Wikipedia talk:WikiProject Mathematics/Archive/2009/Jan

Quaternion (disambiguation) nominated for deletion

Silly Rabbit's mention of quaternions above reminded me that I want to put Quaternion (disambiguation) up for deletion. See the discussion at

Wikipedia:Articles for deletion/Quaternion (disambiguation).

As always, give reasons for your opinions. Ozob (talk) 09:32, 3 January 2009 (UTC)

Nomination withdrawn by Ozob. Martin 15:02, 5 January 2009 (UTC)

amscd package

I would like to shorten the vertical arrows of the diagram this (the source code is attached). Any ideas? GeometryGirl (talk) 14:50, 5 January 2009 (UTC)

Correction: It's the horizontal arrows that need to be shortened. siℓℓy rabbit (talk) 14:53, 5 January 2009 (UTC)

Two more or less stupid ideas, but probably effective: You could try typing it with \rightarrow and \downarrow etc. Or simply take a graphics program and shrink them in the processed image. Jakob.scholbach (talk) 14:56, 5 January 2009 (UTC)

Using a graphics program would either involve shrinking the whole thing, which would make the Hs look too thin, or a lot of manual realignment.

If you don't mind learning Xy-pic, it can do this sort of thing for you. Try the following code:

\documentclass{amsart}
\usepackage[all]{xy}

\begin{document}
\begin{equation*}
\xymatrix@C=1em{
\cdots\ar[r] &
H_{n+1}(X_1)\ar[d]_{f_*}\ar[r] &
H_n(A_1 \cap B_1)\ar[d]_{f_*}\ar[r] &
H_n(A_1) \oplus H_n(B_1)\ar[d]_{f_*}\ar[r] & 
H_n(X_1)\ar[d]_{f_*}\ar[r] &
H_{n-1}(A_1 \cap B_1)\ar[d]_{f_*}\ar[r] &
\cdots \\
\cdots\ar[r] &
H_{n+1}(X_2)\ar[r] &
H_n(A_2 \cap B_2)\ar[r] &
H_n(A_2) \oplus H_n(B_2)\ar[r] & 
H_n(X_2)\ar[r] &
H_{n-1}(A_2 \cap B_2)\ar[r] &
\cdots \\
}
\end{equation*}
\end{document}

A quick explanation: Each diagram entry corresponds to a matrix entry. Arrows do not get their own diagram entry. Instead, each \ar[x] creates an arrow that starts in the present entry and goes in direction x (d=down, r=right). The down arrows are subscripted with f_*s. The key spacing command is the @C=1em at the beginning, which says "Set the intercolumn spacing to 1em". Ozob (talk) 18:49, 5 January 2009 (UTC)

I was going to suggest xypic as well. Unfortunately, xypic is a brilliant piece of software with less-than-brilliant documentation. siℓℓy rabbit (talk) 22:53, 5 January 2009 (UTC)

For the most beautiful and easy to code diagrams, Paul Taylor's commutative diagrams package is hard to beat. And no, I am not Paul Taylor. Happy diagram coding :-) Geometry guy 23:09, 5 January 2009 (UTC)

Slowness, inactivity?

Is it just me, or is are the mathematics articles on Wikipedia less comprehensive than most other topics of the same importance? There are relatively few mathematics featured articles, and many of the subprojects seem to be, well, dead. Leon math (talk) 04:04, 3 January 2009 (UTC)

It may simply be that you know more about this part of wikipedia. I'm not sure how one would measure it but it seems to me that a number of other subjects I'm interested in are also fairly dead on wikipedia, then again the sales rank of books that I buy from amazon never seems to be less that some tens of thousands :) Dmcq (talk) 14:50, 4 January 2009 (UTC)

The point about FA is that the criteria are not really designed for mathematical exposition. Charles Matthews (talk) 15:32, 4 January 2009 (UTC)

The criteria still fit reasonably well, though, I think. They are: well-written, comprehensive, accurate, neutral, stable, appropriate lead, appropriate structure, consistent citations, good style in general, appropriate images, and appropriate length. I don't see anything wrong or anything missing... But if there is something that gives mathematics articles and unfair disadvantage at becoming FA's, we should go to the criteria talk page and propose changes. Leon math (talk) 21:21, 4 January 2009 (UTC)

You know, mathematicians don't really see the point of padding out articles, of adding inline citations for points that aren't important to justify (in a survey - obviously mathematics is more rigorous than anything else on the site), of adding pictures as illustration rather than really adding anything. Rather than the things that happened in the past with the reviewing, I think there is more enthusiasm for generally raising the standard over a range of articles that are really designed to cover part of a field. Certainly that would speak for me, though I'm not particularly active on mathematics articles currently. In the past I thought there was more point in driving the coverage closer to the current state of the art: that still seems to me to be the important aim. Charles Matthews (talk) 21:32, 4 January 2009 (UTC)

In addition to the above, most math articles involve subjects that are too technical and too abstract, and thus require sufficient specialized knowledge for improving them (even more so than technical articles on other scientific topics because of the abstract nature of math). This makes them ill-suited for the FA process, except for articles on the most general and basic math topics, like the recently promoted Group (mathematics). Most editors who are typically involved in the FA process have little background in math and it would be hard for them to provide informed and correct opinions as to whether a given article is comprehensive and accurate. There may be substantial ommissions and even inaccuracies in an article, but non-experts may easily miss them. E.g. take a look at Poincare conjecture - certainly a nice article on an important subject but well beyond the scope of non-experts in terms of commenting on accuracy and comprehensiveness. There are relatively few active Wikipedia editors with sufficient expert knowledge in any given reasonablty advanced mathematical topic. As Charles notes above, most of them are more interested in writing/expanding more advanced math articles in their fields rather than working on polishing existing math articles on very basic math topics that may actually have a chance to succeed in the FA process. Nsk92 (talk) 21:56, 4 January 2009 (UTC)

Articles on very basic math topics should be polished not by experts but by undergraduates etc. Right? Boris Tsirelson (talk) 15:30, 5 January 2009 (UTC)

No, I don't think either is preferred. Undergrads might not clutter up the article with allusions to advanced topics or be snobbish about presentation or metamathematics, but someone without long and broad experience might (and often seems to) also suffer from tunnel vision and think that the truth is only what they know, in the exact way they learned it. More articles should, perhaps, be read by undergrads, however. Ryan Reich (talk) 18:06, 5 January 2009 (UTC)

Probably I understand what is "snobbish about presentation"; but what do you mean by "snobbish about metamathematics"? (I ask since I like to avoid this sin.) Boris Tsirelson (talk) 02:20, 6 January 2009 (UTC)

You know, something like the argument over whether a ring should be assumed to contain a multiplicative unit. The literature is divided, and different fields will tell you different things about which one is more useful. It's basically a question of what examples of rings you consider most natural whether you think a non-unital "ring" is really a ring. I'm not sure which side is the snobbish one here (perhaps both), but it doesn't change the fact that noncommutative ring is a redirect, so this argument is comparitively a waste of time.

That could be taken to be a matter of presentation (though it has metamathematical roots). Another example of snobbish metamathematics could (arguably) be what happened at least-squares (discussion starts at Talk:Least squares#A major proposal) a while ago, when one expert vastly expanded and reorganized the article and its cousins according to what he took to be the right mathematical perspective—a perspective unfamiliar to anyone who had only learned least-squares from, say, an introductory linear algebra course, according to its detractors. Still, the article is good now and hasn't changed back. Ryan Reich (talk) 04:52, 6 January 2009 (UTC)

Yes, I saw the noncommutative ring redirect, and was very astonished. But if algebraists do it this way, I probabilist do not interfere. You ise the word metamathematics in somewhat unexpected (to me) way, but never mind. Boris Tsirelson (talk) 07:13, 6 January 2009 (UTC)

I had in mind for "metamathematics" a meaning like "not what the theorems say, but what they really mean". That's probably just mathematical philosophy, though. Ryan Reich (talk) 18:21, 6 January 2009 (UTC)

I have contributed a great deal to content review processes, and they are entirely compatible with mathematics articles, partly (in the case of GA) through my efforts. However, in my own edits to mathematics articles, I am much more interested in bringing a range of mathematics articles to B-Class, than taking any of them further. Of Wikipedia's 2.5+ million articles, less than 10000 are GAs or featured (0.4%). Improving the dross to a reasonable standard is far more important a goal than making a handful of articles exceptionally good.

The main historical failing of mathematics articles is the lack of sources. Just check out a few mathematics articles at random. Many have no sources at all. There seems to have been some idiotic belief that mathematics sources itself. I don't say this with my content review "verifiability" hat on, but as a user of Wikipedia. Wikipedia is now a great resource for looking up mathematical information. However, stubby mathematics articles would be so much more useful if they provided references (preferably online) to sources which fill in the gaps. Clicking on an article and finding inadequate content with no references is a depressing experience. Geometry guy 23:39, 4 January 2009 (UTC)

I agree wholeheartedly with your last paragraph that lack of sources is a serious problem for mathematics articles. Just yesterday I was discussing a forthcoming paper with a colleague who was eager to find some sources for a theorem due to Gaspard Monge. I suggested that he should look at the Wikipedia article (an article which I wrote, although I didn't volunteer this information). He reluctantly agreed to do so, but only after expressing a sentiment with which I was sympathetic: Wikipedia articles on mathematics tend to give fairly eclectic sources, often reflecting current trends in pedagogy or obscure areas of research, and rarely giving appropriate primary sources or good historical scholarship. Unfortunately, there also seems to be a sort of folk dogma on Wikipedia that perpetuates the notion that primary sources are bad and secondary sources are good, often to the exclusion of the former in favor of the latter. siℓℓy rabbit (talk) 23:53, 4 January 2009 (UTC)

It's not folk dogma, it's a matter of policy. See Wikipedia:No original research#Primary, secondary and tertiary sources. The policy even says, "Without a secondary source, a primary source may be used only to make descriptive claims, the accuracy of which is verifiable by any reasonable, educated person without specialist knowledge." If papers are primary sources, then we have no acceptable sources for many research-level math topics. That's ridiculous, and it's completely non-standard for a math encyclopedia.

I'm not even sure how one should interpret "primary source" in a math context. Are all those standard textbooks on abstract algebra referenced in Group (mathematics) primary sources or secondary ones? They prove everything from scratch; but they don't claim any originality. Does Borel and Serre's paper on Grothendieck-Riemann-Roch count as a primary source because it's the first publication, or a secondary one because Grothendieck had already presented it in a seminar talk? I can't tell.

My own feeling is that this is a case for Wikipedia:Ignore all rules. WP's sourcing guidelines aren't well suited to the process used in mathematics. We should source articles as well as we can with whatever sources are best suited, primary or not. Ozob (talk) 01:29, 5 January 2009 (UTC)

Yes, the policy statement is clearly problematic. Allow me to clarify: the statement of WP:OR explicitly refers to primary sources in a historiographic context, rather than a general scientific context. Our own article on primary sources adopts a much broader definition: "In scientific literature, a primary source is the original publication of a scientist's new data, results, and theories." A primary source of the latter sort is perfectly allowed, provided it meets the other criteria under the WP:OR policy. So, indeed, it is merely "folk dogma" which proscribes primary sources in mathematics and the sciences. siℓℓy rabbit (talk) 01:53, 5 January 2009 (UTC)

The notions of primary, secondary and tertiary sources are poorly understood throughout Wikipedia, and even more so at this project. First, they are not absolute: a source can be primary for one fact and secondary for another. Second, and this is Silly rabbit's point, primary sources are not a bad thing: we need primary sources in articles. This is not just because primary sources are better than no sources, but because primary sources are an important part of any encyclopedia article. Borel and Serre's paper is a secondary source for Grothendieck's contribution to the Grothendieck-Riemann-Roch theorem, but a primary source for its own novelties and presentation. Why is that so hard to understand? I have seen a case in which an article by Newton was used (appropriately) as a secondary source, even though the work of Newton is usually primary source material. Secondary sources are needed to evaluate the contributions of others. Standard textbooks on abstract algebra are obviously secondary sources for the material they detail, whether they prove everything from scratch or not. They show that original work has been accepted as standard knowledge. I am amazed that intelligent editors find this hard to comprehend. Geometry guy 02:13, 5 January 2009 (UTC)

I do not know much about the GA process; my general impression that, per individual article, GA process requires much fewer users than does the FA process. So the GA process is probably more math friendly, although even there I would imagine that a math article on a reasonably advanced topic would have a difficult time. For FA, the problem really is not with the process itself but rather with the fact that there is, at least for now, not a sufficient critical mass of active WP editors with sufficient expert knowledge for the FA process to work well for math articles on non-basic math topics. I have written a few reasonably complete math articles, such as Small cancellation theory, van Kampen diagram, Dehn function, Bass-Serre theory, and a few others. However, I think that these types of articles are completely unsuitable for the FA process and possibly even for GA process, since there are too few active WP editors with the requisite background knowledge. I agree with the Geometry guy that the lack of sourcing in WP math articles is a widespread and serious problem. I think the reason is that most mathematicians who do edit WP articles, tend to write them in a similar way as they write their regular math papers, worrying more about mathematical correctness and completeness of the presentation than about references. That is why many math WP articles read like WP:OR essays. Such articles are still quite useful, but they certainly would be more useful if properly sourced. (In my own defence I should say that I am a bit of a reference freak when I write WP math articles, and I am probably guilty of overreferencing).

I have a suggestion that is indirectly related to this discussion. I am still very uncomfortable with the idea that initial ratings are supposed to be assigned by the article's creators. This seems to represent a basic COI to me and I personally would feel very uncomfortable assigning my own article any rating above Start class; it feels like refereeing one's own paper, certainly a no-no. I prefer to keep my articles unassessed that to assign to them a B-rating myself, even in the cases where I think B-rating is deserved. It just does not feel right. I think it would be beneficial to institute a regular process where creators of new math WP articles can request their initial assessment by other members of WikiProject Math. Some other wikiperojects, like Wikiproject Biography, actually have such arrangements in place and I think we should too. There will be an added benefit of new math articles receiving substantive third-party feedback relatively quickly and, hopefully, progress to something around B class. Just a thought. Nsk92 (talk) 00:59, 5 January 2009 (UTC)

Self-assessment at the early stages works because we are our own best critics. Also a rating means "the article is at least this good", even though it might be much better, so a conservative self-assessment is better than no assessment. All four of the articles you list do not meet WP:LEAD and would stand very little chance at GAN. They are however, all at least Start class, and need maths ratings. Some might be close to B-Class, but such a judgement could be left to other editors. We can learn from content review processes even while remaining critical of them. Geometry guy 01:13, 5 January 2009 (UTC)

As I said, I am not really critical of the GA/FA review processes as such but I think that, apart from the matters of style, they need a certain critical mass of people sufficiently well familiar with a particular topic in order to work well. I believe that in most cases such critical mass is currently absent for math articles on non-basic topics. Regarding initial assessment, I still think it would be very useful to institute a regular system for requesting assessment by a third party. It would at least ensure that new math articles receive fairly quick substantive feedback. It should be easy enough to institute such a system. E.g. one could create a section of Wikipedia:WikiProject Mathematics called "Requests for third-party article assessment" (or something like that). People could add unrated or author-rated articles to a list in such a section, and, once another editor rates the article, that editor can remove it from the list. Nsk92 (talk) 02:06, 5 January 2009 (UTC)

The only way to address a perceived lack of critical mass of expert editors is to contribute. Our A-Class assessment scheme failed for the lack of contributions and is now moribund. In that respect, please contribute to WP:Featured article candidates/Mayer–Vietoris sequence. It is hard to take any editor's concerns seriously if they can't even contribute to the only current mathematics FAC. Geometry guy 02:21, 5 January 2009 (UTC)

I'll take a look at the Mayer-Vietoris nomination, although I am leaving on a week-long trip abroad tomorrow morning and I don't know if I'll have enough time to say something substantive before then. Until now I have had little interest in FAC process since it had seemed to me largely inapplicable to math articles, and also because as a matter of personal preference I find it more interesting and enjoyable to work on creating new content rather than deal with things like GA/FA (which does not mean that FA/GA projects are not important). However, I am interested in the workings of the more basic math assessment process (Start, B and maybe A, also C if it is introduced as a math rating). It seems to me that getting the more basic math rating process work more efficiently and meaningfully is a higher priority that promoting more math articles to the FA status (although the latter is, of course, good when it happens). I don't think my opinions on that are invalid or should not be considered even if I don't participate in the FAC discussion for the Mayer–Vietoris sequence. Nsk92 (talk) 02:42, 5 January 2009 (UTC)

As noted above, I have pretty much the same priorities when it comes to editing math articles. However FACs in mathematics are rare enough that it is worth contributing. Geometry guy 02:46, 5 January 2009 (UTC)

Let's not focus on what part of WikiProject Math is more important. It seems that our overall conclusion is that there aren't enough editors that possess all of the following traits: (1) have the knowledge/ability to help, (2) are willing to put information on Wikipedia, and (3) are concerned with the organization, procedures, and conventions of Wikipedia. (I fail number 1.) Hmm... this problem is not easily solved. I guess it's just like Geometry guy said; we can only do as much as we can, and there's really nothing that can be done to drastically improve the situation. Leon math (talk) 03:00, 7 January 2009 (UTC)

Track transition curve

This complex clothoid/Euler spiral is used everyday, being used in roads and on railways to blend together curves of differing radii (or straight sections). An editor recently has introduced a large amount of new material in the form of including PDF page screen shots into the article (rather than TeX notation). I have copied this material to User:Ling Kah Jai/Track transition curve for their improvement, but it would be useful to have some wider review of what is appropriate (the 8-page proof is perhaps more than necessary for a Wikipedia article).

Track transition curve, User:Ling Kah Jai/Track transition curve, Talk:Track transition curve#Formulation of Euler spiral. —Sladen (talk) 05:53, 7 January 2009 (UTC)

Category:Historical treatment of quaternions

This category, and its two current inhabitants, Classical Hamiltonian quaternions and The vector of a quaternion, should in my opinion be transwikied to WikiBooks. I feel that these are both needless and unsanctioned content forks of quaternions. They seem to be filled with the personal opinion and original research of the author, and are rather poorly written. siℓℓy rabbit (talk) 03:46, 3 January 2009 (UTC)

I've worked a lot on the quaternion article, and I agree that those two articles would be better placed at Wikibooks. You might consider contacting User:Hobojaks, who is the primarily responsible for writing those articles. As far as I can tell, he believes that classical quaternions are superior to linear algebra for most purposes. ("Classical quaternions" are distinguished from modern quaternions because the classical viewpoint is that i, j, and k are new primitive symbols, not elements of an R-vector space. At least, this is the impression that I get from Hobojaks; see Talk:Quaternion/Archive_2#A more pragmatic point of view.) I don't know how he would feel about transwikiing those two articles, but he is not always easy to talk to. (See Talk:Quaternion/Archive_2#Modern Cast system????) Ozob (talk) 04:42, 3 January 2009 (UTC)

Ok. I'm not sure what to do. I'm not good in one-on-one situations that could be potentially confrontational, which seems likely given your warning. Would it be better to take these articles to AfD? siℓℓy rabbit (talk) 02:03, 5 January 2009 (UTC)

Sorry for taking so long to get back to you. I think AfD is appropriate for both articles. They're both mostly content forks of quaternion, and the only thing they have going for them is all the historical citations. In the future it might be possible to write a real article on classical Hamiltonian quaternions which would describe how Hamilton's viewpoint differed from the modern viewpoint of H as an R-vector space. But that will have nothing to do with the present article of that name. Ozob (talk) 00:58, 9 January 2009 (UTC)

Invariants of a tensor ?

Came across invariants of tensors and noticed that it currently focuses exclusively on rank 2 tensors i.e. matrices. Matrix invariants are already covered at characteristic polynomial and related articles. Is there a more general article that could be written here about how determinant, trace etc. generalise to higher rank tensors, or is this a dead end ? Gandalf61 (talk) 17:10, 8 January 2009 (UTC)

I don't know anything about tensors, but this book: Introduction to non-linear algebra talks about generalizing linear algebra including determinants to non-linear situations, using tensors. Charvest (talk) 21:49, 8 January 2009 (UTC)

I would guess that "tensor" in that article means "tensor field", mostly because it makes a comment about a coordinate system. So there's something not entirely trivial there, I think, but the article doesn't make that clear.

There are things you can do to generalize various notions of linear algebra to vector bundles. The determinant of a vector bundle is just its top wedge power. I think EGA IV has some stuff about taking the norm of a vector bundle somewhere (sort of like taking the norm in Galois theory). IIRC it seemed to me once that there was something you could do to generalize the elementary symmetric functions, but I forget now. I don't think I found a use for it. Ozob (talk) 01:11, 9 January 2009 (UTC)

I have an incredably stupid question

An editor had earlier comment at the page Iowa class battleship that the two mathematical formulas in the paragraph below were actually the same:

That same year (1935), an empirical formula for predicting a ship's maximum speed was developed, based on scale-model studies in flumes of various hull forms and propellers. The formula used the length-to-speed ratio originally developed for 12-meter (39 ft) yachts:

${\mbox{Speed}}={\sqrt {1.408\times {\mbox{waterline length}}}}$

and with additional research at the David Taylor Model Basin would later be redefined as:

${\mbox{Capital Ship Speed}}=1.19\times {\sqrt {\mbox{waterline length}}}$.

It quickly became apparent that propeller cavitation caused a drop in efficiency at speeds over 30 knots (56 km/h). Propeller design therefore took on new importance.

Sine I have failed four separate remedial level math classes at collage, and haven't passed a math class with a grade better than C- since seventh grade, I was wondering if someone from this project could independently verify that the two formulas are in fact the same. TomStar81 (Talk) 04:08, 10 January 2009 (UTC)

$1.19\times {\sqrt {\mbox{waterline length}}}={\sqrt {1.19\times 1.19\times {\mbox{waterline length}}}}={\sqrt {1.4161\times {\mbox{waterline length}}}}$

So it is pretty close. --fvw* 04:13, 10 January 2009 (UTC)

They are indeed the same thing (except that in the second equation a lower precision is used). Specifically,

${\sqrt {1.408}}\approx 1.187$

which rounds up to 1.19. In math (or science), one would say that for the second equation one just "took out" the "1.408" from under the square root. Also, for future questions of the sort, you can go to Wikipedia:Reference desk/Mathematics. Cheers. RobHar (talk) 04:21, 10 January 2009 (UTC)

The "new articles" list on the "current activity" page

...is working again. Michael Hardy (talk) 17:48, 10 January 2009 (UTC)

A better "prime"

Look at this:

Ψ(t) = −log(π) + Re(ψ(1/4 + it/2)), where ψ is the digamma function Γ′/Γ.

In "displayed" TeX, I'd write the digamma function as

${\frac {\Gamma \,'}{\Gamma }}$

or in some contexts like this:

$\Gamma \,'/\Gamma \,$

I don't want to change an "inline" thing to TeX, since that causes comical mismatches of size and alignment, but the "prime" is barely visible. Is there a better, more legible, way to write a "prime" in non-TeX notation, and if not, can one be created? Michael Hardy (talk) 16:26, 11 January 2009 (UTC)

Well I am certainly no expert on formatting matters, one hack may be to change the font size on the prime. One simple way to do this would be:

Γ′/Γ or Γ′/Γ

But I think there are more refined ways to control the font size. I suppose neither of these look that much better. Thenub314 (talk) 16:59, 11 January 2009 (UTC)

Γ´ uses an acute accent rather than an apostrophe Γ' (too vertical) or a single quote Γ‘ (too curly). I think it's a little better as an acute accent than as the other two. If you don't know how to type it (on my Mac keyboard it's option-e space) you can copy-and-paste from this example. —David Eppstein (talk) 17:10, 11 January 2009 (UTC)

Measure (mathematics)

I am not sure how this article ever got to GA (luckliy it was demoted). I am starting a rewrite now; any help there would be appreciated (in particular, a good lede is necessary). --Point-set topologist (talk) 18:17, 11 January 2009 (UTC)

It was listed for 3 months in the early days of GA, before the criteria became more exacting. Geometry guy 19:21, 11 January 2009 (UTC)

What are you dissatisfied with? Boris Tsirelson (talk) 18:59, 11 January 2009 (UTC)

Well for a start, the article does not explain many important concepts in measure theory, nor does it include any applications to probability theory (apart from the Lebesgue integral) etc... I would think that it is fairly clear that the article is not up to par but as you are a measure theorist, it would be good to know your opinion. PST

I see. If you really feel you can do it better, then of course you should try. Yes, I know many things about measures that do not appear now in the article. However, 14 more specialized articles are mentioned in "See also". Do you want to (partially) merge them to "measure"? Or do you want to add something not present in these 14 articles? In the latter case, are you sure it should be added to "measure" rather than to these more specialized articles? Boris Tsirelson (talk) 21:46, 11 January 2009 (UTC)

I want to add some brief descriptions of these specialized concepts. In particular, something has to be there on the Lebesgue integral and the Haar measure. PST

Modulo cleanup

Go to modulo and click on "what links here".

• Some of these times should be rewritten to say [[modular arithmetic|modulo]] so that the reader sees "modulo" and clicks and sees modular arithmetic.
• Some of these times should be rewritten to say [[modulo operation|modulo]] so that the reader sees "modulo" and clicks and sees modulo operation.

In the modular arithmetic article, 63 and 53 are congruent to each other modulo 10.

In the modulo operation article, "modulo" is a binary operation and (63 modulo 10) = 3.

The modulo article is far more general than just arithmetic.

—Preceding unsigned comment added by 75.72.179.139 (talk) 22:02, 11 January 2009 (UTC)

Michael Hardy (talk) 21:51, 11 January 2009 (UTC)

......I've now taken care of the most egregious cases. Next there are the subtler cases that may require more delicate thought. Michael Hardy (talk) 23:23, 11 January 2009 (UTC)

The Princeton Companion to Mathematics

I just got the book a a preset a very pleased I am too with it. Of course I immediately dipped into he centre and also started looked up things I know about in the index. Very interesting. I didn't find much or anything about the things I thought of which indicates if it really was comprehensive it would be a bookcase of books - it is pretty huge as it is. I seem also to have been corrupted by Wikipedia, I kept thinking I should edit this to add wikilinks and better citations. Where it differs from WP mainly is it is much more chatty and readable with things like "Why should nonequivalence be harder to prove than equivalence? The answer is that in order to show....", or "For fun, one might ask a fussier question:". On further references it can say things like "For further details n sections 1-4 the reader is referred to standard textbooks such as ...". I can thoroughly recommend the book.

The book has a small section in its introduction on "What Does The Companion Offer That the Internet Does Not Offer?" (I feel like quoting WP:STYLE about the capitalization!) and I have to agree with what it says: that the internet is hit and miss, sometimes there's a good explanation sometimes not. The articles are drier just concerned with giving he facts in an economical way and not reflecting on those facts. And it doesn't have long essays on the fundamentals and origins, the various branches , biographies of mathematicians and the influence of mathematics. Not that I agree with all that, basically I think what it amounts to is one wouldn't make oneself comfortable, get a cup of coffee and curl up to read the articles in wikipedia. The book has a problem with that too as it is so heavy but otherwise it is a far better read overall.

Does a book like this have lessons for us? Should WP style be a bit more chatty? Or should we be dry and economical and just inhabit a different domain from books like this? Dmcq (talk) 12:18, 9 January 2009 (UTC)

It's more than being a little less chatty; at the moment Wikipedia's policies sometimes run counter to very standard mathematics conventions. If we can't even say "we" or "note that" in proofs, it's a while before will get anywhere near informal, comfortable chattiness. If this ever makes it to a vote, we could argue that style manuals do want prose to be "engaging"...

Unfortunately, it's difficult to write chatty prose while still covering everything in an appropriate sequence like an encyclopedia should. Leon math (talk) 03:31, 10 January 2009 (UTC)

If you ask me, Wikipedia is not suited for mathematics articles. Most of these current policies are rather useless... --Point-set topologist (talk) 18:15, 11 January 2009 (UTC)

You can still write a good article. That's what matters. Ozob (talk) 01:34, 13 January 2009 (UTC)

Additive number theory

I recently created Category:Additive number theory and I'd like help/feedback.

• What should the category name be? Additive number theory seemed best to me, but any of {arithmetic | additive} {number theory | combinatorics} would seem to be possible, and there are surely others.
• Should the category be under Category:Number theory or the narrower Category:Analytic number theory? It's usually considered one of the major branches of analytic number theory because of its heavy use of the circle method and related techniques, but they're a priori distinct.
• What other articles should be included? I just did a quick pass, but I'd expect that there are more.
• What should the category page say? I just have boilerplate text at the moment, which could be fine, but if there are any distinctions that need to be made ("not to be confused with Subtractive Number Theory") or related fields ("similar to Combinatorial Subtraction, but different because CS uses butterflies and rainbows instead of sumsets").
• Any other comments?

CRGreathouse (t | c) 20:28, 12 January 2009 (UTC)

Additive number theory sounds like a good name. IMO it should be a sub-category of Analytic number theory. That's all my opinions. RobHar (talk) 22:03, 12 January 2009 (UTC)

Something has to be done about this junky article

I am seriously concerned about the article on manifolds. First of all, it seems (from an uninvolved user's point of view) that a group of people rejected this article from becoming featured simply because they couldn't understand this. I am glad at least that it was rejected but there should seriously be some restrictions on the people who vote (some people seem to think that if they can't understand it, no-one else can) (if anyone has the time, just have a read through the article). But here is a specific section (the article is never going to be featured at this rate):

Other curves

Manifolds need not be connected (all in "one piece"); an example is a pair of separate circles. They need not be closed; thus a line segment without its end points is a manifold.

By definition, a 'closed manifold' is a compact manifold without boundary. A line segment without its end points is just R and is therefore a trivial manifold. Why mention these obvious facts? PST

And they are never countable; thus a parabola is a manifold.

????????????? For a start, they can be countable (0-dimensional manifold), and does the implication make sense (even assuming that the first statement is true)? Its like saying that X is never Y; so if Z is not Y, it must be X. PST

Putting these freedoms together, two other examples of manifolds are a hyperbola (two open, infinite pieces) and the locus of points on the cubic curve y² = x³−x (a closed loop piece and an open, infinite piece). However, we exclude examples like two touching circles that share a point to form a figure-8; at the shared point we cannot create a satisfactory chart. Even with the bending allowed by topology, the vicinity of the shared point looks like a "+", not a line (a + is not homeomorphic to a closed interval (line segment) since deleting the center point from the + gives a space with four components (i.e pieces) whereas deleting a point from a closed interval gives a space with at most two pieces; topological operations always preserve the number of pieces).

Nothing wrong with this fortunately. :) PST

I can give (if necessary) similar criticizm of almost all other sections. Recently I re-wrote the lede: I would seriously consider re-writing the whole article and deleting some of the sections there. --Point-set topologist (talk) 20:59, 12 January 2009 (UTC)

From a quick glance the article seems to be better than 98% of our articles. Deleting content is pretty delicate. What is trivial to you may not be so to other readers, so be very careful and thoughtful. Jakob.scholbach (talk) 21:23, 12 January 2009 (UTC)

From another glance at this change log it looks like most of the changes you made were unconstructive

Not true: I expanded the lede as well as made some cleanup to other sections in the article. --Point-set topologist (talk) 22:00, 12 January 2009 (UTC)

, if not harmful. For example, removing reasonable content as per "delete nonsense section" is pretty bad.

I rewrote this section in a much better manner (that is why I used 'nonsense') and merged it into the lede. So in effect, I did not delete it. --Point-set topologist (talk) 22:00, 12 January 2009 (UTC)

I have reverted your recent edits. Jakob.scholbach (talk) 21:33, 12 January 2009 (UTC)

Hi Jakob,

I did not intend my edits to manifold to be unconstructive. I deleted that section because I had already summarized it in the lede (so basically I merged that section into the lede). Maybe I should have made this more explicit (I guess this is kind of what Taku did (on a major scale) to ring (mathematics) although his intentions were good). I also rewrote the lede in the way I did after reading why this was rejected in FA; so basically I made it more accessible. I am adding that section back but if you still feel the same way you can revert it. I just feel that there has been a misunderstanding.

PST (Point-set topologist)

I reverted. It appears that you have delted a lot of my additional material in your rv. Could you please have a look at that diff (of your rv)? --Point-set topologist (talk) 21:57, 12 January 2009 (UTC)

I have to say I side with Jakob.scholbach. The introduction should be short and to the point describing what he article is about. The edits put too much into the introduction. And even if the introduction does say something it should probably be mentioned again in a more precise way later rather than stuff being removed elsewhere to put into it. The introduction should be chatty and accessible and just introduce the article so people know whether they are looking at the right place and have a quick summary. Dmcq (talk) 09:03, 13 January 2009 (UTC)

Freak software bug

I just did a minor edit to Cauchy principal value. After the edit, every line of TeX in the article looked like this:

Failed to parse (Cannot write to or create math output directory): \lim_{\varepsilon\rightarrow 0+} \left[\int_a^{b-\varepsilon} f(x)\,dx+\int_{b+\varepsilon}^c f(x)\,dx\right]

I've seen this a number of times lately. It will probably go away soon, but just when is completely unpredictable. Why is this happening? Michael Hardy (talk) 19:41, 13 January 2009 (UTC)

Because someone broke a server. For now a purge should fix it. See WP:VPT#Error_message_in_http:.2F.2Fen.wikipedia.org.2Fwiki.2FPlanetary_gearing. Algebraist 20:04, 13 January 2009 (UTC)

Shannon–Hartley theorem

There are a number of (bolded red) parsing errors in this article, related - I think - to mathematical equations. Would someone more familiar with this area take a look? Thanks! -- John Broughton (♫♫) 20:56, 13 January 2009 (UTC)

Looks fine to me. Most likely a transient server-side problem; this happens from time to time. --Trovatore (talk) 21:02, 13 January 2009 (UTC)

This sounds like the same thing as the thread above. Algebraist 21:05, 13 January 2009 (UTC)

Topic outlines

I think that these articles should be deleted: Topic outline of algebra, Topic outline of arithmetic, Topic outline of calculus, Topic outline of discrete mathematics, Topic outline of geometry, Topic outline of logic, Topic outline of mathematics, Topic outline of statistics, Topic outline of trigonometry. Charvest (talk) 20:12, 11 January 2009 (UTC)

Why? — Carl (CBM · talk) 01:07, 12 January 2009 (UTC)

Against apparent consensus here (there is a somewhat abortive thread in the archives), User:Transhumanist has gone ahead and moved all of the articles [[List of basic X topics]] to [[Topic outline of X]]. This is a bit distressing since, as far as I am aware, there is no indication anywhere in the manual of style on this massive proposed change (which has its source somewhere off in the rarely-used "Portal" namespace). This entire project appears to be Transhumanist's pet project, and has not been handled in a transparent manner. Instead of going through and changing huge numbers of articles, without attempting to obtain consensus (or disregarding a lack of consensus), an appropriate course of action would have been to draft a suggested Wikipedia guideline, and then solicit comment. The current proposal does have some discussion, but mostly in sundry talk-page archives. In this light, Charvest's request is quite reasonable, if a bit WP:POINTy. These changes should be reverted since the current articles do not follow the standard naming conventions for lists. siℓℓy rabbit (talk) 01:38, 12 January 2009 (UTC)

First of all, wikipedia is an encyclopedia, not a fixed syllabus, so "topic outline" is not appropriate - the state of art of knowledge is a constantly changing. Secondly, most of these articles are pretty rubbishy and I don't see the point in them. Take Topic outline of algebra for example. Even if this is changed back to List of ... it is still rubbishy. What does this article say that isn't already in the main algebra article ?

My opinions on these articles are:

• Topic outline of algebra - delete,
• Topic outline of arithmetic - merge with arithmetic,
• Topic outline of calculus - delete ,
• Topic outline of discrete mathematics - merge with discrete mathematics ,
• Topic outline of geometry - merge with geometry,
• Topic outline of logic - there's a lot here so keep or merge,
• Topic outline of mathematics -delete
• Topic outline of statistics - merge with statistics,
• Topic outline of trigonometry merge with trigonometry

Charvest (talk) 09:58, 12 January 2009 (UTC)

modified Charvest (talk) 21:55, 14 January 2009 (UTC)

Are you aware that these were titled List of basic algebra topics, etc., until they were unilaterally renamed a couple days ago? — Carl (CBM · talk) 12:57, 12 January 2009 (UTC)

I wasn't initially aware, but Silly Rabbit pointed this out above. A list which consists simply of the most commonly used terms is basically a glorified see also section and might as well be put in the main articles, rather than have separate pages, unless they are particularly extensive lists. Charvest (talk) 15:38, 12 January 2009 (UTC)

I would suggest that the portal is the ideal place for these pages. Martin 13:24, 12 January 2009 (UTC)

Having a look at the portals: Portal:algebra, Portal:geometry etc it seems the portals are much better presented and contain most if not all of the information in the lists. Between the main articles, the portals and the lists there is massive overlap. The lists should go. Charvest (talk) 15:38, 12 January 2009 (UTC)

I think the lists are useful, in the "List of basic topics" form. I agree they are glorified "see also" lists, but that makes them very good for including in the "see also" section of basic articles like Algebra, where it would be impractical to include a long list of links, but where naive readers are likely to be interested in a list of topics to browse. — Carl (CBM · talk) 23:52, 12 January 2009 (UTC)

Okay, so some people find them useful so they should be kept. But would a different namespace be more appropriate (i.e. Portal)? Personally I think categories do a better job of helping someone browse or find the article they want. Martin 00:03, 13 January 2009 (UTC)

I think this should be done on a case-by-case basis. Maybe most "List of basic X" really are "Topic outlines" and should be moved over to Portal namespace. I don't know. But I am definitely opposed to any blanket move from "List of basic" to "Topic outline" in the mainspace since, in principle, these denote different things. For instance, "Topic outline of geometry" ideally would contain some rather non-basic things such as differential geometry (which isn't there!) or algebraic geometry (also not there!). siℓℓy rabbit (talk) 02:13, 13 January 2009 (UTC)

I think that topic outlines for major parts of mathematics is a great idea. But to call the execution merely 'lacking' is too kind. Can these reasonably be improved? If not, I'd prefer deletion to keeping them in their present state. **CRGreathouse** (t | c) 03:59, 13 January 2009 (UTC)

To make these useful I think a greater amount of description is required. Topic outline of ecology adds a brief sentence to each term which makes it into more useful article. --Salix (talk): 08:11, 13 January 2009 (UTC)

I've nominated the worst of these articles for deletion at: Wikipedia:Articles for deletion/Topic outline of algebra Charvest (talk) 22:09, 14 January 2009 (UTC)

How to make SVG diagrams

This question sometimes comes up and it bears answering as often as possible, since a lot of people have never heard that we should be using SVG, and of those who have, few seem to have an easy way of actually accomplishing it. This is addressed at Help:Displaying a formula#Convert to SVG, but their proposed solution relies on a somewhat arcane and arbitrary invocation of two different utilities, followed by a roundabout filtration through two major software packages, which is necessitated by one of them (pstoedit) requiring a costly proprietary plugin to work properly. And the end result is still unusable if your diagram has diagonal lines. Here's the right way:

pdflatex file.tex
pdfcrop --clip file.pdf tmp.pdf
pdf2svg tmp.pdf file.svg
(rm tmp.pdf at the end)

Both pdfcrop and pdf2svg are small, free (if new and somewhat alpha) programs that work properly. I advocate pdflatex since with the alternative, you might be tempted to go the route of latex→dvips→pstopdf before vectorizing, and that runs into a problem with fonts that has to be corrected with one of the arcane invocations above. (There is a correct route, which is to replace that chain with dvipdfm, that I have never seen anyone suggest. Somehow, the existence of this useful one-step solution to getting PDFs from plain latex is always ignored.)

I have proposed at the talk page of that Help article that this procedure replace the existing one. It has been road-tested on, most notably (for the complexity of its images) Triangulated category and found to work quite well. Since the interested parties hang out here more than there, I'm soliciting feedback from whatever TeXperts and hackers might be lurking. Ryan Reich (talk) 04:23, 14 January 2009 (UTC)

Thanks for this, I'm quite happy to know this. Also, btw, on macs texshop uses pdflatex as default since pdf's are native on macs. RobHar (talk) 04:59, 14 January 2009 (UTC)

Since writing this, I have investigated Inkscape's internals and found that the following pstoedit invocation is also good:

pstoedit -f plot-svg -dt -ssp tmp.pdf tile.svg

It also makes smaller SVG files, sometimes (with the large ones) by quite a bit. This invokes the GNU libplot, and I cannot decide whether this piece of imperfect software is preferable to the one which is pdf2svg; let it be your call if you use it. Ryan Reich (talk) 20:59, 14 January 2009 (UTC)

...except that it couldn't make a nice SVG out of the pictures now at Cone (category theory), whereas pdf2svg could. I don't think I can really recommend pstoedit for this task. Ryan Reich (talk) 04:26, 15 January 2009 (UTC)

brahmagupta and Cauchy

Please see Negative and non-negative numbers. Katzmik (talk) 18:10, 14 January 2009 (UTC)

A meaningful illustration of vector spaces

Does anybody have an preferrably an illustration (or an idea for one) to illustrate the concept of vector space? I'd like to nominate that article for FA soon, but I feel without a good lead section image it's only half as beautiful. Thanks! Jakob.scholbach (talk) 20:56, 14 January 2009 (UTC)

List of mathematics categories

We have Wikipedia:WikiProject Mathematics/List of mathematics categories which is used as worklist by mathbot to fill in the list of mathematics categories.

Question: can this list of categories be also useful to Wikipedia readers, after some formatting changes or prettifying perhaps? Then we could move it to the article namespace, at list of mathematics categories, and treat it in the same way as the other mathematics topics. Oleg Alexandrov (talk) 07:08, 15 January 2009 (UTC)

Cut paste move

I tagged Krull–Schmidt theorem with {{db-histmerge}}, since there was a WP:CUTPASTE move done to it. The ndash article has no new (relevant) history to it, all of the history is in the hyphen article, which is now a redirect. Can an admin fix this? JackSchmidt (talk) 00:28, 15 January 2009 (UTC)

Done, I think. — Arthur Rubin (talk) 02:01, 15 January 2009 (UTC)

Thanks! JackSchmidt (talk) 14:22, 15 January 2009 (UTC)

What a mess

Can anyone help with Grey relational analysis? Michael Hardy (talk) 05:49, 16 January 2009 (UTC)

Gauss–Jacobi mechanical quadrature

Gauss–Jacobi mechanical quadrature is vaguely written. In particular, what does the function p_n(x) have to do with the statement that follows it? Could someone who knows the answer to these questions clarify by editing the article. Michael Hardy (talk) 05:26, 16 January 2009 (UTC)

The article was indeed vaguely written, so I rewrote it. -- Jitse Niesen (talk) 16:36, 16 January 2009 (UTC)

For me (in this article) all the equations fail to parse. GeometryGirl (talk) 16:55, 16 January 2009 (UTC)

Purging the server cache should fix that. Algebraist 17:05, 16 January 2009 (UTC)

stable module category: many formulas not rendered

http://en.wikipedia.org/wiki/Stable_module_category —Preceding unsigned comment added by 77.4.181.225 (talk) 12:33, 16 January 2009 (UTC)

Yes, there is an intermittent problem that sometimes causes a "Failed to parse ..." message to appear instead of Tex formulae. If you have a Wikipedia account, logging in seems to cure the problem. Gandalf61 (talk) 12:41, 16 January 2009 (UTC)

I've purged the cache for IPs, so it should display fine when logged out now. Algebraist 12:50, 16 January 2009 (UTC)

This occasionally happens on math articles regardless if logged in or not. Clicking on edit and preview makes the formulas render for me; then the problem may go away. I wonder if there is a simpler way. Jmath666 (talk) 01:12, 18 January 2009 (UTC)

As I stated above, purging should work as a temporary measure, but brion said this should be fixed 'pretty soon' more than five days ago now. Anyone feel like bugging him about this? Algebraist 01:18, 18 January 2009 (UTC)

Vandals again

As usual vandals are up to no good at geometry. Having scanned through the editing history for 2008, it appears that vandals were at the peak during mid year; their activity lowest around December. But since January they are back for more. I am worried about this article because everyone knows what geometry is and at least one tenth of people who come across this article are out to vandalize. So this article is never going to be safe against vandalizm. Instead of wasting our times reverting edits there every hour of the day (that article will probably fill up 80% of anyone's watchlist), can we take some action? --PST 13:59, 17 January 2009 (UTC)

There have been 5 vandalizing edits from IPs since the last semiprotection ended on 23rd December. That doesn't seem enough to require protection, and it certainly won't be filling up my 1000-page watchlist. Algebraist 14:46, 17 January 2009 (UTC)

Wow! My watchlist has only 20 pages. But the point that I am trying to make is that this is never going to stop. I stand corrected but look at the article's history in February and you are going to see only reverts and vandalizm (no improvements). Instead of wasting future time, can't we see that it stops immediately. I think that the reason that vandalizm was not there from the 23rd to the 10th is because that was the holiday season. --PST 23:36, 17 January 2009 (UTC)

One of Wikipedia's great strengths is that anyone can edit it. Wikipedia is a huge success, and its predecessor Nupedia was a complete failure, and the difference between them is that anyone can edit Wikipedia. Each protected page takes away a little bit of that great strength. —Dominus (talk) 01:01, 18 January 2009 (UTC)

Featured article nomination

The article on vector spaces is up for featured article nomination. Please opine here. Jakob.scholbach (talk) 16:00, 17 January 2009 (UTC)

bang, drum, and flag

I would be interested in comments as to the appropriateness of the following comment by Gandalf61:

Katzmik, we all know where this is going. You want to bang your non-standard calculus drum and assert calculus could be taught without the concept of limits and so they can't be central to calculus. And you could be right - in theory. However, in practice, limits play a central role in the field of calculus as it is taught and used by most mathematicians, and most mathematicians would be happy with the first sentence of this article as it stands, and your contention that this is a misconception is a tiny minority view. Now you may say that is just my opinon. But if you are really interested in what the wider community thinks, then I suggest you go ahead and flag this discussion at WT:WPM. Gandalf61 (talk) 10:23, 20 January 2009 (UTC)

— Preceding unsigned comment added by Katzmik (talk • contribs)

That (from a discussion at Talk:Topic outline of calculus seems to be an entirely reasonable, appropriate and accurate comment. Algebraist 13:12, 20 January 2009 (UTC)

I'm not certain which aspect you would like comments on.

• The idea that limits are central to calculus is a very common view. Searching google books for "limit concept fundamental calculus" shows many sources in the first few pages. Richard Courant goes so far as to say, "The fundamental concept on which the whole of analysis ultimately rests is that of the limit of a sequence".
• The "bang your drum" sentence might be viewed as strongly worded, and could have been written in a way that doesn't imply the existence of a campaign. However, you have been advocating for more coverage of nonstandard calculus in various articles, so I can understand where Gandalf was coming from. Unless there is a pattern of comments like this, I would brush it off.
• The neutral point of view policy says, "Neutrality requires that the article should fairly represent all significant viewpoints that have been published by a reliable source, and should do so in proportion to the prominence of each." The prominence of nonstandard analysis is not high in mathematics as a whole and in elementary calculus is particularly small. I think that articles like list of basic calculus topics should be written in a way that matches the majority of calculus texts, which proceed through limits to derivatives and integrals, along with applications such as Lagrange multipliers, arc length, and center of mass.

— Carl (CBM · talk) 13:37, 20 January 2009 (UTC)

I like nonstandard calculus. In fact, nonstandard analysis is the primary reason I haven't discarded (in my zeal for simplicity) the Axiom of Choice. But nonstandard calculus is not a part of the usual calculus curriculum, which always includes limits. CRGreathouse (t | c) 13:56, 20 January 2009 (UTC)

But for me the axiom of choice (beyond the countable dependent choice, of course) is rather an interesting mathematical toy (or a brave mathematical experiment), as well as all its consequences, including nonstandard analysis. Boris Tsirelson (talk) 19:43, 20 January 2009 (UTC)

No doubt. But it was nonstandard analysis that opened the door for me. CRGreathouse (t | c) 20:35, 20 January 2009 (UTC)

(Boring part) Wikipedia cannot advance an agenda. We simply reflect what reliable secondary sources say, with due weight. The NSA and constructivist viewpoints both deserve mention in some contexts, but they are most usually an aside.

(Less boring part) I don't much like the axiom of choice as it can be terribly convenient to suppose every subset of the real numbers is measurable. However, regarding NSA, I laugh at your feeble invertible infinitesimals and the fussing over standard parts :-). Real infinitesimals are nilpotent: dx squares to zero, obviously. You fools tie your hands by doing mathematics in the wrong topos :-) Geometry guy 20:59, 20 January 2009 (UTC)

What else could we do while waiting for you the genius? Boris Tsirelson (talk) 21:22, 20 January 2009 (UTC)

:-) Nobody can do much until the insights of Grothendieck and Lawvere are realised and assimilated as something comprehensible to lesser mortals. (I hope I am not giving too much away here by confirming that I am neither Grothendieck or Lawvere.) Maybe 20-30 years...? Geometry guy 22:12, 20 January 2009 (UTC)

It's not really about whether you "like" the axiom of choice. The axiom of choice is true. This I claim is self-evident, once you understand the objects whose behavior the axioms are intended to describe (the ones that appear in the von Neumann hierarchy, where the taking of subsets at the successor stages is done lawlessly).

As for having all sets of reals measurable, you have all you're likely to need of that: All sets of reals that appear in L(R) are measurable, and that's includes all the ones you're likely to encounter "explicitly" whatever that means. This claim is not provable in ZFC alone, but it follows from sufficient large cardinals. The existence of the large cardinals is not self-evident, but it has become clear, in a semi-empirical fashion, that it is true. --Trovatore (talk) 22:14, 20 January 2009 (UTC)

Those who enjoy erudite disputes will always find something to appreciate at WT:WPM. EdJohnston (talk) 22:16, 20 January 2009 (UTC)

I don't see "fun" in the title. :) --PST 22:28, 20 January 2009 (UTC)

LOL. I hope Trovatore's tongue was as firmly planted in his cheek as mine was in mine. Of course such erudite disputes should strictly be banned here as they have nothing to do with improving the encyclopedia. But my, they are at least more fun than arguing over notation or the latest AfD :-) Geometry guy 22:33, 20 January 2009 (UTC)

I was 100% serious. If you take a realist approach to sets, and understand which sets are intended, the axiom of choice is self-evidently true. --Trovatore (talk) 22:36, 20 January 2009 (UTC)

That's surely one viewpoint. Luckily I don't work in set theory or logic or category theory (neither did Grothendieck) so these things tend to make me smile rather than frown seriously. If you believe the real numbers can be well-ordered, that is fine by me. In your preferred model of ZF, they can be. But so what? Geometry guy 22:46, 20 January 2009 (UTC)

Well, the point is that "my" preferred model is the intended one, the one that takes all subsets at each stage. The only way you can make the reals non-wellorderable is to leave out some sets of reals (well, sets of sets of naturals) when you're forming V_ω+2. --Trovatore (talk) 23:00, 20 January 2009 (UTC)

(←) Hey cool, we find our way back to policy. "At each stage"? According to whom? And what interpretation of "stage"? "The only way" according to whom? "Intended model" according to whom?

No viewpoint has a right to hegemony or even undue influence on Wikipedia. There are plenty who believe that set-theoretic foundations and questions such as these are entirely the wrong approach, but there are others who dedicate their lives to resolving them. So we must try our best to keep our personal prejudices to one side, and report on what reliable sources say, with due weight. </boring> Geometry guy 23:33, 20 January 2009 (UTC)

As always, you are right Geometry guy. Except for factors of one-half. Then you're usually wrong. siℓℓy rabbit (talk) 23:51, 20 January 2009 (UTC)

Hey you must know me IRL! But don't forget the minus signs. Minus signs and factors of 1/2. Yup I'm wrong almost every time on those... :-) Geometry guy 00:27, 21 January 2009 (UTC)

OK, gg, you're conflating two things here. Of course, from a WP point of view, the realist viewpoint must be accorded its due weight, neither more nor less. No one is arguing about that. With respect to claims that go into article space, "who says so?" is an entirely appropriate question.

However, from the realist viewpoint, there is no ambiguity about the interpretation of stages. Each successor stage is supposed to consist of all subsets of the preceding one. If you have two (wellfounded) models, just find the first rank where they differ. If model M contains a subset of the preceding rank that model N omits, then model N is wrong, period. That doesn't mean model M is completely right; it might omit other subsets, but at least it's right about that one.

Following this reasoning, you can see that if V_ω+2 exists at all, then it is unique (up to a unique isomorphism), and therefore (for example) the continuum hypothesis is either really true or really false, even if we don't currently know which (and quite plausibly may never know). This was first pointed out by Ernst Zermelo. --Trovatore (talk) 00:57, 21 January 2009 (UTC)

Who is gg? And who defines what are "all subsets"? What rules are allowed to select elements from a set and call it a subset? Geometry guy 01:13, 21 January 2009 (UTC)

You don't need rules at all — that's what I was pointing out earlier. The subsets are taken lawlessly. All of them are taken lawlessly, even the ones that turn out, after the fact, to obey some law.

For example, when picking subsets of the naturals, you start through the natural numbers and start throwing some into your subset and some not, completely at whim. At the end, it may turn out, just by coincidence, that you happened to pick all the even ones, and none of the odd ones, and therefore the set of all even naturals gets into the next stage. But it doesn't get into that stage because it happens to satisfy a law. --Trovatore (talk) 01:18, 21 January 2009 (UTC)

Sounds suspiciously like second order logic to me, but whatever, I'm not a logician. Even with laws, the set of well-orderings of the reals is already an interesting example. It's a subset of something, but what subset? Geometry guy 01:27, 21 January 2009 (UTC)

(ec) And it sounds also like a presumption of choice. Any subset is okay. Even among an uncountably infinite set of pairs of socks there is a subset containing one sock from each pair. It is no wonder you believe the axiom of choice is true: it is built into your model. I'm agnostic about this question or perhaps better, my answer is: mu. Geometry guy 01:58, 21 January 2009 (UTC)

The point is that your mu position is incompatible with a realist conception of sets. If one accepts sets as real, that it becomes impossible to be indifferent to the axiom of choice (it's a well-defined question about real objects, so it must have an answer), and very difficult to avoid Trovatore's conclusion that it is obviously true. Algebraist 02:07, 21 January 2009 (UTC)

A naive question: this view of set theory tells you when something isn't the right model: when it is non-maximal, because some other model includes a set that it doesn't. But why should I be convinced that there exists any maximal model? Maybe there are plenty of models but they are all non-maximal? —David Eppstein (talk) 01:51, 21 January 2009 (UTC)

Yes, a priori, that could be. But would imply that the powerset axiom is false. I view the powerset axiom as something like a conjecture in Popper's sense — potentially falsifiable, has not been falsified, gives us useful information about the world — and so, taking a quasi-empiricist epistemological position I consider it true. --Trovatore (talk) 02:09, 21 January 2009 (UTC)

Well actually the powerset axiom is the beast isn't it? What is the set of all subsets when there is uncertainty about what a subset is? This axiom not only raises questions about the axiom of choice, but also the continuum hypothosis. Geometry guy 02:17, 21 January 2009 (UTC)

But there is nothing uncertain about what a subset is. --Trovatore (talk) 02:20, 21 January 2009 (UTC)

What are the subsets of the real numbers? Geometry guy 02:26, 21 January 2009 (UTC)

The subsets of the real numbers are those sets whose every element is a real number. What is "uncertain" about this? --Trovatore (talk) 02:36, 21 January 2009 (UTC)

There is some ambiguity about the collection of "all" subsets in first order logic, though. — Carl (CBM · talk) 02:28, 21 January 2009 (UTC)

But why do you want to limit yourself to first-order logic? --Trovatore (talk) 02:36, 21 January 2009 (UTC)

I'm sure you're familiar with the literature on that. — Carl (CBM · talk) 02:39, 21 January 2009 (UTC)

The issue of there being no maximal model was also discussed by Zermelo. The issue is not so much with V_α for any particular α, but with the issue that given any model of ZF the set of all ordinals in it is again an ordinal, suggesting that the model is just an initial segment of some larger model. Indeed, the potential axiom "every model of set theory is embeddable as a countable submodel of another model of set theory" has some aesthetic appeal to me.

Trovatore, I was just reading Maddy's "Mathematical Existence" and I'd be curious to know your personal take on "thin realism", maybe on my talk page. — Carl (CBM · talk) 02:28, 21 January 2009 (UTC)

Back to the nonstandard analysis... I did not say that the choice axiom is wrong in my favorite universe of sets. Rather, for me a proof via the choice axiom is considerably less illuminating than a choice-free proof (if exists, of course; and countable dependent choice is OK, of course). This is why I prefer to prove uniform continuity of a continuous function on [0,1] without nonstandard analysis. Boris Tsirelson (talk) 07:52, 21 January 2009 (UTC)

Whatever about non-standard or standard analysis I think the bit about limits in the article is unnecessary. What follows about differential and integral calculus describes the subject much better. Talking about limits just distracts as it is a general part of analysis and applicable to much more than calculus. And on the other hand whereas limits are I feel by far the best way to introduce calculus they really don't come into the subject much in a practical sense. Just because someone is banging a drum doesn't mean he is wrong in all circumstances. Dmcq (talk) 09:42, 21 January 2009 (UTC)

I do think it is necessary to discuss limits in the article, and I think mentioning them in the lead paragraph is appropriate. While limit proofs don't come into the subject much in a practical sense, I do think that limits do enter the subject early and often. Thenub314 (talk) 10:39, 21 January 2009 (UTC)

Percussive folks might like to work on Non-standard calculus which needs a lot of work. Not clear in intro which century the work is in. Lots of one sentence paragraphs and very bitty presentation. I could not find out from the article why the axiom of choice was important for the NSA. Also there seems to be a need for Category:Non-standard analysis.--Salix (talk): 10:40, 21 January 2009 (UTC)

Calculus just isn't about limits. The sentences saying it is about instantaneous change and areas is much closer to the mark. Calculus led to analysis because of the need to prove results rigorously and analysis with limits is now a huge subject in its own right. Non-standard analysis is another way of dealing with limits. Limits are a tool for proving results in calculus but the first statement is like saying number theory depends critically on the concept of sequence. Dmcq (talk) 11:25, 21 January 2009 (UTC)

I see your position better now. I tend to think of calculus as a small part of real analysis, comprising limits, derivatives, integrals, and applications, rather than a separate subject from real analysis. I often tell students that the thing which separates analysis from algebra is its focus on approximation and limits. — Carl (CBM · talk) 12:51, 21 January 2009 (UTC)

I tend to disagree that calculus isn't about limits. To defend my point of view let me mention that when I look at the calculus books I have had to teach from they have statements like "We could begin by saying that limits are important in calculus, but that would be a major understatement. … Every single notion of calculus is a limit in one sense or another." and "The concept of limit is surely the most important, and probably the most difficult one in all of calculus." Further Google searches also reveal several books about calculus which describe limits as central to the subject of calculus. For these reasons, I stick by the first sentence of my previous comment. Thenub314 (talk) 14:57, 21 January 2009 (UTC)

Combinatorial map and Generalized map

These two articles are in an unsatisfactory state. They look as if they could probably be phrased in such a way that any mathematician could understand them. But the author seems to assume knowledge of some related topics that most mathematicians don't have, and seems to lack knowledge of some things that most mathematicians know. I doubt that the person who wrote these two article can do what needs to be done, and I could do it only with more work than I'm going to put into it today or this week. Michael Hardy (talk) 18:23, 19 January 2009 (UTC)

I agree. From what I can make out, both articles are on the subject of topological graph theory (I have really only used graph theory in the context of algebraic topology). Combinatorics is not my strong point but I agree that it is certainly not easy to understand (too many complex terms). --PST 20:39, 19 January 2009 (UTC)

The dread words data structure suggest that the author is a computer scientist, which would account for Michael Hardy's observation. (I'll have my saucer of milk now, please, like a good cat.) Septentrionalis PMAnderson 02:23, 27 January 2009 (UTC)

I are an expert both in data structures and in topological graph theory, and I don't find the article very intelligible either. When I tried to read it I got the strong impression it referred to the same thing as a rotation system, one of the ways of encoding embedding graphs on two-manifolds, and I'm still pretty sure that's what the bulk of the article is about. But the author removed my {{mergeto}} tag, assuring me it actually referred to higher dimensional things as well, as the "general definition" section claims but never clearly describes. As for "generalized map" it seems to be a copy of only that section, making the signal-to-noise ratio even worse. —David Eppstein (talk) 02:32, 27 January 2009 (UTC)

List of topics named after Bernhard Riemann

I've created a new page titled List of topics named after Bernhard Riemann. It is of course incomplete. Please help expand it by doing two things:

• Add topics you know of that are not there.
• Add topics you can find by a systematic search of Wikipedia that are not there.

Michael Hardy (talk) 01:08, 22 January 2009 (UTC)

I've added all the wikipedia articles with Riemann in the title or in a section title that refer to a topic named after Riemann. Also added some redlinks from Google. Now somebody needs to turn the redlinks blue. Charvest (talk) 14:35, 22 January 2009 (UTC)

World Mathematics Challenge

World Mathematics Challenge is up for deletion as a possible hoax. Ben MacDui 19:43, 27 January 2009 (UTC)

Deletion proposal

See Complex argument (continued fraction) and Talk:Complex argument (continued fraction). A "prod" tag proposes deletion. The article is very clearly and cleanly written and that's quite unusual for dubious material. Michael Hardy (talk) 03:02, 20 January 2009 (UTC)

It seems to me that, assuming that there are sufficient references for the continued fraction definition of the argument function, the tag should be a proposed merge instead of a proposed deletion. However, the title is not a likely search term, so maybe a merge + delete redirect would be appropriate. — Carl (CBM · talk) 03:14, 20 January 2009 (UTC)

Sorry for not doing this myself before it was deleted, but can someone please make that article available for me to copy into userspace? It wasn't mine originally, I just wanted to check it out. Cheers, Ben (talk) 07:51, 23 January 2009 (UTC)

OK done at User:Ben Tillman/Complex argument (continued fraction). --Salix (talk): 10:19, 23 January 2009 (UTC)

Thanks Salix. Cheers, Ben (talk) 11:14, 23 January 2009 (UTC)

Did the continued fraction get merged into some other article? Michael Hardy (talk) 21:31, 31 January 2009 (UTC)

Carol number

Carol number has been nominated for deletion. Gandalf61 (talk) 11:53, 28 January 2009 (UTC)