Talk:Lists of mathematics topics/Archive 2004-2005

If I had seen list of theorems on this page, I might have assumed that was an appropriate place to list Stanley's reciprocity theorem, which I wrote on Friday, and failed to notice that another page, list of mathematical theorems, also exists, on which my listing the new article would be appropriate for the same reason. I've put in cross-references, making the absurd situation clear. Those two pages should be merged. The fact that some propositions conventionally called "theorems" may not be entirely mathematical or entirely rigorous does not mean it is necessary to create a separate page when such huge overlap exists. Michael Hardy 00:47, 25 Oct 2004 (UTC)

Renaming this page
Can we rename this page? List of lists of mathematical topics seems unwieldy. Maybe We currently have a redirect from the original name (which isn't much better): Okay, maybe there's no good name. I guess it doesn't really matter. Other suggestions are welcome. -- Fropuff 22:21, 2005 Apr 21 (UTC)
 * Metalist of mathematical topics
 * List of mathematical topics (by subtopic)
 * List of mathematical subtopics
 * List of mathematical topics (lists)


 * How about renaming:


 * List of mathematical topics to List of mathematical articles or List of mathematics articles


 * and


 * List of lists of mathematical topics to List of mathematical topics


 * Just a crazy idea. Oleg Alexandrov 22:32, 21 Apr 2005 (UTC)

Oooh, I like that much better! Of course, that's going to cause some headaches/confusion for those people who have List of mathematical topics bookmarked. If we do this, we should then rename the alphabetical pages as List of mathematical articles (A), etc. for consistency. -- Fropuff 00:02, 2005 Apr 22 (UTC)


 * Yes, this seems like a good idea, although I think it should be "mathematics articles" and "mathematics topics" not "mathematical" (just like it would be physics not physical). Paul August &#9742; 03:15, Apr 24, 2005 (UTC)


 * List of lists may be ugly, but it is more accurate than the uniterated form. Actually, maybe we should consider doing this: where the line now says 'list of group theory topics', make it read 'group theory - list of group theory topics'. Then it really would be a 'list of mathematical topics', supported by lists. There would be a few anomalies, but this might be the way to progress our classification. Charles Matthews 10:36, 24 Apr 2005 (UTC)


 * I think "list of mathematical topics" makes more sense, by analogy with the fact that an article referring to sub-articles is not called an "article about articles". The current List of mathematical topics page should really be in the Wikipedia: namespace since it is aimed at editors. Fredrik | talk 02:21, 5 Jun 2005 (UTC)


 * How about List of mathematical lists? Seems the obvious choice to me. Tompw 15:12, 21 October 2005 (UTC)
 * Looks better. My real gripe is with the list of mathematical topics. That list does not list topics, it lists articles, and the name should reflect that. Oleg Alexandrov (talk) 00:18, 22 October 2005 (UTC)
 * I quite like that, even though it is slightly ambiguous. Elsewhere, Paul August said: "I wouldn't oppose that name, I don't see how it is particularly better though". -- Jitse Niesen (talk) 18:23, 22 October 2005 (UTC)

OK... I would like to re-name this page List of mathematical lists, unless there is significant oposition within the next few days. I was tempted to just go ahead and re-name it, but I thought it best to ensure there's a consensus on this. Tompw 23:24, 9 December 2005 (UTC)


 * Agree. Although I think we should go with mathematics as opposed to mathematical as per Paul's suggestion above. That is, we should have
 * List of mathematics lists (this page), and
 * List of mathematics articles (currently list of mathematical topics), as well as
 * List of mathematics articles (A)
 * List of mathematics articles (B)
 * etc.
 * We definately need a consensus here as this is bound to break some scripts. -- Fropuff 00:21, 10 December 2005 (UTC)


 * I suggest somebody copies it to Wikipedia talk:WikiProject Mathematics. Tompw, please don't move this without discussion, it has caused disagreements in the past. Oleg Alexandrov (talk) 01:59, 10 December 2005 (UTC)


 * I have absolutly no intention of moving this without full and proper discussion. I prefer "mathematical lists" to "mathematics lists", but that's just personal feeling - I wouldn't opose the later. Tompw 12:41, 10 December 2005 (UTC)

Since nobody seems to be commenting here, I'm going to bring this up on Wikipedia talk:WikiProject Mathematics. Redirect further discussion to that page. -- Fropuff 03:21, 15 December 2005 (UTC)

The reason for my recent edits
... was the commentary on the list of nominations for featured lists. Michael Hardy 19:55, 1 Jun 2005 (UTC)

categorized version
I made another version User:Samohyl Jan/List of lists of mathematical topics, which lists lists by category rather than alphabetically. I tried so that the categorization and lists under 'basic mathematics' would be accessible to a person with general high school knowledge of mathematics. Any comments are welcome. Samohyl Jan 10:38, 5 Jun 2005 (UTC)


 * I like the categorial version very much. Some changes are necessary, as Lie groups are I think more differential geometry than algebra, and boolean algebras are more logic than algebra, but I would vote to replace the current uncategorized version with the categorized version. Oleg Alexandrov 19:48, 5 Jun 2005 (UTC)


 * Thanks, I changed that. You are of course invited to make any changes to my proposal. Samohyl Jan 21:36, 5 Jun 2005 (UTC)

Michael, I disagree with your recent changes to the list. You seem to misunderstand the categories (headings). Here is what I conceived: That said, I disagree with: Anyway,I can be wrong even within my system. Regards, Samohyl Jan 20:44, 9 Jun 2005 (UTC)
 * Fields of mathematics should contain lists that collect all articles related to a single mathematical theory.
 * Methodology should contain lists about topics how to do mathematics (by the way, shouldn't there be a list of schools in mathematics?).
 * Mathematical statements should contain lists of meta-logical statements in mathematics (eg. although theorems are mathematical objects in logic, the list of theorems is not made from logical point of view).
 * General concepts should contain lists about concept which may overlap several or many fields of mathematics and doesn't constitute a single theory.
 * Mathematical objects should contain lists of mathematical objects of the roughly same type.
 * List of convexity topics, List of curve topics, List of circle topics, List of partition topics, List of order topics under some field heading, because they usually span many fields and are general concepts (for instance, in List of circle topics, there is also circle group and could be also circle in graph theory, on the other hand there are many circles outside of mathematics; the same is true for the other lists). The first three are also twice in the list.
 * List of wave topics because with the exception of two or three articles, it's all physics.
 * List of mathematical examples should go in the statements section, because it's not a list of objects of the same type.


 * List of mathematical examples should go in the statements section, because it's not a list of objects of the same type.
 * ... and they're not statements of the same type. But examples are not statements.  So if that's how you want to do it, then I think you should re-name the section. Michael Hardy 21:15, 9 Jun 2005 (UTC)


 * I think we should make distinction between examples and more-or-less comprehensive list of objects of some type, although there are some borderline cases. Any object can be considered an example if you constrain it enough. I think of example as a (famous) illustration of a concept, rather than any specific object (which is a different view from List of mathematical examples). There is even more disputable List of examples in general topology, which I honestly think should be renamed to list of topological spaces. But you're right, they're also not quite statements. Maybe we could put them into methodology section? And what about my other remarks? Samohyl Jan 07:10, 10 Jun 2005 (UTC)

Mathematics Subject Classification
I'm guessing there would be value to mapping the Mathematics Subject Classification (MSC) to this list and vica versa. Do we have any documentation of the MSC on WP as yet? --- Charles Stewart 14:25, 13 October 2005 (UTC)
 * I don't think it is a good idea. MSC is for mathematicians, this list is for general audience. This is also reason why some wikipedians rejected use of MSC for categories. Samohyl Jan 15:20, 13 October 2005 (UTC)
 * I recall the proposal and argued against it, but I'm not suggesting a restructuring of this list or any content on WP, rather providing in addition means of moving between the two classifications. For that subset of users familiar with the MSC, knowing which codes are covered by a list is cogent information. --- Charles Stewart 16:19, 13 October 2005 (UTC)


 * All fine, but let's not import any sclerotic notions from elsewhere into our own thinking. The big advantage wiki has is that it is configurable. Charles Matthews 16:44, 13 October 2005 (UTC)


 * Areas of mathematics is as close as we got to the MSC. Oleg Alexandrov (talk) 06:17, 14 October 2005 (UTC)
 * It's not far from what I wanted. I see that page has some but not many of the lists on this page: it would, I take it, be an improvement to add them all and link to the page from this page. --- Charles Stewart 14:18, 14 October 2005 (UTC)

List of category theory topics
Should this list go under the logic section? I'd say it was more of an algebra topic. --- Charles Stewart 04:21, 19 October 2005 (UTC)


 * If you listen to the category theorists, everything would go under it! Actually is homological algebra at heart, so under algebra. Charles Matthews 09:09, 19 October 2005 (UTC)


 * Two for, none against. I'll move it. --- Charles Stewart 00:17, 20 October 2005 (UTC)

Introductions
At the FLC discussion at Featured list candidates/List of lists of mathematical topics, some people bemoaned the lack of accompagnying texts introducing the various lists. I happen to agree with this criticism. I wrote some introductions, so that we do not talk about abstract concepts. I welcome suggestions (including that the introductions should be removed; I am not convinced yet that they're actually useful).

I moved the sections on meta-lists down, since I am not sure how useful they are. The section ==Fields of mathematics== seems to contain the most natural lists. -- Jitse Niesen (talk) 18:23, 22 October 2005 (UTC)


 * I think they are quite useful, thanks! I hope that introductions can be added for the remaining sections as well.  One comment:
 * Topology developed from geometry by looking at those properties that do not change even when the figures are deformed by stretching and bending, like dimension.
 * It was my impression that (the popularity of mapping doughnuts into coffee-cups aside) the main motivation for the development of point-set topology was to develop notions of continuity and continuous functions that did not rely on a metric. Am I mistaken?  &mdash;Steven G. Johnson 04:09, 23 October 2005 (UTC)


 * I think that's not the historical perspective, at least as I understand it. Sets of points, i.e. quite general subsets of the real line, were studied for example in relation to Fourier series. There was a kind of bifurcation into general topology and descriptive set theory that went on 1910-1920. Various foundational things happened at that time (Brouwer, Weyl, Hausdorff I suppose); Weyl's book on Riemann surfaces (c.1913 IIRC) is a locus for an 'abstract space' definition. Charles Matthews 09:36, 23 October 2005 (UTC)

To be honest, I haven't got a clue. I found out that writing the introductions is much harder that it seemed. This sentence comes from topology, which says that "Topology is concerned with the study of the so-called topological properties of figures, that is to say, properties that do not change under bicontinuous one-to-one transformations (called homeomorphisms)." I cannot reconstruct anymore what brought me from this to the statement that topology started historically by looking at homeomorphisms.

As often here, the introductions were written swiftly and I'm not really happy with them, so they do need to be worked on (yes, I know, it's a bit of a cop-out, but such is life). -- Jitse Niesen (talk) 11:56, 23 October 2005 (UTC)


 * I think that taking a line or two from the major article covering each section is the way to go, assuming that people see these introductions as Good Things. That way, at least, users get some consistency between documents if they click on to the main article.  Ben Cairns 09:15, 24 October 2005 (UTC).

As one of the people who made the criticism on featured list candidates, can I commend the work that's gone on here, and add that (for me personally) these section intros make an enormous difference to the quality of the list. I'm close to switching to supporting this as a featured list. I do think the introduction to the list as a whole still needs beefing up a bit. Can anything be added about difficulties of mathematical classification, and how closely this list matches the AMS classification? --OpenToppedBus - Talk to the driver 12:46, 24 October 2005 (UTC)

Links to non-lists
I don't want to dilute the "list of lists" nature of this article, but if there are to be introductions shouldn't there be some links to other content? I would propose a guideline stating that in the introduction one (1) link to the appropriate subject page for that section be included. For example:


 * ===Mathematical physics===


 * Mathematical physics is concerned with "the application of mathematics to problems in physics and the development of mathematical methods suitable for such applications and for the formulation of physical theories".

Note that I'm not suggesting that physics be linked here -- I don't mean to clutter the list, just provide a link to more information about the subject at hand. Anyone have any opinions on this? Ben Cairns 12:16, 24 October 2005 (UTC)


 * My first reaction was against it because it distracts from the links to the lists, which are the purpose of the page. However, I now think that it may be a good idea if we indeed restrict ourselves to one link (well, for the prob and stats section we may need two links). My experience is this restriction will be hard to maintain, but it's not impossible. So, as far as I am concerned, go for it. By the way, thanks for helping out. -- Jitse Niesen (talk) 22:24, 24 October 2005 (UTC)

The restriction should be that it should serve the page's purpose, rather than a restriction on the number. Michael Hardy 00:59, 25 October 2005 (UTC)

Difficulty editing
I'm getting some odd error while editing the article and it just gives me the edit screen again when I hit save, with no explanation. I just need a place to put this description for Mathematical statements in the meantime.


 * A mathematical statement amounts to a proposition or assertion of some mathematical concept, formula or construction. Such statements include axioms and the theorems that may be proved from them, conjectures that may be unproven or even unprovable, and also algorithms for computing the answers to questions that can be expressed mathematically.

Forgot to sign: Ben Cairns 21:55, 24 October 2005 (UTC)

And it worked again. Hooray! Ben Cairns 21:59, 24 October 2005 (UTC)


 * Are you sure it gave you ONLY the edit screen, rather than the edit screen followed by a preview? Giving you that when you hit "save" has been a recurring bug. Michael Hardy 01:01, 25 October 2005 (UTC)

Yeah, I think that's it exactly, although I had already previewed so it was basically just giving me what I had. I shut down my browser and it worked again after that (although I couldn't say that was the fix). Ben Cairns 08:48, 25 October 2005 (UTC)

Ref to WP
The current opening sentence reads This article contains all the lists collecting articles about mathematics in Wikipedia., which, on the face of it, is a violation of WP:ASR.

In fact, this is a somewhat tricky issue. Normally articles should not refer to the whole encyclopedia of which they are a part, but lists such as these that try to be a comprehensive need to in order to say what they are there for.

I think we should generalise this to talk about this reference work. Note an issue with this: syndicates of this work may include more content than this, or less, and so the statement can only be read as faithful for this work and its exact syndicates. I think this is a problem for the syndicator, not us, hence the proposed change. --- Charles Stewart 16:07, 25 October 2005 (UTC)
 * Maybe a Template:ThisReferenceWork is a better solution? --- Charles Stewart 16:10, 25 October 2005 (UTC)

proposed page move
As we discussed earlier in the "featured list" proposal, I propose to move this page to "list of mathematics lists". "List of lists" is a jarring phrase, because it hints at "list of lists of lists of lists of X", in which you need to count as you go along. Comments? Michael Hardy 02:45, 15 December 2005 (UTC)
 * You may want to post this instead at Wikipedia talk:WikiProject Mathematics s there more people will participate in the discussion. Oleg Alexandrov (talk) 02:56, 15 December 2005 (UTC)


 * I'm going to bring this up on Wikipedia talk:WikiProject Mathematics. Redirect further discussion to that page. -- Fropuff 03:21, 15 December 2005 (UTC)