Wikipedia talk:WikiProject Mathematics/Archive/2007/Jun

Topologists, help wanted at neighbourhood (mathematics)
Sorry to bring this up again, but two of us disagree rather strongly on whether one should define first the neighbourhood of a point, or the neighbourhood of a set, with no compromise in sight.

While the issue may be trivial, the concept of neighbourhood is important enough in mathematics, that perhaps more people should get involved. The discussion is at Talk:Neighbourhood (mathematics). Thanks. Oleg Alexandrov (talk) 01:46, 1 June 2007 (UTC)

Orphan talk page
Why does Template talk:Numerical algorithms exist when its template does not? JRSpriggs 08:18, 1 June 2007 (UTC)
 * Admin error! I have fixed it. There is an archived discussion concerning the former template here. Physchim62 (talk) 08:55, 1 June 2007 (UTC)
 * Sorry, I forgot to delete it. Oleg Alexandrov (talk) 15:39, 1 June 2007 (UTC)
 * JRSpriggs probably knows about this already, but for those who don't: you can use db-talk to tag a talk page whose main article is deleted, to have the talk page deleted as well. There is a list of these templates at Template:Deletiontools. CMummert · talk 16:31, 1 June 2007 (UTC)
 * Thanks to Physchim62 for fixing the problem. Thanks to CMummert for the pointer to Deletiontools; I was not aware of it. However, I probably would not have used the "db-talk" template in this case because I had forgotten that the template was deleted (not paying enough attention); so I did not know why the talk page was there without a template. I do not necessarily think that leaving the talk page for a little while after the article is gone is a bad idea, but there should be some indication on it of what happened to the article and that the talk page will be deleted eventually. JRSpriggs 07:22, 2 June 2007 (UTC)
 * There's always admin discretion to leave a talk page when the main article has been deleted, but usually such situations are simple errors (admins are only human, after all!). Thanks for bringing it to people's attention. Physchim62 (talk) 12:50, 2 June 2007 (UTC)

Zero
I have been going through the Z articles, and I have found quite a few stubs in the zero section, Zero_ideal, Zero_set, Zero_tensor, Zerosumfree_monoid, Zero_matrix, Zero_module, Zero_order. Is there any way we can unify these articles in a meaningful way. As it stands I don't see these articles growing all that much. Perhaps we could create something along the lines of the List of prime numbers article. Maybe "List of mathematics terms that include zero".--Cronholm144 05:50, 2 June 2007 (UTC)

I will take the silence as a "go for it C" and create something in my sandbox :) --Cronholm144 18:15, 2 June 2007 (UTC)


 * Zero set clearly has potential to be expanded into a solid article; Zero order may have as well, and I would give Zerosumfree monoid the chance to flourish or perish on its own merits (a redirect might be more appropriate). The other four articles are all zero elements/objects in one way or another, and there isn't much one can say about them individually. There may indeed be scope here for a list, or other unifying article, on such zero objects: in which case, "go for it C"!

Done List_of_zero_terms with redirects in place. I didn't redirect Zero matirx, just relisted it. Now all of the horribly weak stubs can grow together in one place. Feel free to move the page to a better name, just be sure to warn me so I can reset the redirects to the appropriate locations--Cronholm144 18:46, 2 June 2007 (UTC)

BibTex for Wikipedia?
It often happens to me that I want to include a reference to, say, Hartshorne's book "Algebraic Geometry". It is somewhat annoying to always look for it at some page where the reference already is. Is this only a problem / issue of mine or do also other people wish there would be a BibTex-like system on Wikipedia? In the simplest case it would be a page including references to (at least) major math books. It might look like

Jakob.scholbach 17:35, 30 May 2007 (UTC)

PS. Of course, much more helpful would be a mechanism generating the above reference by something like . Jakob.scholbach 17:47, 30 May 2007 (UTC)


 * If you have the ISBN, you can use the Wikipedia template filling tool referenced at WikiProject_Mathematics/Reference resources. For ISBN 0-387-90244-9 it produces  , which displays as:
 * --Lambiam Talk 20:41, 30 May 2007 (UTC)
 * --Lambiam Talk 20:41, 30 May 2007 (UTC)


 * If Wikipedia as a whole does not keep a database, at least WikiProject Mathematics could. (I note with interest that another — more focused — wiki has adopted a scheme of giving each citation its own page.) It would be very nice to have a list, for several reasons.
 * citation data would be easier to find
 * corrections and additions could benefit everyone
 * conventions and standards might be easier
 * I have proposed this in the past, but encountered an apparent lack of enthusiasm. Also, what is involved in creating and maintaining the data, can we do better than cut-and-paste to use it, and who will do the work? --KSmrqT 04:09, 1 June 2007 (UTC)
 * It is not hard to parse all the math articles and extract all citations in a list. I don't know if it is worth the trouble though, the Wikipedia template filling tool mentioned above does a decent job I think. Oleg Alexandrov (talk) 04:12, 1 June 2007 (UTC)
 * The template filling tool is nice to have in our arsenal, but is rather limited. First, it requires an ISBN for a book, and does not accept ISBN-13. So I tried it on a real example, ISBN 0-875-48170-1, and got the following


 * I deliberately used an improperly hyphenated ISBN (it should be ISBN 0-87548-170-1), and got the same back. The citation I had actually used in the article splits the two authors, splits first and last names for both, links the first author, provides a URL to an on-line copy of the work, links the publisher, provides a correctly hyphenated ISBN-13, and supports automatic linking from a Harvard-style reference in the text.
 * I deliberately used an improperly hyphenated ISBN (it should be ISBN 0-87548-170-1), and got the same back. The citation I had actually used in the article splits the two authors, splits first and last names for both, links the first author, provides a URL to an on-line copy of the work, links the publisher, provides a correctly hyphenated ISBN-13, and supports automatic linking from a Harvard-style reference in the text.


 * There is a substantial difference in favor of the latter. And how am I supposed to come up with the following (from the same article)?
 * There is a substantial difference in favor of the latter. And how am I supposed to come up with the following (from the same article)?


 * No ISBN applies, and I have no ID number; and even if I did, the tool will not provide that marvelous URL. --KSmrqT 05:26, 1 June 2007 (UTC)
 * No ISBN applies, and I have no ID number; and even if I did, the tool will not provide that marvelous URL. --KSmrqT 05:26, 1 June 2007 (UTC)


 * I think it could be useful. I have a file with half a dozen of references I use quite often. Something similar is at User:Shotwell/Standard references. I'm not so sure whether it's worth the effort for journal articles, but who knows. We can always set something up and see whether people will use it. It would be nice if we could use it in a more intelligent way than copy-paste, but I'm not sure that's possible. I would however be against extracting all the citations from articles; by doing it by hand we have some quality control. -- Jitse Niesen (talk) 15:37, 1 June 2007 (UTC)


 * Bear in mind that each editor should cite the particular version of a source they used: so if you have a different edition of a book from another editor, you should use a citation for that edition (with the ISBN from your copy of the book) rather than just reusing the other editor's citation unmodified. This is less of an issue for journal articles (in that fewer have such multiple versions), but citations of those are also likely to be less widely reused.


 * Another question with reusable citations: when should links to authors (or journals, etc.) be included in them? Policy on links would suggest that a particular author should be linked just once in the references for an article; reuse would suggest that the citation shouldn't depend on the article it's being used in, so all or none (with a given author) should link to the author. Joseph Myers 18:36, 1 June 2007 (UTC)

So, I understand that there is some interest in a Wikiproject-wide list of references. I'm willing to put some effort into it, but I don't know the inner mechanisms of Wikipedia. Is it possible to create and maintain etc. a database inside Wikipedia? Otherwise I would volunteer to set up some reference database outside WP which can be edited by everybody. A mere list of references is a nice thing, but is still kind of a hassle to manually look for the item one needs, especially when the lists grows bigger and bigger as everybody adds his favourite references. It is probably also unefficient because everytime the whole list has to be saved when someone adds a new entry. The advantage, pointed out by KMSrq, of including an URL is definitely something we should not miss, because giving an URL is (at least for me personally) practically more important than the volume no. and the journal's name, at least until one is actually writing a paper and needs the paper-reference, but then good old BibTex does the job anyway. Besides the URL of the paper or book (if there is one) it would also be nice to allow the URL of a review, for example like on MathScinet. Concerning Joseph's remarks: different editions of a book are no particular problem, I guess, they should just be listed as different database entries. Whether to give a wikilink to the author's page or not might be decided by the user by checking or unchecking some checkbox "wikilink the author(s)" etc. Jakob.scholbach 17:30, 3 June 2007 (UTC)

New month, new collaboration
Hey everyone, It's June first and you know what that means... A new Mathematics Collaboration of the Month! The victor, by an overwhelming margin of 3 votes, is Integral. Everyone here should be able to contribute on this one (no excuses this time!). With a little polish and elbow grease, this article will be at A class in no time at all. See you there--Cronholm144 06:21, 1 June 2007 (UTC)


 * I am not in the habit of participating in these events; few are. However, I'd like to put in a special request for "integral". If this esteemed assemblage of editors could just briefly stop by the page and skim it (it's quite short), then leave feeling embarrassed at the poor state of such a key article, that would be progress. If you feel like a minor edit, or perhaps an observation on the talk page, that would be better still.
 * Unlike Cronholm144, I've been around long enough to know that topics like this (as described below) are a huge challenge. It is a gateway topic, visible to far more readers than an expert topic like Poincaré duality. It is one of the deepest topics in mathematics, with massive amounts of material to tap. Many editors will have encountered integrals in a simplistic way, and think they know more than they really do. And the topic can be introduced and organized in many ways, with each editor drawing on different taste and training. It scares me.
 * That said, integral is so weak that even a little effort could make a visible difference.
 * So, please, take a few minutes of your time and have a look, and perhaps give it a nudge towards improvement. Thanks. --KSmrqT 07:03, 3 June 2007 (UTC)


 * I'd like to reiterate my suggestions for facilitating the collaboration by proceeding in phases:
 * Phase 1 is like a peer review, in which we identify what the problems with the current version are.
 * Phase 2 is a discussion phase in which we reach consensus on the target: what are (and what are not) problems and what to do about them.
 * Phase 3 is implementing this.
 * --Lambiam Talk 08:21, 3 June 2007 (UTC)

Flagged revisions (stable versions)
There is a proposed policy at Flagged revisions about stable versions. The idea is that some pages would be "flagged" and then the flagged version would be shown by default to users who aren't logged in. This has obvious implications for vandalism fighting and quality control.

This has been in development for years, but now the code is apparently finished modulo final approval. Although it is still not certain that flagged versions will be enabled on en.wikipedia.org, the proposal is an attempt to determine some community consensus on the issue. &mdash; Carl (CBM · talk) 17:40, 3 June 2007 (UTC)

ratings
User:Geometry guy is perhaps the most prolific assigner of "ratings" on math article talk pages. He ranke deformation theory as of "mid" importance and degrees of freedom (statistics) as low. Is there some standard according to which that is not idiotic? (I'd have said "low" for the former and "high" for the latter. And "high" for any other topic that, like this one, is covered every statistics course from kindergarten through Ph.D.-level.) Has anyone attempted to codify standards for these ratings? Michael Hardy 22:35, 1 June 2007 (UTC)

OK, at WikiProject Mathematics/Wikipedia 1.0/Assessment it says "low" means "Subject is peripheral knowledge, possibly trivial." By that standard, ranking degrees of freedom (statistics) as "low" is profoundly illiterate. Nothing kinder can be said about it. Michael Hardy 22:38, 1 June 2007 (UTC)


 * I have occasionally come across ratings I didn't agree with, and adjusted them accordingly. For example (if I recall correctly), measure theory and harmonic analysis were also low.  Real analysis and complex analysis were mid (should have been top).  And so on.  It might do to cruise through the ratings from time to time and see if there are any eyesores.  I think that, rather than a codified standard, it seems to be a free-for-all in which the ratings reach a sort of equilibrium value.  During some discussion, unrelated to the present one, G.Guy brought up an analogy with simulated annealing, which seems to be apt for the rating system as a whole.


 * By the way, I have been assigned the task of putting together an FAQ on the subject of ratings. So far, I've completely procrastinated, but now might be a good time to get it up and running.  Silly rabbit 22:44, 1 June 2007 (UTC)


 * OK, here's a counterexample, Michael. I'm going to say something kinder about it. Geometry guy is working very hard to provide a summary page where the rest of us can consult ratings vs. importance, grouped by broad subject areas. I think he's doing a great job, that everybody is human, that mistakes are inevitable, and that we will foster a better spirit of community by helping each other out than by spewing venom on this talk page.
 * At least I think that's a counterexample. I might be wrong, though – I've been characterized as a troglodyte in this venue before today, and I suppose it may happen again. ;^>  DavidCBryant 22:55, 1 June 2007 (UTC)

Hello all, thank you for your comments. I am attempting to do two things simultaneously right now. The first is to make up for the patchy coverage of the maths rating scheme by attaching maths ratings to approximately 1/3 of the 15000 articles in the List of mathematics articles. The second is to try and refine and understand what importance ratings are for, and how to assess them. These two processes feed into each other.

Importance ratings are always going to be subjective and will fluctuate, but the goal of the second task is to reduce this subjectivity and fluctuation. In the meantime, however, the first task is flawed in many ways: first, I (and others who join me in this effort) will make subjective judgements; second, we will make mistakes; third, the criteria on which these judgements are made have not yet been fully elucidated. I can only ask others to have patience, and also bear in mind that this is a wiki: anyone can fix or update a maths rating. I am saddened by how the harder I work, the more complaints I receive on my talk page. No one needs to complain: just fix the rating.

Importance seems to cause more trouble than anything else. I am beginning to wonder if it should be renamed "priority" (which is the term used by some other WikiProjects): it is not about how important a subject is, but how high a priority it is for us to have a good article on the subject (in the context of related articles.) This does not mean that there will be fewer mistakes, only (I hope) that editors will be less upset by them. Anyway, I think that the word "priority" should at least be mentioned much more in our assessment pages. Recent experiences only serve to reinforce my opinion that the terms "peripheral" and "trivial" should be eliminated as soon as possible from the summary of the low-priority rating. (These words are not actually part of the WP 1.0 scheme, which uses the term "specialist" instead, although this is problematic as well.) I will try to fix this tomorrow.

In the meantime, bear in mind that there is a lower importance rating than "low": unrated. If you know an article which has not been rated which you think should be, please rate it. So far, I have got as far as Dei, so if your favourite article comes before this in the alphabet, don't come to my talk page to complain: assess it! Best wishes to all... Geometry guy 00:09, 2 June 2007 (UTC)


 * I agree with DavidCBryant that Geometry guy is making substantial contributions. When I was saying nothing kinder could be said I was speaking ONLY of that one rating of that one article.
 * I suspect Geometry guy is seriously confused about the content of statistics, and maybe also about its importance. Michael Hardy 00:37, 2 June 2007 (UTC)
 * I suspect Geometry guy is seriously confused about the content of statistics, and maybe also about its importance. Michael Hardy 00:37, 2 June 2007 (UTC)


 * Sadly very few statistics articles have been given maths ratings so far: the subject really needs a champion to go through and assess them. The maths ratings project has been active for quite some time now (at least six months), but even a month ago, there were only 29 assessed probability and statistics articles; now there are 147. This five-fold increase is largely a result of my efforts: I hope this shows I am aware of the importance of statistics, even if I am confused by its content!
 * As I mentioned above, there is a lower importance/priority rating than "low", which is "unrated" (the bottom 2/3rds, in my view). I've had to skip over many stats articles for lack of expertise: if I were a statistician, I would be more up-in-arms for the stats article that remain unrated than for the ones whose rating is wrong. The ones to which I have added a rating are the ones I thought desperately needed to be put "on the map" for others to rate more accurately.
 * Anyway, in case it is any reassurance, most of the articles I am skipping over right now, with no rating, are obscure irregular polygons (sometimes in five dimensional space!). You wouldn't believe just how much of this kind of stuff there is! Geometry guy 01:05, 2 June 2007 (UTC)
 * I strongly believe that comments above involving the word 'idiotic' should be retracted. I would like to express support and highly praise Geometry guy for undertaking an incredibly difficult task of rating broad swaths of articles (literally, thousands). In addition to that, he and others have written rather extensively on the criteria used in ratings on this talk page, although some of the discussion is now archived. It was no sneaky action on his part, as one might erroneously infer from Michael Hardy's comment in the beginning. The unfortunate part is that we did not reach a consensus on what terms should be used for rating importance, and did not establish the clear criteria to be used (of course, individual application of any criteria will always remain subjective). In my opinion, this happened not because of any deep disagreement (indeed, most of the proposals were very close), but due to the general lack of interest to codifying the results of the discussion. As a consequence, there are now multiple attempts to adjust the ratings based on a whole slew of criteria, from the discredited and obsolete four levels to multiple interpretations of the alternative schemes that were discussed, and additionally, the adjustments that are not based on anything save highly opinionated personal choices. I feel that it's TOP PRIORITY to establish at least a draft of reasonable rating scheme that can be used as a reference.


 * Mid for Deformation theory is correct, in my opinion. I am not a statistitian, but in my classes from kindergarten through the university level, degrees of freedom (statistics) did not establish notability on a par with Euclidean geometry, Fractal, or Riemann sphere, to quote the first three high importance rated articles in the field of geometry. The article itself does not make for an easy determination of the importance (regardless of how you might define importance). As I have pointed out earlier in a discussion of ratings, it is difficult to rate undeveloped (start/stub class) or messy aricles in context and especially for a non-expert. Subjective judgements and even mistakes are inevitable, and we would all benefit from restraint in descriptions of others' contributions, be they posted on this page, talk pages, or as summary of edits. In this I wholeheartedly agree with DavidCBryant's comment above.


 * Let me repeat some earlier remarks that we should keep in mind one of the main goals of the rating enterprise: to facilitate improvement of mathematics part of Wikipedia, by identifying the key areas needing improvement and matching limited editing resources with a multitude of articles that compete for our attention. It is emphatically not an endorsement of the absolute importance of the subject of the article for mathematics as a whole, or our beloved special area! Having said this, I'd like to point out the fairly broad agreement in previous discussions that only a few articles be rated top importance and relative limited numbered high importance. I mention this, because Silly rabbit has increased importance ratings in many cases that were a lot less compelling than Real analysis, creating an impression that any important topic he would like to put into top and high classes. Hopefully, the newest Geometry guy's thoughts on the rating scheme can serve as a basis of a good rating scheme that we can all agree upon. Arcfrk 01:19, 2 June 2007 (UTC)


 * Has there been some discussion on my recent upgrades that I was unaware of Arcfrk? The only case anyone bothered to bring to my attention was image (mathematics), which I promptly downrated from high to mid, favoring the isomorphism theorem for high instead.  This, I hope, is significant enough that we can all agree belongs in high.  Similar upgrades to asymptotic analysis, character theory, representation theory.  I didn't think these would be at all controversial, but since it's clear you don't want other editors adjusting the ratings, I'll refrain.  I'll just revert my ratings and let someone else handle it.  BTW:  Maybe you could write the FAQ, too. Silly rabbit 01:50, 2 June 2007 (UTC)

I am grateful to all for both supportive and critical comments. I would emphasise that anyone can adjust ratings. It can be a thankless task sometimes, but please don't be discouraged by disagreement! I have been trying to build on the discussions held here previously to improve the importance page and hence provide better guidance for these ratings, but it is still work in progress. I am acutely aware that this is a high priority, and I will try and push it forward later today. Geometry guy 02:13, 2 June 2007 (UTC)


 * I expect the importance of an article to be highly correlated with the number of articles linking to it (not counting "List of ..." articles and redirect or disambiguation pages). For Deformation theory I count 17 linking articles, and for Degrees of freedom (statistics) 41. Is it possible to collect this information automatically, for a sanity check of already rated articles and also for checking if some important articles failed to get an importance rating? --Lambiam Talk  08:39, 3 June 2007 (UTC)
 * I see such a list exists already: User:Mathbot/Most linked math articles. --Lambiam Talk  08:44, 3 June 2007 (UTC)


 * One of the approaches taken by Cronholm and me for adding maths ratings (following Oleg's suggestion) is to go down this list from the top. However, the correlation of this statistic with importance/priority is not entirely reliable for several reasons. First it tends to overrate articles of a more general rather than specialist nature. Second, it can be inflated by links between similar articles: see for instance the articles on polyhedra and tilings. Third it tends to underrate articles in poorly developed areas of the maths project, which are often the areas which most need our support and further development.


 * Furthermore, I strongly believe that articles should be assessed in the context of related articles. It doesn't make a lot of sense to compare Deformation theory and Degrees of freedom (statistics). The former seems firmly Mid to me, in comparison with related articles. I clearly slipped up rating the latter as Low, as it is certainly in the Mid-High range, not because it is "more important than deformation theory", but in the context of other statistics topics. Geometry guy 13:42, 3 June 2007 (UTC)

One difficulty with statistics is that coverage is feeble by comparison to most math topics. One can readily imagine 30 or 40 articles in a list of topics related to degrees of freedom in statistics, but they're not there. Similarly analysis of variance is a vast topic on which one could write several thick volumes, but the article is pretty stubby. Michael Hardy 01:06, 4 June 2007 (UTC)

Help with article in "unconventional computation"
The article Non Universality in Computation has come to my attention. While the papers by Selim Akl that it cites don't appear to be completely incorrect, they are not actually reflective of classical computability theory because they place restrictions on the models of computation that are not permitted in the standard theory of computability. In particular, the papers assume some sort of time scale such that "computers" must complete calculations in a certain number of steps, which is incompatible with the standard definitions.

So while the articles are not completely incorrect, some of the claims that Akl makes are not correct, or overstated at least, and these claims are repeated in the WP article. The claims were also added to the Turing machine article, but someone else removed them.

I think that there is a place on WP for this information, once it has been rephrased to use standard terminology. But the article as it stands is likely to leave readers with false impressions.

I have asked the author of the WP article, User:Ewakened, to comment here, and I would appreciate hearing other opinions on the matter. CMummert · talk 23:12, 29 May 2007 (UTC)


 * The first cited paper by Aki (that the article is based on) seems to argue quite reasonably that the standard model of computability is not adequate. But there are some unfortunate confusing statements in the introduction that sound like they try to provide a counterexample to universality (in the classical sense) of the Turing machine. This is what went into the WP article. It becomes clearer later on in the paper that the author understands universality differently and basically searches for its meaning by a series of examples. In my opinion, not notable. Jmath666 07:36, 4 June 2007 (UTC)

Name change: CMummert &rarr; CBM
My username was recently changed from CMummert to CBM (log). This change will be seen in page histories and your watchlist, if my user pages are on it. &mdash; Carl (CBM · talk) 14:32, 4 June 2007 (UTC)

Normal set on AfD
Prod had expired; de-prodded. --Trovatore 03:54, 5 June 2007 (UTC)

Cofactor expansion
After viewing the Determinant article I was surprised to see that cofactor expansion (obviously one method for determining the determinant of a square matrix) doesn't have an article nor does it even serve as a redirect. I thought that I should bring it to the attention of the Wikiproject.--Jersey Devil 20:28, 2 June 2007 (UTC)


 * I guess I'll eat the bullet on this one. I'll create the stub tonight.--Cronholm144 07:34, 3 June 2007 (UTC)
 * P.S. In my sandbox, I hate to put unfinished work onto the mainspace.


 * I'm puzzled; is there something we want to say about cofactor expansion that does not belong in the determinant article? --KSmrqT 11:26, 3 June 2007 (UTC)


 * Me too ;) Is this really the same KSmrq who recently said to me "For those of us using popups, articles with definitions — even brief ones — are appreciated." ? :) Geometry guy 13:58, 3 June 2007 (UTC)
 * Yes, and I'm being consistent. For a definition only relevant in one place, it's better to include the definition in that article. For an extreme example, look at eigenvalue and eigenvector. --KSmrqT 18:50, 3 June 2007 (UTC)


 * A redirect  #REDIRECT Determinant  ought to have been fine here. The problem is that the Determinant article uses the term, but fails to explain it; and neither does our article Minor (linear algebra), which defines "cofactor" but not "cofactor expansion". The article in statu nascendi at User:Cronholm144/Cofactor expansion should perhaps more properly be called "Cofactor (mathematics)" and could, in finished form, replace the current redirect page of that name (now redirecting to Minor (linear algebra)), with Cofactor expansion being a redirect to Cofactor (mathematics). However, I wonder if it is not better to merge the sandbox article into the existing Minor (linear algebra) article. --Lambiam Talk  14:18, 3 June 2007 (UTC)


 * Midway through the writing I realized the same thing and changed my article's focus to the general cofactor. I am still writing. I think I will withhold my own judgment on the merge (which is valid, but the articles have different aims at the moment) until I finish. --Cronholm144 14:40, 3 June 2007 (UTC)

Is the Cofactor expansion not the same thing as the Laplace expansion ? Jheald 15:29, 3 June 2007 (UTC)


 * It certainly appears to be doesn't it. :) It certainly looks like there are going to be an interesting set of mergers once I get done. As it stands now I think the redirect for C exp. should definitely go to L exp.--Cronholm144 15:49, 3 June 2007 (UTC)


 * Well, considering none of us thought to look for it under Laplace expansion, maybe the redirect would be better Laplace exp -> Cofactor exp. But yes, it looks like this whole group of articles could use some merging/refactoring, so it's a good thing you're on the case. Jheald 16:02, 3 June 2007 (UTC)


 * And we did not read through to the end, because Laplace expansion is mentioned there, and explained as well. It is stated to be efficient for small n. All methods are efficient for small n, but isn't it rather very inefficient for large n? Or is there some clever trick to obtain the cofactor expansion in substantially fewer than n! operations? --Lambiam Talk  16:38, 3 June 2007 (UTC)


 * If you read even further down, at Determinant, you'll learn the answer ;) However, I think that it doesn't happen that often in practice that you want to compute the determinant of a large matrix. -- Jitse Niesen (talk) 19:15, 3 June 2007 (UTC)
 * I know that the "obvious" way of using Laplace expansion to compute determinants, computing the determinants of the minors recursively with the same method, requires on the order of n! steps (obviously). I also know that there are more efficient methods that do not use Laplace expansion. Using the "naive" method of Laplace expansion, in total floor((e−1)n!) times a determinant is computed, one for the whole matrix, the others for minors, minors of minors, and so on. However, there are only 4n square sub-matrices, a number that is soon dwarfed by n! as n grows, so an awful lot of these minors get their determinants recomputed quite often. My question was, in essence, whether some clever way (other than dumb memoization) is known for organizing the computations in such a way that these recomputations are avoided. This question, which is not answered in the article, is more theoretical than practical; but, presumably, the same method could then be used for speeding up the computation of permanents. --Lambiam Talk  20:16, 3 June 2007 (UTC)


 * Have any of you heard of Lewis Carroll's method of matrix condensation? It was a rather interesting read, but I believe it partially bypassed the problems presented by large n, but I can't quite remember. aha! found it mid-write mathworld. The original article is available in JSTOR's catalouge, only six pages and a delightful read. --Cronholm144 20:36, 3 June 2007 (UTC)


 * It's discussed in Volume 2 of The Art of Computer Programming. I can look it up if you don't have a copy handy. Silly rabbit 20:19, 3 June 2007 (UTC)


 * Oops... I think it must be in one of the new installments. Here is Knuth's paper on it. Silly rabbit 20:29, 3 June 2007 (UTC)


 * Thanks, you beat me to it (edit conflict) BTW since I am on an algebra writing kick... How does Methods for computing determinants sound?--Cronholm144 20:36, 3 June 2007 (UTC)


 * There's also a related technique, due to Edgar Bareis (?), using Sylvester's identity. I believe this is optimal for large n. Silly rabbit 20:21, 3 June 2007 (UTC)


 * ..and modular methods for integer determinants using the Chinese remainder theorem, implemented for instance in Victor Shoup's Number Theory Library. Which, I think, work better particularly in parallel processing environments.  Yes, a new article seems to be called for.  Silly rabbit 20:43, 3 June 2007 (UTC)


 * I am surprised that no one mentioned Gaussian elimination (and related methods, such as QR decomposition) yet! Surely, these are more efficient than any expansion tricks, giving O(n3) complexity for computing the n by n determinant straight away. As far as I can remember, nothing like that exists for computation of permanents. This provides a philosophical 'explanation' why cofactor expansion, condensation, etc that apply equally to determinants and permanents cannot be (even close to) optimal in the determinant case.
 * Concerning Lewis Carrol method: besides in-house Dodgson condensation, see Bressoud's book referenced in Alternating sign matrix. Arcfrk 01:07, 4 June 2007 (UTC)


 * Yes, numerical analysts (like Jitse?) typically use LU decomposition (with partial pivoting, of course), then take the product of the diagonal elements. However, for abstract algebra we must also consider matrices over a ring for which division is not generally available. For example, Mathematica says that it "uses modular methods and row reduction, constructing a result using the Chinese Remainder Theorem" when it cannot use the floating point methods. The computer algebra system Fermat claims to be particularly good at determinants, but I do not know the methods employed. --KSmrqT 10:23, 4 June 2007 (UTC)


 * But Dodgson condensation is O(n3). I think that LU is used primarily to avoid underflow issues.  Of course, per KSmrq, for non-floating point matrices LU has certain obvious problems.  Silly rabbit 12:12, 5 June 2007 (UTC)


 * Indeed, I'd use LU decomposition. I had never heard about Dodgson condensation. I doubt underflow is an issue here. My guess would be that it is unstable, or too slow, or that nobody thought properly about it (in decreasing probability); but as I said, I'm only guessing. -- Jitse Niesen (talk) 22:55, 6 June 2007 (UTC)

Lie algebra bundle
The recently created article Lie algebra bundle starts with the word 'definition' and consists of a rather dull definition and a list of 9 references. I cannot even think of a tag to place on it (if it's not straight AfD) — any ideas? Arcfrk 18:03, 6 June 2007 (UTC)


 * This is a terrible start to an article on a worthy subject. Lie algebra bundles are rather important in the theory of connections (as adjoint bundles). I suggest that the best thing to do is to get the talk page going. Geometry guy 19:43, 6 June 2007 (UTC)


 * For now I've added a tag.  --Lambiam Talk  19:46, 6 June 2007 (UTC)
 * Good call! So good in fact, that Salix Alba and I tried simultaneously to do just that. He won :) Geometry guy 20:19, 6 June 2007 (UTC)
 * Thank you both for so promptly obeying my command :) --Lambiam Talk  22:37, 6 June 2007 (UTC)

Problem of points
A relatively recent addition, but in a desperate state. It is pretty hard even to work out what it is about. Has anyone heard of this problem? If so, can you elucidate? Geometry guy 16:26, 29 May 2007 (UTC)


 * I've heard of it at some time or another. It's a fairly significant historical problem in probability theory.  It has something to do with the fair division of a number of stakes in a game of chance given the number of points scored among multiple players (or something along these lines).  It is, if I recall correctly, the European origin of Pascal's triangle.  Silly rabbit 16:37, 29 May 2007 (UTC)


 * Thanks. This appears to be consistent with the contents of the article! Geometry guy 20:32, 29 May 2007 (UTC)


 * The problem is notable and famous, but I have never heard it referred to by that name. Blaise Pascal briefly mentions it, without giving it any name. de Méré's problem seems to be a different problem. –Henning Makholm 20:58, 29 May 2007 (UTC)
 * (I must admit, however, that Google finds a number of non-Wikipedia uses of the "problem of points" name –Henning Makholm 21:03, 29 May 2007 (UTC))


 * If I understand the article and the history correctly, de Méré's problem is unrelated, but Pascal (and Fermat) worked on a different problem, also posted by the Chevalier de Méré, which is a special case of the problem of points. de Méré asked Pascal to consider a game in which the players threw dice, scoring one point for each successful roll, until one player had accumulated six points and so won the game and the pot.  Suppose the players must abandon the game when the score is five to four.  How should they split the pot?  de Méré said they should split it 3-1, but his associate said that they should split it some other way, maybe 5-4, or 2-1, or something.  Pascal and Fermat agreed that 3-1 was correct.


 * In any case, I do believe that the problem is historically significant. -- Dominus 21:41, 29 May 2007 (UTC)


 * Thanks all: any chance someone could transfer these clarifications to the article? It doesn seem to be an important one, and I'm kind of busy right now. Geometry guy 21:50, 29 May 2007 (UTC)

I have rewritten Problem of points and think it to be in decent shape now. However the somewhat related article Chevalier de Méré is in need of somebody's loving attention. The current article, translated from French, tells an improbable story that de Méré managed to bankrupt himself by betting even odds on being able to throw at least one six in four throws of one fair die, and complained to Pascal that he had expected a 4*1/6 chance of winning. However, one easily computes that de Méré would actually have a few percent's advantage on such a bet, not likely to bankrupt him unless he bet his entire fortune on a single game. My sources agree that what de Méré actually asked of Pascal was an explanation of why the known better-than-even chances for throwing one six in four does not scale to better-than-even chances of throwing one double-six in twenty-four throws of two dice each. However even here the disadvantage is less than a percent, not likely to drive a non-idiotic gambler into immediate bankruptcy.

I might take a stab at this myself, but my available sources are very sparse with actual biographical information about de Méré. Anybody got something better? –Henning Makholm 22:08, 3 June 2007 (UTC)


 * .. on further investigation, the nonsense story about wrong odds and bankruptcy was not part of the original article that was translated from French, but was inserted later by a vandalism-only account. I have deleted it now. Some work to put reliable content in its stead still remains. –Henning Makholm 00:43, 4 June 2007 (UTC)


 * According to this article in French, which appeared in the Gazette des Mathématiciens, a periodical published by the Société Mathématique de France, the problem posed to Pascal was this: "how often must one throw two dice to have a priori at least a one on two chance of obtaining a double six? is it 24 or 25?" This sounds quite plausible to me; the chevalier de Méré must have known that 23 was too little and 25 sufficient.but see below! I don't know if the periodical counts as reviewed, but their website states that submitted articles will be examined by the editorial board before being accepted.
 * Here are some bits and pieces I found:
 * French writer (1607-1684). After studies with the Jesuits of Poitiers, he conquered Paris where he made himself well known in sophisticated society, and established ties of friendship with Guez de Balzac and the Duchess of Lesdiguières.
 * He was born in Boueux near Angoulême and was, supposedly, the first instructor of Françoise d'Aubigné.
 * He is responsible for quite a few aphorisms, such as: Admiration is the daughter of ignorance.
 * --Lambiam Talk 00:58, 4 June 2007 (UTC)
 * P.S. While plausible, the formulation of the SMF article is not actually supported by the text of the letter that Pascal sent to Fermat. He writes that the man − although of great wit, not a mathematician, a grave defect − complained that "... If one undertakes to make a six with one die, one is in the advantage to undertake it in 4 ... If one undertakes to make [double six] with two dice, one is in the disadvantage to undertake it in 24. And yet, 24 is to 36 ... as 4 is to 6 ...". 01:19, 4 June 2007 (UTC)

This turned into a really nice article. Thanks and congratulations to everyone who worked on it, particularly Henning Makholm. -- Dominus 15:01, 7 June 2007 (UTC)


 * I'm so happy that this incidental query had such a positive outcome. I agree that Henning Makholm in particular deserves much appreciation for his efforts. Thank you! Geometry guy 18:19, 7 June 2007 (UTC)

David Eppstein for admin
I nominated one of us, David Eppstein, for administrator. If you are familiar with David's work, you are welcome to voice your opinion at Requests for adminship/David Eppstein. Oleg Alexandrov (talk) 16:39, 31 May 2007 (UTC)


 * I'm pleased to say David Eppstein's nomination passed with 87 users in favor and none opposed, which is a remarkable show of support. &mdash; Carl (CBM · talk) 17:29, 7 June 2007 (UTC)

AfD for 1000000000000 (number)
There's some discussion about deleting it at Articles for deletion/1000000000000 (number) 2nd nomin. Someone asked "Is there a Wikiproject or something discussing these? [large numbers]". I thought perhaps the members of this wikiproject might be interested. --Itub 12:55, 7 June 2007 (UTC)

Wikiproject numbers is the project that you want.--Cronholm144 14:40, 7 June 2007 (UTC)
 * Oops, I supposed that such a project would exist, but I tried Wikiproject numbers with no success. It's with a capital N. :) --Itub 15:43, 7 June 2007 (UTC)

Importance ratings progress
I thought I would start a new section on this, so that the old ones can be archived. Today I have done some of the things I promised to do.
 * I have made some progress on WikiProject Mathematics/Wikipedia 1.0/Importance. I have not yet summarized/developed the discussions here on context, but I have come up with a table of priority/importance descriptors, which I hope will prove to be more helpful than the general descriptors of WP 1.0.
 * I have removed our own "peripheral/trivial" description for low importance articles and replaced it (temporarily) with the WP 1.0 "specialist" description. Untimately, I think we should replace all of the WP 1.0 descriptors by our own ones, because the former have many flaws. I intend to feed these thoughts back to the WP 1.0 project.
 * I have added an additional row to the priority ratings to emphasise that there is a lower rating than low, namely "unrated". This is where the terms "peripheral" and/or "trivial" may apply, although not always. Sometimes an article could be not sufficiently relevant, or might be too specialized or technical, for it to be worth rating within this project.
 * I have threaded the word "priority" a little bit more into the whole system in order to clarify the point, which User:Arcfrk articulated previously, that "importance" ratings are about how important it is for this project to have a good article on a subject, rather than an endorsement of the absolute importance of the subject. In particular, just as quality gradings use terms such as "A-Class", it may be more helpful to use terms like "Top-priority" for importance ratings. Geometry guy 22:50, 2 June 2007 (UTC)

Erm, I guess I should have said explicitly: please start making comments on WikiProject Mathematics/Wikipedia 1.0/Importance, either here, or on the talk page. Geometry guy 23:42, 2 June 2007 (UTC)


 * Yes I agree priority is a nicer word. The description on importance linked above seems a good start. Nice to emphesis that its for editors, if it was for readers you could say thats its OR. --Salix alba (talk) 12:21, 3 June 2007 (UTC)

I've now bitten the bullet, and drafted the "context" section. I added some information on the scope of the assessment project as well. Also, we didn't discuss articles about mathematicians: I raised the issue before, but no one commented on it. Anyway, I have proposed that we don't make substantial use of the WikiProject Biography scheme, since I believe it is flawed, particularly in the mathematics context. Full details at WikiProject Mathematics/Wikipedia 1.0/Importance. The latter page is now rather long and verbose, but I thought it would be better to do it that way while the guidelines are still being developed. Geometry guy 18:03, 3 June 2007 (UTC)

Okay it looks like the plan to use X-Priority instead of X-Importance will go ahead, but the term "importance" will still be used frequently (as in "Articles by importance", "importance level" and so on). I will now also use the new importance table to update our summary table. This will be hard to get right, so other editors' input may be crucial! Geometry guy 20:37, 6 June 2007 (UTC)

Summary table now updated at: WikiProject Mathematics/Wikipedia 1.0/Assessment. Geometry guy 11:45, 7 June 2007 (UTC)


 * I suggest that we go ahead with renaming everything, as there have been no objections here. &mdash; Carl (CBM · talk) 14:50, 8 June 2007 (UTC)

Categories and #redirect pages
I've been looking at the new math pages for a couple of months now, and one thing I've observed really has me puzzled. From time to time, somebody hangs a "category" tag on a redirect page.

That really doesn't make any sense to me. What purpose does such a tag serve? I would just take the tags off, but I've encountered a few editors who seem quite vehement about keeping them in place (although they haven't explained why this matters in terms that I can understand). So I'm asking the question here. Should we have a general policy about category tags on redirect pages? Thanks! DavidCBryant 16:39, 7 June 2007 (UTC)


 * The argument in favor of it is that it allows a user to browse categories like a topical index. The argument against is that the point of categories is to categorize articles, not topics. I usually remove categories from redirects when I see them and then forget about it if someone reverts me. There general WP policy does not forbid them. &mdash; Carl (CBM · talk) 17:49, 7 June 2007 (UTC)




 * I think that in general categories in redirects should be avoided, but they might be useful in a few cases when an article is called by two different names that are not universally known, and you want both names to be listed in the category to make it more accessible. I'm thinking of cases such as Zucchini/Courgette or Eggplant/Aubergine. (Note that none of those use categories in the redirect page, but perhaps they should.) I've noticed that when a redirect is listed in a category page it appears in italics, which can help in identifying them. --Itub 08:10, 8 June 2007 (UTC)

GA and math ratings
The discussions on Wikipedia talk:Good articles aimed at reforming the GA system seem to be going nowhere. Would there be support here for removing GA as one of the visible article quality classes on the maths rating template? The GA rating doesn't seem to have much to do with how we view the quality of math articles, and doesn't really fit into a linear scale with the other stub-start-b-a classes. Removing it from the scale would free us to assign GA articles "start" class if we feel they deserve it (for instance, Geometry Guy's "start" rating of Klee's measure problem, which I fully agree with), and it would avoid confusion about how GA and our own A-class rating system are supposed to interact. In any case if this change is made the GA status would still be visible in the separate GA banner on the talk page. —David Eppstein 20:21, 2 June 2007 (UTC)


 * I made a proposal about this above, but it is probably worth repeating it here. Basically, I proposed a less substantial change, because I think there may well be maths editors who like to have GA in the scheme, and I don't think it is necessary to remove it, only to clarify its meaning.


 * What I propose is a merger of B+ with GA. This would amount to the following: replace the horrible lime green colour of B+ by the darker green of GA; ask VeblenBot nicely to count and list B+ and GA articles together; and adjust some of the wording in our grading scheme to reflect the merger. In particular, an article can only be rated GA in our scheme if it is both B+ quality by our standards, and also a good article. (In particular, my rating of Klee's measure problem as Start class is entirely compatible with such a system.) Further, we can emphasise that achieving GA status has nothing to do with progression from B+ to A.


 * As I mentioned above, we might also want to make our B+ grading more robust, so that GA becomes, effectively, "B+ with added footnotes". Geometry guy 20:42, 2 June 2007 (UTC)


 * Given what I have seen of GA and its talk page, I agree with David Eppstein that needed reform seems unlikely anytime soon. That doesn't mean we must go stripping GA tags from articles, but it does mean we should eliminate GA from our ratings. As I have suggested repeatedly, to deafening silence, in principle tags like GA could be akin to barnstars, in that any group could tag articles by any criterion they prefer. (We could have "good use of subtle humor", for example.) Such tags should be orthogonal to our system, not part of it. --KSmrqT 00:28, 3 June 2007 (UTC)


 * Geometry guy's merger proposal seems to rest on the assumption that some maths editors may prefer to retain the GA rating in our scheme. Being rather fond of the Polder Model, I'd prefer the merger proposal if such editors indeed exist. If not, then it's better to eliminate the GA rating (and also the section on WikiProject Mathematics). So, could the people in favour of having GA in our scheme come forward? -- Jitse Niesen (talk) 04:02, 3 June 2007 (UTC)


 * In the current climate, I think it is rather unlikely that regulars here (G-guy included) will have a good word to say about the GA process! So I was thinking more about "the editor in the street".
 * However, my proposal doesn't rest on this assumption. There are other reasons why eliminating GA entirely from the scale might not be the best way forward.
 * Most of Wikipedia 1.0 uses GA, and retaining it will help ensure compatibility, and enable us to argue that our B+ is equivalent to WP 1.0 GA, and not to WP 1.0 B.
 * It is usually wiser to proceed slowly: we introduced B+; now let us make it a valid replacement for GA; then, later, we can consider whether we want to remove GA altogether from the scheme.
 * (Closely related.) For all our misgivings about GA, and recent events, we need to be able to hold our heads high in future discussions. A too-strong knee-jerk response could marginalise us, whereas a more measured response might convince some other WikiProjects of the merits of our approach.
 * On the other hand, forgetting the wiki-politics, there is essentially no difference between my proposal and removing GA from our scheme. The only difference is that B+ quality articles which are also good articles will be permitted to use the letters GA instead of B+ in their quality grading. I emphasise that good articles which do not meet our B+ standards would not be so entitled, and that good article status would be even more irrelevant for progress to A Class than it is now. Geometry guy 18:59, 3 June 2007 (UTC)


 * I'd be very reluctant to merge B+ and GA. One reason is the political, we are in danger of isolating ourselves from the greater mass of wikipedia who do acknowledge GA. A situation where the maths pages become a law unto themselves could be very disruptive in the long term.
 * When I first though up B+, it was intended to be a little short of GA, generally well written articles which failed in one respect, often a lack of history or illustrations. The idea was that it could be used as a holding ground for articles that could be put forward to GA.
 * I've now put Klee's measure problem of WP:GA/R as I think it fails 3a of WP:WIAGA, lacking in illustrations, context of related problems, also the claimed use in computer graphics could do with a citation. --Salix alba (talk) 21:27, 3 June 2007 (UTC)


 * I entirely agree about the political aspect, as I mentioned already. Anyway, my compromise is rather flexible: it can instead be viewed simply as an enhancement of the current B+ rating. We already allow A-Class without good article status, so I don't a problem in regarding GA as "B+ with external quality assurance". Geometry guy 02:00, 5 June 2007 (UTC)


 * That is exactly how I view GA, and why I don't think B+ should be eliminated or merged. Similarly, I view FA as essentially "A class plus external quality assurance", and would not want to merge them. &mdash; Carl (CBM · talk) 02:07, 5 June 2007 (UTC)


 * Yes, B+ is a great innovation of this project. I'm surprised by your view of FA-Class, though: in my view there is quite a jump in quality between A-Class and FA-Class. The latter is, after all, the Wikipedia gold standard. If this project takes the view that FA is "A plus external quality assurance", then quite a few A-Class articles need downrating, and the criteria for A-Class should be strengthened! I would be very much against doing that, as I think A-Class provides an important stepping stone between GA/B+ and FA. Geometry guy 16:46, 5 June 2007 (UTC)


 * Perhaps "external quality assurance" isn't the right phrase. But look at the FA requirements. Only one of them relates to the content of the article independent of presentation (1b), and that one only requires that the article "does not neglect major facts and details." That's not a high fence to jump. The remainder of the FA requirements, and the bulk of the FA review process based on what I've seen, is devoted to copyediting, making sure every detail of the manual of style is followed, copyediting, etc. I just scanned through WP:FAC and it looks like most of the comments still fall into the general scope of "copyediting". One of the goals I had in mind when we made the A-class review for this project was to try to avoid that. &mdash; Carl (CBM · talk) 18:30, 5 June 2007 (UTC)


 * My view of Featured Articles is more pragmatic; these articles will be featured on the Wikipedia welcome page, to impress the world with the wonders of open editing. This is not a "gold standard", but something more. A specialized mathematics article could be excellent for our purposes, yet never suitable for featured status. It is not a matter of quality control, but of purpose. For quality control, Wikipedia has a peer review option (though there may be some question about who is a suitable peer).
 * My view of Good Articles is that the project began as an attempt to recognize small articles and others that might not merit featured status, but has since lost its way.
 * Where does that leave mathematics? We have very broad coverage of mathematics topics, yet almost every one of our articles could benefit from attention. Despite the excesses of the inline citation squad and the silliness of WP:V, we can surely agree that we would like each article to cite at least one place to read more. Often the English language is roughed up, as is TeX and wiki markup. Specialized articles need not overly pander to the lay reader, but even mathematicians might appreciate more genial introductions. And here and there a figure could be wonderfully illuminating for us visual thinkers. I don't trust (many of) the current GA reviewers to assist us, but their stated criteria seem close to my own. I would hope our A-class articles meet similar standards. --KSmrqT 18:48, 5 June 2007 (UTC)
 * Our A-Class review is another great innovation. I agree that on the surface FAC suffers from many of the same concerns as GAC. but in practice it seems to me to be a whole different ball game, especially for technical articles. Yes, FAC editors usually criticise form, and often only add fact tags to articles, but this is frequently accompanied by a real drive to improve the article. I have participated in a couple of FACs: Encyclopedia Britannica and Equipartition theorem, but I was impressed in both cases by the result. (1b), (1c) and (4) all refer to content (as does (1a) to some extent), but (1b) is the big one, because "comprehensive" is a big word; FAC is a high fence to jump in practice. At the B+/GA level, the story is different, because the content is not fully developed, and the GA process is mostly only able to address presentational and policy issues for technical articles.
 * We should also be careful not to confuse FA and FA-Class. Our descriptors of FA-Class make quite clear the distinction between A-Class and FA-Class. The latter articles are described as "definitive" and "outstanding". I would not like to place such strong requirements on A-Class articles. Geometry guy 19:49, 5 June 2007 (UTC)
 * As to the content vrs presentation aspect of FA, this is perhaps all which could be expected. The people at FA are not in general going to be content specalists so it assesment in that factor will be hard. Maybe this is where A-class review fits in as a place where the subject specalists can assess the content. Also we should not underestimate the importance of presentation, a well presented article is more likely to get read than one which is not. Indeed this a a case where the FA process can help improve the article, there a lot of english majors there who can spot, and hopefully correct, an awkward turn of phrase. This is something which mathematicians have not. as a rule had much training in, its also something which is vital for mathematics articles aimed at a large audience. --Salix alba (talk) 20:05, 5 June 2007 (UTC)


 * I agree entirely. And sometimes quite amazing things happen at FAC! Geometry guy 20:13, 5 June 2007 (UTC)

Consensus?
From the above there does not appear to be consensus for removing GA-Class from our ratings, especially while this is still used and accepted by most of the rest of Wikipedia 1.0. On the other hand, we are exceptional in having a B+ class rating, and there seems to be some consensus that GA-Class amounts to B+ Class with external quality assurance (at least in issues of presentation and policy).

I therefore believe that we should update our grading scheme to reflect this consensus. I also think that the other practical suggestions I made are worthy of consideration: Please comment on these concrete suggestions. Geometry guy 20:45, 5 June 2007 (UTC)
 * 1) replace the lime green colour for B+ articles with the same green colour used for GA articles; this might actually help us to incorporate our approach into the general WP 1.0 scheme;
 * 2) list B+ and GA articles together on maths ratings pages (this is much less essential, but is mainly cosmetic).

I'm going to start tweaking our grading scheme descriptors both to cover this issue, and also the issue that our articles often start off being technically correct but inaccessible, rather than accessible but needing expert input. I won't move on the two numbered issues yet (although I am sorely tempted to get rid of the lime green ;) Geometry guy 20:45, 6 June 2007 (UTC)


 * I don't understand this. I thought we agreed that a GA tag was orthogonal to our ratings. Indeed I thought instances were noted in which an article with serious mathematical problems nevertheless received a GA tag. For that matter, a FA tag can also be earned without a sound technical review. Once again, I claim that a checklist is the way to go. Our best articles must be technically correct and readable and include at least one citation. A featured article must be pretty (and of general interest?) as well.
 * 
 * Is it:
 * correct?
 * reasonably complete and balanced?
 * clear?
 * compelling?
 * reasonably accessible, given the topic?
 * grammatical, correctly spelled, and well typeset?
 * appropriately illustrated?
 * well linked?
 * helpful in providing references and additional resources?
 * 
 * But I repeat myself. --KSmrqT 21:29, 6 June 2007 (UTC)


 * Indeed you do :) Please read the comments of Salix Alba and Carl (CBM) above. Geometry guy 22:02, 6 June 2007 (UTC)


 * I'm convinced by Geometry guy and Salix Alba's arguments. Let's merge B+ and GA. And please get rid of the lime green. -- Jitse Niesen (talk) 23:03, 6 June 2007 (UTC)


 * Changing the color is trivial. What does the merge mean, really? Would it still be possible to assign B+ ratings independent of GA? &mdash; Carl (CBM · talk) 01:51, 7 June 2007 (UTC)


 * Most definitely yes! Perhaps I shouldn't have used the word "merger" for my compromise proposal. Actually it is more like a definition:
 * GA-Class := B+-Class $$\cap$$ {good articles}.
 * In this way the Stub-Start-B-Bplus-A scheme is independent of WP:GA, and also GA-Class is only assigned to good articles of B+ quality. In a sense this makes WP:GA orthogonal to maths ratings, yet also keeps GA-Class within our scheme as "B+ with external quality assurance". I hope this gives some satisfaction both to supporters of GA and to editors who want to have nothing to do with it. Geometry guy 10:02, 7 June 2007 (UTC)
 * Further to KSmrq's suggestions above, perhaps this checklist could be part of our A-Class review process? I also think we should make sure that FA-Class math articles have been reviewed by this project, particularly for their content. Geometry guy 10:25, 7 June 2007 (UTC)


 * I think we would have to come up with a new name for the merge, using the GA tag will cause confusion. Changing lime green is a little tricky, is where the colour is set and would require discussion at Template talk:Grading scheme, creating a new template could be the way forward. The colour of  is yellow, very easily changed.
 * Options seem to be
 * Create a new class the union of GA and B+
 * Treat GA as orthogonal, allow a GA tag to appear in the rating template and but with an appropriate A/B+/B/Start/Stub grading as well.
 * Just forget about GA altogether, GA listed as seperate banner on talk pages but not included in the template.
 * Keep things as they are
 * My preference would be for orthogonality.
 * I do wonder how great the problem is, are there other GA articles which have a differet maths rating, if so it might be best to put these articles on good article review. When Klee's measure problem went to GA/R there was unanamous support for delisting, this may be the case for other problematic articles.--Salix alba (talk) 10:46, 7 June 2007 (UTC)


 * I definitely shouldn't have called it a "merge"!! Just when there appears to be some consensus, four new proposals come along! Anyway, by "lime green" I was referring to the yellow-green colour of B+ (B-Class is yellow). Sorry for any confusion, but I did spell this out. We cannot and should not change the colour of GA-Class. Salix Alba himself has argued strongly that we should maintain compatibility with the rest of WP 1.0, so GA-Class should be kept as a possible rating. I do not see the confusion here: we already use A-Class for good articles which are better than B+. I see no harm in extending this principle and only using GA-Class for good articles of B+ quality. As Salix Alba points out, this is unlikely to be an issue in practice, as good articles which have lower quality will almost certainly be delisted.
 * In terms of the list, this is a compromise between "orthogonality" and "keeping things as they are". Geometry guy 11:13, 7 June 2007 (UTC)
 * Without orthogonality, we create the impression that an article must pass GA before it can achieve A-class. We have no consensus for such a requirement, and I think it an unsupportable idea given our current lack of comity with the GA reviewers. --KSmrqT 16:54, 7 June 2007 (UTC)

(unindent) As far as I am aware, it has never been a requirement to pass good article to achieve A-class, neither here nor within WP 1.0 in general. I believe that there is consensus for this policy (not merely "no consensus" for its contrary). I am not aware of there being a false impression about this: plenty of A-Class articles have not passed WP:GA. Anyway, I report with pleasure (and from the above it sounds like Jitse will be happy to) that I have now replaced the horrible B+ colour with the same green used for GA-Class. This should further clarify our policy, as will some changes to the B+ and GA descriptors which I promised to make above. Geometry guy 17:47, 7 June 2007 (UTC)

I've now updated our quality grading scheme to clarify the issues discussed in this forum. Tomorrow, I will use this, together with any comments, to refine WikiProject Mathematics/Wikipedia 1.0/Assessment. Geometry guy 20:30, 7 June 2007 (UTC)

I've now refined and updated the Assessment page. Geometry guy 20:35, 8 June 2007 (UTC)

E (mathemathical constant) nominated for Good Article status
E (mathematical constant) was just nominated for Good Article status by. If anyone wants to polish it to try to get it to pass, go for it. JRSpriggs 07:32, 8 June 2007 (UTC)


 * The review process seems to consist mostly of removing information which is allegedly "not important", such as some of the continued fractions and series. Personally, I would have preferred to leave them in the article. JRSpriggs 10:05, 9 June 2007 (UTC)


 * A subarticle (e.g. "Representations of e") containing some of this information may be a way forward. Geometry guy 10:24, 9 June 2007 (UTC)


 * We let non-mathematicians explain to us what is important, to achieve their notion of "Good Article"? No, put the information back. I read a recent claim that reviewers were not editors, so who is doing the removing anyway? Even in academia reviewers must engage in a dialog with authors; both must be satisfied, because the author's name is on the paper and the reviewers are responsible to the journal. Grow a backbone; push back. Both sides, and especially the readers, will benefit.
 * Often in such a process we must "read between the lines". Reject the ill-conceived fix, but try to understand what caused the reviewer to propose it. For example, maybe better organization would help; maybe the reviewer feels lost in an unmotivated disorganized sprawl. If the continued fraction is mathematically important (note: it is), then don't make the reason a mystery for the reader. Remember, most reviewers (and readers) know almost nothing about e and less than that about continued fractions.
 * Side note: following Bill Gosper, I like to write the continued fraction as
 * $$ e = [ 1;0,1, \, 1,2,1, \, 1,4,1, \, 1,6,1, \, \ldots, \, 1,2k,1, \, \ldots ] . \,\!$$
 * Try it; the first triple is equivalent to 2, and this form makes the pattern more dramatic. --KSmrqT 15:42, 9 June 2007 (UTC)
 * And it generalizes nicely to
 * $$ \exp\{x^{-1}\} = [ 1;x-1,1,\,\,1,3x-1,1,\,\,1,5x-1,1,\,\,1,7x-1,1,\,\,\ldots,\,\,1,(2k+1)x-1,1,\,\,\ldots]\,,$$
 * which works for all values of x, except of course 0. --Lambiam Talk  19:45, 9 June 2007 (UTC)

On the Equilibrium of Heterogeneous Substances
Started monumental paper, please feel free to chip in. Thanks: --Sadi Carnot 15:30, 10 June 2007 (UTC)

Fermat's last theorem
I've nominated Fermat's last theorem for A-Class review. This article gets a lot of attention, pop-culture links, and (of course) vandalism, so I thought it might be worth giving the mathematical content a brush-up. Geometry guy 20:17, 11 June 2007 (UTC)

Just to clarify: this article was promoted to A-Class last October, before A-Class review was introduced in March. I (and a few others, it seems: see the article talk page) do not believe it currently meets the criteria, so some input would be most welcome. Geometry guy 23:08, 11 June 2007 (UTC)

Current activity
Does anyone have an explanation for strange behaviour of the Current activity page? I've noticed in the past that certain articles keep reappearing in the tables of supposedly newly created articles (e.g. Transformation geometry). However, recently it seems that the majority of 'New articles' are not only old, but were not even been edited on the date under which they are listed. For example, look at the list for June 10 (as an even more specific example, see Cartan's criterion, which hasn't been edited for weeks). It does make one wonder whether, conversely, all new (or renamed) articles are faithfully represented in the table. And a related question: if the name of a new article is stricken out, what does it mean? (certainly, not that it was deleted!) Arcfrk 05:06, 11 June 2007 (UTC)


 * You probably need to ask Oleg and/or Jitse – the current activity page is maintained by Jitse's bot, which reads input from Oleg's bot. If there really is a problem, the fault probably lies with Oleg's "Mathbot", since Jitse's bot just reformats Oleg's list (when it comes to "new" articles). Oh – the crossed out entries have been deleted from the list of mathematics articles.
 * I did notice some very odd activity lately. On Friday, June 8, a great number of articles were added by Oleg's bot. Then, on Sunday, June 10, the same articles were deleted from the list. I think this had something to do with Category:Modal logic and Category:Economics curves. Most likely, Oleg decided to include those two categories in a list of categories that feeds his bot, and then changed his mind. Or maybe somebody else added new categories to the list, and then Oleg took them out. It was probably something like that.
 * Anyway, the bots work correctly most of the time, and help us keep a handle on the math articles. I regard the occasional malfunction as par for the course. This is a volunteer effort, after all. DavidCBryant 15:27, 11 June 2007 (UTC)


 * That's more or less what happened: Mathbot can add categories automatically, but sometimes it makes mistakes (it isn't as good at math as Oleg), so Oleg fixes them. Geometry guy 16:01, 11 June 2007 (UTC)


 * One more thing. This subject was kicked around in February. You can find some relevant discussion in the archive, at Wikipedia_talk:WikiProject_Mathematics/Archive_22 and also at Wikipedia_talk:WikiProject_Mathematics/Archive_22. Happy reading! ;^>  DavidCBryant 15:58, 11 June 2007 (UTC)


 * Thank you for the links! I had suspected at first that strange behaviour had something to do with categories, but on a closer examination, the conjecture did not hold. Namely, some articles have only one category, for example, Cartan's criterion has Category:Lie algebras; Classifying space for O(n) has Category:Mathematics stubs, and it would appear to be highly unlikely if that category appeared and disappeared from the list of mathematics on alternate days (also, the fact that other articles such as Quasi-Lie algebra with the same category as their only category did not make it to the list of new articles contradicts the conjecture). Is there another possible explanation? Arcfrk 22:16, 11 June 2007 (UTC)


 * You're right, Arcfrk. It's a poser. I took a look at Cartan's criterion. Oleg's bot showed it as a new article on May 24, with no activity since then. Jitse's bot shows it as a "removed article" on June 9, then as a "new article" on June 10. It sort of looks as if Jitse's bot may have hiccuped.
 * I noticed something similar earlier this year, with an article entitled corresponding conditional (logic). I asked Jitse about it – you can read that discussion over here. I guess I accepted Jitse's explanation (that the bot may malfunction occasionally, but it's no big deal) and now I just overlook the occasional glitch. DavidCBryant 23:19, 11 June 2007 (UTC)

Yes the weird activity is due to me. I added in Category:Modal logic and Category:Economics curves with a bunch of other categories the other day (as remarked above by David), but did not check these two carefully enough. They have a huge amount of nonmath, especially the first, so I cut them out. Sorry for the mass changes. I don't know what to do about these two categories. Comments? Oleg Alexandrov (talk) 03:07, 12 June 2007 (UTC)


 * The few articles in Category:Modal logic that should be counted can be included in other math logic categories easily enough, and there are very few of them, so it seems OK to me to leave that category off the list. &mdash; Carl (CBM · talk) 04:48, 12 June 2007 (UTC)


 * I looked into centering matrix one or two days ago, which also disappeared and reappearing in the current activity. In that case, the cause was that Oleg rolled back a few weeks' worth of edits of Mathbot at List of mathematics articles (C). I think that the issue with transformation (geometry) and transformation geometry is that Mathbot is programmed to consider them as identical, and so it puts sometimes one and sometimes the other on List of mathematics articles (T). -- Jitse Niesen (talk) 10:21, 12 June 2007 (UTC)
 * I now made the bot distinguish the two articles as above. Sorry for the mass rollback at the C list (I thought nobody was watching this! :) I'll pay more attention in the future. By the way, as mentioned a while ago, having more people taking a look at the recent additions is rather helpful, as that's the right time to catch misformatted articles, welcome the new people, etc. Oleg Alexandrov (talk) 16:01, 12 June 2007 (UTC)

Revisiting naming of "Boolean algebra" article
Please take a look at talk:Boolean algebra. --Trovatore 23:26, 13 June 2007 (UTC)

Infobox graph
I've put together a tentative infobox for articles on specific graphs (and, in a few cases, graph families). I'd like some feedback on the template before I deploy it on 19 articles, particularly from someone who knows more about graph theory and can better point out which properties are most important to mention. ~ Booya Bazooka 22:49, 10 June 2007 (UTC)
 * One thing I'd suggest is changing the title so it appears inside the box. You might like to look at Template:Infobox Polyhedron which is similar. --Salix alba (talk) 07:35, 11 June 2007 (UTC)

Template:Infobox graph is now operational. ~ Booya Bazooka 20:13, 14 June 2007 (UTC)

proposed deletion
The proposal to delete Zaimi-Marku inequality may well make sense, but the people commenting at Articles for deletion/Zaimi-Marku inequality aren't being very intelligent about it yet. Michael Hardy 23:49, 15 June 2007 (UTC)

Cleaning house at the K- articles
The following articles are very weak and I am planning on prodding or AfDing them unless there is an objection here. Any and all feedback is appreciated. Cheers--Cronholm144 05:00, 14 June 2007 (UTC)
 * K-loop-redirect to Bol loop? -resolved
 * K-opt -resolved
 * K-set (geometry) -resolved
 * Kahan summation algorithm -resolved
 * Kalman-Bucy filter-consider merge with Kalman filter -resolved
 * Kampyle-PROD? On the List of curves -resolved
 * Kaplansky conjecture-weak and what others? -resolved
 * Kappa statistic-weak(no prod)
 * Karman-Trefftz transform-no context -resolved
 * Kauffman polynomial -resolved
 * Kaup–Kupershmidt equation -resolved
 * Klerer-May System -removed maths cats
 * Knot -removed math cats
 * Kulkarni-Nomizu product -resolved
 * Ky Fan inequality -resolved


 * The K-set (geometry) problem (specifically, bounding the number of k-sets that a set of n points can have) is arguably the most important unsolved problem in discrete geometry. It definitely deserves an article (a much better one than what's there). I'll add it to my to-do list, and request that you not AfD or prod it. I have no strong opinion on the others. —David Eppstein 05:12, 14 June 2007 (UTC)
 * Done. —David Eppstein 22:14, 16 June 2007 (UTC)


 * Oh, and I went ahead and merged K-opt into a larger article that gives it better context. —David Eppstein 05:19, 14 June 2007 (UTC)


 * I would argue that Kauffman polynomial needs a better article, but should not be deleted. I'll put it on my to-do list unless Chan-Ho gets to it first. :) VectorPosse 08:05, 14 June 2007 (UTC)
 * ... or Salix Alba as the case might be. Thanks for the quick patch.  I'll still put this on my to-do list as it could be expanded a tiny bit more.  (Perhaps not much more.)  VectorPosse 08:08, 14 June 2007 (UTC)
 * Knot now removed from maths categories. --Salix alba (talk) 09:32, 14 June 2007 (UTC)


 * K-loop should be merged into and then redirect to Bol loop.
 * While the Kahan summation algorithm is presented in pseudocode, it is not immediately clear what would be a better way of presenting it.
 * Kalman-Bucy filter could be merged to Kalman filter.
 * Kampyle is a strange case. There is the apparently unrelated Kampyle of Eudoxus, simply called "Kampyle" in this gallery of plane curves; see . The equation in our article is that of the Lemniscate of Gerono; the image does not fit the equation. No references. Indeed, away with it.
 * Kaplansky conjecture: don't know; is it notable? The stub states, ominously: "There are numerous other 'Kaplansky conjectures'".
 * Kappa statistic: useless, delendum est.
 * Karman-Trefftz transform could be merged to Joukowsky transform.
 * Kaup–Kupershmidt equation has context and references; while not strong, I don't see what is gained by deleting it.
 * Klerer-May System: uninformative; is it notable?
 * Kulkarni-Nomizu product: no context; is it notable?
 * Ky Fan inequality: ditto.
 * --Lambiam Talk 11:52, 14 June 2007 (UTC)


 * I've expanded Kulkarni-Nomizu product slightly. This old-fashioned operation in differential geometry is never going to be a great article, but it is notable. I've also made minor tweaks to some of the others. It is usually easier to provide redirects or add links to backlinks than to PROD articles. Michael Hardy may be able to provide notability for Ky Fan inequality, as he has edited it in the past. Geometry guy 12:10, 14 June 2007 (UTC)


 * I have tweaked Ky Fan inequality and added a reference. Gandalf61 13:30, 14 June 2007 (UTC)


 * Kaplansky conjecture is notable, it is related to Kadison idempotent conjecture, aka Kadison-Kaplansky conjecture, and Baum-Connes conjecture. The statement about numerous other Kaplansky conjectures is correct, but misleading (there are, but why mention them here instead of writing a separate article?). Arcfrk 15:58, 14 June 2007 (UTC)
 * And it is the List of statements undecidable in ZFC, which is a substantial claim to notability (as Kaplansky's conjecture, which should be straightened out; I'm not sure which is idiomatic). Septentrionalis PMAnderson 16:05, 14 June 2007 (UTC)
 * This seems to be yet another Kaplansky conjecture. Geometry guy 16:26, 14 June 2007 (UTC)
 * PS. I'm a bit surprised that Baum–Connes conjecture is still red. Can someone make a stub? Geometry guy 16:41, 14 June 2007 (UTC)


 * Kaplansky made dozens of conjectures. I've spent an hour reading Math Reviews, and the vast majority of them are either better known by other, more descriptive names, or referred to as Kaplansky's conjecture. I suggest that the latter be made into a disambiguation page. The conjecture mentioned by PMAnderson is one of the notable exceptions. Arcfrk 16:31, 14 June 2007 (UTC)


 * I've added more info from this page, and prepped the article to become a dab at a later date. Geometry guy 22:07, 14 June 2007 (UTC)
 * PS. Credit to Cronholm for turning another redlink blue!


 * Kappa statistic should probably be a dab between Fleiss' kappa and Cohen's kappa. I have no opinion on whether either of them is notable, and one of them appears to be a trivial generalization of the other; I'm only judging from the articles. Septentrionalis PMAnderson 16:13, 14 June 2007 (UTC)


 * I guess we need one of our expert statisticians to comment on this one. Geometry guy 22:44, 14 June 2007 (UTC)

I have found a webpage on the Lemniscate of Gerono that compared its equation to the rather similar equation of the Kampyle of Eudoxus. In the conviction that this was the source of confusion resulting in the wrong equation to be ascribed to the Kampyle, I've rewritten the latter article (still a stub) and moved it to Kampyle of Eudoxus. For simplicity, I've omitted a parameter making this a family of similar curves, where the similarity transformations (rescaling) leave the origin fixed; after all, other similarity transformations (e.g., rotation) are usually not dealt with either. --Lambiam Talk 22:49, 14 June 2007 (UTC)

Proposed merges to Partial fraction
I've proposed that the two articles named Partial fraction decomposition and Partial fraction decomposition over the reals be merged into the article named Partial fraction. You can explain why this is a terrible idea at, respectively: --Lambiam Talk 08:13, 18 June 2007 (UTC)
 * Talk:Partial fraction, and
 * Talk:Partial fraction.

More weak stubs
Hello again everyone, thanks for your swift action on the K articles (Kappa statistic is the only one left). I have found more articles in need of attention so here goes. :)--Cronholm144 06:26, 17 June 2007 (UTC)

I guess I need to make myself a little more clear. These articles will be on AfD if they don't improve.--Cronholm144 06:26, 17 June 2007 (UTC)

Weak:

 * Kaczmarz method--one sentence
 * Kendall's W--three sentences
 * Jacobi-Lie bracket--two sentences
 * Jarnik's theorem--one sentence
 * Jensen-Shannon divergence--two sentence and two references...
 * Jenkins-Traub method--one and one source


 * Jacobi-Lie bracket is a clear AfD case. Arcfrk 06:48, 17 June 2007 (UTC)


 * Isn't it just a redirect to Lie derivative? Geometry guy 09:27, 17 June 2007 (UTC)

I have cleaned up everything but Kendall's W (which was already done before I got there, thanks Lambiam and David) and Jarnik's theorem. Furthermore, I think that the latter might be wrong, the Jarnik's theorem I found has to do with diophantine approximation. I need input on this one. Also I am going to dab Kappa statistic if their are no more objections. cheers--Cronholm144 04:21, 18 June 2007 (UTC)


 * I still think we need a statistician to look at kappa statistic. It seems to be that this has developed into a general concept of which Cohen's kappa and Fleiss' kappa are the key examples. I've added a bit to the lead, anyway. Geometry guy 12:16, 18 June 2007 (UTC)

I guess I will give it more time, hopefully Michael will fix it. I saw him playing with it.--Cronholm144 17:46, 18 June 2007 (UTC)


 * Well, we have worse stubs than this one. Jarnik's theorem is more troublesome. I wasn't able to find any reference to such a result known by this name. Of course Vojtech Jarnik proved many things, and there are a couple of notable results called Jarnik's theorem, one in diophantine approximation, another about the existence of lim sups of difference quotients (mentioned by Erdos in the Annals, no less). However, neither of them are the result which this article is attempting to state. Geometry guy 18:29, 19 June 2007 (UTC)

Other:

 * Juxtaposition --shouldn't be a math article
 * Joint Board for the Enrollment of Actuaries --I don't know what to do with this
 * I've removed the math cat from the second of these. The first is a wiktionary link, so I've removed it from the list, as suggested. Geometry guy 09:56, 17 June 2007 (UTC)

Boolean algebra again
The term "Boolean algebra" usually means (to mathematicians) a type of algebraic structure, and (to non-mathematicians) a way of manipulating propositional variables. My last try at gathering a consensus on how to disambiguate, went nowhere, and we still have the problem. I'm trying again at talk:Boolean algebra, hopefully with a statement of the problem that takes into account what I learned from the last discussion. --Trovatore 08:08, 20 June 2007 (UTC)
 * Oh, of course sometimes mathematicians, also, use the "way of manipulating variables" sense of the word. The point is that there are two quite distinct meanings, and there are in fact two articles (though both need significant improvement), but Boolean algebra itself needs (IMHO) to be a disambiguation page because neither of the two well-demarcated meanings is in fact primary. --Trovatore 09:00, 20 June 2007 (UTC)


 * The reason to have different articles for Quotient ring and for Modular arithmetic, for example, is not that one is a count noun for abstract algebraic structures and the other a mass noun for a collection of mathematical operations, but that modular arithmetic involves only one very specific class of quotient rings Z/mZ. Suppose that class was an object of serious mathematical study in its own right, as a subfield of Ring theory, and we had an article on those "Modular rings" (as they are sometimes called). Then (in my opinion) there would be no very good reason to separate the articles on (1) the algebraic structures that are these "modular rings", and (2) the "modular arithmetic" of such structures. I still don't see what makes Boolean algebra so different. We could of course make a dab page, both of whose disambiguating links point to the same article. :) But please weigh in with your insights at Talk:Boolean algebra. --Lambiam Talk  11:17, 20 June 2007 (UTC)


 * This reminds me a bit of a common situation in which editors debate the choice of words in the lead of an article whose content is inadequate. In that case, a good piece of advice is to improve the content and then write the lead. Any disagreements about the content can then be resolved during the course of improving the article rather than on the talk page, and once the content is good, it is usually pretty easy to write a good lead. Maybe something like that is needed here. Once the content is right, the names of the articles might be less contentious. Geometry guy 11:45, 20 June 2007 (UTC)


 * Having said that... a compromise solution occured to me (see the article talk page), motivated by the observation that there is a category here, Category:Boolean algebra. Now, like any self-respecting category, this ought to have a main article, presumably called Boolean algebra, which should neither be a dab, nor focus on one of the particular meanings of the term. The particular meanings could then be elaborated in subarticles. Geometry guy 16:56, 20 June 2007 (UTC)

We have two meanings, and two articles. What's wrong with a dab header from each to the other? Why do we need to have everybody click through a dab page? Septentrionalis PMAnderson 18:06, 20 June 2007 (UTC)
 * Mainly because of links. Editors repeatedly add wikilinks to Boolean algebra, intending one meaning or the other (and generally it's quite well-defined which meaning), without bothering to check whether the article actually reflects that meaning. I don't see that changing. If the link goes to the wrong article it may stay that way for a long time. If it goes to a dab page, presumably someone will notice and do something about it. --Trovatore 18:12, 20 June 2007 (UTC)


 * The main article I am suggesting would, of course, begin with a dab header to the two main meanings. The advantage of this approach, however, is that even if editors don't notice that they should disambiguate, a link to the main article is still useful, and possibly even educational. Geometry guy 18:44, 20 June 2007 (UTC)
 * But it's not the article that either sort of editor is intending to link to. --Trovatore 19:27, 20 June 2007 (UTC)
 * So an editor of either persuasion will at some point fix it. Meanwhile, readers might even benefit :) Geometry guy 19:39, 20 June 2007 (UTC)
 * I don't see how, as in my opinion there is no sensible way to write such an article, except by making it primarily about the mass-noun sense, which gives us the current linking problem, but just reversed. --Trovatore 19:44, 20 June 2007 (UTC)
 * No, there is also George Boole, the algebra of sets, and numerous other issues in the category to be discussed. But, if your mind is so made up, Trovatore, that you are not able even to imagine alternatives to your point of view, then why bring the issue to WT:WPM? I made another suggestion above, which is to make the content of the articles match your vision. You may be contested, because this is not www.trovatore.com, but at least content would be added to the articles. Geometry guy 20:10, 20 June 2007 (UTC)

Signal subspace
Could someone take a look at the above page? It's newly created, and a little incoherent at the moment. I've wikified a couple of the links, but anyone who's familiar with the term might want to have a look. Thanks! -- simxp (talk) 10:21, 20 June 2007 (UTC)
 * What's the problem? It seems clear to me, except for the use of "almost completely" for "not quite 100%" instead of the usual mathematical meanings of "almost". I'll see if I can fix that. Septentrionalis PMAnderson 17:58, 20 June 2007 (UTC)


 * You were looking at a version several revisions later than the initial request. The diff between the versions can be seen here. --Lambiam Talk  23:33, 20 June 2007 (UTC)

Mathematical eyes sought
Over at integral, the fabulous Mathematics Collaboration of the Month, Loisel and I are discussing an image purporting to show the difference between Riemannian and Lebesgue integration. There is some prior unresolved discomfort with the image at Lebesgue integration, and the section of that article in which the image appears ends with the completely unacceptable remark: "See the discussion page." (May I just say, yuck.) The French, German, Russian, and Japanese pages do not use the image.

I'm keen on fostering intuition, and work hard to provide appropriate images. The question for all you analysts and pedagogues: Is this image correct and helpful? Please come share your views! Thanks.

(Feel free to guide evolution of the integral article in other ways as well; one prior view is here.) --KSmrqT 18:00, 17 June 2007 (UTC)


 * I think both points of view have some validity here. The image is partly helpful in understanding the difference between Riemann and Lebesgue, but also partly misleading. Roughly speaking, Riemann integration involves slicing up the domain, Lebesgue integration the codomain, and the picture captures this. Although it does not represent how the Lebesgue integral is usually defined (see Talk:Lebesgue integration, the "unresolved discomfort" linked above), it could be defined in this way.
 * The key difference between the two forms of integration is that Riemann integration exploits the connected topological structure of the domain, whereas Lebesgue integration does not. On the one hand, this means that Lebesgue integration generalizes to any measure space. On the other hand, the Riemann approach can be extended to integrate the derivative of any function (the generalized Riemann integral of Kurzweil and Henstock), whereas the derivative of $$ x^2 \sin(1/x^2)$$ is not Lebesgue integrable across zero (the absolute integral diverges); indeed no theory of integration on measure spaces can handle such a function because its integrability relies on local cancellation, one of the deepest aspects of real and harmonic analysis.
 * I would therefore suggest that the image could be helpful, but its use must be qualified explicitly. I will make a start at Lebesgue integration by removing the reference to the talk page, which is not only unacceptable (to delicate souls like KSmrq and myself), but not permissible on Wikipedia. Geometry guy 20:12, 17 June 2007 (UTC)
 * PS. I second KSmrq's encouragement to work on Integral, although I have not been nearly so virtuous as he has in this respect!


 * The picture does not help foster my intuition of the Lebesgue integral at all. I prefer the "splitting up the range" versus "splitting up the domain" approach that Geometry guy said above (besides, that's basically what's going on). The picture actually makes me think that I don't understand the Lebesgue integral (while, as it stands, I believe that I do)l. The picture does not look that good (in my eyes) anyway. I suggest that it be done away with.
 * And I should add, I don't like the picture because when computing "area between curves" in a Calculus 2 course, sometimes integrating along the y-axis is more helpful; it seems to me that the picture confuses the Lebesgue integral with this kind of approach. –King Bee (&tau; • &gamma;) 20:23, 17 June 2007 (UTC)


 * Well I made a poor first effort at Lebesgue integration, but that might be the best way to encourage others to improve it :) Geometry guy 20:27, 17 June 2007 (UTC)


 * In the real analysis class that I teach, I explain that the Lebesgue integral involves splitting up the y axis instead of the x axis, and I make basically the same drawing as the figure. Loisel 20:30, 17 June 2007 (UTC)


 * Is this not like arguing about whether (a+b+c)+(a+b)+(a) is the same or different from (a+a+a)+(b+b)+(c)? JRSpriggs 08:40, 18 June 2007 (UTC)


 * I don't like the Lesbegue integration diagram because it gives the impression that Lesbegue integration just consists of replacing $$\int y(x) dx$$ with $$\int x(y) dy$$. It does not give a intuitive feel for why the Dirichlet function, for example, is Lesbegue-integrable even though it is not Riemann-integrable. The "contour map" explanation that goes alongside the diagram in the Lebesgue integration article suffers from the same problem. How do you draw contours on the Dirichlet function ? Seems to me that if you can draw contours then the function is Riemann-integrable anyway, so this explanation begs the question. Gandalf61 09:40, 18 June 2007 (UTC)
 * Yeah, that's what I was getting at with my "area between curves" thing above. I agree entirely; most of the interesting functions that are Lebesgue integrable cannot be "graphed" or "drawn." –King Bee (&tau; • &gamma;) 10:19, 18 June 2007 (UTC)
 * I think this is a red herring. These pictures have nothing to do with which functions are integrable: they are about how the integral is defined. Indeed the difference being illustrated (partition of codomain vs partition of domain) is irrelevant to the question of which functions can be integrated. The Dirichlet function can be integrated by Riemann summation: all you have to do is allow the width of the strips to vary with position in the limiting process.
 * The Dirichlet function has Riemann sums, but by an appropriate choice of partitions we can make the Riemann sums over a unit interval converge to either 0 or 1. Since the limit of the Riemann sums depends on the choice of partitions, the Dirichlet function is definitely not Riemann-integrable - the fact that we can engineer the paritions to make the Riemann sums converge to the "right" answer is irrelevant. Indeed, the Dirichlet function is used as an example of a function that is not Riemann-integrable in the Riemann integral article. Gandalf61 21:44, 18 June 2007 (UTC)
 * Yes, but it is generalized Riemann integrable, Gandalf: all Lebesgue integrable functions are. For all &epsilon;, there exists a gauge &delta;(x) such that any &delta;-fine Riemann sum is within &epsilon; of the integral. The (essentially trivial) modification of the Riemannian definition is to let the control parameter &delta; depend on position. Geometry guy 21:59, 18 June 2007 (UTC)
 * The "contours" in the Lebesgue approach are given by a simple function approximating the given function. They are typically undrawable, but then, the Weierstrass function can't really be drawn either.
 * As I mentioned in above, the key difference between the two definitions is that the Lebesgue approach generalizes to measure spaces (whereas the Riemann approach does not), while the Riemann approach allows local cancellation (the Lebesgue approach does not).
 * It is certainly important to discuss differences between which functions are integrable in different theories, but this is a separate issue and requires a separate discussion. Geometry guy 12:51, 18 June 2007 (UTC)


 * Consider the figure shown right. I claim that it is exactly the right picture for both a Riemann sum and a Lebesgue measurable "simple function" sum. The simple function consists of piecewise constant steps, and the measure of each step is the length of the real interval under it. Thus the sum of the Lebesgue integral is exactly the same as the sum of the Riemann integral.
 * The example function, f(x) = &radic;x, is deliberately monotonic. A non-monotonic function could have separated intervals with the same simple function value. The measure for that term of the sum would combine those interval lengths. But in neither case is it correct to depict the summation using horizontal slabs.
 * Teaching is an art, and each class and each teacher is different. If Loisel finds it helpful to use incorrect figures in an attempt to convey correct intuition, best of luck. I am not comfortable with that approach, and don't think Wikipedia should follow suit. Need I add, IMHO? --KSmrqT 17:21, 18 June 2007 (UTC)


 * This is both a Riemann sum (provided one allows variable width strips) and a simple function, but so what? Just because you can draw a picture which fails to illustrate the difference between the two methods of summation doesn't mean that they are the same. In your case the simple function has the form
 * $$\sum_{i=1}^n a_i 1_{[x_{i-1},x_{i}]},$$
 * where $$0=x_0<x_1<\cdots <x_n=1$$. Now try drawing a picture to illustrate a simple function of the form
 * $$\sum_{i=1}^n b_i 1_{[x_{i-1},1]}.$$
 * (With $$ a_i = \sum_{j=1}^i b_j$$, this is the same function.)
 * The intuition that Loizel is attempting to capture is that the Riemann integral can be obtained by a limiting process in which the width of the strips tends to zero, whereas the Lebesgue integral can be obtained by a limiting process in which the height of the increments tends to zero: this is a fundamental distinction between the two methods. Just because Loizel's picture doesn't convey that intuition for you and your class does not mean it is "incorrect". It just needs to be properly explained. Geometry guy 17:50, 18 June 2007 (UTC)


 * Sorry, your example is not cast in proper "simple function" form, which partitions the domain as pre-images of the range:
 * $$\begin{align}

s &{}= \sum_{i=1}^{n} a_i \, 1_{A_i} \\ A_i &{}= \{ x \colon s(x)=a_i \}. \end{align}$$
 * Nor is there a limit, per se, merely a supremum over all suitable s. The step heights ai are always vertical, the measurable sets Ai are always unions of horizontal intervals, the measures are sums of those interval lengths, and so each term is a collection of vertical slabs.
 * I agree that an s with more steps, more "vertical partitions" as it were, can more closely approach the supremum. I agree that we might like to tickle the intuition. But I contend that horizontal slabs do not match the definitions; they do not correspond to anything in the sums.
 * We are allowed only a finite number of heights for s, and the support of each height must be a measurable set. And although we require s &le; f, the heights need not touch the function. (In the square root example, we could use s = 1&frasl;2 if 1&frasl;3 &lt; x &lt; 2&frasl;3, and s = 0 otherwise.)
 * It might be possible to depict something showing the finite number of distinct range values, maybe using horizontal lines traversing the entire width of the plot. But, please, no sum of horizontal slabs. --KSmrqT 19:19, 18 June 2007 (UTC)


 * Lebesgue integral and simple function both define a simple function to be a finite linear combination of indicator functions of measurable sets. That does not mean your definition is wrong, of course, only that there are different points of view. There are several minor variations that one can employ in the definition/construction of the Lebesgue integral. In particular, it could be defined in terms of horizontal slabs, even if this is neither a common definition nor your preferred definition. Let me emphasise, though, that I am not wholeheartedly endorsing horizontal slabs picture. I just think there is something being captured here that some editors seem to value. But it seems your mind is made up. Geometry guy 20:01, 18 June 2007 (UTC)
 * I'm vigorously asserting a position, which is not quite the same thing. ;-)
 * An ideal image would show both the similarities and the differences of Lebesgue and Riemann. Strengths of Lebesgue include two kinds of generality: peculiar functions and diverse domains. Weaknesses include the need for measure and for absolute convergence (if |f| doesn't work, Lebesgue fails). I think the key novelty is that although a measurable set can be a collection of intervals, it can also be much more flexible than that. Thus the function
 * $$\begin{align}

f \colon [0,1] &{}\to \R \\ x &{}\mapsto \begin{cases}0, & \text{if }x \isin \mathbb{Q} \\ 1, & \text{otherwise} \end{cases} \end{align}$$
 * is a "simple function" (in the technical sense!), and the success of the Lebesgue integral in coping with it is all down to the fact that the pre-image of 0 and the pre-image of 1 (the only two values in its image) are both measurable sets. We have no need for a limit of increasingly thin horizontal slabs!
 * This we cannot depict; but we can make the same point by using zero (or arbitrary values) at only a finite number of exceptional spots.
 * I am, of course, thinking aloud, searching for a concept and an image than comes closer to everyone's ideal. --KSmrqT 22:00, 18 June 2007 (UTC)


 * You are indeed: I encourage you to learn about the generalized Riemann integral, which I have mentioned in several of my posts here, but (apart from your reference to absolute integrability) you appear not to have responded. The problem with your approach is that you are trying to do several different things at once. The generality of an integral in terms of the functions it can integrate, and it terms of the spaces on which it is defined, are really two quite different ideas. Conflating them just adds to the confusion. Geometry guy 22:06, 18 June 2007 (UTC)
 * Why do you think I was conflating kinds of functions and kinds of spaces? I deliberately listed them as two separate items! I have not mentioned it, but I was already familiar with Henstock–Kurzweil and have been thinking about whether to bring gauges into this. In fact, by replacing a constant delta over all sub-intervals by a gauge function assigning a delta to each tag location we can integrate a broader class of functions than Riemann or Legesgue; however, Lebesgue apparently generalizes to other spaces more nicely. (Ironically, I actually had Schechter's page open for inspiration as I was typing my previous post!) More to the point, the Henstock–Kurzweil integral clearly does not use horizontal slabs; it builds on Riemann sums.
 * Set that aside. Is not my final example a death blow to the horizontal slab idea? (This is, of course, the kind of nowhere continuous function that Gandalf61 wanted to address.) My question is, what kind of image retains the idea of a finite collection of range values, but without the slabs? Can we inspire intuition about measurable sets with a picture? --KSmrqT 03:49, 19 June 2007 (UTC)
 * Because the purpose of this picture is not to explain the fact that more pathological functions can be integrated by the Lebesgue integral than the Riemann integral; it is to explain the idea that by partitioning by codomain instead of domain, the integral can be defined on a wider class of spaces.
 * I agree indeed that it is precisely to the point that the Henstock–Kurzweil integral "does not use horizontal slabs; it builds on Riemann sums": this means it is a generalized Riemann integral, not a generalized Lebesgue integral (it makes no sense on measure spaces). But we seem to be talking at cross purposes because of different nuances in the words. For instance, in your final example, there is just one undrawable slab. The slab picture is hopeless for inspiring intuition about ungraphable functions, but that is not its purpose. Geometry guy 10:59, 19 June 2007 (UTC)

I think this discussion is resolved with the following reference:


 * Folland summarizes thusly: "to compute the Riemann integral of f, one partitions the domain [a,b] into subintervals", while in the Lebesgue integral, "one is in effect partitioning the range of f".

Loisel 22:10, 18 June 2007 (UTC)


 * But the meaning of this statement must be explained, Loisel. We are not in the business here of promoting a point of view, but in providing encyclopedic information about a topic. The point of view you express has some validity, in my opinion (see above), but it must be accompanied by riders and explanation, or it is simply misleading.
 * Please everyone, look for compromise here. You know it makes sense! Geometry guy 23:11, 18 June 2007 (UTC)

Ordinarily, for math articles I'm not too much about "compromise" and "NPOV" and "no original research", because math is typically true or false. Unforunately in this case, it is quite obvious that there are strong opinions. In this situation, I will resort to WP:NPOV, WP:VER and WP:NOR. If you want to modify this part of the article, you are welcome to do it, subject to WP:NPOV, where you must phrase things in a neutral way, WP:VER, where you must cite a source which says pretty much exactly what you want to say, and WP:NOR, where you cannot come up with your own explanation.

As far as I know, Rudin and Lang have said nothing on this subject. You are welcome to find a source that says something else. You are also welcome to add something like "Rudin and Lang draw no such analogy between the Riemann and Lebesgue integral". Loisel 00:30, 19 June 2007 (UTC)


 * Jawohl, mein General! Arcfrk 00:38, 19 June 2007 (UTC)

Ah, if you want, you can actually give a formula, by gluing the right bits of Folland, which does give a formula in terms of the horizontal slices of the function, like the picture. Loisel 00:47, 19 June 2007 (UTC)


 * So you are saying that for a simple function that takes on two values, say a and b with a < b, Folland gives the formula for the sum (b-a)v + a(u+v), where u is measure of the preimage of a and v is the measure of preimage of b, instead of simply au + bv? I don't have access to the book right now, so I can't check myself.  --C S (Talk) 01:23, 19 June 2007 (UTC)


 * More or less, although it's of course not said in such a simple way. You have to look up the theorem that Folland gives, which says that there is a sequence of simple functions converging to f in L^1, and how to build this sequence. Then you glue it with the definition of the integral of a simple function. Loisel 02:33, 19 June 2007 (UTC)


 * I just realized I'm not sure your formulae are right, but what I replied is true, I think. Loisel 02:35, 19 June 2007 (UTC)

I have two copies of Rudin (real and complex, and principles of analysis), which one were you looking at? Also, I am compiling a bevy of resources that talk about Lebesgue, I think I will stick all of the excerpts in my sandbox and link them here if there are no objections.--Cronholm144 00:53, 19 June 2007 (UTC)

R&C analysis is the one that discusses the Lebesgue integral (chapter I). I may be wrong, but your PoA one is probably the first year Riemann integral text, in which case it does not talk about the Lebesgue integral. I don't think his other books discuss the Lebesgue integral either. Loisel 01:07, 19 June 2007 (UTC)

Thanks, I will look there first. I have found four books so far and I am about halfway through my books.--Cronholm144 01:12, 19 June 2007 (UTC)

Here it is User:Cronholm144/Lebesgue. I gathered together all the resources that bothered to address the integration geometrically(many didn't). From my own reading, I can see how the picture could be misleading, if we are to include it, (I am leaning against it) we must be extremely careful about how we explain it. The possibility exists that the reader might just see the picture and and come away with a flawed understanding of the concept. It seems to me that it might be more of a liability than help.--Cronholm144 02:04, 19 June 2007 (UTC)

I feel some of Geometry Guy's comments need to be expanded on, particularly the comment on how the picture does not match the usual definition of the Lebesgue integration but does match an "unusual" definition. The picture, to me, clearly indicates a definition of the Lebesgue integral as an improper Riemann integral. I think Loisel would agree that what is "really going on" is we are taking limits of sums as the mesh of the subintervals of the range gets smaller; each sum has a term that looks like (length of subinterval with bottom endpoint y) * (measure of all domain points x that map to greater than y). The function that for every y gives the measure of all domain points x that map to greater than y is in fact a Riemann integrable function, as it is monotone decreasing.

Let me emphasize there is no need for simple functions here, because we are doing a Riemann integration. I think part of the problem in this whole discussion is that Loisel wants to do something like I just explained but also wants to use the machinery of simple functions. However, when using simple functions, the ahem, simplest thing to do is take the sum in the obvious way, i.e. each value of the simple function gets multiplied by measure of the value's preimage, not to create these "slabs" as in the picture. On the other hand, if one wants to think of the Lebesgue integral as the result of slicing up the range and doing an analogous thing to the Riemann integral, one can! It is then in fact a real (improper) Riemann integral. --C S (Talk) 02:32, 19 June 2007 (UTC)


 * Well, for the purpose of the article, I want nothing more than to quote Folland.


 * For the purpose of math...


 * The notion that partitioning the range is of crucial importance in many proofs of the Lebesgue integration theory, starting with the density of continuous functions in L^1 and including Chebyshev's inequality, etc...


 * In addition, partitioning the range is not equivalent to partitioning the domain. If you partition the range in intervals and do the right thing, you get the Lebesgue integral. If you partition the domain in intervals, you get Riemann and not Lebesgue. Loisel 02:45, 19 June 2007 (UTC)



Illustration of a Riemann integral (top) and a Lebesgue integral? JPD (talk) 10:58, 19 June 2007 (UTC)


 * I don't think so. To my trained eyes, they look the same except for the color. Loisel 15:06, 19 June 2007 (UTC)


 * It does capture something for me, because in the first picture the strips have equal width, whereas in the second, the height differences are equal. Perhaps the function could be made less flat to make the difference more pronounced?
 * On the other hand I agree with Loisel's earlier comments that the slab picture isn't really a Riemann integral: you need the function to be invertible for that. The indicator function of the irrationals, as KSmrq pointed out, is a counterexample to such an interpretation of the integral of a simple function. Geometry guy 18:42, 19 June 2007 (UTC)


 * If you are referring to Loisel's response to my earlier remarks, it's not clear to me that s/he (and you) understand my comments. The function need not be invertible.  But slicing up the range does in fact give a Riemann integral of a different function.  This function is obtained by taking the measure of all points in the domain that map above a certain value.  So if the original function is f, then the new function F(y) = measure of the set of x such that f(x)>y.  The Riemann integral being illustrated is then simply \int[0, \infty] F(y)dy (assuming f only took nonnegative values).  It seems to me that this is exactly what you and Loisel have been talking about with the horizontal slabs.  There is no need for simple functions here as you can just take the Riemann integral directly.  --C S (Talk) 06:51, 20 June 2007 (UTC)


 * Thanks for explaining, Chan-Ho, and sorry I didn't get it before. This is quite clever, and I agree that this is one way of looking at what is going on, although one might argue that computing measures before integrating is "cheating" in the context of the Riemann integral. Geometry guy 11:19, 20 June 2007 (UTC)


 * To Chan-Ho Suh: If I understand you correctly, I think you are using the wrong Riemann integral to approximate the Lebesgue integral. You want
 * $$- \int{y \, d F(y)} $$
 * which is actually a Riemann-Stieltjes integral. JRSpriggs 11:47, 20 June 2007 (UTC)


 * Hehe, nope, I wrote what I wanted. Just take a Riemann sum of the integral I defined and a Riemann sum for the one you defined.  Rearrange.  Rinse and repeat.  You will see they give the same answer with the appropriate choice of y in the subintervals. Your integral is corresponds to the usual picture for an integral of a simple function, but my point is that "my" integral corresponds to a horizontal slab kind of picture: for nice functions, each term in a Riemann sum for the integral will indeed be horizontal slab (or a disjoint union of such).  I prefer to use just a Riemann integral since it makes the following pedagogical point better: a Lebesgue integral is nothing more than an improper Riemann integral of a related function.  Of course, as Geometry Guy mentions, it may be kind of "cheating" as one still needs the Lebesgue measure theory, but I wasn't aware I was trying to get away with something here :-).    --C S (Talk) 18:12, 20 June 2007 (UTC)
 * Oh. Are you doing integration by parts and did not tell me? Using that y=0 at the lower limit and F(y)=0 at the upper limit (when y=+infinity). I guess the joke is on me. JRSpriggs 07:00, 21 June 2007 (UTC)

The visual distinction here is almost invisible to me, and I know what point is being made. What's wrong with the traditional illustration of the Lebesgue integral, with horizontal slabs? Septentrionalis PMAnderson 02:15, 20 June 2007 (UTC)




 * Late to the party, eh? What's wrong with it is the question on which this discussion began (see right). --KSmrqT 03:02, 20 June 2007 (UTC)


 * Fashionably late, I would say :) The use of the word "traditional" here is interesting, though. Geometry guy 11:19, 20 June 2007 (UTC)

To add something concrete to the discussion, see (green) Rudin's proof of theorem 1.17 on simple functions: every non-negative measurable function is the pointwise limit of a non-decreasing sequence of simple functions. The technique is to divide up the range into finer and finer rectangles. The link with Lebesgue integration is clear: monotone convergence. Silly rabbit 12:55, 20 June 2007 (UTC)

Proposal for a new image
So here's an idea I'll throw out for a new image, which maybe can be hammered out into something agreeable to everyone. Draw a function that oscillates infinitely many times. Start with some up and down humps that get smaller and smaller, then put some "dot dot dots", then some more humps that get larger. When you draw horizontal slabs for a level, there will now be pieces that get smaller and smaller. So hopefully the idea that is conveyed is that for a slab level you need to multiply the height of a slab by a "width", but here the "width" must be some kind of measure thing.

This kind of picture would (hopefully) avoid the the "it's just inverting the function and Riemann integrating" pitfall that several people have mentioned. On the other hand, it illustrates a right way to interpret the Lebesgue integral as a Riemann integral that has been discussed above. In particular, it still captures this slicing up the range idea, while indicating that all the "nastiness" gets pushed to understanding measures of these preimage sets. Boy, I guess it'd be nice if I actually made a picture, but I'll leave that to someone more industrious for now. --C S (Talk) 18:50, 20 June 2007 (UTC)

Mathematics portal
Interest in maintaining the portal seems to be at an all-time-low. I guess it had been heroically and almost single-handedly maintained by Fropuff for a while, but he appears to be less active on Wikipedia these days: Tompw was another vital contributor, who may or may not still be interested in the project. The "article of the week" would have broken last week and this week, if I had not repeated Golden ratio and then copied an old portal article (the Pythagorean theorem) into the latest slot.

Although I maintained the page in Fropuff's absense (with Fractal, Map projection and Golden ratio, and thanks to suggestions and advice from this forum), I doubt I am sufficiently heroic to keep this up on my own (and admire Fropuff all the more that he did). I would therefore propose to continue the process, which I started this week with Pythagorean theorem, to recycle old portal articles in order, omitting only those which no longer meet our standards. Comments welcome, volunteers even more so.

In addition to this proposal, there is a more general point I would like to make. One of the reasons I would prefer to reuse old portal articles (for the time being) is that it is extremely difficult to find additional mathematics articles which are suitable. Among our articles of Bplus quality and above, the ones that are sufficiently accessible and appealing for the portal have already been used. Some editors may have noticed that in s, I am being a bit harsh on articles that are less accessible than they could be (and have tweaked the B and Bplus descriptors in the grading scheme to reflect this). This does not mean I believe that an article on an advanced mathematical topic should be accessible to the layman, only that each article should be as accessible as is appropriate for its content.

I encourage everyone to create more articles that could appear on the portal! Geometry guy 19:59, 19 June 2007 (UTC)


 * Hmmm, probably "portal interest" is an oxymoron, and "apathy" would be a more appropriate adjective. I wish I had the talent for controversy that KSmrq has used to generate interest in Integral! Anyway, things being as they are, and the portal being dull, I've recycled some old articles. This will satisfy the "article of the week" up to week 40 of this year. Can someone set a wiki-alarm clock? Geometry guy 23:00, 20 June 2007 (UTC)


 * If you want controversy, pick someone's favorite article and have the Portal:Mathematics cite it as an example of how not to do mathematics -- the substandard article of the week. JRSpriggs 07:05, 21 June 2007 (UTC)

Somer pseudoprime
A "" template has been added to the article Somer pseudoprime, suggesting that it be deleted according to the proposed deletion process. All contributions are appreciated, but the article may not satisfy Wikipedia's criteria for inclusion, and the deletion notice explains why (see also "What Wikipedia is not" and Wikipedia's deletion policy). You may contest the proposed deletion by removing the  notice, but please explain why you disagree with the proposed deletion in your edit summary or on its talk page. Also, please consider improving the article to address the issues raised. Even though removing the deletion notice will prevent deletion through the proposed deletion process, the article may still be deleted if it matches any of the speedy deletion criteria or it can be sent to Articles for Deletion, where it may be deleted if consensus to delete is reached.

I'm including this warning here rather than on the page creator's page because the creator was an anonymous IP address that hasn't been active since 2005, and since it's likely to get more appropriate attention here. —David Eppstein 04:06, 20 June 2007 (UTC)
 * The article has an OEIS link; A085046, which is noticeably better than our article in explaining these. They alternate between odd squares and (even squares minus one); I have no idea why they're called pseudoprimes. I am not tempted to contest. Septentrionalis PMAnderson 17:54, 20 June 2007 (UTC)


 * Well, we need to be careful about allowing entries that are only sourced by OEIS. I've learned something about their process from someone who accepted and edited submissions.  They basically accept any sequence that people submit.  In some cases, cranks will submit some semi-garbage, and then the editors and some others can clean it up into something reasonable.  They aim to collect all interesting number sequences.  Wikipedia has a different goal.  We generally want recognized scholarly work.  --C S (Talk) 21:58, 20 June 2007 (UTC)


 * I don't see how the formula in the article generates A085046, and looking at A085046 I don't see why these should be called pseudoprimes. All but the first two are composite: either D2 or D2−1. And what has Somer (Lawrence Somer?) got to do with this? What does it mean that the only Google hits for "Somer pseudoprime" are to this article? --Lambiam Talk  23:28, 20 June 2007 (UTC)
 * There's a typo in the formula; someone got confused by the even or odd case. Chan-Ho's explanation seems good for the absence of hits. But if it's going away, why worry? Septentrionalis PMAnderson 18:26, 21 June 2007 (UTC)

Non-universality in computation on AFD
I've nominated Non-universality in computation for deletion. See also Wikipedia talk:WikiProject Mathematics/Archive 26. --Lambiam Talk 13:04, 20 June 2007 (UTC)
 * User:Dhaluza has extended the discussion of this issue to the Village Pump. EdJohnston 18:52, 21 June 2007 (UTC)

Partial derivatives
I always write


 * $$ \frac{\partial^2 f}{\partial y \, \partial x}$$

rather than


 * $$ \frac{\partial^2 f}{\partial y \partial x}$$

Should we have a norm prescribing this usage?

Names and links

 * This was proved by Pincherle (1880).

I think the usage above makes sense only if the list of references has an item labelled


 * Pincherle, S. "Blah Blah Blah", Journal of Whatever, 1880.

Opinions? Michael Hardy 18:49, 23 June 2007 (UTC)


 * I agree that a year in parentheses should always indicate a Harvard-style citation, and should be reworded ("by Pincherle in 1880") if it is meant to just make a claim about a year. &mdash; Carl (CBM · talk) 19:36, 23 June 2007 (UTC)


 * Just as an additional note for those who don't already know (I found out about this combination of templates only this week), citation and harv, harvnb, and harvtxt work well together to make Harvard-style citations. As in and  . Advantages of doing it this way over formatting it manually are that it's likely to be more consistently formatted, that it generates COinS metadata, and that the Harvard citation in the text gets html-linked to the appropriate line in the references. The different harv templates produce different formatting, but the one here with only the year in parens is harvtxt. —David Eppstein 20:19, 23 June 2007 (UTC)


 * Is this templatic synergy worth mentioning at or near WikiProject Mathematics/Reference resources? I never use Harvard style myself. --Lambiam Talk  04:20, 24 June 2007 (UTC)


 * Added --Cronholm144 05:10, 24 June 2007 (UTC)


 * Apparently I've been too subtle. I've been using and promoting the Harvard citation templates for some time now. (See "area of a disk" and "integral", for example.) I like them for all the reasons David mentions, and because one template handles books and journal articles and everything else. (I'm also familiar with a weakness or two.) They definitely deserve an explicit mention at reference resources.
 * &lt;soapbox&gt;For web pages especially, Harvard style is superior to footnotes. On a printed page, moving the eyes suffices to read a footnote, yet it's still a distraction from the flow of the text. On a web page, hover popups or sidenotes would be the closest equivalent, but we don't have those and we'd have to train users to hover. Web "footnotes" are a misappropriation of a print idea; the to-ing and fro-ing is awkwardly jolting. (Properly, they're "endnotes".) As well, Harvard references often tell me enough from just the author(s) and date when I'm reading in a field I know, whereas a mere number tells me nothing; thus even in print Harvard style can be less distracting. Harvard style takes more space at the point of reference, which has the benefit of highlighting the absurdity of flurries of footnotes.&lt;/soapbox&gt; --KSmrqT 05:51, 24 June 2007 (UTC)

Some featured articles, or are they?
In response to a request made some time ago, I have, from time to time, been checking unsigned ratings and signing and dating them.

In the course of doing this I found a few FA-Class articles which don't, in my opinion, currently meet the featured article criteria (which is a requirement for FA-Class in the grading scheme). The articles I have in mind are Cryptography, Galileo Galilei and Monty Hall problem, which I reckon are about Bplus-Class.

Now I can't sign a rating I don't agree with, and I don't want to pass them over. Does anyone think these meet the criteria? Geometry guy 12:39, 23 June 2007 (UTC)

PS. There are also a few good articles I am not sure about: see Nash equilibrium, Best response and Probability theory.

PPS. Category:Mathematics articles with no comments now has less than 200 articles in it, so why not take a look and sign a maths rating today! :)


 * For the featured articles at least, there are links from the talk page to the discussions when the FA status was granted or reviewed. Those discussions may provide insight into what problems were seen during the review. You can always nominate an FA article for review, but that will be more beneficial if you're willing to stay with the review and fix the issues raised, since the reviewers are often reluctant to make even trivial changes themselves. &mdash; Carl (CBM · talk) 14:30, 23 June 2007 (UTC)


 * The problem here is that FA standards have changed so much even in the last year, and only Monty Hall problem has been reviewed recently. This last review began with an unedifying argument over inline citation and never fully recovered in my view, although a lot of effort was poured into copyediting. I'm reluctant to take it to FAR or GA/R again, although reviewers at the latter are working on improving their process, and do now quite often make edits to articles themselves. Geometry guy 15:44, 23 June 2007 (UTC)


 * Concerning Cryptography, I've found your (signed) comment a bit, ahem, cryptic. Plenty of inline citation, and what about the lead? Arcfrk 05:21, 24 June 2007 (UTC)


 * Yeah, it is a bit. I'm getting into the bad habit of thinking everyone knows WP:LEAD back-to-front. But forget about what I think, that isn't why I'm posting here. What do you think about the article? Geometry guy 10:02, 24 June 2007 (UTC)

Some Good Articles, or are they?
In addition to Nash equilibrium, Best response and Probability theory, Sylvester's sequence appears not to meet the criteria. The problem is again the lead, which at the moment is a definition/first section, rather than an overview. This should be fairly easy to fix, but I think other editors may be able to do a better job than I can. Anyone? Geometry guy 15:28, 24 June 2007 (UTC)


 * I made another pass at Sylvester's sequence. Criticism welcome. —David Eppstein 15:56, 24 June 2007 (UTC)


 * Thanks David, that was quick! I never knew that the Sasakian Einstein metrics on spheres were linked to this sequence. Very nice. Geometry guy 16:30, 24 June 2007 (UTC)

E is for ugly
Another exiting post by me, everyone! E for some inexplicable reason is in quite a poor state. Here are some things I have found:

Lie groups
These are not problem articles but all of the polytope articles are stubs. Is some kind of merger in order?
 * E6 (mathematics), E6 polytope
 * E7 (mathematics), E7 polytope
 * E8 (mathematics), E7½, E8 lattice, E8 manifold, E8 polytope
 * I thought of proposing a merger of some of the polytope articles in the past. A similar case is the various hyperbolic tessellation articles (see the Order_*_tiling articles in Category:Tiling).  These remind me of Wikipedia's zoology articles: nice infoboxes on stub articles, with information presented clearly and uniformly.  Maybe it's better to have a broader discussion on polytopes, tilings, and other articles of the mathematical "zoo" independently of the fact that the above examples happen to start with the letter E. Silly rabbit 10:24, 24 June 2007 (UTC)

Yes, I believe that would be appropriate, E just happened to be the catalyst. To start things off, should there be a merger? or are the free-standing stubs just an inevitability?--Cronholm144 10:32, 24 June 2007 (UTC)


 * Short answer: no.
 * Long answer... My point of view on this is that there is a clandestine WikiProject out there, which I will call WikiProject:Polytopes and tilings, which, for reasons known only to itself, wants every polygon, polyhedron, polychoron, tiling, tessellation or lattice, no matter how regular, irregular, stellated, or truncated, to have its own article. As Silly rabbit notes, WP:PAT have generated a lot of uniformly presented information, with nice infoboxes and classification tables.
 * I think it is inevitable that there will be such articles. They have a certain taxonomic appeal. Some of the information is arguably indiscriminate rather than encyclopedic, but I would rather not worry about it. If we merged En polytope into En (mathematics), we may well be depriving WP:PAT of three of its most notable articles.
 * So, when I see an article on a polytope or a tiling, I think to myself, "that is part of WP:PAT", then move quietly on.


 * Most other mergers of the above are untenable: the five exceptional Lie algebras/groups/root systems are distinct and notable enough to deserve separate articles, and the E8 lattice is a key building block in the theory of unimodular lattices. Geometry guy 11:09, 24 June 2007 (UTC)

Fair enough, I will treat WP:PAT articles the same way that I treat WP Numbers articles. I will think to myself "my goodness, that seems rather indiscriminate...oh well" and move on :)--Cronholm144 11:17, 24 June 2007 (UTC) P.S. Even E 7.5 is unmergeable?


 * Many of the tessellation articles are unreferenced, although most could probably be referenced with Grunbaum's "Tilings and patterns" tome. I don't have a copy at my disposal at the moment, but I have written Template:Grunbaum which optionally accepts a |pages=  and/or  |chapter=  option.  So if anyone wants to tackle these articles, please do so.  (Note: I don't know for how long Template:Grunbaum is going to be allowed in the main space, so use subst.) Silly rabbit 11:23, 24 June 2007 (UTC)


 * Hi. I can't tell if I'm making anything worse on the E groups, but I'm coming from the polytope side, and just added a sort of "family" page at: Semiregular_E-polytope. I'd definitely prefer to keep polytope pages separate, mostly because there's a whole family of uniform polytopes with each semiregular form. Tom Ruen 02:46, 12 July 2007 (UTC)

Should they be listed?

 * Ecliptic latitude, Ecliptic longitude
 * Eddy covariance
 * Edge of chaos
 * Notable popular idea in complex systems theory. I don't see the problem? -- Jheald 11:20, 24 June 2007 (UTC)
 * Edgeworth conjecture
 * Early stopping
 * Notable mathematical method (well, hack) in training neural networks. I don't see the problem? -- Jheald 11:20, 24 June 2007 (UTC)

I think these mostly belong to the category of articles that are mathematical enough to be on the List of mathematics articles but not relevant enough to WPM to need a maths rating. The one I'd be most tempted to rate is Edge of chaos; the one I'd be most tempted to remove from the List of mathematics articles is Eddy covariance (check "What links here" for that one). Geometry guy 11:21, 24 June 2007 (UTC)

Okay, as long as we are fine with them being listed(I though maybe some of them had slipped through the cracks).--Cronholm144 11:26, 24 June 2007 (UTC)

Should they be prodded?
Okay then, I will try to expand it. Does anyone have a copy of his original paper? It was published in the journal of research for the national bureau of standards, I think.--Cronholm144 09:57, 24 June 2007 (UTC)
 * Eclectic probability Probably not ;) although it might be worth an AfD to prod someone into sourcing it. Geometry guy 11:34, 24 June 2007 (UTC)
 * Edge-to-edge tiling I merged this with tessellation. -- Jitse Niesen (talk) 09:59, 24 June 2007 (UTC)
 * Edmonds matrix No.  Reference provided, definition expanded slightly. Notable (but will likely never be more than a stub). Silly rabbit 09:48, 24 June 2007 (UTC)
 * Edmond's algorithm No. A quick googling for the reference Edmonds, “Optimum Branchings” establishes some degree of notability for this algorithm (the paper is referenced quite often).
 * Effective descriptive set theory . And risk upsetting both Trovatore and CBM (who have both edited the stub)?! Not a wise move... :) Geometry guy 11:34, 24 June 2007 (UTC)

You don't have to worry about upsetting me, at least, but this article is a shame. EDST is an extremely important branch of contemporary set theory but our coverage is minimal. For example we don't have an article on Glimm–Effros dichotomy, a result on simple invariants (or lack thereof) in mathematics. Trovatore is an expert in the area, but I'll take a stab at expanding the article myself. &mdash; Carl (CBM · talk) 13:06, 24 June 2007 (UTC)


 * Thanks Carl - of course I was joking: what I was really saying, beneath the attempted humour, is that if you and Trovatore have both edited it, then it is obviously an important topic and so doesn't need to be prodded. Bon courage with the expansion! Geometry guy 14:32, 24 June 2007 (UTC)

Fair enough, Suggestions? .Notable sources? It hasn't changed much since 2003(!). I can go Googling and JSTORing but it would be good if I had an author or two. --Cronholm144 09:09, 24 June 2007 (UTC)
 * EGARCH. Merge with GARCH? Geometry guy 11:36, 24 June 2007 (UTC)
 * Effective results in number theory Most certainly, not! Arcfrk 09:01, 24 June 2007 (UTC)
 * Note that the absence of references in an article is in no sense a justification for deletion!

The article has an identity crisis, and you should ask Charles Matthews, who edited it recently, for suitable references. Lang's Diophantine Geometry would be good as a general reference. Arcfrk 10:13, 24 June 2007 (UTC)

Are you referring to Lang's Survey of Diophantine Geometry or are there two different books? I will ask him (BTW, the threat of deletion is a great motivator, notice that no one has commented anywhere but the prod section...sigh, I merely propose that the articles be proposed to be deleted, if no one comments like at Jarnik's theorem, then I PROD them)--Cronholm144 10:30, 24 June 2007 (UTC)

I've added two clean-up tags to this. CBM has edited it, and may be able to come up with references. Geometry guy 11:41, 24 June 2007 (UTC)
 * Effectively calculable
 * I merged it with Church-Turing thesis. The term is rarely used anymore except in that context, and the article was really just a poor version of the Church-Turing thesis article. &mdash; Carl (CBM · talk) 13:06, 24 June 2007 (UTC)

Merger? + poorly written

 * Ecological correlation, Ecological fallacy
 * Edge-transitive, Edge-transitive graph
 * This one is the usual distinction between geometric things with edges (polyhedra, tilings, etc) and combinatorial things with edges (graphs), visible also e.g. in the split between vertex (geometry) and vertex (graph theory). It doesn't help that the polyhedron article links to the MathWorld graph article... Any attempt to merge the two article would have to wrestle with some subtle definitional differences, e.g. one can have a polyhedron with an edge-transitive graph as its skeleton that is not edge-transitive geometrically (simplest example: a scalene triangle). —David Eppstein 10:40, 24 June 2007 (UTC)

I am only 50 articles in so there is more to come. :)--Cronholm144 08:28, 24 June 2007 (UTC)

By the way, I am willing to make most/all of these changes myself, I just need direction and consensus before editing, I would like a little more participation than at the J articles(are my constant posts scaring you away? :. Anyway, Cheers--Cronholm144 08:38, 24 June 2007 (UTC).


 * As for constant posts, if others feel it is too much the details could be moved to a project subpage, but I think this is an appropriate place to look for comments. You might also look through User:VeblenBot/Oldpages which lists some pages that have not been edited for over a year. &mdash; Carl (CBM · talk) 13:06, 24 June 2007 (UTC)

Cool link, :) but you know this just means more delightful comments from me. In all seriousness though, I plan to go through every math article pruning and posting as I go. I imagine this will take several months but the combined effect could burn people out(including me). The only worry that I have is that a subpage will go the way of the dodo and the math portal. I think that I will wait and see how it goes. In any case, I plan to post fewer articles next time. --Cronholm144 13:19, 24 June 2007 (UTC)


 * Rumours of my extinction have been greatly exaggerated. The Mathematics Portal 14:35, 24 June 2007 (UTC)

AFD on Probability derivations for making low hands in Omaha hold 'em
This looks like it might be a fairly interesting AFD discussion. I expect there may be conflicting opinions even among members of the WikiProject, so I thought I would advertise it here. --C S (Talk) 14:34, 24 June 2007 (UTC)

BibTex for Wikipedia?, the second
After the discussion a couple of days ago, I programmed a database to facilitate the creation and use of consistent and correct and complete references like this (automatically generated) one:

You may find the first result of these efforts here.

Right now, there are three intertwined databases, one for books, one for authors and a third one for publishers. The design of the database is intended to meet the needs of WP references, e.g. books are linked to their (co)authors etc., hence wikilinks to authors will appear (if there are any). Besides this, the main distinction between the database and this Template of User:Diberri is, that one may look up a book by its title, which seems more reasonable than by its ISBN.

I think, at the current state it's reasonable to call this a feasibility study. I would like to hear people's ideas about it, whether it's a reasonable thing to pursue further. Obviously, right now the database is practically void, so besides further programming (which I volunteer to do), it needs willing people to inhale life to it, i.e. data. This may probably be done automatically or semi-automatically, using the references which already exist in WP articles (or Math articles or whatever). At the moment this latter feature is not yet programmed, other reasonable things like looking up the ISBN database when one has the ISBN of a book, adding a similar database for articles in journals etc. are also not yet done. If the database is considered to be useful to you guys, I will implement these shortly, as well as other ideas emerging of your impressions. So, tell me what you think. Thanks. Jakob.scholbach 03:41, 18 June 2007 (UTC)


 * I think this is a great idea and would encourage you to continue the feasibility study, especially methods for the the automatic and semi-automatic population of the database. I suggest it be developed into a "proof of concept" for mathematics articles. Geometry guy 12:56, 18 June 2007 (UTC)


 * This is great indeed, a true database fillable by editors. Much better than everybody keeping their own subpages.


 * A somewhat related comment is that today I found out that one can get BibTeX info from Google Scholar (one has to enable one's preferences to see a link to BibTeX citations for each search result). This can be great help when writing papers. :) Also, it is easy to write a script to convert BibTeX to cite book format, although the quality of the result won't be high (no ISBN, last name/first name order, etc.). Oleg Alexandrov (talk) 02:00, 19 June 2007 (UTC)


 * I haven't looked at the details of any of this, but let me just voice my support for something like BibTEX for Wikipedia. Loisel 02:03, 19 June 2007 (UTC)

Thanks. Is it possible to parse the Mathematics WP articles and automatically retrieve all the contained references? Jakob.scholbach 17:04, 19 June 2007 (UTC)


 * It is, but there are others here with much expertise in this kind of thing who will be able to answer in more detail. You mught also find WikiProject Mathematics/References useful. Geometry guy 18:50, 19 June 2007 (UTC)
 * In fact, I suggested this some months ago, and Carl seemed willing to help (though he has since become an admin, so may be frittering away his time in other ways now).
 * I do hope this project succeeds magnificently. And it would be such sweet irony if we mathematicians, who have so vigorously opposed the inline citation squad, are the ones to bring easy, reliable citations to Wikipedia. :-) --KSmrqT 00:13, 20 June 2007 (UTC)
 * I can provide, on demand, a list of all the contents of all cite templates used on math articles or the contents of all references sections of math articles. The more difficult thing would be processing this data into a database. I'm sure many sources are duplicated, likely with errors in some, and it would take a lot of manual effort and verification.
 * Let me also point out User:VeblenBot/Unreferenced, a list of math articles that an automatic scan thinks have no references or external links section. &mdash; Carl (CBM · talk) 01:20, 20 June 2007 (UTC)
 * When you say "all cite templates", does that include citation templates? (I hope!) --KSmrqT 02:58, 20 June 2007 (UTC)
 * OK, good. I will get back to you, Carl, when I'm done with the programming necessary prior to this. Jakob.scholbach 02:03, 20 June 2007 (UTC)
 * Jakob, please take your time, I can do it whenever. Ksmrq, yes, I can pull any template(s) you're interested in. The most difficult thing is just downloading all the math articles. &mdash; Carl (CBM · talk) 20:48, 20 June 2007 (UTC)

Can I say that I really detest the inversion of names in references? I really find it a negative, searching the site as much as I do, to have to search "Gauss, C. F." and so on with all the variants of "C. F. Gauss". In other words, it doubles what you have to do with an exhaustive search. The virtues of inversion seem to be mostly in the world where one does searches by scanning down columns. In other words, this is a paper habit. Charles Matthews 21:01, 25 June 2007 (UTC)


 * Yes, this is probably something you should tell those guys developing the template and the other ones. I find it somewhat natural to sort a list of references by the last name of the author, though. As far as the database is concerned, first and last names will be stored separatedly, so any reasonable formatting will be possible to implement. Jakob.scholbach 22:05, 25 June 2007 (UTC)

Links to natural topology
A certain User:Karada has been linking every occurrence of the phrase natural topology to the non-existent article natural topology. I've reverted a few of them, but there are many more articles to go through. To the best of my knowledge, natural topology typically does not have a prescribed meaning (in the sense of natural transformation) although I can easily imagine some uses where the term is "natural" in the categorical sense. Since there is no article on the subject, is there a consensus here that these edits should be reverted? Silly rabbit 19:50, 24 June 2007 (UTC)

Another possibility is to write an article, such as natural (mathematics) covering the basic (imprecise) uses of the word natural in mathematics. I have no idea what such an article might look like, though. Thoughts? Volunteers? Silly rabbit 20:02, 24 June 2007 (UTC)


 * Thank you for your comments. "Natural topology" seems to be, at the very least, a mathematical jargon term, like "up to", with a specific meaning in topology, even if it does not have a precise formal meaning. If we can't explain what we mean by this, we are doing our readers a disservice. If it hasn't got a meaning which can be articulated, we shouldn't be using it at all.


 * The problem is that the phrase "natural topology" is used, but nowhere defined, throughout many topology-related articles, and is indeed used in ways specific enough to be able to write papers with titles such as "There is no natural topology on duals of locally convex spaces" . Clearly, "natural topology" must mean something in this context, or the paper wouldn't get published in a peer-reviewed journal: but what? Saying "it's informal" is like saying "it's a secret, we can't tell you", or "we're handwaving here, please ignore this bit" or "oh dear, did you miss that lecture?".


 * It's clear that "natural" means something a bit more precise than just "obvious" or "simple" in this context: if it just meant something as subjective as "obvious" or "simple", it would be hard to talk about the nonexistence of such a topology in a mathematical paper. From what I can see, "natural" must have a specific (even if informal) meaning in the context of topology.


 * My best guess is that "natural" in this context means something like "induced by the partial order(s) used in the construction of this structure". Is this correct? If not, can we find someone who does know what "natural" means in this context? -- Karada 20:17, 24 June 2007 (UTC)

I think it's usually a bad idea to write such articles, but if our hand is forced, then we have to be very upfront and clear about the fact that the term has no precise meaning (and hope no one asks for a citation, because hardly anyone bothers to note explicitly that terms with no precise meaning have no precise meaning). This is a very dangerous situation and can easily result in disaster articles like definable real number that can neither be easily fixed nor deleted. --Trovatore 20:27, 24 June 2007 (UTC)


 * Thank you! That's exactly what I was trying to get at by making those links. Either "natural" in this sense has a precise meaning, or it doesn't, and if it doesn't, its meaning should either be be possible to explain as a piece of informal jargon, in an article similar to "up to", or the usage should be avoided entirely, and the articles in question reworded to be more precise, more newbie-friendly, or both. -- Karada 20:31, 24 June 2007 (UTC)

By the way, if by chance Karada is right and the paper from the Springer journal does intend a precise meaning for the phrase "natural topology", then it must be a meaning from some specific subfield of functional analysis, and any article written about it should have a title with a parenthetical disambig phrase for that subfield. Otherwise there's the danger that the usual usages of the phrase, which have no precise meaning, will be inappropriately linked to the article for that precise meaning. --Trovatore 20:35, 24 June 2007 (UTC)


 * Here's an example: Wikipedia's ordinal number article contains a sentence that says, in full, "Ordinals have a natural topology." Now, that either means something precise, or it doesn't. If it means something formal, we should be able to create a natural topology article, about the subject of that sentence. If it means something informal, we should say that in sufficient detail for it to be understood. (Could this mean something like "A very simple topology can be induced on the ordinals using the 'greater than' order relation between them, and this is generally referred to by mathematicians as their 'natural' topology"?) For other examples of similar usages throughout Wikipedia, please see Special:Whatlinkshere/Natural_topology -- Karada 20:40, 24 June 2007 (UTC)


 * It is a worthwhile term: the point is to make a particular map or collection of maps continuous. Often there is a "best" topology which does this. I've made a start. Please expand and add your own examples. Geometry guy 20:53, 24 June 2007 (UTC)
 * G-guy, I really think that was a bad idea. The problem with writing articles on imprecise terms is it tends to make them seem more precise than they are. You may think you've abstracted the commonality from the varied usages and made them genuinely precise, but that's original research. I think the best course of action now would be for you to request deletion of the new article -- if no one else has yet edited it, that can be done without further formalities. --Trovatore 20:56, 24 June 2007 (UTC)


 * Any ambiguity and imprecision does not rest with this article. The article could actually be made quite precise, and it reflects most standard usages of the term. The imprecision rests with question "what are the natural operations or maps in a particular context": I certainly would not want to write an article on that (an overarching statement here surely would be original research). So I don't see the need for right now, but thank you for the suggestion: if no one has anything further to say on the topic, it might be useful. Geometry guy 21:06, 24 June 2007 (UTC)
 * PS. If everyone here things that the idea of a "natural topology" as the finest or coursest topology (if such a topology exists) that makes a map or collection of maps continuous is original research, please let me know, and I will write a paper on it and send it to a top journal. God knows, I need the publications... Geometry guy 21:36, 24 June 2007 (UTC)
 * In that paper, it probably wouldn't hurt your reputation as a topologist to spell "coarsest" correctly. Michael Hardy 22:00, 24 June 2007 (UTC)
 * Thanks! Luckily, I'm not planning to build a big reputation as a topologist, but at least I spelt it right at natural topology. Geometry guy 22:28, 24 June 2007 (UTC)
 * PS. Hmmm, I see the latter is only right because someone else fixed it. I must be losing my mind. Can someone recommend a good clinic? Geometry guy 22:35, 24 June 2007 (UTC)


 * Just because something is imprecise, doesn't mean we can't have an article about it, even in mathematics. Handwavey ideas like up to are perfectly useful, even if it needs to be explained that they are informal; indeed, an article which explains that it is not a precisely defined term, and how and why it is used informally, seems to be just what is needed here to help the baffled beginner.


 * And, reading the comments above, we probably need to go further and have an article about natural operation as well, even if it has to explain that it is a jargon term with no formal meaning, and is the subject of great debate among mathematicians as to whether it has one at all. -- Karada 21:09, 24 June 2007 (UTC)


 * That's an easy redirect: the most common (i.e., sourced) way to make this precise is the notion of a natural transformation. Geometry guy 21:17, 24 June 2007 (UTC)

A few thoughts:
 * I hope everyone here understands that, just because something is "original research" in the WP sense, that doesn't mean it's original enough to publish. In context it means it's going outside the encyclopedist's purview, not that he's necessarily done anything very creative.
 * Just the same, it is possible that I overreacted in this case. What I really want to avoid is a clusterf*** like definable real number, where you have a necessarily imprecise notion, used all over the place in the literature but with meaning entirely context-dependent, but where many of the authors seem to think it has a unique precise meaning and write as though it did.
 * So for example large cardinal property is another concept where there is no generally accepted precise definition, but also little if any disagreement about whether an individual candidate qualifies as a large cardinal property, and it's too important to ignore. Is "natural topology" really in that category, or is it more or less just jargon?
 * Finally, I disagree with Karada about the utility of jargon articles like up to. I think they're a blight. --Trovatore 22:06, 24 June 2007 (UTC)


 * I more or less agree with Trovatore that it is a bad idea to link every occurrence of natural topology with the recently created article. Nevertheless, I have reverted all of my reverts save one: Euclidean space, where I feel that "...the natural topology induced by the metric" is clearly what was intended rather than "...the natural topology induced by the metric".  Let me say that, per Trovatore, I still object to a blanket decision on linking every occurrence of the term natural topology on Wikipedia to this particular article, though.  In the case of Euclidean space, this is a detriment rather than an improvement to readability, for example.  Silly rabbit 22:27, 24 June 2007 (UTC)


 * I agree with Silly rabbit's choice of links. Natural topology isn't a great stub, so I encourage editors to (a) improve it, and (b) link to it with caution. I still think it is an article worth having, though. Geometry guy 22:40, 24 June 2007 (UTC)


 * How about simply adding a few sentences to Mathematical jargon instead of creating an article? Arcfrk 23:37, 24 June 2007 (UTC)


 * After checking out a few of these links to Natural topology, I came to the conclusion that such blanket linking a is really bad idea, since no matter what is at that page, it would not help understanding the meaning of the linked terms in the instances that I've reviewed (which is frequently subtly or completely different). Or to put it differently, there is no such an overriding thing as Natural topology as far as these linked articles are concerned. Arcfrk 00:49, 25 June 2007 (UTC)


 * And now I've gone over all of them manually, and after checking that the linking is inappropriate in each case, unlinked. Arcfrk 01:22, 25 June 2007 (UTC)

My impression of the topic is that the meaning of "natural" is sociological or psychological: it has nothing to do with coarseness or making things continuous, it just means that there is one topology that most experts on the topic would pick as the most appropriate to use. I think that trying to nail the term down any further would be a mistake. The best we can hope for is a stubby article that says as much and points to a widely-varying collection of uses of "natural topology" in the literature to back up that point. But to do so would most likely be original research by synthesis. —David Eppstein 06:19, 25 June 2007 (UTC)


 * I'm glad you brought in original research by synthesis. That really brings the issue into focus for me.  Linking natural topology to a particular use of the term would need to be cited, particularly for things like "the Zariski topology is natural" or "the Euclidean topology is natural".  Both are true, but since neither is commonly introduced as a natural topology (in the strict sense), it would need to be referenced somehow. Silly rabbit 10:09, 25 June 2007 (UTC)


 * Long ago, I put the sentence "Ordinals have a natural topology." into the lead of ordinal number. It was not intended to be jargon or to have any formal definition. I was just putting the reader on notice that there is a topology which has a special relationship to ordinals. The details are covered in a section further down in the article (now farmed out to order topology). linked "natural topology" to his new article natural topology.  reverted that and added a comment saying "This is an obscure claim. Are ordinals a topological space? Or even a set? What is the topology? Needs a bit of clarification." which shows a lack of understanding of the topic.  reverted that and changed the sentence to "Any ordinal number can be made into a topological space by endowing it with the order topology." which is correct, but not appropriate for the lead since it will scare off unsophisticated readers. JRSpriggs 09:27, 25 June 2007 (UTC)


 * Reply to JRSpriggs. I prefer the original version, but I see some logic in putting details in up front. Would a better way to say it be "Ordinals have a natural topology: the order topology.  This seems less scary than the current revision, but has the advantage of saying what the "natural" topology is.  Silly rabbit 09:35, 25 June 2007 (UTC)


 * A bit unclear, because ordinals don't form a set (which is what puzzled Arcfrk above): instead " Any ordinal has a natural topology: the order topology. " Tobias Bergemann has just fixed it in a similar way, but avoiding the use of the word "natural" Geometry guy 10:49, 25 June 2007 (UTC)


 * Ha! Yes, that's what I meant.  Not ordinals are a topological space, but any ordinal... (etc.)  Silly rabbit 10:52, 25 June 2007 (UTC)

I wonder if it would help to keep in mind a distinction between "a natural topology" and "the natural topology". In quite a few contexts people write "Equip it with the natural topology". It seems to me that something quite specific is meant here, and a link to an article which explains that could be helpful. On the other hand, in the ordinal example, the language "any ordinal has a natural topology: the order topology" is quite different. Here we don't want to link to natural topology, only to topological space and order topology: if we had to link the word "natural", then probably the best we could do is link it to wiktionary!

PS. Just curious, and I haven't thought it through, but what are the left and right order topologies in this case? Geometry guy 11:05, 25 June 2007 (UTC)


 * An overexposure to category theory with its technical use of "natural" makes me automatically expect such a sense when I see the term in mathematics. Clearly, many authors do not bear that burden, and use the word "natural" as naturally as they breathe. An analogy, for those who do not relate to categories, is "group", which carries no technical meaning for a lay reader. I wonder if there are a multitude of such examples that we fail to see. I expect we will see more. --KSmrqT 22:57, 25 June 2007 (UTC)

Lead
I have noticed lead problems with most mathematics articles, at least as far as the general editing advice at WP:LEAD goes. For instance, they often fail to give an adequate summary of the article. I realize that there are possibly good reasons for not abiding by some of the lead recommendations in many math articles in the spirit of Make technical articles accessible. Does the math project offer any more specific guidelines on the lead? Silly rabbit 14:46, 25 June 2007 (UTC)


 * Yes, most mathematics articles do have lead problems. However, it is perfectly possible to have a decent article without satisfying WP:LEAD. Often the problem is purely cosmetic (e.g. the lead material really belongs in the first section, or the lead is a one-liner but the first section contains good lead material). Even if it isn't, an article which is accessible to someone is much better than no article at all. We have a lot of pretty decent B-Class articles, and for me, it is only really when we want to lift them to B+/GA-Class and above that issues such as the lead, and "is it accessible as it could be?" really start to bite. I'd be interested to know what other people think. Geometry guy 19:04, 25 June 2007 (UTC)

Perhaps we should start a new thread, since clearly my question doesn't have an easier answer (along the lines of "Why yes, SR. That was discussed 8 months ago in [this thread].  See [this new policy recommendation].")  A case study is my recent foray into bringing exterior algebra up to scratch. The lead has definite problems: it aims to give both a summary of the article and to be partially accessible to a general audience. I think its clear that these objectives are incompatible here (unless some more brilliant editor wants to take a stab at it.) Silly rabbit 20:08, 25 June 2007 (UTC)


 * For the exterior algebra, solution seems fairly obvious: delete the second paragraph of the lead and only keep a non-technical sentence or two from the third one, mentioning what additional structures are present on exterior algebra, possibly, emphasizing those applications where that structure is important. Also, what are the guidelines about citations from the lead? Arcfrk 20:19, 25 June 2007 (UTC)


 * In cases like this it sometimes helps to have an "Informal introduction" in section 1. If the lead is a summary then the accessibility of the lead should reflect that of the article. In other words, much of the lead should be as accessible as much of the article, but if there are important technical points or definitions, then I don't see why they can't also be mentioned in the lead.
 * As for citations, I've seen different things in different places. One argument is that since the lead should contain no information which is not expanded in the body of article, this information can be sourced there instead. The counterargument is that if any lead information is "likely to be challenged" it might be more helpful to provide a cite in the lead anyway. I guess this rarely applies in math though. Geometry guy 20:49, 25 June 2007 (UTC)


 * To me, WP:LEAD is a stylistic choice — there are plenty of other ways to begin a piece of expository material. But it's a stylistic choice that doesn't hurt us, I think, and one that's been made Wikipedia-wide, as part of a set of choices to make the content here more unified. Is there a good reason to depart from it for math articles? —David Eppstein 20:20, 25 June 2007 (UTC)


 * It is slightly more than a stylistic choice, because for some articles, the lead alone will be included in some fixed editions of Wikipedia. In any given article, though, there are good reasons to depart from it initially, in that one cannot write a lead for a stub, or for an article in development. However, once a mathematics article reaches about B-Class, it seems to me that its further development and WP:LEAD are perfectly compatible, and I agree that there is no reason to depart from the latter. Geometry guy 20:49, 25 June 2007 (UTC)

I'm inclined to say any mathematics article that begins with the word "Let..." is horribly wrong in its intro. My favorite example of this sort of thing remains an article on something other than mathematics. It's called schismatic temperament. Given the usual meanings of those two words, I guessed that it was about a psychiatric disorder. Nothing in the first sentence (when I first looked at it) told the lay reader that it was not about chemistry, politics, fiction writing, etc. I changed it so that it starts with the words "In music,...". Such a brief phrase, but worth a lot. (Of course, there's more to lead sections than that.) Michael Hardy 22:35, 26 June 2007 (UTC)


 * &hellip; and here is the diff: The article looks way better now Arcfrk 00:12, 28 June 2007 (UTC)

New nav template on logic articles
User:Gregbard has created a new Logic template and put it at the bottom of some logic articles, including a few in math logic. Now, I have to say it's quite a bit slicker than the navigational templates we've seen in the past. It's relatively unobtrusive, just a thin horizontal bar across the bottom of the article with a "show" button in the right-hand corner. If you click on "show" it pops up a bunch of subfields and related articles.

There's at least one of his categorizations I don't entirely agree with, but that can be dealt with. The question is, is this sufficiently different from the nav templates we've rejected in the past, to reconsider whether to allow it? I'm undecided myself. --Trovatore 08:58, 27 June 2007 (UTC)


 * I like show/hide wikitables, and I think this is a very appropriate use of them. I don't know what arguments have been made in the past, but in my view, navigation templates are not entirely encyclopedic content because they "label" the article and link to other articles without providing relevance or justification: they provide a "See also" section with no option to prune the list. On the other hand, for many readers, they are a great convenience. So I find a "collapsible collapsed" navigation template a nice compromise: unobtrusive, but available. I think we should consider doing that with more of our navigation templates: it is quite straightforward to add this functionality. Geometry guy 17:30, 27 June 2007 (UTC)

Hack attempts/paranoia
I've recently started to receive emails containing "temporary passwords" to my WP login account. I beleive that these are what one gets if one checks the "I forgot my passord" box on the WP login page. As it happens, I haven't forgotten it, and someone else is making these requests. Being slightly paranoid, I am concerned that someone is hoping to catch one of these emails in-flight (they're mailed out in cleartext, so the temporary password is clearly visible), and is thus hoping to hack my account. Any recommendations on how I should deal with this? Ignore? Retry? Abort? linas 23:56, 27 June 2007 (UTC)


 * I don't know how anyone could catch one "in flight" unless they have access to your ISP or a major carrier, in which unlikely case you aren't safe anyway. More likely they are just trying to annoy you. You can ignore the emails and use your ordinary password. &mdash; Carl (CBM · talk) 23:59, 27 June 2007 (UTC)


 * This is definitely worth reporting to someone who can look into the source. Depending on where you read your mail, there might be an easy way for someone to tap communications close to you. But even if your account is never compromised, the attack (if that's what it is) bears investigation. And if it is not an attack, but a piece of misbehaving software, that is still worth investigating. I wish I could tell you who to contact, but this is new to me. --KSmrqT 04:52, 28 June 2007 (UTC)
 * I came across this before when the attack was malicious. I seem to recall that the IP responsible was blocked WP:AN/I is probably your first place to look for assistance. --Salix alba (talk) 07:36, 28 June 2007 (UTC)

It is that time of the month again
Hey everyone, June is almost over and it is time for a new collaboration of the month WP:MATHCOTM and we need some votes so we can decide what article will receive this high honor. Mosey on down and place your vote or go ahead and suggest a previously unlisted article, all contributions are welcome!--Cronholm144 22:15, 28 June 2007 (UTC)

P.S. I think this diff demonstrate the raw power of a good collaboration. Thanks again to everyone who worked hard on Integral

Symplectic geometry or symplectic topology?
I have discovered, to my great surprise, that there is no Category:Symplectic geometry. All symplectic articles are being filed under Category:Symplectic topology instead, even though the vast majority of them is really about geometry. I was wondering what people here think of renaming the category? Arcfrk 06:12, 26 June 2007 (UTC)


 * I agree with the rename. Symplectic topology is an important modern branch of symplectic geometry. In the long run, I expect it will make a good subcat. Also note that the same issue applies to the Symplectic geometry article, which is currently a redirect! Geometry guy 09:14, 26 June 2007 (UTC)


 * This is priority one on my to-do list, but until I graduate, I can't justify writing articles for Wikipedia when I should be writing my dissertation! :)  (I shouldn't even be checking my watchlist as often as I do.)  But if anyone has the drive, time, and energy now, more power to you.  VectorPosse 18:20, 26 June 2007 (UTC)
 * Nonsense. No one outside your thesis committee is likely to read your dissertation, and they may not read all of it; but people all over the world and for years to come will read your Wikipedia contributions! Besides, once you have your sheepskin in hand, you'll likely be employed as an assistant professor whose tenure track duties include trying to teach first-year calculus to students who don't want to learn it. After a year or two of that you may not wish to explain anything to anyone who is not already a mathematician. ;-D --KSmrqT 23:29, 26 June 2007 (UTC)


 * Disturbingly close to the truth, I'm sure. Hopefully the world will not have to wait more than a few more months!  VectorPosse 07:46, 27 June 2007 (UTC)
 * If getting a diploma were fun, everbody would want one. But do not despair. Some students will be like you; they will be bright and curious and motivated and will inspire their teachers. You may find it refreshing to relate to faculty as a colleague rather than as a student. You can start paying off debts instead of accumulating more. Besides, is it so bad to hope that your thesis is not the best work you will ever do? :-D --KSmrqT 08:21, 27 June 2007 (UTC)


 * Very wise! Meanwhile I think we should rename the pages/categories as recommended. Geometry guy 22:43, 26 June 2007 (UTC)


 * Yes, this part should be pretty easy to take care of for now. What I had in mind for the (hopefully) near future is a complete rewrite of all this stuff (on the symplectic and contact side&mdash;the issues are similar for both).  VectorPosse 07:46, 27 June 2007 (UTC)


 * Oleg has suggested to me that for a rename, it would be best to take the category to CFD. An alternative would be just to create Category:Symplectic geometry and make Category:Symplectic topology (which doesn't have much edit history) into a subcat. Any preferences? I'm happy to do the CFD nomination if that is what people prefer. Geometry guy 16:17, 27 June 2007 (UTC)


 * Best just to do it. It's a bit technical for CfD, and everyone here seems to think it's pretty uncontroversial good sense.  Best just to be bold and go ahead.  Jheald 16:33, 27 June 2007 (UTC)


 * Yes, but do what? I have change the cats in all symplectic geometry articles which are not symplectic topology. So do we move Category:Symplectic topology, or create Category:Symplectic geometry. My own preference is for the move, to preserve the (admittedly small) edit history. We can then decide whether we want Category:Symplectic topology to remain as a subcat. However, the move needs an admin, which I am not. Geometry guy 19:57, 28 June 2007 (UTC)


 * I'd just create a new one, and in the new edit summary say where you're pulling over some of the text from. We pull text over from one article to another all the time - no difference here.  That way seems much the simplest.  Jheald 20:05, 28 June 2007 (UTC)

I thought the point was that Dusa McDuff said the subject could now be called symplectic topology; and many people were going along with that. Just creating a supercat Category:Symplectic geometry, and moving out things that would be annoying to have in Category:Symplectic topologyy, seems an obvious solution. Charles Matthews 14:04, 29 June 2007 (UTC)

Duplication of adjoint representation
A discussion on the reference desk brought to my attention the existence of two similar articles: (1) adjoint endomorphism, to which "adjoint representation of a Lie algebra" redirects, and (2) adjoint representation. Could someone with a little time and interest look into this apparent duplication? --KSmrqT 04:48, 29 June 2007 (UTC)


 * On the first glance, the first article is about the Lie algebra adjoint representation, and the second article is about the Lie group case. Arcfrk 05:20, 29 June 2007 (UTC)


 * And I suppose, in principle, we could have independent articles. However, these are closely linked, and I think both articles mention both concepts, and both cite Fulton &amp; Harris, where Ad and ad appear together. Anyway, I'm trying to concentrate on integral as the end of the month fast approaches, and the last thing I need is yet another distraction. :-) --KSmrqT 11:47, 29 June 2007 (UTC)

Residual sum of squares
This article has had a merge tag on for a while now, and it's beyond my knowledge to assess it. Could someone here take a look. Cheers Kevin 08:38, 29 June 2007 (UTC)