. The Lie theory is a touchy one. To me, Lie theory fits within representation theory and geometry. There are analytic and topological aspects, but to me they aren't what the subject is about. When you look at the IMU list's subtopics in the Lie theory section, they might all fit pretty cleanly into either geometry or algebra. But perhaps this is another subject that, like algebraic geometry, could use a field of its own. Before doing that, I'd like to make sure that it doesn't imply that all sorts of other broderline subjects should have their own field. As for education, there was some discussion above that seemed to suggest there aren't very many such articles, and that for now at least they could fit into "general". Regarding dmcq suggestion of a "recreational mathematics" field, I could see the use in this, though I wonder if placing an article in that field might offend some people in some cases; maybe that's not an issue though. I think I'll stop now. [[User:RobHar|RobHar]] ([[User talk:RobHar|talk]]) 15:19, 20 March 2010 (UTC)
::::About "recreational" math, firstly we don't have too many article to warrant a new field. Secondly, as pointed out, it might be hard to classify and may offend some people (like is Tetris being NP-complete recreational math?). --[[User:RobinK|Robin]] ([[User talk:RobinK|talk]]) 16:38, 20 March 2010 (UTC)
:::::We already classify quite a few article as such under [[:Category:Recreational mathematics]]. Most of them don't seem to have been tagged as maths and those which have are variously discrete maths or general or some such non-descript field though I see the origami ones are classified as geometry. [[User:Dmcq|Dmcq]] ([[User talk:Dmcq|talk]]) 17:24, 20 March 2010 (UTC)
::::::It is worth discussing better ways than the current "basics" and "general" to distinguish between fundamental routine mathematics and recreational general interest mathematics, bearing in mind that this distinction is for editors, not readers, and so need not have anything to do with the category classification system. ''[[User talk:Geometry guy|Geometry guy]]'' 23:02, 21 March 2010 (UTC)

===2. Allow multiple fields per article===
Currently, you can only specify one field in the maths rating template. I'd like to propose allowing more than one. Math isn't always so clear cut. [[User:RobHar|RobHar]] ([[User talk:RobHar|talk]]) 23:40, 19 March 2010 (UTC)
:As Carl suggested above, this seems like a very useful feature to have. I don't think too many people would oppose this idea. --[[User:RobinK|Robin]] ([[User talk:RobinK|talk]]) 03:57, 20 March 2010 (UTC)
::I agree with RDBury's comment above that we should first find out what we want to have this categorisation for. Currently every article can only be categorised in one field, and that potentially has advantages because it partitions our articles. If we allow several fields per article, that might also have advantages. We can't tell which is better unless we know what we wont to do with the fields.
::So what is it that we (can or want to) do with the fields that we can't do with the normal category system? [[User:Hans Adler|Hans]] [[User talk:Hans Adler|Adler]] 15:45, 20 March 2010 (UTC)
:::If Wikipedia was able to do database operations on categories it would certainly solve a few problems. [[User:Dmcq|Dmcq]] ([[User talk:Dmcq|talk]]) 21:41, 20 March 2010 (UTC)
::::The only problem might be overclassification: remember that WikiProject assessments are for editors, not readers, and editors are likely to have a greater understanding of the limitations of any classification system. ''[[User talk:Geometry guy|Geometry guy]]'' 22:53, 21 March 2010 (UTC)

:Re Hans: I think the main benefit of the fields is to make grouped tables such as [[User:WP 1.0 bot/Tables/Custom/Mathematics-1]] and [[User:VeblenBot/MainTable]], and to let people make lists of articles in a certain field that are of a certain quality and/or priority. The main math table has about 7,700 articles, which is great, but it's too big to browse. Personally, I only want to browse articles related to my specialty, and I would guess some others feel the same way. 

:The real issue between using fields in the wikiproject template and using categories on the article is on how we prefer to do the maintenance. If we use fields, then we need people to update them on each article, so there is ongoing maintenance to fix up newly-tagged articles. If we use categories, then we need to maintain a list by field of the categories that should be read to make a list for that field. This list requires ongoing maintenance as categories are created and deleted. 

:Either of those methods works, it's just a question of which sort of ongoing maintenance we prefer. Actually, right now I feel more in favor of the category system. I was planning to use the categories anyway to update the field ratings once we settle on a new selection of fields. I could just change the whole system to work with article categories.  &mdash;&nbsp;Carl <small>([[User:CBM|CBM]]&nbsp;·&nbsp;[[User talk:CBM|talk]])</small> 12:05, 22 March 2010 (UTC)

::Using the field updates a relevant category of class by field. The update is immediate but it is more of an effort to maintain.Using categories would mean a bot would have to go through the categories every so often and perhaps update things overnight but would be much more flexible. I think yes I'm inclining more to supporting a bot and forgetting about the field. [[User:Dmcq|Dmcq]] ([[User talk:Dmcq|talk]]) 12:23, 22 March 2010 (UTC)

::(ec) Thanks, that makes sense. I guess I wasn't thinking very clearly when I asked: I thought it would be enough to use the top-level categories for this purpose. But of course some articles are in subcategories that imply membership in the parent category, and others are in subcategories that don't imply such a thing. So it seems there could be a real maintainability nightmare with that.
::I have an idea for a system using hidden categories, but will take it to your talk page. [[User:Hans Adler|Hans]] [[User talk:Hans Adler|Adler]] 12:27, 22 March 2010 (UTC)

===3. Add C rating (leave B+ rating)===
Currently, the possible quality ratings for math articles are Stub, Start, B, B+, GA, A, FA. There was a [[Wikipedia_talk:WikiProject_Mathematics/Wikipedia_1.0#Proposals_for_change_of_math_ratings|discussion]] at the assessment talk page about changing this. I'd like to propose adding a 'C' rating to this scheme. I find there are articles better than a 'Start', but not yet a 'B'. Additionally, most (all?) other projects have a 'C' rating (so sometimes our articles end up with C ratings, which we must correct). [[User:RobHar|RobHar]] ([[User talk:RobHar|talk]]) 23:40, 19 March 2010 (UTC)
:Agreed. Adding C is a good idea. Leaving the B+ rating as it is makes this a smooth and easy transition. --[[User:RobinK|Robin]] ([[User talk:RobinK|talk]]) 03:37, 20 March 2010 (UTC)

:There was pretty much a consensus to add C except for [[User:CBM]] who argued, if I may paraphrase, that C isn't needed in general, much less in WPM. I for one am going to be bold and just start using the C rating where it seems appropriate. If no one else wants to do it I'll try to write up a draft for changes to the rating criteria.--[[User:RDBury|RDBury]] ([[User talk:RDBury|talk]]) 07:02, 20 March 2010 (UTC)

::Seems good to me. B+ is useful where you think the article is well written but don't want to faff around with GA. [[User:Dmcq|Dmcq]] ([[User talk:Dmcq|talk]]) 10:37, 20 March 2010 (UTC)
:::C may be unnecessary for WPM, but it is also harmless. ''[[User talk:Geometry guy|Geometry guy]]'' 22:51, 21 March 2010 (UTC)

===Biographies===
If we include biography & history as suggested above, there needs to be some cooperation with the Wikiproject Biographies, which is doing their own separate article assessment. At least it doesn't make much sense sense when the article's discussion pages get 2 competing templates.--[[User:Kmhkmh|Kmhkmh]] ([[User talk:Kmhkmh|talk]]) 17:02, 20 March 2010 (UTC)

:Actually this already occurs quite often. For us, especially with the wiki project physics and computer science amongst others (e.g [http://en.wikipedia.org/wiki/Talk:General_relativity], [http://en.wikipedia.org/wiki/Talk:Quantum_mechanics], [http://en.wikipedia.org/wiki/Talk:P_versus_NP_problem]). I think I've seen bots (and people) come around and set all ratings to the same class on such pages, though I'm not sure that's a good idea. Also, note that we already have the field "mathematicians" and that I was mostly just suggestion renaming this biography and merging it with history. [[User:RobHar|RobHar]] ([[User talk:RobHar|talk]]) 18:01, 20 March 2010 (UTC)

::I don't think that we should use "biography" as a synonym for "history". For example, [[Principia Mathematica]] is an article on a topic from history, but not a "biography". &mdash;&nbsp;Carl <small>([[User:CBM|CBM]]&nbsp;·&nbsp;[[User talk:CBM|talk]])</small> 11:55, 22 March 2010 (UTC)

== Special functions ==

Our special functions articles are, by and large, in a dreadful state.  They are typically nothing more than a minimally differentiated list of formulas.  This situation appears to be exacerbated by the edits of {{user3|A. Pichler}}, whose contributions to the project have, for a long time, consisted almost entirely of adding unreferenced identities to special function articles, some of which are quite dubious.  [[User:Stevenj]] has warned him than once in the past to give references for the content he adds, but he continues not to give them.  So Stevenj continues to revert many of this editor's contributions.  More expert eyes on the contributions of this editor would be helpful.  I've already gone one round with him.  [[User:Sławomir Biały|<span style="text-shadow:grey 0.3em 0.3em 0.1em; class=texhtml">Sławomir Biały</span>]] ([[User talk:Sławomir Biały|talk]]) 10:43, 22 March 2010 (UTC)
== [[Augmental homology]] ==

This article requires attention from an algebraic topologist. It appears to contain some recent research (see the refs), and I'd like to have some idea of the notability of the topic. There is now a version at [[Künneth theorem]] that contains the material; and after [[Stanley–Reisner ring]] was updated by [[User:Arcfrk]] some other related material was reposted at [[Stanley-Reisner ring (binary operations)]]. There is an underlying point at the chain level about simplicial complexes, it seems, but if it is worth inclusion here, it might be more in the nature of a remark that should be in [[simplicial complex]] or [[simplicial homology]]. [[User:Charles Matthews|Charles Matthews]] ([[User talk:Charles Matthews|talk]]) 13:50, 22 March 2010 (UTC)

: Blatantly clearly the work of a newbie who is a mathematician.  I can't do everything tonight.  This person needs to get introduced to Wikipedia conventions, etc. [[User:Michael Hardy|Michael Hardy]] ([[User talk:Michael Hardy|talk]]) 06:24, 23 March 2010 (UTC)

: I haven't read the article carefully yet, but it <strike>reads like an essay</strike> seems to be inflating the value of the research made by the person who wrote the article ([http://arxiv.org/abs/math/0412552]). [[User:Aenar|Aenar]] ([[User talk:Aenar|talk]]) 18:10, 23 March 2010 (UTC)

:: Based on the username, I'd guess there's some [[WP:COI]] going on. [[User:CRGreathouse|CRGreathouse]]<small> ([[User talk:CRGreathouse|t]] | [[Special:Contributions/CRGreathouse|c]])</small> 20:02, 23 March 2010 (UTC)

:::But that doesn't need saying, and doesn't speak to what mathematical value the contributions have. [[User:Charles Matthews|Charles Matthews]] ([[User talk:Charles Matthews|talk]]) 21:32, 23 March 2010 (UTC)

== [[Laplace–Beltrami operator]] ==

This article's talk page is currently blank. 99% of the time, when I come across such an article, I try to attach a wikiproject banner to the talk page - though most of the time I can't say very much useful about the article rating, I know that the wikiproject involved usually finds this useful and particularly so if they subcribe to an automated article alerts service. However, when I naively tried to add {{tl|WP Mathematics}} I got a rather scary-looking warning sign. Should I simply add {{tl|maths rating}}, even though I wouldn't know how to rate it, in the hopes that somebody else will notice the blank template, come along and do so? Or are there WP Math reviewers who have a big list of unreviewed articles, regardless of whether they have a template on the talkpage, and are steadily working through the lot? Or infact, do y'all actually care about your project ratings at all, given that your articles (including this one) are included in comprehensive lists? I suppose what I really want to know is (a) if I come across such an article again, should I make an effort to bring its lack of a {{tl|maths rating}} to somebody's attention, or even make an attempt at filling out the more obvious parts of it, or just leave it alone; and (b) the rather naive question, why isn't {{tl|WP Mathematics}} a redirect to {{tl|maths rating}}, since the latter seems to fulfil a similar if not entirely analogous purpose to the "WP Whatever" templates of other projects? [[User:TheGrappler|TheGrappler]] ([[User talk:TheGrappler|talk]]) 15:23, 23 March 2010 (UTC)

:The "deprecation" route seems to have been around for a long time; but it does apparently miss out on the possibility of having the WikiProject template as a way of adding to a maintenance category. Perhaps the thinking could be reviewed; presumably quite a high proportion of relevant articles have been rated now. [[User:Charles Matthews|Charles Matthews]] ([[User talk:Charles Matthews|talk]]) 22:21, 23 March 2010 (UTC)
== Discrete geometry ==

And why the name [[discrete geometry]] ? Do we have a better definition than the article currently uses: "the study that does not essentially rely on the notion of continuity."  I mean [[circle packing]] involves arranging objects which are continuous, within a space which is continuous, in such a way that the circles only touch at tangent points (i.e. at infinitesimal points). What the heck is discrete about that ?  ;-p Seriously though, surely [[combinatorial geometry]] is a better name. [[User:Bethnim|Bethnim]] ([[User talk:Bethnim|talk]]) 21:22, 24 March 2010 (UTC)

:Combinatorial geometry is a better name, but it means something different. Combinatorial geometry is about finite [[incidence structure]]s — abstract systems of points and lines that have similar properties to the entire system of points and lines in Euclidean or projective or hyperbolic geometry. Discrete geometry is about combinatorial properties of Euclidean points and lines (or sometimes hyperbolic or spherical, but in any case finite subsets of continuous geometries). —[[User:David Eppstein|David Eppstein]] ([[User talk:David Eppstein|talk]]) 22:00, 24 March 2010 (UTC)

:* I reworded that phrase: "the study generally does not rely on the notion of continuity."  It might need some more work. <b><span style="color:green;">Jwesley</span>[[User_talk:Jwesley78|<sub>78</sub>]]</b> 22:30, 24 March 2010 (UTC)

:* It can be hard to define mathematical research fields in the negative (e.g., "the study does not..."), since there are often exceptions to such a "rule". (Breakthroughs sometimes occur when someone finds a [[synergism]] between two previously disparate fields.) <b><span style="color:green;">Jwesley</span>[[User_talk:Jwesley78|<sub>78</sub>]]</b> 22:30, 24 March 2010 (UTC)
:I agree that discrete geometry is a confusing name, particularly because I've seen it used recently for a rather different topic in computer science, considering questions about discretised geometric data: questions such as how to define rotations of bitmaps over non-square angles while preserving essential information, so that after multiple transformations the bitmap does not endlessly degrade. Possibly there are even other radically different subjects at the frontier (or intersection?) of the geometric and the discrete. [[User:Marc van Leeuwen|Marc van Leeuwen]] ([[User talk:Marc van Leeuwen|talk]]) 08:01, 25 March 2010 (UTC)

David, I notice that on your page http://www.ics.uci.edu/~eppstein/junkyard/combinatorial.html you say "This is a difficult topic to define precisely without including all of discrete and computational geometry." Jwesley, for now I've added a concise non-negative definition to the article: "'''Discrete geometry''' and '''combinatorial geometry''' are about combinatorial properties of ''discrete collections'' of geometrical objects.". The article is of course a stub at the moment, but do you think there should eventually be separate articles for Discrete geometry and combinatorial geometry, or not ? [[User:Bethnim|Bethnim]] ([[User talk:Bethnim|talk]]) 07:56, 25 March 2010 (UTC)
:I named that web page a long time ago and I'm no longer sure I picked the right name for it, since it's mostly about what I would now call discrete geometry. Note that the line you quoted is about ''computational'' geometry, not ''combinatorial'' geometry — computational geometry tends to be about algorithmic problems in discrete geometry and tends to ignore combinatorial geometry, and you can find lots of books (and a good journal) with "discrete and computational geometry" as their title. —[[User:David Eppstein|David Eppstein]] ([[User talk:David Eppstein|talk]]) 00:45, 26 March 2010 (UTC)

== [[John Tate]] ==

Tate has received an [[Abel Prize]] (couldn't have happened to a nicer guy). The page is currently linked from the Main Page, so please watch for vandalism. [[User:Charles Matthews|Charles Matthews]] ([[User talk:Charles Matthews|talk]]) 19:48, 25 March 2010 (UTC)
== Requested move from [[omega automaton]] to [[ω-automaton]] ==

The ω in the title is the smallest infinite ordinal, and is not usually spelled out as ''omega''. I thought the move to what I consider the only correct title would be totally uncontroversial, but apparently all page titles with non-Latin letters are currently on the blacklist for page moves. So I requested the move, and currently the situation at [[Talk:Omega automaton]] looks as if it might not pass due to the number (not quality) of objections – all by editors with no editing history in mathematics or computer science articles. I guess this is because of editors frequenting [[WP:RM]] who treat this ''ω-automaton'' if it was a silly trademark.

The case is similar to sigma-algebra/σ-algebra, but not the same: ''sigma-algebra'' appears more often than σ-''algebra'' in Google Books, but ω-''automaton'' appears much more often than ''omega-automaton''.

Do we have consensus within the project? [[User:Hans Adler|Hans]] [[User talk:Hans Adler|Adler]] 08:21, 27 March 2010 (UTC)
:It seems reasonable but what was the rational for blacklisting Greek letters in the first place? If it's just a convenience thing then it would be better to do the move, but if it would break Wikimedia for some arcane technical reason then there really isn't a choice.--[[User:RDBury|RDBury]] ([[User talk:RDBury|talk]]) 13:50, 27 March 2010 (UTC)
::There are no technical problems. It's intended to stop confusing things like [[Αbelian group]] <small>(the initial letter is a capital alpha)</small>. [[User talk:Algebraist|Algebraist]] 14:01, 27 March 2010 (UTC)
::The reason for the blacklisting of Greek letters is page move vandalism. The vandals try to move pages to titles that include a certain word. After all titles containing the word were blacklisted, they started to use χṝęăτίυê ṣpe̽ǁɨŋɠ, and now apparently all non-Latin letters were blacklisted. We can still create articles with them, just not move them there. The problem is that if you move a page such as ANI with thousands of watchers, they will all see the new title on their watchlist, even after the page has been moved back. [[User:Hans Adler|Hans]] [[User talk:Hans Adler|Adler]] 15:48, 27 March 2010 (UTC)
:::I think there is a technical limitation in that an article name can't start with a lower case letter, so the article name would have to be Ω-''automaton'', though you can get it to display as a lower case letter as in [[eBay]]. Other technical restrictions exist, e.g you can embed a [ in an article title for obvious reasons, but I couldn't find any that apply in this case. There are policy rules that say Greek letters have to be transliterated but there are exceptions such as [[α+β proteins]]. So it makes sense that the blacklist is purely an antivandalism measure, though I couldn't find anywhere it was discussed.--[[User:RDBury|RDBury]] ([[User talk:RDBury|talk]]) 19:41, 27 March 2010 (UTC)
::::"There are policy rules that say Greek letters have to be transliterated". I think that's a bit misleading. I looked for such a rule in [[WP:TITLE]], and here is what I found:
{{quotation|1=
{{See|Wikipedia:Naming conventions (use English)}}
The choice between anglicized and local spellings should follow English-language usage [...]

If there are too few English-language sources to constitute an established usage, follow the conventions of the language appropriate to the subject [...]

Names not originally in a [[Latin alphabet]], such as Greek, Chinese or Russian names, must be [[transliteration|transliterated]]. Established systematic transliterations, such as [[Hanyu Pinyin]], are preferred. However if there is a common English-language form of the name, then use it, even if it is unsystematic (as with [[Tchaikovsky]] and [[Chiang Kai-shek]]). For a list of transliteration conventions by language, see [[Wikipedia:Romanization]].
}}
::::When non-Latin-based names are used in English, they are normally transliterated, so it makes sense to do the same for names that don't occur in English sources. It would be absurd to read this as an instruction to transliterate non-Latin letters in names that are already normal English ''with'' the non-Latin letters. That this isn't meant becomes even clearer in [[WP:Naming conventions (use English)]]. [[User:Hans Adler|Hans]] [[User talk:Hans Adler|Adler]] 22:56, 27 March 2010 (UTC)
:::::See the page [[ω-consistent theory]], which was moved to that title in November 2006. I believe that we should use whatever spelling is seen as most appropriate by mathematicians. In this case, the topic would probably be spelled as [[ω-automaton]]. In the past, people might have worried about using Greek letters in titles due to indexing and cataloging issues. But Google has no trouble with such letters. If you put 'ω-consistent' into a Google search box, guess what pops up as the first hit?  Our Wikipedia article. A Google for 'omega-consistent' gets you to the same place, so the situation poses no problem to people who decide to spell out the Greek letter in their search query.  [[User:EdJohnston|EdJohnston]] ([[User talk:EdJohnston|talk]]) 01:50, 28 March 2010 (UTC)

== Codomain of a random variable: observation space? ==

The technical term "observation space" for [[codomain]] of a [[random variable]] was used by [[User:Winterfors]] on 14 Feb 2008 in [[Bayesian experimental design]], then by [[User:3mta3]] on 7 May 2009 in [[Probability distribution]], by an anon on 26 Aug 2009 in [[Random variable]], and by [[User:Stpasha]] on 27 Nov 2009 in [[Probability density function]]. Now [[User:WestwoodMatt]] and a `random passerby' are unhappy with it, see [[Talk:Probability distribution#Observation Space]].

As far as I understand, the term is used mostly by non-mathematicians, and its use in such articles as [[random variable]] is a bit [[Off-label use|off-label]]. On the other hand, it could be rather convenient here. Maybe we should mention it, but use sparingly.

However, the very idea to define a random variable as a measurable map from a probability space to an arbitrary measurable space could be a [[WP:POV]]. Maybe some sources use such terminology, but not the mainstream. Checking four books, "Probability: theory and examples" by Richard Durrett, "Probability with martingales" by David Williams, "Theory of probability and random processes" by Leonid Koralov and Yakov Sinai, and "Measure theory and probability theory" by Krishna Athreya and Soumendra Lahiri, I observe in all the four cases that a random variable is a measurable map from a probability space to the [[real line]]. More general objects are called random vectors, random functions and, most generally, random elements (of a given measurable space).

Any opinions, please? [[User:Tsirel|Boris Tsirelson]] ([[User talk:Tsirel|talk]]) 16:36, 27 March 2010 (UTC)

: My immediate reaction, then, is to do one of two things:
:: a) Find a way of rigorously defining "observation space" with the caveat that it is generally used as an imprecise concept;
:: b) Define "random variable" without using "observation space", and also indicate that it can be defined in two ways:
::: i) The "usual" way, that is, as a map to the real line;
::: ii) In a more general way that is rooted in measure space concepts, in which the image of the random variable is a more general measure space - and providing a link to the explanatory definition that specifies that a real line ''is'' an instance of a  measure space, thus showing that the more specific is an instance of the more general. I see that's sort of already been done, but I believe it could be made more rigorous and precise.--[[User:WestwoodMatt|WestwoodMatt]] ([[User talk:WestwoodMatt|talk]]) 17:07, 27 March 2010 (UTC)

: In the article on [[Bayesian experimental design]], I used the term "observation space" in the sense "the set of all possible observations", which if you define the observation as a (conditional) random variable will be its codomain. In the context of Bayesian experimental design the alternative term "data space" is often used, but I prefer "observation space" since "data" is more ambiguous than "observation". 

: I think the term is appropriate in the article on [[Bayesian experimental design]], but not in the articles [[Probability distribution]], [[Random variable]] or [[Probability density function]] since these describe more general cases not necessarily relating to the probability of making a particluar observation.
:-- [[User:Winterfors|Winterfors]] ([[User talk:Winterfors|talk]]) 18:31, 28 March 2010 (UTC)

== [[Franklin graph]] ==

The [[Heawood conjecture]] states that "''the minimum number of colors necessary to color all graphs drawn on an orientable surface of that genus (or equivalently to color the regions of any partition of the surface into simply connected regions) is given by <math>\gamma(g)</math>...''". I'm unable to understand how a ''particular'' graph can be a "''counterexample to the Heawood conjecture''" - as far as I can imagine, a "counterexample" should consist in some particular surface (presumably, the klein bottle in this case) ''and'' a proof that ''any graph on that surface'' can be colored with less than <math>\gamma(g)</math> colors.

I obviously don't mean that Franklin was wrong, I just have the impression that the way this is stated on the two pages is by far too simplicistic... --[[User:Toobaz|Toobaz]] ([[User talk:Toobaz|talk]]) 21:39, 28 March 2010 (UTC)
:Better now? —[[User:David Eppstein|David Eppstein]] ([[User talk:David Eppstein|talk]]) 22:37, 28 March 2010 (UTC)
::Totally - I also removed an erroneous part of image caption. --[[User:Toobaz|Toobaz]] ([[User talk:Toobaz|talk]]) 23:13, 28 March 2010 (UTC)

== A moderately subtle TeXnicality? ==

I found this in an article:
: 
: <math>l\sim\frac{\ln{N}}{\ln{\ln{N}}}.</math>
: 
I changed it to this:
: 
: <math>\ell\sim\frac{\ln N}{\ln \ln N}.</math>
:
I'd have guessed that the seemingly purposeless extra curly braces, although they might be inconvenient for those who edit (and who cares about ''them''?) would not affect what the reader sees.  But if your browser is like mine, there's a clearly visible difference.  Why?  (I also changed "l" to "\ell".) [[User:Michael Hardy|Michael Hardy]] ([[User talk:Michael Hardy|talk]]) 02:04, 29 March 2010 (UTC)

:Possibly the image was cached from an earlier implementation of TeX?  I don't know, but a bit of experimentation suggests that it has nothing to do with the braces.  E.g., the same formula (with useless braces), but using ''M'' in the numerator instead of ''N'' to force a new image to be generated:
::
::<math>l\sim\frac{\ln{M}}{\ln{\ln{N}}}.</math>
::
:This seems to look more like the updated version. [[User:Sławomir Biały|<span style="text-shadow:grey 0.3em 0.3em 0.1em; class=texhtml">Sławomir Biały</span>]] ([[User talk:Sławomir Biały|talk]]) 02:34, 29 March 2010 (UTC)

:(ec) It isn't really the curly braces. See what happens when you just change "l" to "\ell":
::<math>\ell\sim\frac{\ln{N}}{\ln{\ln{N}}}.</math>
:For some reason when the first equation is [[font rasterization|rasterized]] the strokes of the letters "ln" must line up precisely with the pixels, while in the other equations they are slightly off, so they are smoothed, which unfortunately results in bolder-looking logs. When "l" is changed to "\ell", this explanation makes sense, because "\ell" is slightly wider than "l". I don't understand why there is a difference when the only change that is made is the removal of the curly braces. My guess is that it has something to do with the fact that TeX typesets subexpressions in curly braces with fixed whitespace that will not grow or shrink with the rest of the expression, and this must produce some slight difference that the rasterizer is very sensitive to. —[[User:Bkell|Bkell]] ([[User talk:Bkell|talk]]) 02:35, 29 March 2010 (UTC)

::Actually, I think I like Sławomir's caching explanation better. The shape of the "n" glyph is different between the two renderings—it is wider in the first equation than in the second. —[[User:Bkell|Bkell]] ([[User talk:Bkell|talk]]) 02:38, 29 March 2010 (UTC)

My guess is also that the first expression's image is being cached from a previous version of the mediawiki TeX system. For example, when I copied the same exact code for the first expression to http://meta.wikimedia.org/wiki/Sandbox and previewed it, the appearance was like the second expression. If it was just a rasterizer issue, the appearance should not change when I do that. The server software on meta is going to be identical to the current server software here. I seem to remember encountering this issue before. Usually, just adding some meaningless change to the TeX is enough to force the rendering to update. At some point we should file a bug asking them to purge the oldest images. &mdash;&nbsp;Carl <small>([[User:CBM|CBM]]&nbsp;·&nbsp;[[User talk:CBM|talk]])</small> 02:42, 29 March 2010 (UTC)

:Also, the "last modified" date for the image of the first formula, reported by the webserver, is Sun 28 Jan 2007 11:11:59 AM EST. Other old images, such as [http:/upwiki/math/9/f/3/9f3c73b3c4e8366aa669c8711a466e7e.png], show similar problems. &mdash;&nbsp;Carl <small>([[User:CBM|CBM]]&nbsp;·&nbsp;[[User talk:CBM|talk]])</small> 02:53, 29 March 2010 (UTC)