Wikipedia talk:WikiProject Mathematics/Archive 5

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Educational trampoline

I'd like to propose the creation of a new WP math policy (and category) concerning articles that are of particular educational value. I have in mind articles, such as Pi and Torus, which, if properly written and edited, could be accessible to pre-teens and still be interesting and fun for experts. Articles in this category would provide a portal for bright kids or teens (or even college freshmen) to launch into sophisticated math topics. For example: torus: when I was 9 years old, my teacher wrote formulas for a sphere, cylinder and torus on the blackboard: this is clearly a topic accessible to youth. Yet the article continues on to mention Lie groups and cohomology (and links to modular forms), which are advanced undergrad or grad-student topics. If this article is properly structured, it could provide a fine entrance to many fantastic topics in math.

The suggestion here is then only to create and apply some special editorial guidelines to articles in this class, and to create a special category so that educators could easily find them and thus suggest them for brighter students. If there is general agreement, I'd like to make this an official WikiProject Mathematics policy. linas 03:49, 3 Apr 2005 (UTC)

I'm very confused. Why does the inclusion of Lie groups and cohomology, esp. later in the article, make the elementary discussion any less accessible?? If an article is not accessible enough for the audience you talk about, then what is needed is more attention to the elementary presentation, not a deletion or excision of the advanced material. Of course, if the advanced material starts to overwhelm the entire article, a split may be called for. But not including things about the advanced properties is a disservice to those who are looking for this. The point is, if the elementary treatment is first, then the audience you are talking about it will read it, go as far as they can, and then turn away when they're overwhelmed by terminology or abstraction. And the people looking for an abstract treatment will be mature enough to recognize the various levels presented and navigate around the article. If we're worried about scaring people off simply by presenting an advanced treatment in addition to a wonderful elementary treatment, then we're underestimating the readers. "Knowing where you starting to get lost" is sort of a skill itself that will become more and more important as the information age goes on. And besides, why should we guess where a reader's "level" stops? They might read the elementary part, come back a year or two later and read more, and a year or two after that and read the advanced. The article could become an old friend rather than an enemy. And for me, at least, reading about things I don't quite yet understand often leads me to investigate further and I sometimes end up learning quite a bit I didn't know before. Maybe there are precocious undergrads (or evne high school students) who are really interested what the heck a Lie group is, or what cohomology is. It's not Why close these opportunities off? Revolver 14:36, 12 Apr 2005 (UTC)
It would be very nice to have such articles. I suggest you choose one article to convert/improve as an experiment. Hopefully this could lead to improved structure of all our articles. -MarSch 14:25, 4 Apr 2005 (UTC)
It's Wikibooks that is the designated place for textbook development. The suggestion seems to be along the lines rather of the material in the kind of popularising, accessible book that really does have a chance of interesting readers without much background. Still, it does sound more like a Wikibook, to me. Charles Matthews 14:52, 4 Apr 2005 (UTC)
I don't believe in wikibooks. Yet. I like linas vision of the future of WP. -MarSch 13:51, 7 Apr 2005 (UTC)
Providing an introduction for math articles (or wikipedia articles in general) is a good thing. It makes the articles accessible to a wide range of people. But writing an article which can be used for studying a certain topic is an entirely different matter. Wikipedia is an encyclopedia as such is primarily used for looking up information. The structure of the articles should reflect this and present the information in an accessible and neutral way. A textbook on the other hand should be structured according to pedagogical principles. These principles vary from author to author as does the selection of material. MathMartin 15:25, 7 Apr 2005 (UTC)
I agree with MathMartin. We need to keep the encyclopedic style. So, several styles (described below) which were mentioned in places in the discussions on these pages are not quite encyclopedic. They are:
(a) Writing very concise articles containing just formulas and listing theorems (a la Abramowitz and Stegun)
(b) Writing things in a top-down approach.
(c) Making articles with pedagogical bent.
(d) For that matter, putting proofs in the articles, unless they are useful to the statement of the theorem or are otherwise instructive. Oleg Alexandrov 17:05, 7 Apr 2005 (UTC)
If you want encyclopedic then that is the Bourbaki way and thinigs should be top-down. Nobody wants this. Instead everybody wants our articles to be easily understandable. I believe linas proposed to make some articles _extremely understandable_ and thus accessible to children. In addition he proposed to make these articles more interesting by providing connections with other subjects. Don't we want interesting understandable articles? Also proofs are always usefull, and if someone is not interested than they can be skipped, but they provide a way of checking that a result is properly stated and should always be included. MarSch 12:49, 12 Apr 2005 (UTC)
These generalisations are always only indicative. It is pretty clear that some proofs should be included, others not, and so on. Some articles, particularly on recent work (from the past 40 years, maybe) are likely just to be surveys. Something no one has said yet, I think: accessible often will mean visual, so one direction in which to concentrate efforts is to add many more diagrams, not more words (waffle). Charles Matthews 12:52, 12 Apr 2005 (UTC)

I think Revolver got my meaning completely reversed; I wholly agree with him. In fact, I intended to suggest that an article like "torus" could safely include more links to various complex topics. I also wanted to suggest, that the progression from simple to complex be made a tad less challenging, so that the article becomes slightly easier to follow. However, one must stop short of writing a book. Borwein wrote a book about Pi, but if you look at his book, much of the material in it is already covered by various wikipedia articles. For example, Borwein's book on Pi has a chapter on modular forms or something like that (not sure); whatever that connection is, via Ramanujan's series, it could be spelled out in a a few sentences, followed by a wiki link. Similarly, a torus is a great example of a simple Teichmuller space. We don't have to write the book; but adding the words to establish the link would be good.

Very few articles in Wikipedia have the opportunity to bridge from simple to complex. Pi, Torus and modular arithmetic are a few that come to mind. Most of the rest of the articles cover topics that are either too advanced, or have no natural ties to a wide range of topics. This is why I wanted a special category for the few articles that have this magic property of being broadly relevant. linas 15:27, 13 Apr 2005 (UTC)

Disagree with some of this. As far as I know a torus isn't a Teichmuller space. You can relate π to modular forms if you want; you can relate it to Buffon's needle too - I'd be surprised if there was anything you couldn't relate it to, in mathematics. I'm not here to sell anything specific, and I think Wikipedia policies make it better just to build up 'core material' in a steady way. Charles Matthews 18:40, 19 Apr 2005 (UTC)

Error in rendering of html math

''L<sup>p</sup>'' gives Lp (rendered as <i>L<sup>p</sup></i>)

''L''<sup>''p''</sup> gives Lp (rendered as <i>L</i><sup><i>p</i></sup>)

Apparently, for a lot of users, these expressions are identical but I see something close to Lp for the second (where the p is slightly smaller font). I use the konqueror browser version 3.2.1. My question is: is this a bug in the wiki software or in my browser?

''L''<sup>p</sup> renders the way I would expect: Lp Jan van Male 18:45, 12 Apr 2005 (UTC)

They look the same in Firefox. Ibelievethisis the correctbehaviorfornested tags.
(Although the wiki software seems to remove nested tags! Interesting. Because it assumes they are mistakes? What if you need to print xfs? Oh. That works. But nested supers do not: xfs) hehehe - Omegatron 19:12, Apr 12, 2005 (UTC)
I use Konqueror, they look the same to me. (and both look good). Your choice of default fonts, maybe? linas 15:31, 13 Apr 2005 (UTC)
Using different fonts does not help here. I'll see whether the konqueror bug database turns up anything usefull. Jan van Male 16:22, 13 Apr 2005 (UTC)
Yes. Nested sup/sub tags are broken in MediaWiki!! :( Vote for bug #599 and maybe it will get some attention and be fixed. Dysprosia 03:02, 20 May 2005 (UTC)

Articles needing diagrams

Is there a page listing mathematics articles which are in need of diagrams? If not, we should create one somewhere. There are plenty of articles which could be listed. I am handy at doing commutative diagrams and don't mind doing them but I'm completely inept when it comes to anything requiring artistic talent. I'd like a place where I could put up some requests and handle others. -- Fropuff 17:02, 2005 Apr 14 (UTC)

Well, there already is Wikipedia:Requested_images#Mathematics. - Omegatron 19:20, Apr 14, 2005 (UTC)
There are presently no requests in there. Maybe I'll try populating it and see if I get any turnaround. -- Fropuff 22:04, 2005 Apr 21 (UTC)
I think a separate page for mathematics-related articles would be a good idea. Fredrik | talk 22:08, 21 Apr 2005 (UTC)

Template:MacTutor Biography — what about Template:MathGenealogy like it?

I have noticed a recently created Template:MacTutor Biography — looks like a cool idea. I've found 26 articles on people linking into the Mathematics Genealogy Project database, and thought about creating a template to link to it, similar to the MacTutor one. Does anybody have any objections against me going ahead and doing it? BACbKA 18:54, 16 Apr 2005 (UTC)

Update: I have done the above. Please use the template when linking to the mathematical genealogy project database entries; also you're welcome to improve the template text. BACbKA 12:50, 17 Apr 2005 (UTC)

Plutonium recalculations

Can someone please redo the calculations involving the half life of Pu on pages RTG and Voyager program to reflect the proper half life of 87.7 years instead of 85 year current value? thx.--Deglr6328 01:55, 17 Apr 2005 (UTC)

Have done this on RTG. -MarSch 12:49, 19 Apr 2005 (UTC)

Several proposals to modify the List of mathematical topics

The List of mathematical topics is a very useful resource, as from there one can track the recent changes to all the listed math articles (try Recent changes in mathematics articles, A-C). Its only weakness is that quite a lot of math articles are missing from there (in addition to the 3537 articles listed at the moment, there are at least 2000 not listed — and this is a very conservative estimate, the actual number could be as high as 3000 or more).

Now that we have the math categories, and most math articles are categorized, one idea is to add to List of mathematical topics by harvesting the articles listed in the math categories. I would be willing to do that, especially that I already have written some scripts which do most of the work.

One issue would be how to sort the articles, this is discussed at Talk:List of mathematical topics, and seems to be a tractable problem, even if one needs to sort the mathematicians by last name.

That was the first proposal. I wonder what people think. Now, the second proposal. Charles Matthews suggested (see again Talk:List of mathematical topics, at the bottom), to remove the mathematicians listed there altogether, as they have their own list, List of mathematicians. So, some feedback on this is also needed.

Now, to the third proposal, closely related to the above. You see, adding lots of new articles will make the lists quite big, and even now some are big (for example, List of mathematical topics (A-C) is 58KB, with almost all contents being links). This causes issues when the server is slow, and when updating with new entries (it happened in the past that the lists actually got corrupted because of that). It can also be hard to check the diffs if lots of changes happen. So, the proposal is to further split the lists, with each letter getting its own article.

Backward compatibility can be ensured by using a template-like thing. If we have the articles List of mathematical topics (A), List of mathematical topics (B), List of mathematical topics (C), one can insert in List of mathematical topics (A-C) the lines:

{{:List of mathematical topics (A)}}

{{:List of mathematical topics (B)}}

{{:List of mathematical topics (C)}}

and the appearance of this list would be as before, and can be also edited as before. The link Recent changes in mathematics articles, A-C will still work (I tried these).

So, I wonder what people think of these proposals. Note that they are related, but a decision on one of them need not affect the decision on the other ones. Oleg Alexandrov 02:33, 19 Apr 2005 (UTC)

All the above seems fine to me. Paul August 02:57, Apr 19, 2005 (UTC)
Having heard no objections, I will proceed. I will also create a List of mathematics categories, which I will populate as I move along. I will try to work on this this weekend, or either way do it by next Wednesday. Oleg Alexandrov 21:40, 21 Apr 2005 (UTC)
All three proposals sound good to me. The template trick is rather nifty; I had no idea that worked. -- Fropuff 22:02, 2005 Apr 21 (UTC)

Scanned math monographs of Polish mathematicians

Today after following an external link from Lebesgue-Stieltjes_integration I found the following gem [1]. On this page journals and monographs from Polish mathematicians can be downloaded free of charge. (for example the complete french translation of Stefan Banachs Théorie des opérations linéaires.) If nobody objects I would like to start a section in Wikipedia:WikiProject Mathematics with a list of webpages where older mathematical monographs and journal articles can be accessed. I know there are simialar projects in France and Germany going on. I think it is fantastic that many important math journal articles can now be found online making it possible to link them directly from the relevant wikipedia articles.MathMartin 21:24, 19 Apr 2005 (UTC)

Gathering together our conventions

The new page Wikipedia:WikiProject Mathematics/Conventions is to collect up our current set of working conventions. Please add any more to it, and use its talk page to discuss the adequacy or otherwise of those conventions. Charles Matthews 11:13, 23 Apr 2005 (UTC)

Renaming the List of lists of mathematical topics ?

There is a discussion at Talk:List of lists of mathematical topics#Renaming this list. I wonder what you think about those suggestions, and which, if any is preferred. Thanks. Oleg Alexandrov 00:31, 24 Apr 2005 (UTC)


Someone has listed Pearson distribution for deletion:

For some reason this is picking up a few delete votes, and I don't understand why. It's not my field but I know this is a fairly popular distribution nowadays. Any help with cleanup, keep votes, etc, welcome. --Tony Sidaway|Talk 02:18, 28 Apr 2005 (UTC)

"Things to do" section?

I'm thinking about adding a "Things To Do" section to the project page, some thing like:

Things to do

Looking for something to do? There are several places on Wikipedia where mathematics related requests, suggestions and tasks have been collected together:

What Where
Suggest or edit a mathematics article needing attention Pages needing attention: Mathematics
Suggest or edit a statistics article needing attention Pages needing attention: Statistics
Suggest or write a mathematics article Requested articles: Mathematics
Expand a mathematics "stub" Mathematics stubs
Suggest or edit a redirect which could have its own article Redirects with possibilities: Mathematics
Help move PlanetMath content onto Wikipeia PlanetMath Exchange

Any comments? Paul August 18:26, Apr 28, 2005 (UTC)

Sounds fine with me. Some of these links already show up at the bottom of Wikipedia :WikiProject Mathematics. The PlanetMath Exchange link shows up somewhere higher on the same page. To integrate all of these nicely would be good. Oleg Alexandrov 18:41, 28 Apr 2005 (UTC)

Ok I've added the above to the project page. Paul August 22:03, May 3, 2005 (UTC)

Template:Calculus -- is that needed?

Topics in Calculus

Fundamental theorem | Function | Limits of functions | Continuity | Calculus with polynomials | Mean value theorem


Product rule | Quotient rule | Chain rule | Implicit differentiation | Taylor's theorem | Related rates


Integration by substitution | Integration by parts | Integration by trigonometric substitution | Solids of revolution | Integration by disks | Integration by cylindrical shells | Improper integrals | Lists of integrals

Vector Calculus

Vector | Vector field | Matrix | Partial Derivative | Directional Derivative | Gradient | Flux | Divergence | Divergence Theorem | Del | Curl | Green's Theorem | Stokes' Theorem | Path Integral

Tensor Calculus

Tensor | Tensor field | Tensor product | Exterior power | Exterior Derivative | Covariant derivative | Manifold

I just wonder, are things like Template:Calculus so useful? I put it to the right just for illustration.

(Note: the template refered to above is now at Template:Calculus2 the first template displayed to the right is the "old" template, the "new" template, now at Template:Calculus is displayed below. Paul August 02:19, May 10, 2005 (UTC))

To me, as I followed its evolution, it looks like an ever growing monster of links, popping up in many places. Besides, it is very long and wide, taking up lots of room even on a 19" monitor with high resolution. Also, I thought the category system should take care of linking articles to each other.

I would suggest this template be eliminated, or otherwise be trimmed to the true calculus, which is integrals and derivatives on the real line, no vector calculus, tensor calculus, and what not. Opinions? Oleg Alexandrov 23:08, 29 Apr 2005 (UTC)

I do not like the template. The scope is too broad and it takes up too much space in the article. So either trim down radically or delete entirely. MathMartin 10:03, 30 Apr 2005 (UTC)

My attitude: I have removed it in a number of places. I think it might actually be useful to some readers; but it doesn't need to be on every calculus article. Charles Matthews 12:49, 30 Apr 2005 (UTC)
I agree. It takes up too much space. I think the vector and tensor calculus stuff should go. Perhaps moved to their own templates. Paul August 13:23, Apr 30, 2005 (UTC)

I have an idea. We could put Vector Calculus and Tensor Calculus as topics under Topics in Calculus, get rid of all the subtopics that were under those two headings, and then make the overall sidebar narrower. I think that might sufficiently trim it down. Sholtar 21:25, May 3, 2005 (UTC)

{{#invoke: Sidebar | collapsible }}

I've made a template to show what it would look like the way I suggested. It's located at Template:Calculus2 (now at Template:Calculus see note above Paul August 02:19, May 10, 2005 (UTC)). If you compare it to the former one, I think this one is much more reasonable in size and would be adequate as far as links are concerned as well. What do you all think? Sholtar 22:21, May 3, 2005 (UTC)
Looks good, thanks! But I can't promise that at some later moment I won't feel like trimming more the template. :) By the way, what do you think of creating a Category:Vector calculus? That will put the related topics in the same box. Same might work for the tensors. Oleg Alexandrov 22:25, 3 May 2005 (UTC)
Hmm... yeah, having a Vector calculus category and a Tensor calculus category would probably help. Should they have sidebars, or just categories? Sholtar 22:46, May 3, 2005 (UTC)
I thought the very purpose of categories is to group similar subjects together. And my own humble opinion is that one does a better job that way than by using templates (sidebars, that is). One day, when I get to it, I will carve out Category:Vector calculus as a subcategory in Category:Multivariate calculus. Oleg Alexandrov 22:59, 3 May 2005 (UTC)
This is true, but templates do make for somewhat easier navigation between topics within a category. Anyways, unless there's any disagreement, I'm going to put the slimmer template in to replace the current one and back the current one up in Calculus2 if it's needed for future reference. Sholtar 23:10, May 3, 2005 (UTC)

I suggest limiting the use of templates to articles most likely to be read by high-school and college students, and then only on articles that are widely and broadly taught. They have pedagogical value for a student trying to master the material. Thus, the fat template might actually be a lot more useful than the thin template. However, it should be used on only a few pages. linas 17:02, 14 May 2005 (UTC)

Now on VfD: Evaluation operator

The mathematical article evaluation operator is now on VfD; see Wikipedia:Votes for deletion/Evaluation operator. It is claimed to be original research. Unfortunately, it is now too late for me to investigate it. Related articles are multiscale calculus and theta calculus. -- Jitse Niesen 00:39, 10 May 2005 (UTC)

I should have added that I spotted this while listing an another article, namely John Gabriel's Nth root algorithm. Its VfD entry is at Wikipedia:Votes for deletion/John Gabriel's Nth root algorithm. -- Jitse Niesen 08:15, 10 May 2005 (UTC)

Reminds me of this group: eucalculus, differation, atromeroptics. These seem to be personal definitions/original research, and should presumably go to VfD. Charles Matthews 08:47, 10 May 2005 (UTC)
The evaluation operator surfaced on the german Wikipedia, was discussed at de:Portal Mathematik and put to VfD there. After assuring myself that only the original author uses this term but was rather busy creating a net of articles here, I put it on VfD here. --Pjacobi 09:58, 2005 May 10 (UTC)

I listed eucalculus on VfD, after verifying that I could not find a peer-reviewed article about it. The VfD entry is Wikipedia:Votes for deletion/Eucalculus. -- Jitse Niesen 22:57, 12 May 2005 (UTC)

Discussion on german Wikipedia seems to indicate, that Theta calculus and Multiscale calculus, at least in their current form, are original research by User:Dirnstorfer. Opinions? VfD? --Pjacobi 15:26, 2005 May 13 (UTC)

Evaluation operator has now been deleted, and the other two articles are listed on VfD; their entries are at Wikipedia:Votes for deletion/Theta calculus and Wikipedia:Votes for deletion/Multiscale calculus. -- Jitse Niesen 22:24, 17 May 2005 (UTC)

Major fields of mathemtics

I've added an 'Major fields of Mathematics' template to the Matematics Categories page. It's based on the classification used in The Mathematical Atlas. Any comments or suggestions? --R.Koot 13:38, 10 May 2005 (UTC)

The template in question is at Template:Mathematics-footer.
Now, first of all, the style here is not too use that many capitals. That is, one writes "Linear algebra" instead of "Linear Algebra", and "In mathematics" instead of "In Mathematics".
About the template. I myself do not think it is a good idea. There is already a Areas of mathematics article, having good information.
I would like to note that the very purpose of categories is to group related subjects together. As such, navigational templates should not be used that much, they just become link farms showing up all over the place.
This is my own personal thinking, and I am somewhat biased against templates for the reason above. I wonder what others think. Oleg Alexandrov 20:36, 10 May 2005 (UTC)
On this one, I'm going to have to agree with Oleg Alexandrov. I like templates personally, but they have to be used with moderation. I just don't think this one is neccessary. Sholtar 23:23, May 10, 2005 (UTC)
I agree with Oleg. I am against using a template for this category. Note: I believe that templates are useful and nice in certain pedagogical settings, see debate on the calculus template above. However, a template is inapporpriate for this cat. linas 17:30, 14 May 2005 (UTC)

To be honest I think that this template shouldn't be neccessary, I had two (good) reasons for creating one. The first is that is is also done in the Category:Technology and more importantly, the current categorisations of articles is quite a mess, which makes it very difficult for the non-mathematicain to quickly get an overview of mathematics major fields. --R.Koot 00:32, 11 May 2005 (UTC)

The Category:Mathematics is not a mess. Math has many more facets than just subject areas. The categories reflect this. Oleg Alexandrov 00:47, 11 May 2005 (UTC)
We should probably come to a consensus about whether or not to do this in all categories, but just because someone did it for technology doesn't seem to be a feasible reason to do it for mathematics. I think unless a consensus is reached about the subject, default to whether or not it's neccessary. This one I just don't think is neccessary, especially because there's an article about the major fields. Sholtar 05:23, May 11, 2005 (UTC)

I agree that mathematics is much richer than it's fields. Therefore the template is biased, but adding more links to it make it lose it's purpose so I suggest the following:

  • Remove the template.
  • Put all the articles that are categorized direcly under mathematics in a subcategory, except for the Mathematics article itself, and maybe a select group of introductory articles like Areas of mathematics (articles that help navigate you quickly and would propably be found in a real encycolpedia).
  • Rename a lot of the categories from Mathematical foo to Foo_(mathematics), this would make the index more readable and is the prefered Wikipedia style, I believe.
  • Design a good categorization system and make people aware of it. A suggestion
   Logic             Computer Science                   Literature
   Set Theory        Signal Processing                      Journals
   Arithmetics           Digital Signal Processing      History
   Combinatorics         Transforms                     Recreational Mathemtics
   Number Theory         Wavelets                           Games
   Algebra           ...                                ...

Now you could either put all the categories in the three columns together under Category:Mathematics or put them in their own subcategory (Pure Mathematics, Applied Mathematics), resulting in a rather tiny index, whcih would probalbly be my preference, but I think this might be a bit too controversial? --R.Koot 10:52, 11 May 2005 (UTC)

(This was written before I saw R.Koot's comment above.) At the moment, we have several ways to navigate through the articles:
  • Wikilinks. This works well, but requires the user to read a lot of text to find the link he is interested in.
  • Categories. They are very useful, but in my opinion not very user-friendly. I actually agree that Category:Mathematics is a bit of a mess; part of the problem is that the list is sorted alphabetically, another part is the lists mixes very different kinds of subcategories, like Cellular Automata (a small subfield), Geometry (a big subfield), Formula needs explanation (a category meant for editors) and Theorems.
  • Lists like list of linear algebra topics. They provide more flexibility (one can sort articles as one wants, introduce subheadings, annotations), but the experience shows that these lists are difficult to maintain.
  • Navigational boxes. Again, I think these can be useful, but they take up space (especially when implemented as sidebars instead of footers) and they tend to grow out of control.
Unfortunately, none of these is perfect. I believe Charles Matthews has written a whole piece comparing these navigational aids, but I cannot find it anymore. But it would be good to build some sort of consensus on which to use where. -- Jitse Niesen 11:10, 11 May 2005 (UTC)
The point about our existing systems of lists and categories is that they have grown up organically, in line with the articles. They are not an imposed, top-down categorisation. I support strongly the idea of doing it this way. After all, where do top-down lists come from? They are basically a bureaucratic idea, and not very compatible with wiki self-organising principles. What we need are a few structures to support the existing system. For example, a 'guide' page outlining the category system, and some project page on which to discuss areas where the coverage remains weak. Charles Matthews 08:55, 13 May 2005 (UTC)
This is a very good point. MathMartin 16:44, 14 May 2005 (UTC)

I see that R.Koot went ahead and performed the edits anyway, despite the discussion. I disagree with a number of the edits. About a month ago, Category:mathematics had approx 300 articles. I categorized almost all of them, leaving behind about 30 articles that gave a flavour of mathematics, that dealt with topics that were broadly applicable to all branches of mathematics, or that were inter-disciplinary, giving a sense of the relation of mathematics to broader society. While not perfect, the remaining lone articles in combination with the list of categories, gave a pretty good overview of what math is about. I am rather distressed that the collection of individual articles were shorn out of the category (I started reverting last night, I plan to continue when my spirits increase). linas 17:46, 14 May 2005 (UTC)

As to the 65 subcategories of mathematics, its certain that this list could be cleaned up a bit and shortened; but I'm sure I'd shit the proverbial brick if it was not done correctly. linas 17:46, 14 May 2005 (UTC)

vote for MarSch's adminization

Please visit Wikipedia:Requests for adminship and vote on my application. I want to do some edits on protected pages, but I have too few edits yet to get enough anonymous support, so since you guys know me a little better I'm hoping that my edit count will be less of an issue. So please take a look. -MarSch 14:43, 13 May 2005 (UTC)

Hoaxer is back

Kimberton's Poppages Theorem, now deleted, was the Bryleigh (Cayley/Newbirth) hoaxer again. Not possible to do a long-term block on the IPs used. Everyone please look out for hoaxes. Charles Matthews 14:08, 14 May 2005 (UTC)

Is there a way of monitoring what articles are added to (or removed from) a category? I'm wondering how you discovered the existance of the above page. (No doubt, you're aware of my recent bout of categorization and thus interest in such things.) linas 17:54, 14 May 2005 (UTC)
It's possible to monitor added articles, but not removed articles; see m:Help:Category#Detection_of_additions_to_a_category. Daniel 18:26, 14 May 2005 (UTC)

mathbf or boldsymbol?

Typically, bold font is used for vectors, as in . Note that does not have the desired effect. I think it would be better to use \boldsymbol as in (Igny 23:52, 15 May 2005 (UTC))

Well, we'll use whatever works. We can use mathbf, and when it doesn't work, we can use boldsymbol. Observe also that does not show up the same as , which may be undesirable. Dysprosia 23:49, 15 May 2005 (UTC)
I didn't know about boldsymbol, but I like it. Use whatever is more appropriate. -MarSch 11:43, 16 May 2005 (UTC)
Vector valued variables should be written bold but not italic so you should use \mathbf not \boldsymbol --R.Koot 00:37, 17 May 2005 (UTC)
Agree with R.Koot. Oleg Alexandrov 01:18, 17 May 2005 (UTC)

Problem with the "what links here" feature, affecting the recent changes to list of mathematical topics

If you check what links to the article Osculating circle, one can see that it linked from the List of mathematical topics (O). However, it does not look as if it is linked from list of mathematical topics (M-O), which is very strange, because if you click on that page you will certainly see the article listed.

On the other hand, if you look at what links to Alan Turing, you will see a link from List of mathematical topics (S-U), which is wrong, as if you visit List of mathematical topics (S-U) you will not see Alan Turing listed there. I removed this article from there a long while ago (since it shows up in list of mathematicians).

As such, the "what links here" feature does not show links which exist, and does show links which do not exist. This affects the "rececent changes" from list of mathematical topics. I find this very strange. Anybody having any ideas with what is going on? Oleg Alexandrov 19:15, 18 May 2005 (UTC)

I seem to remember that there are some bugs with What links here when combined with templates. I think you should look in the list with wikimedia bugs for details, or wait and hope that somebody gives you a more precise answer. Jitse Niesen 21:06, 18 May 2005 (UTC)
I've been seeing stuff like this in more than Mathematics, but I can't really help you out in knowing what the problem is. It's probably just some kind of bug with the overall feature, as Jitse said. Sholtar 04:13, 2005 May 19 (UTC)
I went to List of mathematical topics (J-L) and just inserted a comment and saved the thing. Miraculously, the "what links here" feature worked just fine afterwards! The moral I think is that every once in a while applying a dummy edit will refresh the database, and quirks as above -- where linked articles did not show as linked and unlinked articles showed as linked -- will not show up. Oleg Alexandrov 19:39, 21 May 2005 (UTC)

Move of "Mathematical beauty" to "Aesthetics in mathematics", comments?

(Discussion moved to Talk:Mathematical beauty#Move of "Mathematical beauty" to "Aesthetics in mathematics", comments?. — Paul August 20:00, May 27, 2005 (UTC))

Covariant, contravariant, etc.

Here is some discussion from my talk page. -- The Anome 14:57, May 20, 2005 (UTC)

User:Pdn wrote:

The entry Contravariant has a notice: "This article should be merged into covariant transformation. If you disagree with this request, please discuss it on the article's talk page." I very much disagree. I wrote something on the discussion page but the notice is still there, so here I go.

The term covariant has two very different meanings. In relativity theory (and probably differential geometry) it refers to the invariance of a quantity (generally a measurable one) when coordinates are changed, including changes among relatively moving reference frames. For example, the velocity of light is covariant, and the rest mass of an object can be determined in a way that does not depend on coordinate system or reference frame, i.e. a covariant way. But covariant also refers, unfortunately, to certain components of a vector or tensor that do usually change very much when the coordinates change. The simplest example is the vector from one point to another in ordinary three dimensional geometry. In the usual Euclidean metric, the numerical values of the contravariant and covariant versions of the vector are identical. If we perform a coordinate transformation doubling all the coordinates, (x',y',z') = (2x,2y,2z) then all the contravariant coordinates double but the covariant ones are cut in half. The distance, which depends only on the products of the coordinate differences (contravariant times covariant) (summed, and then the square root taken) does not change. It is covariant, but the covariant coordinate increments were all cut in half. The transformation is a covariant one, but does not preserve the covariant components. The invariance of the distance relates to the discussion of "covariant transformation" while the discussion of the changes in individual coordinate values, contravariant vs covariant, belongs in "contravariant". Thus, the notice suggesting merge should be removed. If you want to match "contravariant" with something, then you should create a page "covariant component" as opposed to "covariant transformation." Else you could rename "contravariant" as "Contravariant and covariant components" and I will port some of this discussion in there. These very concepts are rather passé now, at least in relativity theory, as the use of differential forms is supplanting old fashioned tensor analysis, but some folks still use tensors for fluid and continuum mechanics [2], rheology [3], mechanical vibration, crystal optics [4] and other fields not so suitable for the fancier newer maths so the entries should not be dropped. Simple tensor analysis is helpful when a cause (force, mechanical stress, polarized optical beam, e.g.) produce an effect imperfectly aligned with it. Such usages do not lend themselves as much to exterior differential form analysis so there's no reason to toss old-fashioned tensor analysis. Pdn 13:48, 19 May 2005 (UTC)

[...time passes...]

Dear Anome (sorry to put this as a trailer on some vandalism , but I do not know how to create new messages without appending to old.) I'm afraid that the two usages of "covariant" are so very different that your concept of parallel disambiguation pages won't fly. I have never heard of a "contravariant transformation", though you could ask a person more expert than I in differential geometry or differential forms. As I explained, "covariant components" and "contravariant components" are two faces, so to speak, of the same thing. The second one, in the case of the differentials of coordinates (hope I restricted my remark to that case) is an integrable quantity, a thing many people do not realise. Thus, if one totals the contravariant component of "dx" around some closed curve one gets the change in x, a property not generally shared with the covariant component of dx. I do not know how "covariant" came to be used for vector components, but I do not see it as related to the invariance under transformations. The devil of it is that we can't just change "covariant transformation" to "transformation with invariants" for many reasons, including wide usage probably started by Einstein. You could make up a disambiguation page for "covariant" pointing to "covariant transformation" on the one hand and "covariant tensor components" on the other. Unfortunately you cannot just use names like "covariant tensor" and/or "contravariant tensor" because these are two faces of one item. So you would have to work with "covariant tensor components" and make up a page like the existing one for "contravariant" for that case, so you could change "contravariant" to "contravariant tensor components." Actually, now that I think of it you could rename "contravariant" as "contravariant and covariant tensor components" and I'd be glad to fill in the "covariant" portion - you can leave a stub. Then the disambiguation page would fork between "covariant transformation" and "contravariant and covariant tensor components."

I think we probably need to discuss this at the Wikipedia:WikiProject Mathematics I agree with you about the covariant and contravariant components of tensors; tensors seem to be a particularly tricky subject here for some reason. The term "contravariant transform" seems to have been used: see Google for a few examples of what seem at least at first sight to be valid uses. The other terms really need some thought; you've certainly convinced me that a simple merge/redirect alone will not do the job. To that end, I'm copying your recent comments and this reply into the Wikipedia talk:WikiProject Mathematics page. -- The Anome 14:51, May 20, 2005 (UTC)
Some confusion here. Differential forms, which are always contravariant, can only 'replace' tensors that are already contravariant and antisymmetric with respect to interchange of indices. The "components" terminology causes more confusion than anything else in this area, I think. In the presense of a metric you can indeed 'raise and lower indices', so have the option of taking the components of the variance you want; but that is very much not the basic situation with tensors. Charles Matthews 15:14, 20 May 2005 (UTC)
When physicists say covariant, they mean tensorial as far as I know. Since tensors exist without reference to any coordinate system they don't transform.
This is a fine mess we have here. I think the article about covariant transformations is really about coordinate transformations. Then the components of tensors transform co(ntra)variantly as per their nature. Perhaps we should merge the lot with tensor or tensor field. You can only take covariant components and contravariant components of a (co)vector when you have a metric.--MarSch 15:34, 20 May 2005 (UTC)

I am afraid you maths guys are taking the definitions and discussion too far away from what is used by engineers and the more pedestrian of physicists. I have taught relativity using differential forms, but not for a while and had forgotten that part about their always being contravariant. Engineers would be floored by trying to use differential forms and I am not even sure they are useful for elasticity, fluid mechanics in Newtonian theory, birefringent optics, and so on. In all the cases normally used by physicists and engineers, you do have a metric. So the math is getting far afield by discussing cases with and without metric. There are some anomalous theories in physics where the metric is affected by another field (e.g. Brans-Dicke theory and other "conformal" theories,) and it may be that branes can make the usual usage of a metric muddled (path dependent) but you are getting so far from what can be used in most colleges and in university courses in physics or engineering up through second year graduate school, that I am getting queasy. In relativity, we distinguish general covariance and covariance under the special theory of relativity. In the latter case, measurable quantities have to be invariant to the Lorentz transformation (in the most general sense, including translations and rotations, as well as [constant] velocity differences, but not to time-varying rotation). In the former, the measurables must be locally invariant to change to systems in relative acceleration, including time-varying rotation. While coordinate changes are not measurables in the strictest sense, distances are. By "the strictest sense" I mean that a reliable measuring tape or clock does not measure a coordinate, but it measures the distance, including the metric. I will stop here or the debate entries will become too long. Anyway, to physicists "covariant" does not mean "tensorial" in my opinion, it means invariant to certain coordinate and reference frame changes as I described above. Pdn 14:42, 21 May 2005 (UTC)

I'm confused by the confusion. A covariant transformation is the thing that changes the coordinate system on a covariant tensor component on a (mixed) tensor. Ditto for contra. Mass and speed of light are invariant and not covariant. The people who study branes and Brans-Dicke know differential geometry inside-out and upside-down, so I'm not worried about them. The above seems to be implying that there is something else out there, not yet documented in WP, that is called a "covariant transformation" ?? what is that thing? linas 00:19, 22 May 2005 (UTC)

You are absolutely right - sorry - there is no such thing as a covariant or contravariant transformation. If one wants to make up separate names for the operations on covariant and contravariant components, one could use these names, but that would obscure the fact that (when there is a metric) both kinds of components are just different aspects of one thing, the tensor. So I would think that the two items could be combined into one about how to transform tensors, in component form. And also you are right that I should have used "invariant" for scalars that remain fixed in transformation. I just now referred (way) back to Peter Bergmann's book "Introduction to the Theory of Relativity" (Prentice-Hall, 1942) and my memory is returning: equations can be covariant under certain kinds of transformation; the transformation is not the covariant thing. When the equation (such as ) is preserved under coordinate transformations it is covariant. I also agree, and I am glad you agree, that people doing advanced work such as branes and conformal theories do not need any help from Wikipedia; that is why I wanted to steer away from cases where there is no metric, which were referred to by MarSch on May 20. So I suppose we need entries for tensors and their transfromation rules, covariant and contravariant components, and covariance of equations - the exact titles are not clear to me. In regards to the previous comment (also by MarSch): ":::When physicists say covariant, they mean tensorial as far as I know. Since tensors exist without reference to any coordinate system they don't transform." I agree in part - the tensor is "there" and we just see different views of it when we take components in different systems, but we need to retain some of what was taught to engineers, physicists and maybe even some differential geometers, who can't easily be weaned from components. I am now probably going to cease writing here because there is, indeed, so much confusion over covariant, covariant transformation and contravariant, and you mathematicians should be the ones to settle it. I just hope you leave something useable by scientists and engineers who do not want to learn more advanced mathematics than they have to, but want to use tensors.Pdn 03:12, 22 May 2005 (UTC)

Yes I agree, three articles on essentially one topic is too much. All three, covariant, covariant transformation and contravariant should be merged. Yes, the expression "covariant transformation" is a poor choice of language, and the new article should be purged of this expression. Oleg is right, there are times when a metric doesn't exist, or the metric is not invertible, but these cases should be treated in distinct articles (non-invertible metrics occur in subriemannian geometry; a special language exists for this case.). The component notation is just fine for the merge article. (The metric-less and componenent-free case is already dealt with in the pullback/pushforward articles.) Not sure what MarSch is going on about with this component-less thing; I'd like to see him write a computer program that graphs pictures of tensor quantities without using components ;-). If an equation is invariant under a change of coordinates, one calls that equation invariant in modern terminology, not covariant. I guess some folks might still use the term "covariant" in this case, but suspect its anachronistic. I'm not planning on doing any merging myself. linas 06:40, 22 May 2005 (UTC)
Oh, and I do see one point of confusion: the "transformation" of tensors under changes of vector basis is related to, but not at all the same thing as the "transformation" of tensor fields under change of coordinates. Unfortunately, these two distinct concepts often do get conflated. linas 06:48, 22 May 2005 (UTC)

I do not see any difference between a tensor and a tensor field, unless the former is a very special case, being defined at only one point, and therefore of little use. I do not consider terms like "covariant" (for invariance of an equation under special-relativistic transformations) and "generally covariant" for invariance under more arbitrary transformations in GR (I say "more arbitrary" because I want to keep the light cones etc preserved) to be out of date. That's what Einstein used so it is worth preserving; otherwise people need to ask the mathematicians who changed the definition what Einstein meant. This kind of thing is often tried by well-intended people who like, nevertheless, to play "follow-the-leader." One outstanding case was the late (I believe) Parry Moon of MIT. He wrote the article on illumination in the 1956 Encyclopedia Brittannica, wherein he tried to replace ordinary concepts like brightness, illumination, luminous flux, the lumen etc by a new breed of terms such as "pharosage","lamprosity" (sounds like something that invaded the Great Lakes, killing many gamefish), "blondel," "stilb" and "apostilb." The terms have not stuck very well but can be found here and there. Moon and collaborators (such as Domina Eberle Spencer and Euclid Eberle Moon) wrote many bizarre papers. Early on, Moon and Spencer claimed, in J.Opt.Soc.Am. 43,635(1953), that according to relativity, light from distant galaxies could reach Earth in a few hours or days. This was picked up by young-earth creationists, and stil is, but it is nonsense. More recently, the indomitable trio published items supporting a ballistic theory of light in Physics Essays, and for the latest see this: [5]. So be careful about renaming things like the covariance of an equation. It may be a sign of impending senility. OK, nowadays a janitor is a "building engineer" and an overweight person is "gravitationally challenged," but that's harmless, while to side-track people who want to understand the writings of Einstein, Minkowski, Weyl, Pauli, and many capable if not illustrious successors by requiring them to consult Wikipedia talk pages to find out that the "covariance" of an equation is now called "invariance" is uncool. The forgoing was not a filibuster and I am not a filibusterer [6]. One final point: Somebody (I believe he was named Kretschmer) once pointed out that you can make anything into a tensor by defining it in one system and transforming it to any other by tensor transformation rules. So, reflecting on that, we see that "covariance" of a physical quantity or scientific equation means that the same measurement process used to measure it in one system will measure the transformed version of in (transformed using tensor rules) in another system. For example. E^2-B^2 where E is electric field and B magnetic is covariant. E-B is not, but if you measure E-B in one frame and then transform it to other frames by brute force with tensor rules you can claim that it is covariant or invariant etc. So "general covariance" has more to it - that the physical content is carried over to new frames - not just math.Pdn 05:09, 23 May 2005 (UTC)

What I don't like about merging into covariant and contravariant is that those are adjectives, so the article is about a descriptor instead of a thing. As a physicist I came across covariant transformation long before covariant, but that's because we usually define co(ntra)variant vectors by how they transform. If they're going to be merged into one article, how about at least something like covariant tensor. But personally this differential geometry talk is above my head, and I'm just pulling for them ending up somewhere that makes sense to physicists, too. --Laura Scudder | Talk 22:41, 26 May 2005 (UTC)

Since this issue is being clouded by various points-of-view, I think we need to talk structure and organisation first. Nouns are better than adjectives, as Laura implies: so we need to treat covariance and contravariance in some central place. I suggest making covariance and contravariance the 'top level', most general article, and hang things like tensor field (all those indices) off it. Charles Matthews 09:17, 27 May 2005 (UTC)

Talk:Squaring the circle

Perhaps my fellow math-nerds should look at Talk:Squaring the circle. I have taken the position that the article is about the legitimate mathematical problem of squaring the circle and the proof, published in 1882, that it is impossible; that although it should mention crackpots who continue working on squaring the circle, nonetheless that that topic is at most tangential (to the circle?)Pdn 15:10, 21 May 2005 (UTC). As nearly as I can tell, a Wikipedian named Sebastian Helm is saying that squaring the circle is a topic invented by crackpots rather than a legitimate mathematical problem. He seems very angry at my assertion to the contrary, which he called "BS". Michael Hardy 04:06, 21 May 2005 (UTC)

I am sorry about the misunderstanding. What i called BS was your "example of a conspiracy of space aliens". I never said that "squaring the circle is a topic invented by crackpots". And i got angry because you keep putting words in my mouth which i never said or meant (on three counts including this one). You don't even have to assume good faith, if you just stick with the facts. — Sebastian (talk) 16:30, 2005 May 21 (UTC)
I think all of this started with Sebastian putting Squaring the circle in Category:Pathological science, which is kind of undeserved. Oleg Alexandrov 17:45, 21 May 2005 (UTC)

I agree with Michael and Oleg in questioning the appropriateness of the category "pathological science", for this article. In fact, I think that "pathological science" is a problematical name for a category. The description given here seems to imply as much, and Sebastian seems to agree, quoting from here: "I don't like the name "Category:Pathological science", either, but this was the closest i could find." A good category name should be self-explanatory, which this one is not. It should not require a paragraph to define, and then still be not quite clear (to me at least). Having said that, there is some merit to what this category is trying to describe. And it does have some relationship to this article. And there are other mathematical topics which might share this relationship, for example other impossible contructions like angle trisection (do people still try to do this?).

As to the somewhat unpleasant discussion between Michael and Sebastian, I think there has been some misunderstanding going on. I do not see that Sebastian said or implied that "squaring the circle is a topic invented by crackpots rather than a legitimate mathematical problem". Nor do I think he meant to imply that by assigning the article to the category "pathological science", although I can see why Michael might have thought so. I think everyone agrees that "squaring the circle" was a legitimate problem considered by serious and reputable mathematicians, prior to the proof that it is impossible. However, that people nevertheless are still trying to square the circle, is an interesting phenomenon, which is deserving of some thought and discussion, and perhaps even a category. Paul August 21:08, May 21, 2005 (UTC)

Yes, I agree. This is exactly what i meant! Thanks for getting back on topic! Possible names include:

  • pointless scientific efforts
  • misguided scientific endeavours
  • research which flies in the face of facts

Sebastian (talk) 22:10, 2005 May 21 (UTC)

Squaring the circle is not the right article for a more-than-tangential mention of mathematical crackpots. Certainly a separate article could treat that. Michael Hardy 01:24, 22 May 2005 (UTC)

Micheal, I think the request is to come up with a catchy category name that says "this topic is a legit topic that tends to attract crackpots"; not just math but in general. free energy and casimir effect spring to mind. linas 06:56, 22 May 2005 (UTC)
What exactly is the motivation behind creating a category bringing together subjects 'attracting crackpots'? Surely not to attract crackpots more effectively. It seems kind of unencyclopedic to give these things too much attention. Charles Matthews 20:51, 27 May 2005 (UTC)

Perhaps category:pseudoscience is the category which Sebastian is looking for. Although I don't think it would be appropriate for Squaring the circle. And pseudomathematics could be the right place for a more lengthy description of the phenomenon represented by the continued attempts to square the circle. Paul August 21:19, May 27, 2005 (UTC)

I'll say first of all that it's clear all this resolves around the aggressively named category "Pathological science". Let me draw a more modern parallel.

In complexity theory, a classical result is that the class NL, and indeed the entire log-space hierarchy, collapses to NL — that is, NL is closed under complement. I've read papers predating this discovery by the most eminent of researchers, still alive today, that claimed that most researchers reasonably believed that the log-space hierarchy did not collapse, and they based some of their results on this. A similar thing happened with the discovery that SL is closed under complement, widely believed to be false not so long ago and now trivial as a consequence of L=SL.

The short of it is, very smart and very reasonable people have good reasons to believe that things that are false. Neither they nor the goals they pursue are "pathological" or even "misguided"; rather, they are reasonable actions based on available knowledge.

Finally, one more example: I can't remember the name, but one of the founders of noneuclidean geometry actually believed that Euclid's parallel postulate could be derived from the remaining axioms — in other words, his aim was to disprove the existence of any alternate geometry. He assumed that the axiom was false for purposes of contradiction, going on to write a large book deriving many results from noneuclidean geometry, eventually uncovering a "contradiction" which was actually an error and proclaiming the theorem proved. Was he a crackpot? No. Was his effort pointless? Not at all! He didn't achieve the unattainable goal he set, but he discovered a lot of useful things in the process. You don't tell a kid they'll never be an astronaut.

So what's a good category? I vote for Category: Disproven conjectures.

Deco 09:44, 28 May 2005 (UTC)

Possible crackpot pages

Seems that User:Laurascudder has unearthed a cluster of physics pages of highly dubious content. I'm not sure what to do with them. I'd suggest VfD except that I don't quite know that process.

and possibly also

although this last one almost does make sense.

As a whole, these pages seem to be filed with errors, ommisions, indecipherable formulas, a mixture of trite and deep statements, notation pulled from many different areas of physics and mashed together in highly non-standard, incoherent ways. My gut impression is that most of this stuff is dubious "original research" by an out-of-work Soviet nuclear technician who has a strong grounding in physics, but was unable to master quantum field theory as it is taught today. So what's the WP process for stuff like this? linas 16:39, 22 May 2005 (UTC)

Linas, I recommend heading over to Wikipedia:Votes for deletion and going to the bottom of the page, there are instructions there for listing on VfD. Even if these pages end up being worth keeping, it's still a good thing to know. Sholtar 17:11, May 22, 2005 (UTC)

These are all created by the same guy - Rudchenko (no user page, so link shows all contributions to date). Maxwells nonlinear equations looks especially suspect to me... (I always understoof Maxwell's equations are the whole and the entirity of non-quantum electromagnetism). I will try contacing people I know to get some definate answers. Tompw 17:07, 22 May 2005 (UTC)

Gluonic vacuum field should also be looked at. It seems to belong to the same cluster of articles. Paul August 03:28, May 23, 2005 (UTC)
Well, it seems they have gone to VfD anyway, which is a process hard to stop once it is started. Rather than theorising about the author, I think it is important to focus on what we know about the content. Which is indeed about an alternate line of field theory, to standard QFT. There is a key passage on one of the pages, which I will cite when I find it. Charles Matthews 10:01, 23 May 2005 (UTC)
Right, the place to begin is certainly w-field, with its reference to an approach to field theory attributed to Gustav Mie. One approach is to assume that all essentially all these pages are working out consequences of that idea. Original research they may be - I wouldn't know enough about this corner of theoretical physics to know. I don't think they should be deleted simply because the approach is different from standard QED. Charles Matthews 10:08, 23 May 2005 (UTC)
Hi Charles, I'm the one who VfD'ed it. The reason for this is not so much that they're non-standard (you should know by now that I have a weakness for non-standard things), but rather 1) they're pretending to be something they aren't: one could formulate a non-linear electrodynamics, but this isn't what's being done here. 2) They're filled with deductive errors. Sure, the pionic field is pseudo-scalar, (it changes sign under parity), but to argue that this means that the associated (non-relativistic) potential is purely imaginary is bizarre/wrong; the (non-relativistic) Hamiltonian wouldn't be hermitian, which is wrong. I suppose one could try to build up some quantum theory with non-Hermitian pseudo-Hamiltonians, but you'd have to lay oodles of groundwork first, and it might not work out in the end. 3) The same formulas show up in gluonic vacuum field and quantization of pionic field. That's wrong. If it had been called pionic vacuum field, that might have flown, but gluons are non-abelian, they belong to the adjoint rep of su(3); they're very different than pions, which would be a singlet of su(3). One musn't write an article about gluon-anything without saying su(3) at least once. 4) Multiple instances of the usage of the non-relativistically covariant Schroedinger equation, followed by remarks such as "we can use the Klien-Gordon equation". 5) article on coherence condition: one can't write down a kinetic term that way, at least not without oodles of justification. The 'coherence condition', a purported variational minimization of the Lagrangian, is missing a few terms. The presentation turns incoherent shortly thereafter; the variation δ s should not be thought of as "non-fixed numbers".
As far as I'm concerned, this stuff is a word salad of formulas, the likes of which is common in the underworld of flying saucer theory. Sure, one can build alternative theories, but one needs to lay a groundwork, define terms and the like. One mustn't say "D^2s=0" without first explaining what "D" is. And next, one must point out in the preface that these are "alternative theories", rather than pretending that Maxwell had invented some kind of non-linear equations (and thereby implying legitimacy). That's why I VfD'ed them; these articles are beyond repair. linas 14:49, 23 May 2005 (UTC)
FWIW, here's why I expound so confidently: my PhD thesis was on the Casimir effect inside of protons/neutrons, so I know a lot about the quantum vacuum state and QCD in general. This quark vacuum was coupled to a topological soliton made out pions. That's how I got my grounding in math. As to pions ... somewhere (misplaced) I have a copy of the "Pion-Nucleon Interaction", signed by the authors, Andy Jackson (my advisor) and Gerry Brown, (his advisor). Gerry, unwelcome in the US, spent the McCarthy years running around Europe setting up nuclear research centers; one might say things like RHIC and the neutron star equation of state are his legacy. You can find a few of my lame publications from that era on e.g. "Justifying the Chiral Bag", cited by 21, hot damn!linas 15:15, 23 May 2005 (UTC)
One more quickie remark: The standard formulation of a non-linear version of Maxwell's equations is known as Yang-Mills theory, which these days is understood to be a principal bundle with fiber SU(N). Rudchenko's attempts seem to be an effort to use SU(2), given the appearence of the cross-product. Until he explains how it differs from the 'standard' SU(2) formulation, its just bunk. linas 16:51, 23 May 2005 (UTC)
The articles are of such low quality they would have to be rewritten anyway. Further, the only person that seems to know anything about it Rudchenko stopped contributing several months ago. And last but not least I could not find any papers on the subjects (except for w-field and nonlinear magnetic field) meaning this will never be verifyalbe. So I'm in favor of a delete. --R.Koot 12:45, 23 May 2005 (UTC)
Rudchenko is still contributing but is using anon IPs, see:, and probably: and Paul August 16:52, May 23, 2005 (UTC)
I'm confused. From and he tweaked some formulas, which you wouldn't do if this was a hoax. While he has been creating a link farm and given some very strange replies on talk pages from (If your known similar calculation please give sign here. Rudchenko.)? --R.Koot 18:27, 23 May 2005 (UTC)
inetnum: -
descr: Donetsk Regional General Scientific Library
country: UA (Ukraine)
inetnum: -
country: UA
address: Scientific & Technological Centre FTICOM
inetnum: -
descr: Dial-up pools and interface addresses. FARLEP-TELECOM-HOLDING, a subprovider of Farlep-Internet in Donetsk, Ukraine
country: UA
I think it is more likely that these articles are original research than hoaxes. Paul August 19:07, May 23, 2005 (UTC)

Extended Yukawa Potential, Yukawa Potential. Maybe this is of some use to anyone? --R.Koot 13:04, 23 May 2005 (UTC)
Be aware that google and even is blissfully unaware of most modern physics and math. Dead-tree media still underpins the dominant publishing paradigm. linas 16:07, 23 May 2005 (UTC)

Revert to an old version of manifold

(Moved to Talk:Manifold. Oleg Alexandrov 16:59, 27 May 2005 (UTC))

Use of this page

It is better, I think, if discussions on page content are left on the talk pages of the articles. It is perfectly fine if, in the case of an article of basic importance to mathematicians, an invitation to participate is made on this page. I really don't think long discussion threads on specific content issues are correctly placed here. Charles Matthews 10:11, 27 May 2005 (UTC)

Right. Sorry, I did not think it will go that far. Not again. Oleg Alexandrov 15:33, 27 May 2005 (UTC)

I agree with Charles. For obvious reasons, page-specific discussions, usually best occur on that page's talk page. I think there is a tendency to raise page-specific issues here, in order to reach a potentially wider audience, which I must say I do find useful, both as one who wants to "reach", as well as be reached. But as Charles implied, that can, to some extent at least, be accomplished by posting a notice (perhaps together with an excerpt of an ongoing discussion) here, with a request that further discussion occur there. In any event, any page-specific discussions which do occur here, should, at some point, be copied or moved to the associated talk page, so as to preserve a more complete historical record there. To that end, unless anyone objects, I will move the above section "Move of "Mathematical beauty" to "Aesthetics in mathematics", comments?", which I initiated, to Talk:Mathematical beauty. Paul August 16:32, May 27, 2005 (UTC)

By the way, I also wanted to say that I quite value this project's active and vibrant discussions. The more we do it, the better we should get at it. A project needs a certain critical mass of activity to remain viable. This is a great project and it has a great group of participants, and if it takes an occasional "off-topic" discussion to keep it active or to assure ourselves that some of us are still alive and kicking, then it is worth it ;-) (Perhaps, from time to time, we should take attendance!) However, as this page's only archivist, Charles may have mixed feelings about the volume of discussion ;-) — so I pledge to help out with that task in the future and also in accord with my earlier comment, I volunteer to go through all of this page's archives, and copy any page-specific discussions to the appropriate talk page. Paul August 18:02, May 27, 2005 (UTC)

I think we should create a section on this page to note important discussions: obviously if big edits to mathematics, manifold and so on are being mooted, it is of general interest. Charles Matthews 18:07, 27 May 2005 (UTC)

Should there be a distinct math-related VfD page? Are VfD's common in math? At any rate, if any come up, I think announces should be posted at least here. linas 20:34, 27 May 2005 (UTC)
They are not so common. There have been a few 'crank' pages in the past. Mostly poor material can just be dealt with by redirecting. Also, it is not always clear when topics are technically wrong: who knows enough to be an expert in all branches of mathematics? So my policy is not to rush to VfD. Of course sometimes we need it. Charles Matthews 14:08, 30 May 2005 (UTC)

Two math pages set for deletion

Algebra I has been submitted for deletion, and I did the same thing today for Algebra II. They are about courses with the same name. I think does not look encyclopedic. But either way, here are the links:

Oleg Alexandrov 00:10, 30 May 2005 (UTC)

Might I direct your attention to Long-tail traffic as well. It has a VfD banner on it, but isn't on the list. At least one of the pictures seems to be scanned and the rest of the article gives that impression too. Reference [1] are lecture notes on ELEN5007 so this is probalby someone who put his paper on Wikipedia. --R.Koot 00:27, 30 May 2005 (UTC)
This article is part of a collection of articles, which are all part of a class project. They are being discussed here: Wikipedia:Deletion_policy/Teletraffic_Engineering. Paul August 01:45, May 30, 2005 (UTC)
Thanks, I missed that. Very strange though... --R.Koot 11:40, 30 May 2005 (UTC)

Vfd for space mixing theory

The page on space mixing theory seems to be unpublished work. I called for a vote for deletion. I hope this is the right forum for announcing that. If not, I apologize, and would really appreciate it if someone could point me to the right place to discuss deletion of unreal science. Bambaiah 10:39, May 30, 2005 (UTC)

Current active content discussion

Please edit this section to keep it up to date (major topics only)


for some of the more important content discussions now active in this WikiProject.

Nominated article


  • I nominate Lebesgue integral. Charles Matthews 08:17, 19 Feb 2004 (UTC)
    • Hello Charles. I do like the Lebesgue integral article, although it gets bogged down toward the end -- it seems like the discussion sections can be tightened up quite a bit. Comments? Wile E. Heresiarch 02:33, 8 Apr 2004 (UTC)
      • Always room for improvement. I chose it mainly because it touches all the major bases (motivation, some history, towards applications, picture, real content), so is quite a good template. Charles Matthews 06:31, 8 Apr 2004 (UTC)
  • I second the nomination for Lebesgue integral. I'll also nominate Bayes' theorem. Wile E. Heresiarch 02:33, 8 Apr 2004 (UTC)

Other articles I think are good in their ways are Boy's surface (graphics) and Nicholas Bourbaki (perspective and NPOV - I have worked on this one). Charles Matthews 09:19, 15 Jul 2004 (UTC)

Wikipedia:Classifications of mathematics topics

Seems this page was not updated in ages. And right on top is a suggestion to maybe delete. Indeed, what people think? We already have areas of mathematics, list of lists of mathematical topics, and list of mathematics categories. So, Wikipedia:Classifications of mathematics topics seems kind of reduntant. Or does this article have a purpose? Oleg Alexandrov 02:15, 22 May 2005 (UTC)

It proposes 2 categorizations one of which is original work and the second is included in areas of mathematics. Looking more closely this seems to be a talk page not an article? --R.Koot 15:24, 22 May 2005 (UTC)
What do you mean by original work? Oleg Alexandrov 16:01, 22 May 2005 (UTC)
I meant original research. --R.Koot

For now, I redirected Wikipedia:Classifications of mathematics topics to areas of mathematics, as the two aritcles have exactly the same purpose and the latter is more compete and better written. Both pages seem to be concerned with classifying the math on Wikipedia based on the American Mathematical Society's math subject classification, MSC2000.
Also, some content in Wikipedia:Classifications of mathematics topics makes me think that this page was either vandalized, or otherwise very sloppily edited.
By the way, I have a feel that areas of mathematics would need some work, but I don't know exactly what kind of work; it just feels somewhat unfinished. Any ideas on what to do with this page? Oleg Alexandrov 00:22, 2 Jun 2005 (UTC)

question about formatting of standard symbols

I am wondering whether there is any policy in this project about formatting for standard symbols like Q (the set of rational numbers). I sometimes see Q, sometimes Q, sometimes just Q, and on a few occasions the blackboard-bold version wrapped in <math> tags, i.e. . It's particularly jarring when these different versions appear in the same article (or sentence). I realise that if a single article uses both inline and <math> formats, then some inconsistency in appearance is unavoidable. Also I realise there's some conflict here between freedom and rules, with the concomitant effects on productivity. Still, I'm wondering if at least there is some consensus on the 'ideal' notation. Dmharvey 18:47, 31 May 2005 (UTC)

I think one needs to use either Q or . The first is preferable in inline formulas, as the second yields an image, which is undesirable, see Wikipedia:How to write a Wikipedia article on Mathematics. The second one is more preferrable in big formulas I think. Now, to use Q or plain Q for the rationals is not correct; it needs to be changed to one of the two if encountered.
Now, all this is my own opinion, but this seems to be the unwritten tradition. Oleg Alexandrov 01:46, 1 Jun 2005 (UTC)
I like to use both Q and . The blackboard bold should be reserved just for that: the blackboard. --MarSch 16:22, 1 Jun 2005 (UTC)
I think I agree that is a definite improvement on . Certainly in my regular work with LaTeX I stick to . Although usually it doesn't turn out so huge. And it could be argued that, in certain important respects, WP has a lot in common with the humble blackboard :-) If other people agree, perhaps the math(s) project needs somewhere for this kind of notational suggestion to belong. Does it belong under Wikipedia:WikiProject Mathematics/Conventions? Dmharvey 17:38, 1 Jun 2005 (UTC)

I always prefer using blackboard bold even in typeset work, as bold is used for too many things. This will always be a matter of opinion though; there will always be those who disagree. If more browsers supported it I would use ℚ in all my articles. For the time being I stick to Q and . -- Fropuff 18:25, 2005 Jun 1 (UTC)

I'd stick with blackboard bold, not only because I find it more pleasing aesthetically, be because it's a defacto standard. Maybe Wikipedia's policy of no original research should be extended to no original typesetting? --R.Koot 22:07, 1 Jun 2005 (UTC)
I personally like the LaTeX rendering, but I think it would be best to use only when it is not disruptive to the general flow. If an effort were made to set formulae aside from other text, perhaps making the statements first in "math lingo" and then restating what was just stated in TeX with standard English perhaps the entire issue could be resolved. Guardian of Light 5 July 2005 14:46 (UTC)