Wikipedia talk:WikiProject Mathematics/Archive/2006/Oct

WAREL is back again

I wonder if anybody knowing the subject of the articles edited by WATARU could take a look at some diffs and see if it makes sense what he wrote. Oleg Alexandrov (talk) 15:09, 28 September 2006 (UTC)

I think all changes but one have been corrected or removed. I don't know about Japanese sociologists. — Arthur Rubin | (talk) 18:15, 28 September 2006 (UTC)

But he doesn't stop, blocking him seems necessary.--gwaihir 23:37, 28 September 2006 (UTC)

Looking at policy under WP:DE (Disruptive Editing) I think WATARU is somewhere between steps 5 and 6 of the process. According to step 4, a 'Request for Comment or other impartial dispute resolution' should be opened. However this was done back in April '06 [1]. We now seem to have 5, 'Editor ignores consensus'. The suggestions under part 6 are topic ban, site ban or probation. EdJohnston 00:45, 29 September 2006 (UTC)

We reached point 6: 'Blocks fail to solve the problem.'  --Lambiam^Talk 01:46, 29 September 2006 (UTC)

Still up to the same tricks. What's the next step? —David Eppstein 23:15, 30 September 2006 (UTC)

Blocked (along with his IP) for 48 hours for personal attack (against me). I have no objection to a community ban, including the IP. — Arthur Rubin | (talk) 06:00, 1 October 2006 (UTC)

Changed reason to general disruption. The WP:NPA in editing my user page doesn't rise to the level required for a block, but the disruption is still valid. — Arthur Rubin | (talk) 06:26, 1 October 2006 (UTC)

Now Special:Contributions/Suslin --gwaihir 15:40, 4 October 2006 (UTC)

and Special:Contributions/MACHIDA (indefblocked; anyone changing the ja: wikilink on Field or Division ring deservices an immediate temporary block, at this point, and the other edits and style makes it clear what's happening.) — Arthur Rubin | (talk) 12:54, 9 October 2006 (UTC)

and Special:Contributions/MORI (indefblocked), but he seems to have killed the ja: articles. — Arthur Rubin | (talk) 03:10, 10 October 2006 (UTC)

Fourier Transform

Some of us are discussing re-organizing the articles about the fourier transfrom, I thought this might be of general interest, so anyone interested should look at the Topology of articles discussion under the Continuous Fourier transform talk page. — Preceding unsigned comment added by Thenub314 (talk • contribs) (Oops on my part Thenub314 00:29, 30 September 2006 (UTC))

That's not a good page name. How about Fourier transforms on the line? Charles Matthews 07:01, 29 September 2006 (UTC)

There is also a multi-dimensional continuous version, which curiously is mentioned at Fourier transform but not Continuous Fourier transform.  --Lambiam^Talk 11:46, 29 September 2006 (UTC)

The multidimensional version is in there under under a sub-sub-section Extensions. I like the idea of "Fourier Transform on the Line", I had suggested "Fourier Transfrom on R", but no one else seemed to like that idea. But I do dislike the term "continuous Fourier Transform". Thenub314 13:41, 1 October 2006 (UTC)

"Importance" and "vital" tags

I think we need to have a discussion about just what are the criteria for the various "importance" levels, and the "vital" tag, for the {{maths rating}} template. Right now they seem to be the opinion of the person adding the template, which I have no terrible argument with (I certainly don't want to add another level of process), but we need to be aware that there can be disagreements.

My attention was brought to this by Salix alba's addition of "Top importance" and "vital" to the decimal article, an article the need for which I think is frankly marginal, at least from the perspective of mathematics. (I agree it's a very important topic from the perspective of history of mathematics.) --Trovatore 20:20, 30 September 2006 (UTC)

Vital relates to Wikipedia:Vital articles which is actually a cross-language grouping of the vital articles that every language should have. There are about 67 such mathematics articles, most of which are rather basic. The mathematician in this list is: Archimedes, Vladimir Arnold, Diophantus, Euclid, Leonhard Euler, Pierre de Fermat, G. H. Hardy, David Hilbert, Gottfried Leibniz, Muhammad ibn Musa al-Khwarizmi, Henri Poincaré, Pythagoras, Srinivasa Ramanujan, which I find rather arbitary, and does not agree with the list we put together on the main maths assessment page. It is the same list as Wikipedia:WikiProject Biography/Core biographies. The tag is there to have some cross coordination with other efforts.

Yes I wasn't quite sure on the importance of decimal, high importance for school age students, engineers, less important for pure mathematicians.

You do raise a good point about about it being only one persons view. Others may wish to change the ratings, which is fine, indeed encouraged. There have been a few changes in rating happen already. Edit summaries and article talk pages are probably the best places to discuss disputes in the ratings.

The overall definition of importance levels is probably best on the maths assessment page. So far we've only covered about 150 articles, a tiny fraction of the whole mathematics coverage. Quite where the lines should be drawn is still a good question. --Salix alba (talk) 21:13, 30 September 2006 (UTC)

I see; I hadn't understood the exact meaning of the "vital" tag. Maybe the template should be clarified to indicate that. I considered putting "vital=Y" back, but decided to remove decimal from wikipedia:vital articles instead. We'll see how it shakes out. --Trovatore 21:44, 30 September 2006 (UTC)

Have you notices how they have Proof listed under Number theory, I can't quite figure out the best place to put it though! --Salix alba (talk) 21:55, 30 September 2006 (UTC)

As I recall there's a "logic" category there; any reason not to move it there? --Trovatore 22:00, 30 September 2006 (UTC)

I understand that Wikipedia:Vital articles is supposed to be a mirror of Meta:List of articles every Wikipedia should have. However, I spotted quite a few discrepancies.

The following are listed here as "vital" mathematicians, but are not mentioned at Meta: Vladimir Arnold, Diophantus, Pierre de Fermat, G. H. Hardy, Henri Poincare, Srinivasa Ramanujan. Curiously enough, Pythagoras is listed, but in the category "Social scientists"!

The following mathematicians are listed at Meta but not here: Fibonacci, Carl Friedrich Gauss, Christiaan Huygens, Hypatia of Alexandria, Johannes Kepler, Pierre-Simon Laplace, Blaise Pascal, Bernhard Riemann. One could argue that Kepler should be in the category "Scientists", but he is not mentioned at all on our "Vital" list. Same for Pascal as also being a philosopher. Isaac Newton is listed in the category "Inventors and scientists".

Should we do something about these discrepancies, and if so, what is the appropriate approach?  --Lambiam^Talk 22:48, 30 September 2006 (UTC)

I think Wikipedia:WikiProject Biography/Core biographies, it the place most worthy of our attention, as it has the highest profile, being a key part of the WP:1.0 project. The job of selecting just ten mathematicans seems quite arbitary.

Also worrying is the coverage of mathematics in WP:CORE just 5 out of 150 article

Algebra Geometry, Mathematics, Number and Statistics. (Calculus, Mathematical analysis and Non-euclidean geometries got booted off).

WP:CORESUP the suplement with 150 more articles, and only 5 more maths articles

Arithmetic, Equation, Mathematical proof, Theorem, Trigonometry

WP:V0.5 the first itteration of the 1.0 list, has

Georg Cantor, Carl Friedrich Gauss, David Hilbert, Gottfried Leibniz, Blaise Pascal, Alan Turing, John von Neumann, Algebra, Calculus, Game theory, Linear algebra, Margin of error, Mathematics, Measurement, Trigonometric function, Pi, Fractal, Manifold, Matrix (mathematics).

Thats now closed, selection was based partially of GA/FA's and core topics, plus a few we put forward. There will probably be another iteration before the final 1.0 release.

Possibly the best thing for us to do is assemble of list of perhaps 50 mathematics articles, which are of high importance and good quality. We can then pass these lists onto the various other projects as sugestions for inclusion. The 0.5 people were quite responsive, although we didn't have much to offer them at the time. --Salix alba (talk) 00:10, 1 October 2006 (UTC)

For the record... there are currently 76 top-class articles, of which 3 are FAs, 8 are A-class, 4 are GAs, 12 are B+ class, 27 are B-class, 19 are start-class, and none are stubs. These figures include mathematicians. Tompw 22:43, 6 October 2006 (UTC)

Going back to the original point, which is basically asking how we decide what level of importance to give an article. I think several people (myself included) would naturally tend to equate importance with "importance in mathematics" - so something like the Pythagorean theorem would come out fairly low. However, the criteria given in the WP 1.0 subpage relate to an articles importance for a print encyclopedia. To me, this means we have consider importance to the readership as well as importance in mathematics. Consequently, the Pythagorean theorem comes out as top importance. In a nut shell, I give the artitcle an importance of Max{public importance, mathematical importance}. Because the grading of quality and importance is done by oen person, there will always be potential for disagreement. In that case, it's probably best to discuss it in the talk of the assessment page. Tompw 22:30, 6 October 2006 (UTC)

There's a tendency to equate "mathematics" with "contemporary pure mathematics research", visible both here and in the new version of the Geometry article, that I think should be discouraged. As a formula for calculating distances from Cartesian coordinates, in the kind of mathematics that non-mathematicians are likely to use, the Pythagorean theorem is extremely important. —David Eppstein 22:42, 6 October 2006 (UTC)

I agree with you completly... the point I was trying to make (maybe needing a better example) was that we are trying to rate the importance of the article in an encyclopedia, not the importance of subject matter in mathematics itself. Tompw 22:50, 6 October 2006 (UTC)

I concur with Tompw. The "importance" criteria should be something along the lines of, if you were in a math class that assumed you knew "x" and needed to look "x" up, might you try an encyclopedia, or would you try to find a more specific reference? For example, yesterday, I rated complex number as a Top importance article because it's a concept that is very common (yet often misunderstood) in mathematics and probably should be found in a general reference book. On the other hand, something like holomorphic function (trying to stick with the complex theme here) is very important to mathematics, but it is advanced to the degree that no one would try to look it up in a print encyclopedia. --JaimeLesMaths 04:26, 7 October 2006 (UTC)

The Core biographies importance ratings are helpful:

• Top - Must have had a large impact outside of their main discipline, across several generations, and in the majority of the world. (snip)
• High - Must have had a large impact in their main discipline, across a couple of generations. Had some impact outside their country of origin.
• Mid - Important in their discipline.
• Low - A contributor to their discipline and is included in Wikipedia to expand depth of knowledge of other articles.

These are a little more objective, but need a little tweeking to better fit the needs of mathematics articles. So by these Pythagorean theorem is clearly top, whith a very large impact. holomorphic function has a smaller impact outside of mathematics.

Possibly another way of sorting articles would be when they would typically be taught, say primary (up to 11), secondary (11-16), advanced (16-18 and non mathmatics numerate degrees), maths degrees, post-grad. These could be called something other than the emotive importance, say academic level. Possibly also useful as the actual academic level could be compared with the writing style of the article indicating articles with too technical writing for the content. --Salix alba (talk) 09:25, 7 October 2006 (UTC)

New section in Pythagorean theorem should be expanded

I've hastily added a new subsection to Pythagorean theorem on the proof found in Euclid's Elements. Doubtless it could bear further elaboration (since it's not really the full proof, but rather an illustration with an accompanying explanation). Also, could someone who knows how to do such things help with the alignment of the illustration, so the reader can more easily tell which illustration goes with which section? Michael Hardy 01:20, 1 October 2006 (UTC)

I've worked over the illustration layout, introducing right-left alternation, standard thumbnail size, forced clears, and captions.

For those who have little experience with images, there is helpful information at Wikipedia talk:WikiProject Mathematics/Graphics, and at Help:Images and other uploaded files.

Once an image has been uploaded, the standard right-floated thumbnail is produced by a line like the following.

[[Image:Circle ellipse tangents.png|thumb|right|''Figure 1.'' Shared tangents]]

It should immediately preceed the paragraph it accompanies. To force a break, use the following HTML.

<br style="clear:both" />

There's no rocket science here. The hard part is, as always, creating the images. --KSmrq^T 23:05, 1 October 2006 (UTC)

Suggestion to improve most math articles

What I've noticed, in my quick, probably statistically invalid sample of a few articles, is that they could be benfitted greatly from graphs. For example, Venn diagram is clearly illustrated, as is a bit easier to understand than, let's say, Comparison test. Comparison test could benefit from the image on Convergent series, for example... and similar. That, IMO, could help many math articles be a bit closer to FA status. Titoxd^(?!?) 03:03, 1 October 2006 (UTC)

Then you'll be delighted to contribute to Wikipedia:WikiProject Mathematics/Graphics.

Good illustrations don't just happen. Some mathematicians think in pictures, but many do not. So first, someone must have an idea for a figure. Then someone must design it. Then someone must create it. Then it must be uploaded (to Commons) and introduced into the article. You might be surprised how much time and effort can go into a single illustration.

We'd also like more articles, and better introductions for the general public, and more examples, and more references, and more ISBNs for listed books, and more web links, and so on. And, of course, more better writing. (And fewer vandals, and fewer clueless editors, and fewer drive-by "fixit" tags.)

In other words, we may agree with your sentiments, but Wikipedia places the power to make it happen in your hands. Do feel free to ask here, or at Wikipedia talk:WikiProject Mathematics/Graphics, or at the Village Pump if you need assistance. --KSmrq^T 06:06, 1 October 2006 (UTC)

See also Wikipedia:Reference desk/Mathematics#I'm taking image requests.  --Lambiam^Talk 00:51, 2 October 2006 (UTC)

John Dee

John Dee is up for a featured article review. Detailed concerns may be found here. Please leave your comments and help us address and maintain this article's featured quality. Sandy 21:02, 1 October 2006 (UTC)

Major reworking of Geometry

Geometry is just undergoing a major reworking. The previous article was just a history of the topic and has been moved to History of geometry. This now leaves Geometry as a stub, sugestions of how to structure the article welcome on the talk page. --Salix alba (talk) 09:24, 2 October 2006 (UTC)

And this major move had how much discussion? 'Just' a history of geometry - would anyone care to weigh in with a non-historicist discussion of what geometry means? Charles Matthews 09:31, 2 October 2006 (UTC)

Er, no discussion. I guess User:The Transhumanist was being WP:BOLD. Still I think its generally a good idea, as the history only approach was not the best way to structure the article. --Salix alba (talk) 10:14, 2 October 2006 (UTC)

I agree that the earlier incarnation of the article was bloated and didn't give enough of a flavor of 20th century developments, but jettisoning the whole thing was a mistake. I am definitely leaning in the direction of revert. Michael Kinyon 10:31, 2 October 2006 (UTC)

Well, plenty of edits since then. Let it not be said that we (OK, I) ducked the challenge. Charles Matthews 15:02, 2 October 2006 (UTC)

I just assumed you meant the "royal we", Charles. :-) In any case, yes, I'm slowly being convinced this can work. Michael Kinyon 15:36, 2 October 2006 (UTC)

You can call me Prince. Charles Matthews 17:02, 2 October 2006 (UTC)

Though Shing-shen Chern is deceased (so I guess he's not contemporary), it is very odd that he is not mentioned in this article. What is the definition of contemporary again. A fortiori, Cartan I guess would not be contemporary either. --CSTAR 17:10, 2 October 2006 (UTC)

It needs a section just for differential geometry too, of course. Charles Matthews 18:25, 2 October 2006 (UTC)

There appears to be a very long list of topics (in its own article) of articles on Geometry, so I do not think that the main article needs to mention them. It already has a pointer to that list. I would suggest that the main article focus on the most modern concept of Geometry, i.e. David Hilbert's. As the History of Geometry article says "In geometry, there was a clear need for a new set of axioms, which would be complete, and which in no way relied on pictures we draw or on our intuition of space. Such axioms were given by David Hilbert in 1894 in his dissertation Grundlagen der Geometrie (Foundations of Geometry).". JRSpriggs 09:18, 3 October 2006 (UTC)

Axiomatic geometry is interesting, but is only a small part of the subject known as geometry. The article works best as a survey, and seems to be evolving quite well right now. Michael Kinyon 09:43, 3 October 2006 (UTC)

Hilbert's axioms are only 'state of the art' in a very restricted sense. The suggestion that we need a survey based on the contemporary scene is sound; though it shouldn't exclude other things on that page. As for axiomatics, Atiyah says some interesting things about those. I was trying to find where Weil discussed geometry, yesterday, so far without success. The way things are going, we should be finding more quotes to add to various articles. Charles Matthews 09:59, 3 October 2006 (UTC)

Hilbert's axioms provide a great understanding of how mathematics develops and how mathematicians think; You can see that reading any good "mathematical education" textbook (quotes here are used to indicate my disdain for most specialists in education), e.g. Great Theorems of Mathematics: A Journey Through Genius (I forgot the author), that puts side to side Euclid's axioms and Hilbert's. They are a valuable addition to any article on geometry. --Lucas Gallindo 15:10, 3 October 2006 (UTC)

The author is William Dunham. ISBN 0471500305. Gandalf61 15:22, 3 October 2006 (UTC)

I think it is fair to ask how many contemporary papers in geometry are actually based on Hilbert's axioms. Charles Matthews 15:26, 3 October 2006 (UTC)

As far as I know, papers of real relevance, using Hilbert axioms... there are none! But I still think they are enlightening for the newcomer.--Lucas Gallindo 15:40, 3 October 2006 (UTC)

It is also fair to ask how many contemporary papers are based on Euclid's axioms. I don't believe the study of facts about Euclidean geometry on the plane is a major topic in contemporary research. The things mentioned in Geometry about contemporary research in Euclidean geometry, such as geometric group theory, seem like a stretch. CMummert 01:32, 4 October 2006 (UTC)

I take the point abouy geometric group theory, which has a more complicated set of inputs than the other areas mentioned in that section. Euclidean geometry now is the geometry of Euclidean space, or the Euclidean group, post-Klein. Charles Matthews 07:05, 4 October 2006 (UTC)

Synthetic geometry should be more fully described; I know just enugh about it to be cautious of "Euclid-style" without being able to edit myself. Septentrionalis 04:41, 6 October 2006 (UTC)

Numeric spiral

Just a word of warning: The page Numeric spiral was created today by User:Noluz. The same user listed it on List of curves and in the External links of Archimedean spiral, but I just reverted both since Numeric spiral has nothing to do with curves at best, and at worst is numerology. Michael Kinyon 23:29, 3 October 2006 (UTC)

Is this the same or similar to the Ulam spiral? --Salix alba (talk) 00:29, 4 October 2006 (UTC)

Yes, I think so. It is similar, in fact, to at least one of the external links [2] on that page. Michael Kinyon 01:55, 4 October 2006 (UTC)

The thing described is not a Ulam spiral. It is a badly designed visual representation of partitioning the natural numbers into equivalence classes modulo 9 while marking the prime numbers. Putting them in the form of a spiral serves no particular purpose and does not help to bring to light any properties. I've listed this article for deletion.  --Lambiam^Talk 05:04, 4 October 2006 (UTC)

It is simply applying Casting out nines to calculate the equivalence class (as Lambiam said) and then treating the fact that primes (except three itself) are not divisible by three as some kind of magic. Really idiotic. JRSpriggs 05:36, 4 October 2006 (UTC)

Yes, I see it now that I finally thought to click on the figure to enlarge it. And only now can I decipher the nonmagical parts of the article. "Cabilist" indeed! :-) Michael Kinyon 07:01, 4 October 2006 (UTC)

Gang Tian

Hi, it seems that a single-issue user (130.158.83.81) is keen to revert the controversy section of Gang Tian from my edits originally made here. His reversions are here and here.

My edits were intended to improve the quality of the writing of that section, to improve the wikilinks (for example, 130.158.83.81 insists on linking to Yau-Tian affair, which doesn't exist, rather than Tian-Yau affair), to improve the accuracy (according to my limited knowledge) and to add citation requests for unsupported assertions.

A later editor removed the controversy section altogether, after the 130.158.83.81s latest reversion. I have since restored the section for the time being, but perhaps removal is the best option. If we want to keep the section, then the version promoted by 130.158.83.81 seems objectively worse than my alternative. There is much room for improvement, but I just sought to make the section better than awful.

Anyway, I don't think that editor is breaking any rules, and I don't want to enter a daily edit war, but I thought I'd bring it to your attention. All the best--Jpod2 08:59, 4 October 2006 (UTC)

I've made a redirect from Yau-Tian affair, removing one minor bone of contention. The content should be very careful, and adhere to WP:LIVING, staying well away from any hint of defamation. We should also remember and respect the fact that these are important professional mathematicians. Charles Matthews 09:11, 4 October 2006 (UTC)

Agreed. I tried to tone down some of the extreme and unusual language in my edit, or otherwise requested citations. I doubt that this version will stay there, though.--Jpod2 09:14, 4 October 2006 (UTC)

I think your edits helped to improve the section, and helped to remove POV from the article. Thanks. It may be that user Reb's solution of removing the unsourced paragraph may be best for now. Good luck, Lunch 15:08, 4 October 2006 (UTC)

I think that might be the best solution for the moment. All the best--Jpod2 16:31, 4 October 2006 (UTC)

Just a couple quick thoughts as my time editing is limited recently. 1) Per WP:BLP do not merely add "citation needed" tags to dubious, potentially libelous information; remove it immediately - do not move it to the talk page. 2) The intro is rather bad as it overemphasizes his recent monograph with Morgan; that is not his most notable achievement or why he is a titled professor at MIT. It should be moved and noted in some kind of contributions section, with a brief description of his specializations in the intro. Also, for some reason he is listed as being a full professor at Princeton in a section. --C S (Talk) 19:27, 4 October 2006 (UTC)

Actually I had the impression he was at Princeton, so I did a little searching and it seems he is there now, although a few years ago he was at MIT and transitioning to Princeton. So this ought to be cleared up in the article. --C S (Talk) 19:42, 4 October 2006 (UTC)

Sylvia Nasar

Besides the fairly well-patrolled Poincare conjecture, Grigori Perelman, Tian-Yau affair, Manifold Destiny, and newer Gang Tian, those with the inclination should keep an eye on S.T. Yau (which doesn't appear watched as much) and Sylvia Nasar (not watched very much either). Recently there has been a couple rather defamatory edits to the Nasar article (based on what appears to be sheer speculation and poor sourcing). --C S (Talk) 22:30, 4 October 2006 (UTC)

Lie theory

The page use to redirect to Lie group [3] but was changed into a small article which is pretty much barren.--Jersey Devil 10:58, 5 October 2006 (UTC)

Looks like it should be merged into Lie (disambiguation); so I did. Septentrionalis 23:01, 5 October 2006 (UTC)

Citation guidelines proposal support

Wikipedia:WikiProject Physics/Citation guidelines proposal currently states: "... editors in Wikipedia:WikiProject Physics want to clarify how these guidelines should be implemented for physics articles ...". Question: Can we change that to: "... editors in the WikiProjects Physics and Mathematics want to clarify how these guidelines should be implemented for physics and mathematics articles ..."?  --Lambiam^Talk 17:20, 5 October 2006 (UTC)

I would support that change. Madmath789 17:25, 5 October 2006 (UTC)

Me too. I like the proposed guidelines a lot. Especially the new part about how simple examples and rederivations aren't WP:OR. —David Eppstein 17:39, 5 October 2006 (UTC)

Yeah, I'm in. I like them, too. Michael Kinyon 18:19, 5 October 2006 (UTC)

Yes. Editors of the mathematics article are setting citation guidelines for that article. It would be far better to follow more broadly accepted guidelines. --Jtir 18:33, 5 October 2006 (UTC)

<comment deleted -- I had said something about the 0.999... article, well I will not delete my comments again> :) --Vesal 20:21, 5 October 2006 (UTC)

The proposed guideline gives no examples of book-cites at the page level, which are used extensively in [0.999...]]. Another problem is that the example article-cites appear in a random order in the notes instead of alphabetically. --Jtir 20:16, 5 October 2006 (UTC)

I wrote some confusing stuff up there and deleted it, sorry about it... I will explain, at first I thought it was a citation style, but this is something much deeper, it's the verifiability guideline, and well as such I don't think it specifies any style at all. So let's discuss the guideline... I have a number of questions, maybe I will ask them on the guidelines talk page. --Vesal 20:25, 5 October 2006 (UTC)

That would be the appropriate place for any and all comments on the draft. Putting them here makes them invisible to editors in other projects. Comments are welcome from everyone. CMummert 20:36, 5 October 2006 (UTC)

Just question to people in this project... has there ever been discussion or edit wars over the proofs or reasoning presented in mathematics articles? I have not seen any such discussion over mathematical details, so I would support the proposal... However, I would not mind, if all mathematics articles were as cited as 0.999.... I don't really see how such citations make reading or editing more difficult. I wonder what the people who worked on that article think about the excessive citing that was required to get it into FA quality. --Vesal 20:36, 5 October 2006 (UTC)

Has there ever! You only have to check out the talk page of that article and its archives. The general consensus I perceive in hindsight is that mild OR is better than nothing, but I've encountered little resistance to the idea that cited material is better than OR. What do I think about the citing? I think it's hard but worthwhile. Not only does it keep you honest and stem accuracy disputes, the search for citations can lead you to the only really interesting material in an article. Melchoir 21:14, 5 October 2006 (UTC)

I have gone ahead and added mathematics in. Seeing as it is a proposal, anyways, it can't hurt. A number of people on WP:CITE and WP:GA seem pretty happy with the proposal too, so I'm optimistic about the chances for this proposal to make an impact for the better. –Joke 21:43, 5 October 2006 (UTC)

I'd just like to say I am really glad the difficulties physics and maths articles faced over WP:CITE and WP:GA are being addressed. Tompw 22:28, 5 October 2006 (UTC)

I'm glad to see the issue recognized. The unthinking insistence at Wikipedia:What_is_a_good_article? that all articles, whatever their structure or sources, must have in-line citations continues, however. The exception in the proposal is entirely reasonable. Septentrionalis 22:59, 5 October 2006 (UTC)

I don't think anything has been resolved at WP:CITE; this is at best a stopgap measure. And WP:GA applications are going to be a dead end for a while unless we get a large number of scientifically knowledgable good article reviewers. CMummert 00:23, 6 October 2006 (UTC)

That's true, but I take the attitude that the articles that are best off without in-line citations are probably not articles that we really want to become "Good Articles" (or, heavens, Featured Articles). It's crucial to recognize that there is a difference between Good Articles and good articles: this is particularly so, and will likely remain so indefinitely, with physics and math articles. Articles such as the Littlewood-Richardson rule and Bianchi classification (these don't exist yet – hint, hint) could probably be quite easily be made into good articles. But it is not at all clear it would be worth the effort to make them into Good Articles. –Joke 00:16, 6 October 2006 (UTC)

We should write good articles, not Good Articles. The more I see of that process, the less I like it. Septentrionalis 03:47, 6 October 2006 (UTC)

More good GA fun. Derivative was awarded GA today and then imediatly reviewed, inline cites being one of the issues. Folks might like to comment. --Salix alba (talk) 16:29, 10 October 2006 (UTC)

Help with grading articles please?

Just a notice... it would be wonderful if more people could help grade maths articles in Wikipedia:WikiProject_Mathematics/Wikipedia_1.0. Anyone can edit in additional important articles that should be included. It's *not* a job where an excessive number of cooks leads to inferior broth. Tompw 19:40, 5 October 2006 (UTC)

I believe that Wikipedia 1.0 is a broken and misguided project, and should be abandoned or reformulated. No thank you. Septentrionalis 22:01, 5 October 2006 (UTC)

That's very nice, but totally irrelvant :-). Tompw 22:19, 5 October 2006 (UTC)

Its not just about Wikipedia 1.0, its about having a good allround coverage of the mathematics articles. Grading helps us identify the strengths and weeknesses in our maths coverage: important articles which are week and need work to bring them up to speed, and also the better articles which could be put forward to GA or FA status. --Salix alba (talk) 22:42, 5 October 2006 (UTC)

How do the comments in the tables in Wikipedia:WikiProject Mathematics/Wikipedia 1.0 relate to the comments in the {{maths rating}} box? -- Jitse Niesen (talk) 05:31, 6 October 2006 (UTC)

Er, week equality. The tables predate the math rating tag, serving as a sort of scratch pad, where we tried to build up a list of the most important topics. Much of the task at the moment is to go through the list there and adding tags to the talk pages. Eventially the automatically generated Wikipedia:Version 1.0 Editorial Team/Mathematics articles by quality will become the definative list. Mathbot uses the comments stored in say Talk:Blaise Pascal/Comments to fill in the comment in the list and also in the talk page, which will be a mechanism for ensuring consistancy of comments. I need to work out how to switch on including these comments in the list.

Slightly related is the field parameter to the tag. It currently does nothing but could be used as a mechanism to group the ratings by the particular topic area. --Salix alba (talk) 08:21, 6 October 2006 (UTC)

Prime numbers

While looking into an OTRS ticket, I came across this edit. Does anyone know if this stuff is accurate? --bainer (talk) 08:31, 6 October 2006 (UTC)

Pretty good nonsense. It has been reverted. Charles Matthews 10:16, 6 October 2006 (UTC)

Graph invariant: a new category?

Graph invariant is a regular page. I propose to make it a subcategory of Graph Theory. Several pages would then belong to it:

• Algebraic connectivity
• Arboricity
• Betti number
• Clustering coefficient
• Colin de Verdière graph invariant
• etc.

Do you agree/disagree? pom 09:22, 6 October 2006 (UTC)

On the point of grammar, Category:Graph invariants would be the usual style. Charles Matthews 10:07, 6 October 2006 (UTC)

Agree (preferrably with the plural form) JoergenB 12:49, 6 October 2006 (UTC)

On a similar note, I just made a subcat Category:Graph families yesterday. Probably several of the entries there could also be cross-listed under invariants, e.g. Dense graph defines density as an invariant. —David Eppstein 15:04, 6 October 2006 (UTC)

I created the category. I am not really happy with the content of the old Graph invariant page, so I did not copy it. How should graph invariants defined within a more general article be categorized and/or listed in this category? pom 16:22, 6 October 2006 (UTC)

Notable invariants should be worked into the main article as prose, as in Knot invariant. Later on, it may even be useful to complete the coverage with a list article, but not yet. Melchoir 16:32, 6 October 2006 (UTC)

The future

There are several fairly active discussions going on about quality, citations and so on. The Project needs one more thing, really, which is an assessment of coverage and where it is going. At a moment when the coverage as a whole looks satisfactory, saying people should concentrate more on quality makes every sense.

We are not there yet, really. It is somewhat muddling to look at lists of articles, or of red links, and to try just from that to say how broad the coverage is. My gut feeling, though, is that 18 months ago we were mid-1950s, and now more like mid-1960s. That is, there is a historical way of thinking about this, and it is a helpful barometer. (In physics, the 1960s would be quarks and quasars, kind of thing, and it is not so odd there to ask about coverage in terms of what is adequately discussed in encyclopedia terms.)

Extrapolating, we might have a reasonably full coverage in about four years time. Don't groan: it would be an amazing achievement to say we had a survey that good. There are always going to be topics left out, but the criterion is that writing an article to fill a gap would not involve a long trail of red links to further concepts on which it depended. The basic vocabulary would be there.

Charles Matthews 10:28, 6 October 2006 (UTC)

Problem edits on RH

I noticed a number of problematic edits by User:Karl-H on topics relating to the Riemann hypothesis. I tried fixing some, but am out of energy at the moment. I believe that the gist of what he's trying to say is mostly correct, but he is not a native English speaker, and he's not a mathematician, and he's writing up original interpretations of research papers he did not quite understand. The edits wreck to flow of the articles, the language is fractured, ungrammatical, mis-capitalized, and worst: the formulas are fractured, incomplete or wrong; see for example Chebyshev function, Hilbert-Polya conjecture, etc. I just can't get to this stuff in the next few weeks. linas 19:28, 7 October 2006 (UTC)

See an awkward ongoing discussion about claims to have proved RH, on Talk: Hilbert-Pólya conjecture. I'm not rushing into anything, but there are unsupported statements about RH on the pages, not sourced, which may need to be removed as original research. There may also be an issue here about what is a 'reliable source' for rumours, how we treat 'non-withdrawn claims' over time, and so on. My view is that in most cases we can have an article with NPOV that ignores fringe claims; so that cutting out rumours is usually OK. Charles Matthews 09:26, 9 October 2006 (UTC)

Order theory

Whereas I 100% agree with We should write good articles, not Good Articles, I want to bring to everybody's attention that the GA candidateship of Order theory is on hold [4] for failing the criteria 2a, 2b,2c of It is factually accurate and verifiable. --Pjacobi 22:31, 8 October 2006 (UTC)

This is a sad example of the prevailing lunacy. Despite the twisted mindset of some editors that "inline citations" = "accurate and verifiable", this article is well documented. Reputable sources given at the end suffice to allow the claims given in the article to be verified as accurate. Wikipedia must learn that mobs and footnotes are no substitute for editorial competence and diligence. --KSmrq^T 23:31, 9 October 2006 (UTC)

Navigational templates

Trovatore drew my attention to the fact that there is a consensus against navigational templates in maths articles of any kind. I was completely unaware of this... could someone kindly explain why this is the case?

I always thought navigation boxes were one of things that made Wikipedia so much better than any print encyclopedia. Also, Calculus topics all have a box at the top right; and {{mathematics-footer}} exsists and is used, so the rule is clearly not applied in all cases.

This cropped up because I had begun implementing the contents of User:Tompw/maths templates. Tompw 15:10, 9 October 2006 (UTC)

<rant>No, hypertext makes Wikipedia so much better than any print encyclopedia. But not everybody got the concept of hypertext, so the "See also" section was invented. Then the attack of the web designers happened, and everything had to be be boxed, colored and templated. Or something like that.</rant> --Pjacobi 15:14, 9 October 2006 (UTC)

I said "one of things"... I agree hyperlinks are definitely the single biggest thing that make Wikipedia wonderful. However, when I browse wikipedia, I want to know about related topics. If I'm looking at the History of Nunavut, I may want to read about the Geography of Nunavut. This wouldn't be linked within the text of the former, but is linked via the nav box. Also, such boxes draw your attention to topics you might have been unaware of. Tompw 15:19, 9 October 2006 (UTC)

Calculus I think is allowed to be an exception: as a service to students, a box provides quick navigation between standard topics. Otherwise templates are much hated. For one thing, if you put both an algebra and a topology box on algebraic topology, you are starting a nasty build-up. This illustrates one point: boxes were used before categories existed, and categories are superior. For another thing, the choice of topics in a box is arbitrary in a potentially annoying way. Who would be able to make a definitive box for group theory? It again looks like subcategories is a better solution. Charles Matthews 15:23, 9 October 2006 (UTC)

(edit conflict). I woudl disagree with the statement "templates are much hated"... more to the point, the advantage of nav boxes is that they are selective, whereas a category has to contain anything and everything taht is vaguely relevant. I agree such selectivity has the potential to cause disputes, but that does not means such disputes cannot be resolved. Tompw 15:38, 9 October 2006 (UTC)

It doesn't mean they are worth having, either. That is a genuine reason for the dislike. Say there is a good selection to be made, for a student at a certain level. Who chooses the level, though? First course in topology, second graduate year in algebraic topology ... ? No end in sight. Charles Matthews 16:34, 9 October 2006 (UTC)

I am very displeased by the {{Geometry-footer}} and {{Analysis-footer}} templates. They are huge, and this kind of things tend to only grow over time. I believe in general that navigational templates are bad, except perhaps by {{Calculus}} as mentioned by Charles and maybe {{mathematics-footer}}. Categories are much preferred. I would suggest these templates be deleted. Oleg Alexandrov (talk) 15:31, 9 October 2006 (UTC)

(Btw, I never intended to create these as finished products. I always knew that they would get changed, probably quite substantially from my intial creation. If people think they are too long/short/weird, then edit the thing. This is a wiki, after all :-) Tompw 15:38, 9 October 2006 (UTC))

Those footers are awful ({{Geometry-footer}} & {{Analysis-footer}}). They are a bunch words strung together with no organization, not even alphabetical. And how is "Category:Geometry" a topic in geometry? IMO, a lack of hierarchical organization is a deficiency in many subject areas that makes it hard to take in the "big picture". The Encyclopædia Britannica has a Propædia that organizes all knowledge in a hierarchy. Since WP is electronic there can be several hierarchies. --Jtir 17:18, 9 October 2006 (UTC)

Fair comment. ({{Geometry-footer}} is now much changed. Will do {{Analysis-footer}} in morning, assuming someone else hasn't got there first :-). Tompw 23:44, 9 October 2006 (UTC)

While hyperlinks are good we need to distinguish between inline hyperlinks and hyperlinks in lists/templates. For purpose of navigation inline links are not ideal, they require the user scan the whole text searching for a given link, they may occur in a narative order rather than a logical/hyerarchal order. I'd quite like to see important related topics in a see also section even though they already appear in the main text. It makes it easier for people to navigate.

Tompw raises a good point about categories in how they tend to get too full to allow the important items to be easily found. One solution is to actually expand the text in the category so a more organised list is displayed. This is what we've done at Category:Polyhedra.

The other approach to a nav box style is to follow the German scheme, where there is a standard configurable box, which may had fields like parent topics, sibling topics and child topics. Each page could then set these fields as needed, avoiding problems with the giant nav boxes. --Salix alba (talk) 17:27, 9 October 2006 (UTC)

Sounds interesting, can you provide an example? I couldn't find one on de.wikipedia.org. --Jtir 17:38, 9 October 2006 (UTC)

There is a familiar precedent for displaying hierarchies: Windows Explorer. When collapsed, an entire hierarchy fills exactly one line. Indeed all modern computer file system browsers allow collapsing and expanding of any part of the hierarchy. The Nautilus file manager that is part of many Linux distributions is good example. --Jtir 17:55, 9 October 2006 (UTC)

Example of German navboxes: DE:Halbgruppe. But they're not used consistently throughout math there. —David Eppstein 18:29, 9 October 2006 (UTC)

Thanks. That looks promising. Now if only those bullets were clickable so the subcategories could be displayed or hidden at will.

Could someone translate these headers? BabelFish doesn't do too well on them.

Here are the German headers with English translations:

• berührt die Spezialgebiete ("touches branches/areas [of math]")
• ist Spezialfall von ("is a special case of")
• umfasst als Spezialfälle ("contains as special cases")

--Jtir 19:28, 9 October 2006 (UTC)

I don't see it as promising. I see it as promoting a view of math as a very rigid hierarchy, which conflicts with my view of math as a highly interlinked non-hierarchical graph of connections. E.g., to name two topics I've been working on very recently: Happy Ending problem is categorized as Category:Discrete mathematics while until very recently Erdős–Szekeres theorem was categorized only as Category:Ramsey theory — viewing things hierarchically, Discrete Geom => Geom => Math and Ramsey theory => Combinatorics => Math are very far apart. But they come from the same original paper and originally one was used to prove the other. I think a hierarchical view of the world as promoted through navboxes would downplay that connectivity as well as needlessly cluttering the pages and making it harder to find the actual text of the article. —David Eppstein 20:07, 9 October 2006 (UTC)

Literal translation: "touches branches/areas [of math]", "is a special case of", "contains as special cases".--gwaihir 20:17, 9 October 2006 (UTC)

I think each branch would need to be handled a bit different. Some things partition well, others don't. Some pages would have very short boxes, some could have longer. - grubber 21:01, 9 October 2006 (UTC)

I have tossed around the idea with a couple other WPers about the idea of starting a project to develop some math templates like the ones used in the German wikipedia (see de:Gruppetheorie for an example). I think it would be nice to get together some people interested in this, and hash out some ideas and guidelines about what we could use in the English WP. If we were to let a template system grow organically, I think it will quickly get out of control and become inconsistent... being more of an annoyance than a help. But, if we can plan out from the start, I think we could set up a very nice, usable navigation aid that will not detract from the articles. How would you all feel about such a project (it could be a separate wikiproject or a subproject of this one)? - grubber 19:01, 9 October 2006 (UTC)

The link de:Gruppetheorie leads to "Gruppetheorie ... Diese Seite existiert nicht", which I would roughly translate as "No such article". --Jtir 19:19, 9 October 2006 (UTC)

de:Gruppentheorie --gwaihir 19:21, 9 October 2006 (UTC)

The boxes on German wp are incomplete, partly misleading, partly wrong. They originated in the (not uncommon) misconception that algebraic structures should be understood by comparison to "similar" structures. Of course, a given object like the integers has all the aspects of ring, abelian group, monoid. But group theory is not just abelian group theory without commutativity, and ring theory is again completely different from studying the additive and multiplicative structure separately. I do not update these boxes any more, nor create new ones. But I'll ask for other opinions on dewiki.--gwaihir 19:27, 9 October 2006 (UTC)

I wouldn't want a copy of the German version either. But, I believe there is something between "no boxes at all" and "German-version boxes" (plus something new) that would work really nice. It will take a bit of time and debate and organization to hash it all out, but I think it's very doable. - grubber 20:20, 9 October 2006 (UTC)

Group
Field
Algebra
Related topics
Ring
Field
Sub topics
Abelian group
simple group

I quickly hacked together a demo User:Salix alba/Maths navbox shown on the right. It only supports two siblings and two children, but could be extended for more (I'd recomend no more than six for usability reasons). Its adapted from the taoxobox.

Code: {{User:Salix alba/Maths navbox|color=lightgreen|title=Group|parent=[[Algebra]]|sibling1=[[Ring]]|sibling2=[[Field]]|child1=[[Abelian group]]|child2=[[simple group]]}}

Yay! Lots of people are engaging in a mature and adult discussion about this idea. :-) More to the point, I'm not sure a parent/sibling/child box is the answer. The trouble is that one area of maths doesn't always relate to other areas in a hierachichal (sp) fashion. It's not like bilogy, where a genus is considered as a member of a fmaily, in comparison with that family's other genuses, and as collection of its species. So, the concept of sibling areas doesn't really hold. That said, the parent/children bit works far better. With groups, the parent is Algebraic Structures (and Alegbra in general), and the children are things like Abelian Groups, simple grouprs, quotients, products, sub-groups, major theorums etc. The trouble this leads to is a large number of children - see #3 below. People's complaints about my navigation boxes seemed to fallinto three categories:

1. Categories are better than navigation boxes: My reply is that both can co-exsist quite happily. If you want to to naviagte by category, then the exsistence of nav boxes doesn't prevent you
2. The layout/organisation/content is bad: This is a wiki. Change it. I created those boxes in the same was I create a stub article - for someone else to come along later and improve it.
3. What to include will lead to disputes and its cousin These boxes will get too large as people add more articles: The answer to this is a bit more involved. I was planning on creating navigation boxes to cover the next level of detail. For example, Group theory is just represented by two links in the Algebra box. I intended to create a nav box for gropu theory, containing such topics as Abelian Groups, simple grouprs, quotients, products, sub-groups, major theorums. (This deals with the problem mentioned above of excessivrt children). So, if a box gets too many items, simply split off a section into a new box. (Like splitting off History of XXX from the article on XXX). Now, if you think "This means some articles will ave loads of boxes", then you'd be wrong. At worst, an article (such as group theory) would have two navigation boxes - one covering sub-topics, and one cover super-topics (as it were). Tompw 22:19, 9 October 2006 (UTC)

Further, some areas of math are more hierarchal. Abstract algebra breaks down into a tree pretty decent, but number theory may not. Further, if we designated a central area to organize the nav-box content, then all opinions can be collated and we can maintain some consistency. - grubber 23:44, 9 October 2006 (UTC)

Of course, categories and navigation boxes can co-exist. However, combined they take up even more space, distracting from the meat of the article. Let's take the navbox on groups demonstrated by Salix Alba above. When reading group, how important will it be to the reader that groups are studied in algebra, or that the concepts of ring and field are related? How many will follow these links? I'd say that these things are only of minor importance when compared to the other topics of the article. Therefore, I think the article is better off without such an attention grabbing box at the top. -- Jitse Niesen (talk) 05:44, 10 October 2006 (UTC)

I wasn't ever intedning to put the boxes at the top - I was intending to put them at the bottom. In fact, I don't like nav boxes at the top for precisely the reasons you give. Tompw 14:19, 10 October 2006 (UTC)

I am still left with the idea that those navigational templates are a bad idea. For example, {{Analysis-footer}} contains a random bunch of things, starting with calculus, going to harmonic analysis, then List of integrals and Table of derivatives, to finish with the entire Category:Calculus. Linkcruft basically.

I strongly disagree with any hierarchical navigational boxes as suggested above. That would basically duplicate the category system.

If anybody is full of energy, what this project trully needs is to work on categories containing a huge amount of articles, splitting them into smaller one by topic which would also make navigation easier. Oleg Alexandrov (talk) 02:05, 10 October 2006 (UTC)

OK, this is begining to get repetitive....If you don't like it, change it. Please. The argument is here is not about whether one particular nav box is good or bad, but over whether to use the things at all. Tompw 13:10, 10 October 2006 (UTC)

I strongly agree with Jitse and Oleg. The categories need work, so why use potentially different hierarchies in garish boxes at the top bottom of the article that just get in the way? VectorPosse 06:55, 10 October 2006 (UTC)

"why use potentially different hierarchies..." actually, I would regard having an alternative hierachy as a good thing, to allow users the choice.

"...in garish boxes..." garishness is something that can be changed to accomadate tastes (You really these are garish? I'm surprised)

"that just get in the way". Why would they get in the way? It's not as though the exsistence of the box make it any harder to scroll to the bottom of the article where the category links are. Tompw 20:59, 10 October 2006 (UTC)

Okay, so when I said "garish" I was refering more to the other sorts of boxes given as examples in the preceding discussion. (Lots of colors and somewhat more "in the way".) The boxes you showed are not exactly that, so point taken. Let me also clarify my comment about hierarchies. It is clear that there are two different types of hierarchies we are discussing. This has been discussed here at length and seems to be a matter of "top-down" versus "bottom-up" organization. I am merely asserting (as several others have done here) that both types are already present in articles in the context in which they are more natural. (And I agree that "natural" is a subjective word. I am basing my idea of natural on the standards that are currently in place in Wikipedia and seem to function well already.) Categories provide the bottom up approach of reading an article and using its category to go up to the higher level and understand the context in which the specific article functions. As for top-down organization, this is already present in the hyperlinks in the article that will refer to related concepts, and "See Also" sections that do exactly what you propose to do in an extra box. I agree with you when you say that users might want a choice to go "up" or "down" a hierarchy. I'm simply pointing out that such a choice already exists and that more boxes might be redundant. And yes, they would still be a bit "in the way" since they will be basically repeating a lot of the "See Also" section when it exists and appearing right next to a box of categories that might also be saying a lot of the same thing as well. VectorPosse 23:16, 10 October 2006 (UTC)

I agree that the boxes could be partly redundent in some cases. (Although the exsistence of search and hyperlinks arguably makes categories redudent, but I digress). However, WP doesn't have space restrictions, so there is no reason not ave a belt and braces aproach. (The anology is apt - some people like belts, some people like braces. Me using one doesn't stop you using the other).

Where links in the "See also" section are duplicated, then they could be removed from the "See also" section. One of my pet peeves is a huge long list (e.g. Fluid_dynamics#See_also, especially before I put it columns). Also, a category link maens openign up the acetgory page, possibly going to a sub-category (or super-caetgory), browseing through a list organised alphabetically rather than by topic, and then (and only then) seclting a related article... and if you wish to browse through a series of related articles, then you have to repeat the process. A nav box means you can go to a related page in just one click. For those with slow connections or computers, this is defiante plus. Tompw 12:42, 11 October 2006 (UTC)

See, now you're talking about, not only making the text harder to find by surrounding it with more boxes, and not only making the article harder to maintain by keeping redundant connectivity information in the text and in the boxes, but actually degrading the information in the text to support these useless boxes. Also note that a see also section could and maybe should (even though they often don't) have brief notes explaining why one might want to see also, while in the navbox all that textual context is lost and only the link information remains. And your belts-suspenders analogy implies to me that you are pushing for greater inconsistency of formatting in WP — articles maintained by people who like boxes being very different to navigate than articles maintained by people who don't I am strongly opposed to the suggestion of removing see also links from the main article to boxes, and I think due to that more strong in my opposition to boxes. —David Eppstein 14:57, 11 October 2006 (UTC)

Yep, while Wikipedia is not on paper, there is no point in making articles much less usable by cluttering them with boxes. The primary means of navigating between pages is links in the text; the right link at the right time. Oleg Alexandrov (talk) 15:08, 11 October 2006 (UTC)

<--- First up, I am not talking about "cluttering" aryicles with boxes. It's not like there will be hundreds of the things lurking round every paragraph, ready to pounce on and confuse some unfortunate reader. Also, this is *not* a choice between boxes and alternative methods of navigation. We can have both, so that people can choose whichever they prefer. Yes, I agree that inline links as the primary method of navigation, but that doesn't mean they are the only one. (Categories, the search engine, and the address bar being others that spring to mind).

David Eppstein mentioned adding prose to "see also" lists to add context, and preumsably then the list will probably (hopefuly) end up becoming a proper section on "related areas". That be would be wonderful, and I'd like to see that wherever apropriate. So, I have no problem with "see also" lists remaining. (That said, if they did get removed by somone, an editor could still draw on the nav box as a source for related areas). (Yes, I've changed my mind as a result of your argument). Tompw 16:34, 11 October 2006 (UTC)

I think boxes at the top and bottom would be appropriate on some pagss. Some information is "vertical" (like math->algebra->group->ring->field) and others are more of a "level set" (homomorphism, group action, types of groups, etc). - grubber 15:39, 10 October 2006 (UTC)

That would go against the principles of Wikipedia where you connect to relevant related articles via links in text, and categories a the bottom. Such a "bottom-up" approach works much better than the suggested "top-down" approach of going through a lot of articles and making them have a box of related links. Oleg Alexandrov (talk) 15:55, 10 October 2006 (UTC)

Not really. Sideboxes are used quite often for that purpose: to show it relation to other similar things (German language, Dog), to show what its basic properties are (Cesium, Austin, Texas), or to show its position in a series (History of the United States (1918–1945)). Sometimes it is nice to have these types of relationships excised from the text and stated succinctly. - grubber 19:08, 10 October 2006 (UTC)

I don't want to put too much pressure on the people who have so far proposed some templates but...I don't really like what I've seen thus far. I understand that these are works in progress, but unless I see a concrete example that I like, right now these navigation templates seem like more trouble than they're worth. They seem like the infoboxes on bios, which are often, in my experience, just cluttered or useless. I suppose people have been harping about similar things so I'll stop with that.

Let me just reiterate a "philsophical" argument, due to David Eppstein, which I believe has been missed as it is not listed, for instance, in the list of arguments above. I believe the desire to create this kind of hierarchical system is really unnatural for a lot of mathematics. For some areas, it may "work". But here "work" doesn't mean that it really reflects an inherent hierarchy of concepts, but someone's training. So, for example, with group theory, many in the U.S. learn group theory in this rather pedestrian (albeit elegant) way where one starts with the group axioms, proceeds Bourbaki-style, learning eventually about group actions, etc. But for people with a different background or philosophy, this is really quite strange. For example, I believe there are major Russian schools of mathematics that would not teach group theory this way. Ok, enough philosophizing.... --C S (Talk) 08:34, 10 October 2006 (UTC)

Hmmm... interesting. I think in Russia they start with groups as symmetries of some object or set, and define everything that way. (I remember reading an article by Vladimir Arnold complaining bitterly that the axomatic way of teaching group theory left students with no understanding about what was actually Going On.) But I digress. The point Chan-Ho Suh is making is that different groups of people will order things in different ways as a result of their own educational experience, and this applies especially in mathematics. However, I think this would be resolvable, in that there would be general consensus on what topics would be included under group theory (sticking with groups). Yes, people learn about the topics in different orders, but that doesn't stop them from grouped togther in a similar way.

Also, this is the English-language wikipedia, and as such, articles should be written and organised with the English-speaking world as a target audience. Tompw 13:39, 10 October 2006 (UTC)

Funny to take Bourbaki as a representative anglophone. And Chan-Ho has some very good points about the Russians. We would benefit greatly by having more from their angle here. Charles Matthews 15:07, 10 October 2006 (UTC)

I'll weigh in with the majority opinion, that nav-boxes are inherently evil. My complaint is that I find that they provide a distorted view of the world, echoing some structure that was fashionable three decades ago. They typically give prominence to some inane topic while completely snubbing something more important. A well-written article will already contain all of the needed links to all of the topics that need to be linked. The nav-box offers nothing more than a quick escape for those with a short attention span. linas 05:57, 12 October 2006 (UTC)

If you think a given nav box is as you describe, then why don't you change it? Tompw 10:54, 12 October 2006 (UTC)

Changing the navboxes only makes sense if one already agrees that navboxes are a good idea. Some of us do not so agree. —David Eppstein 14:39, 12 October 2006 (UTC)

Circular argment... "Nav boxes shoudln't exsist because they are bad. But if they are bad they should be improved. But they shoudln't be improved because they shouldn't exist, because they are bad." Tompw 17:42, 12 October 2006 (UTC)

It is not a circular argument. We have three choices: (1) use the navboxes we have, (2) make the navboxes better, (3) don't use navboxes at all. All I'm saying is that some of us prefer (3) over the other two choices. —David Eppstein 17:55, 12 October 2006 (UTC)

I removed {{analysis-footer}} and {{geometry-footer}} from articles. The discussion here shows that people would prefer not to have these nav-boxes. Oleg Alexandrov (talk) 15:35, 12 October 2006 (UTC)

Fixing the Categories in Mathematics

As stated in the section above on Navigation Boxes, the Category system is better. However, many categories are over-full, for example, Category:Set theory. In such cases, we should create more subcategories (and subsubcategories, etc.). And we should also remove excessive categories from the articles. A good example is Category:Large cardinals which is a subcategory of Category:Cardinal numbers with little or no overlap. Unfortunately, overlap is common in other cases. JRSpriggs 07:54, 10 October 2006 (UTC)

Yes, Category:Set theory has nearly 250 articles. As a rule of thumb, I would say 100 articles in a category is quite enough.

The trouble can be that you may need an expert to make subcategories that really convince. I wouldn't necessarily trust myself to go into the set theory category and do the right thing for it. Charles Matthews 08:41, 10 October 2006 (UTC)

(I think the discussion in the above section says that some people think the category systems better, while others think nav boxes are better.) If an article can be said to belong to a category and a sub-category, then it should just go in the sub-category. That's why Category:Mathematics doesn't contain every single maths article on wikipedia. Tompw 13:25, 10 October 2006 (UTC)

It's a bad idea to make that a cast-iron rule, though. There are going to be a few exceptions, and it is excessively tidy-minded to enforce it. Charles Matthews 15:05, 10 October 2006 (UTC)

I haven't poked around much through the Wikipedia math categories so this is a bit naive, but I have a question: how well do the categories comport with the Mathematics Subject Classification (MSC) of the AMS? Dave Rusin has a general overview here and uses it in his articles [5]. The AMS has some descriptions of it here and here. I guess I'm thinking it's worthwhile to not re-invent the wheel. Lunch 22:18, 10 October 2006 (UTC)

Thanks for pointing this out. The AMS article has this to say: "... it is not always clear how to classify a mathematical paper or theorem, as these fields and subjects are far from disjoint." --Jtir 22:30, 10 October 2006 (UTC)

In a nutshell: they don't. The AMS classifications are different from the way the categories have evolved. (See Areas of mathematics for somethign more akin to the AMS classification). I did consider at one poitn drawing up a map from Wikipedia categories to AMS classes, but I don't think it would've been of much use for Wikipedia. The important thing to remember is that the AMS system classifies mathematical papers; the WP categories clasify encyclolpedia articles. Tompw 12:25, 11 October 2006 (UTC)

Any fixed system of categories is going to suffer from sclerosis. It is basically very un-wiki to say 'here, use this already-fabricated classification'. Works for biology, perhaps, but in mathematics you are for example going to have areas of combinatorics that take on their own identity as things move ahead. Charles Matthews 15:24, 11 October 2006 (UTC)

Yes, I know the MSC is used for categorizing contemporary research papers. Yes, I know a fixed set of categories isn't going to cut it.

But the MSC has evolved. And it is the result of a bunch of professionals (experts?) who got together and said, "hey, this is a useful way of categorizing stuff in mathematics."

What I'm suggesting is that it is a useful reference point. That papers/articles often fall in multiple (sub)categories. And for anyone looking to improve the verbal descriptions of categories on their pages, or looking for ways to split large categories into subcategories, the MSC might help point a way.

I hadn't seen areas of mathematics before, thanks. Lunch 19:20, 12 October 2006 (UTC)

By the way, there is a new Category:Systems of set theory. Check it out. Add or remove articles as appropriate. Once it settles down, I may remove the members of it from Category:Set theory of which it is a subcategory. Unfortunately, it is on the second page of subcategories (on my screen, at least). JRSpriggs 07:23, 12 October 2006 (UTC)

Of course it is harder to check out right now, because the weird way subcategories are listed means it is on the second page of Category:Set theory... Categories really should not be allowed to go over 200 entries. You really need to refine categories on a page into one or more subcategories, not just add them, or this problem gets no better. Charles Matthews 09:12, 12 October 2006 (UTC)

In the last day, Charles Matthews has made a Herculean effort to improve the organization of Category:Set theory and its subcategories. I hope you will all join me in expressing our profound thanks to him. JRSpriggs 07:14, 13 October 2006 (UTC)

I'll comment that the biggest change was the creation of Category:Basic concepts in set theory, for the counting-on-your-fingers level of things like the union of two sets, and in fact all the standard concepts of naive set theory. Charles Matthews 16:38, 13 October 2006 (UTC)

Proof by symmetry

The Proof by symmetry looks kind of encyclopedic to me. Any comments on that? Oleg Alexandrov (talk) 03:09, 12 October 2006 (UTC)

Surely you mean UN-encyclopedic. Inarticulate and probably OR as well is what I say. Nor is it about "proof" by symmetry at all, but about some more nebulous concept of symmetry in mathematical expressions. It seems to have about the same encyclopedic status as Michael Hardy's "three kinds of induction" that generated such huge debate and was eventually partially merged into mathematical induction. This is the sort of attractive heuristic that someone really skilled in metamathematics could spin into a paper on "equations of balanced symbolism" or some such, but that the author just decided to stick on Wikipedia since it's less work and more public. Ryan Reich 03:26, 12 October 2006 (UTC)

Proof by symmetry was written by User:Aklinger. It refers to Patterns in numbers, written by a certain Allen Klinger, professor emeritus of the computer science department at UCLA. The manuscript is listed as a draft here. I'm thus PRODding it as OR (I assume that Oleg meant unencyclopedic). -- Jitse Niesen (talk) 04:07, 12 October 2006 (UTC)

Sorry, I did mean UN-encyclopedic. Oleg Alexandrov (talk) 15:31, 12 October 2006 (UTC)

The wiki article is rather vague; the linked Klinger preprint slightly less so. However, there is no reason to accuse either of 'original research' in mathematics as such. Both the article and the preprint stresses points that have to do with problem solving methods and with mathematical didactics, not the (IMO rather mediocre) mathematics.

Both present a somewhat exaggerated view of the difference between Klingon's approach and more normal ones. (However, the greatest error was the addition of Category:algebra to the article, to which User:Aklinger seems innocent.) The merits or lack of merits ought to be discussed in a more pedagogical context. Does en:wiki have such pages? Does there exist comments on Pólya's problem solving approach; or even information on the regular international mathematical olympic games and their outcomes? Actually, Klinger does not offer a simpler solution of the problem; but it may be argued that his 'pivot' approach yields yet another approach to the problem, and therefore could be of use e.g. in training high school math athlets. It is also worth to note that he does quote a few printed articles, but in Science and similarly, none in a clearly professional mathematical context.

Of course, pattern searching is important; for interested kids, for the adult layperson, for graduate students, and for established math pro's. Actually, there are patterns for the pythagorean triples, too, which Klinger doesn't mention. Instead, he writes

While students often learn about the Pythagorean theorem and some specific instances, neither the name nor the values in any such triple possess power to stimulate.

One should recall that data equivalent to the Pythagorean triples have been found on mesopotamian cuneiforms, and clearly indicate that the ancient author knew the pattern - and followed it for its own sake, far beyond any practical usage. However, it is correct that we seldom teach the pythagorean triples patterns - or encourage students to find them on their own. My conclusion is: We should have categories on mathematical puzzle solving, more serious problem solving, mathematical competitrions, and approaches in mathematical teaching. In such contexts, an improved version of the article (also based on the published pattern recognition papers) might have some merits; but not in the field of describing mathematics itself. JoergenB

A brief account for the mathematical lack of content: I stopped reading the preprint at page 2, sat down a couple of minutes, and solved the problem by an equation for 'the lowest number', instead of one for 'the pivot (central) number' as Klinger proposes. Then I read on, and found that Klinger's solution hardly differs in complexity. If we got the question at the reference desk, I think some might deny to answer, referring to the 'no home assignments' rule. Klinger does also discuss a few variants of the problem, and how the pivot method illuminates their similarities.

The first problem may be stated thus: Given a positive integer n, find a positive x, such that

$x^{2}+(x+1)^{2}+\ldots +(x+n)^{2}=(x+n+1)^{2}+\ldots +(x+2n)^{2}\!$ . My solution was: Move all but the first l.h.s. terms to the r.h.s., pair $-(x+i)^{2}\,$ with $(x+i+n)^{2}\,$, and sum. This quickly yields $x^{2}=2n^{2}x+2n^{3}+n^{2}\,$ and $(x-n^{2})^{2}=(n(n+1))^{2}\,$.

Klingers solution: Instead, solve for x in

$(x-n)^{2}+(x-n+1)^{2}+\ldots +x^{2}=(x+1)^{2}+\ldots +(x+n)^{2}\,$, by moving all but the last l.h.s. term to the r.h.s., and pairing $-(x-i)^{2}\,$ with $(x+i)^{2}\,$; proceed as before. This is not OR in pure mathematics. JoergenB 18:07, 12 October 2006 (UTC)

A more pertinent question is whether "proof by symmetry" is a neologism, which wikipedia avoids (WP:NEO), or an established term. In the latter case, since several editors say they have never heard of it, a collection of in-print references would be helpful. CMummert 20:02, 12 October 2006 (UTC)

I don't think anyone suggested that it was the mathematics itself that was original. The OR referred to is indeed more along the lines of neologisms, etc. JPD (talk) 08:48, 13 October 2006 (UTC)

So it may be. However, I think that is an abuse of the term 'original research' (possible a common use, still an abuse). An article that does not contain new mathematics could be righteously brandished in many ways, but not by the OR label.

I found some mathematical competition articles, but not (yet) articles on pedagogical aspects of mathematics, or on problem solving. Since IMO these are the only contexts in which any of the proof by symmetry content (duly migrated) might be of any encyclopædic value, I'd appreciate hints where to find them. JoergenB 16:04, 13 October 2006 (UTC)

You could try Category:Heuristics in general, How to Solve It in particular. Charles Matthews 16:10, 13 October 2006 (UTC)

Euclidean group

The article Euclidean group is a large amount of little factoids, which added together make, in my view, a pain to read. The article is primarily the work of User:Patrick. I like much more the original version by Charles Matthews (see current version and good old version). I would vote for a rewrite of the article using the older version or a revert. Comments? Oleg Alexandrov (talk) 04:23, 13 October 2006 (UTC)

Wikipedia:Embedded list is relevant, I think. (I'm guilty of perpetrating lists sometimes as well, but that doesn't mean I think it's generally good style.) —David Eppstein 04:49, 13 October 2006 (UTC)

I always support good writing over grab bags; please do revert and rewrite. --KSmrq^T 05:18, 13 October 2006 (UTC)

I think I added a lot of useful content, in a very orderly way, not as an unorganized collection of factoids. Therefore I am against deleting that. We should be careful in changing lists into prose, it may become less readable (or if we do, keep both, and split off parts if the article gets too long). Constructive input from others would be nice, there has been little activity by others the last year.--Patrick 07:58, 13 October 2006 (UTC)

The new version does have a lot more information, but when I read through it I found it to be very staccato. Some of the lists are clear, but for example the overview of isometries section is very difficult to follow. I don't think a revert is justified, just some editing to make the article flow better. Adding introductory paragraphs to some of the sectins would make the lists more clear, while other lists could be replaced with a series of subsections. CMummert 13:46, 13 October 2006 (UTC)

I've done some work on the ordering of sections, and other tweaks. It shouldn't be too hard to put this into approved 'concentric' style. Charles Matthews 15:35, 13 October 2006 (UTC) OK, that should be somewhat better now. The only point of real concern I have is this: does the article really need the non-closed subgroups enumerated? I would have thought the closed subgroups were enough. Charles Matthews 15:52, 13 October 2006 (UTC)

If the overview is restricted to closed subgroups this has to be mentioned, you cannot say the subgroups are all of type A, B, or C, when there is also a type D. However, to clarify the restriction you have to explain it, so you end up briefly explaining the additional kind anyway.--Patrick 22:08, 13 October 2006 (UTC)

I don't agree: if it is thought of as a topological group, why not just explain the closed subgroups? I don't see the need for any more than that. Charles Matthews 12:23, 14 October 2006 (UTC)

Doesn't this all belong on the talk page Talk:Euclidean group? Let's take it there. CMummert 22:22, 13 October 2006 (UTC)

Good point. I started the discussion here to attract attention, now that people got involved, the discussion can continue on the appropriate talk page. Oleg Alexandrov (talk) 02:29, 14 October 2006 (UTC)

Erdős number categories on CfD

The categories Category:Erdős number 1 etc. (not to be confused with Category:Wikipedians with Erdős number 1) are nominated for deletion. If you have an opinion on this, comment on Wikipedia:Categories for deletion/Log/2006 October 8#Erdős number categories. You probably have to be fast, as the nomination was six days ago. -- Jitse Niesen (talk) 05:40, 14 October 2006 (UTC)

Emmy Noether

I observe that this article has (recently, I believe) become congested with umlauts. Unless, as we are not likely to, we change the spelling of Noetherian ring, this should be straightened out, with a reasonable allowance of "Noether"s for a mathematician who is usually so called in English, and who died on the faculty of Bryn Mawr College. Septentrionalis 15:36, 16 October 2006 (UTC)

And, if I may add, the German Wikipedia also spells the name de:Emmy Noether. So do German libraries, like the catalogue of the Deutsche Nationalbibliothek. And so did she herself. I'm copying this over to the talk page of the article.  --Lambiam^Talk 16:45, 16 October 2006 (UTC)

Lebesgue measure argument

I came across this article recently, and actually made some edits on it. The Lebesgue measure argument (as defined in the WP article) proves the uncountability of the reals via measure theory. As best I can tell the purpose of the argument is that it avoids the use of Cantor's diagonal argument and can be considered constructive,although I haven't actually checked whether the argument is in fact constructive. Googling on Lebesgue measure argument (verbatim) I get only two hits, from wikipedia both. Though the argument is valid and interesting (if actually constructive), does this article not violate WP:OR?

Articles may not contain any unpublished arguments, ideas, data, or theories; or any unpublished analysis or synthesis of published arguments, ideas, data, or theories that serves to advance a position.--CSTAR 17:46, 16 October 2006 (UTC)

This general idea seems to be present in the introduction to Oxtoby, John C. (1980). Measure and Category (2nd ed. ed.). Graduate Texts in Mathematics, no. 2, Springer-Verlag. {{cite book}}: |edition= has extra text (help); you could cite that as a source. —David Eppstein 18:00, 16 October 2006 (UTC)

I don't think it violates NOR, but I also don't think it's a particularly useful article as it stands. The hard part of the argument is that the measure of R as a whole is not zero, and that's not even touched in the article. When you fill everything in, I don't think it's any more "constructive" than the diagonal argument (which is pretty constructive, looked at the right way; for example, it's an intuitionistically valid proof that there's no surjection from ω onto 2^ω). The article also has a very unenlightening title. --Trovatore 18:36, 16 October 2006 (UTC)

It's not original research. It's well-known. I saw it in the first course on measure theory I ever took. I assigned it as an exercise for undergraduates when I taught a probability course at MIT. Of course, Trovatore is right about the "hard" part. Both Cantor's diagonal argument, and also his original argument for uncountability (which is three years older) are of course constructive. Michael Hardy 20:53, 16 October 2006 (UTC)

Oh---now I see that the argument given here is actually more complicated than the one I assigned. The exercise I assigned also avoided the "hard" parts, since the course assumed only first-semester calculus as a prerequisite (at MIT, first-semester calculus is about what first-year calculus is in most other places). See my comments on the talk page accompanying the article. Michael Hardy 20:57, 16 October 2006 (UTC)

Actually my question about whether this was OR concerned not so much whether the proof is OR, but whether the association of the name "Lebesgue measure argument" to the argument is actually supported in the literature. When I first came to WP over two years ago, I wouldn't have given this matter any thought -- any reasonable name would have suitable. However, with what seems the increasing trend toward WP:Wikilawyering at every junction I think this issue has to be addressed.--CSTAR 00:26, 17 October 2006 (UTC)

The name, as I mentioned, is obviously terrible. I'm not convinced the article should exist at all (a small mention in Cantor diagonal argument is probably sufficient) but if kept it should be moved to something more specific. I doubt there's a standard name in the literature, so that's not going to be much of a constraint, or much help. --Trovatore 00:30, 17 October 2006 (UTC)

I think "Lebesgue measure uncountability argument" would be sufficiently descriptive to avoid any claim that we are coining a new name, but as it stands the article is misleading as pointed out above and perhaps should get a disputed tag until the proof is completed.--agr 00:44, 17 October 2006 (UTC)

Based on the above comments, I put a Proposed AfD banner on the article.--CSTAR 02:56, 17 October 2006 (UTC)

This was deprodded by the author, so I smerged it into cardinality of the continuum, but first I prepared by moving the article to Lebesgue measure argument for uncountability of the reals, to avoid the bad redirect. There are way too many Lebesgue measure arguments to have that name reserved for this one in particular (and there's no real chance of a dab page; most of the time an argument doesn't get its own article, unless it has particular historical significance). And I put the redirect on WP:RFD.

If this is reverted we go to AfD. --Trovatore 05:56, 18 October 2006 (UTC)

Oh, just to clarify -- the redirect I put on RfD was Lebesgue measure argument, not Lebesgue measure argument for uncountability of the reals. The latter redirects where the content was merged; it should stay (though it's in my own words, so there'd be no GFDL issue in deleting it). It's the redirect Lebesgue measure argument, created by the move, that I think should be deleted. --Trovatore 06:12, 18 October 2006 (UTC)

"History of numerical approximations of π" really weird edit war---mathematicians please help

Look at the recent edit history of history of numerical approximations of π. User:DavidWBrooks has inserted this bit of wisdom into the article:

“ It has been known for millennia that π, the ratio between the circumference and radius of any circle, ”

("radius"! Sic.)

“ is a mathematical constant, but no method of calculation was available until fairly recently. ”

Of course someone came to clean up this nonsense, but here's what he (user:Henning Makholm) wrote:

“ Unfortunately no practical system for calculating with numbers is able to express π exactly. Though this fact was only proved rigorously in recent time, it has been suspected since the earliest times ”

Is there something remotely approximating some correct statement in that? If so, what is it? (Makholm left the ratio as circumference-to-radius rather than circumference-to-diameter.) Michael Hardy 21:05, 16 October 2006 (UTC)

I think it's all rubbish. Archimedes, like any capable mathematician of his days, knew how to compute the circumference of a regular 3·2ⁿ-gon. While this method is very not practical due to slow convergence, he must have realized, when using a 96-gon to shew that π < 22/7, that he could in theory compute the value to any desired precision. Given all the fuss at some earlier time over the diagonal of a 1 by 1 square not having a rational length, the claim that "this fact [...] has been suspected since the earliest times" has to be bogus. Or was that what the forbidden fruit of the tree of knowledge of good and evil propositions was about? Lacking a definition of what it means that a system is "practical", it is hard to refute the claim about what was proved "recently" (meaning, presumably, 1882).  --Lambiam^Talk 01:24, 17 October 2006 (UTC)

Why presume 1882? That was the year when π was proved transcendental. But that's got nothing at all to do (as far as I can see at this moment) with whether any "practical system for calculating with numbers is able to express π exactly". Anyone who thinks transcendence is about "practical systems for computing exactly" should get committed forthwith to the State Hospital for the Criminally Innumerate. Michael Hardy 02:09, 17 October 2006 (UTC)

Whoa, Michael Hardy shouldn't you be now concerned that a plague of Wikilawyers will descend on that previous claim, invoking countless breaches of this, that or the other rule, policy, guideline, essay, practice or what not and cart you off to wikiprison or maybe even have you wikiexecuted?. You're a brave man, Michael Hardy! --CSTAR 02:19, 17 October 2006 (UTC)

Arbitrarily-precise approximation is different from exact computation: one wants to be able to test, e.g., inequalities of expressions involving pi, and be guaranteed of an answer in a finite time, while you can keep computing as many digits of precision as you like and not be able to tell whether something is or is not equal to zero. And there is a sense in which transcendentalness is a barrier to expressing numbers exactly in a practical computational system, but irrationality isn't: see e.g. this page describing exact representations for algebraic numbers in the LEDA system. It says "LEDA cannot deal with transcendental numbers, at least not without loss of precision - there is no number type class in LEDA that could represent π or e exactly." Of course, the inability to express these numbers in a single system is not the same as a rigorous proof that no such system can exist, and I know of no rigorous proof that it's impossible perform exact computations in the extension of the algebraics by π. So I don't think the statement in the article is quite right... —David Eppstein 06:28, 17 October 2006 (UTC)

Point taken. What I was trying to express was just that one needs to work with approximations in order to do actual computations that involve pi -- but at the same time I was trying to defuse the possible counterargument that one could manipulate symbolic expressions, or juggle around with an entire convergent series of approximations, which is as "exact" as anybody could ask for. Henning Makholm 20:39, 17 October 2006 (UTC)

This should be discussed on the article talk page, but has general interest. Let's not get sloppy about terms. We can represent π exactly in a variety of ways. For example, we can define a series or continued fraction in a finite expression or algorithm. We can also compute π to any desired number of decimal places (or other measure of error). Archimedes demonstrated one approach using polygons to find upper and lower bounds, and we have much faster ways today. Being irrational, no finite computation can give an exact decimal expansion, oddities like the Bailey-Borwein-Plouffe formula notwithstanding. Yet computations with exact rational numbers are already troublesome in, say, computational geometry with lines and planes and so on, because the denominators can grow in a nasty fashion.

As for the article, both the original insertion and its amendment are hopelessly confused, and should be removed. --KSmrq^T 12:06, 17 October 2006 (UTC)

KSmrq is of course right. However, I'm afraid I can make a qualified guess of what the article editors essentially meant. There are too many students who believe that it isn't possible to express 1/3 exact (since they won't get an exact value by pushing 1:3 on their pocket calculator:-). Exact is often identified with exactly expressed in decimal notation with a finite number of decimals. I now and then meet statements such as '1/3 isn't an exact number, but 1/4 is'. Somewhat better informed students may understand that it is possible to 'express 1/3 exactly', if you use numerals with another basis than 10. In other words, I guess that 'no practical system for calculating with numbers is able to express π exactly' essentially is meant to mean 'π is irrational'.

I don't know if it is possible to clarify things enough for eliminating this confusion among some wiki readers; but we may try to lessen it. JoergenB 20:30, 17 October 2006 (UTC)

Oh, and by the way: That some users make this sort of mistake is not sufficient reason enough to accuse them of vandalism, or to call them 'dishonest idiots', however frustrating this kind of misunderstandings may be. JoergenB 20:42, 17 October 2006 (UTC)

My point above was simply that it is possible to express algebraic irrationals exactly, by writing down an integer representation of the polynomial for which they are root together with some disambiguating information to specify which root you mean. It is also possible to express π exactly, by the notation π. But the algebraics as exactly-specified numbers have been made part of a "practical system for calculating with numbers" (namely LEDA reals) while for π we can write "π" and call it a number and compute as many digits as we like but all that isn't sufficient to perform exact computations with it. I don't think the original editor meant an explanation like that, and I agree that the best course of action is to remove the offending statement, but there is a level of explanation at which his statement makes some sense. —David Eppstein 20:43, 17 October 2006 (UTC)

As a matter of fact, something like that was what I was trying to express with "practical system for calculating with numbers". Henning Makholm 20:51, 17 October 2006 (UTC)

David Epstein wrote:

it is possible to express algebraic irrationals exactly, by writing down an integer representation of the polynomial for which they are root together with some disambiguating information to specify which root you mean

By that standard one can also say that "log₂3" expresses a number exactly. Is there some reason to limit it to algebraic numbers? If not, then the year 1882, suggested above, does not seen relevant. If it is possible to define precisely something that Henning Makholm could have meant that is actually correct, then it seems very irresponsible to write in sich a horribly vague way about such a thing, and then claim that something expressed so vaguely was proved. It can't be proved if it can't be precisely expressed. So far we're still left guessing what was meant, even after Henning Makholm's comments here. Michael Hardy 22:58, 17 October 2006 (UTC)

I see your point, David. However, I think you may be mislead by viewing some CASes (computer algebra systems), where you might do exact simplification of expressions involving algebraic roots, but not as easily with π. In the first place, there are CASes and even pocket calculators where e.g. sin π cos π is replaced automatically by exactly -1, if you wish; some CASes may do much more advanced substitutions involving π; and more to the point, already Archimedes performed exact calculations with π (see talk:history of numerical approximations of π#Intro graf). IMO, 'computable' isn't synonymous with 'computable within a present-day CAS'. JoergenB 23:18, 17 October 2006 (UTC)

I made a stupid mistake above, thinking of cos and writing sin. However, I do not think making such ridiculus mistakes make me (or anybody else) qualified for asylums. I actually do know what the elementary values of the trigonometric functions are; believe me. JoergenB 23:30, 17 October 2006 (UTC)

There is, in fact, a specific technical reason to limit things to algebraic numbers: there exist algorithms that allow a computational system to reliably determine whether two given algebraic-number representations represent equal or unequal numbers. Therefore it is possible to guarantee that the result of a test such as x ≥ y, performed as part of some larger computation, will return in a finite time: one applies the equality algorithm first, and only after it returns unequal do you need to evaluate x and y to sufficient precision to tell them apart. There are no similar equality testing algorithms known, and therefore no similar finite-time guarantees, for systems of numbers generalizing the algebraics but also allowing logs, e, or π.

Also, I wouldn't call these systems CAS. They are libraries for performing calculations with numbers as part of computer programs, similar in spirit to a standard floating point library but allowing the representation of exact algebraic numbers in place of approximate floats. But they don't do some of the other operations that a typical CAS would, such as symbolic integration.—David Eppstein 23:41, 17 October 2006 (UTC)

CAS or not CAS is a matter of opinion. In mine, the algorithms by means of which you decide whether or not two expressions for algebraic numbers stand for the same number or not, are rather typical examples for CASes; much more so than is symbolic integration. This is not very important, though. If you restrict yourself to extending the field of algebraic number with one transcendental, e.g. π, you don't really get any harder decision problems than before. If you try to incorporate e.g. all kinds of exponentiation and logarithms, you run into trouble (at least today; I don't know much about the true bounds for undecidability). This is also not very important. The most important point is this: When you use the method of exhaustion by Eudoxos in order to prove that the same constant relates diameter to circumferense and square of radius to circle area, then you are performing exact calculations with the number π, in the best of the modern meanings. This Archimedes did. (This is a rather non-trivial result; as far as I remember, the claims about the constructions in the infamous Indiana Pi Bill implied different values for these two proportions.) JoergenB 00:49, 18 October 2006 (UTC)

There are no similar equality testing algorithms known, and therefore no similar finite-time guarantees, for systems of numbers generalizing the algebraics but also allowing logs, e, or π.

Do you mean ONLY that none is known, or rather that it is known (can be proved) that none can exist? If the former, it certainly doesn't justify saying that it has been PROVED that something specific about π cannot be done. Michael Hardy 23:59, 17 October 2006 (UTC)

I don't think it has been proven uncomputable, I think it's only that none is known. So that part of the statement is I think wrong. —David Eppstein 00:29, 18 October 2006 (UTC)

There are results along those lines. Consider the expressions built up from rational numbers, π, a single variable x, sine, absolute value, addition, multiplication, and composition. The problem "is such an expression equal to zero?" is undecidable. This theorem is due to a certain Richardson and follows from Matiyasevich's theorem. The only reference I have at the moment are some lecture notes, but I probably can find more details if necessary.

Of course, it's a bit of a stretch to refer to this result as "no practical system for calculating with numbers is able to express π exactly". -- Jitse Niesen (talk) 02:17, 18 October 2006 (UTC)

This is a fun and worthwhile discussion for me; I hope I'm not alone in that view.

So far there has been some dancing around the meaning of “practical system for calculating with numbers”, which is intolerably vague.

• I would consider Macsyma, Mathematica, and Maple very practical systems for computing with numbers, as well as more general symbolic expressions.
• I would also consider the implementation of IEEE floating point arithmetic on an AMD Opteron microprocessor chip a practical system for computing with numbers.
• Both LEDA and CGAL are elaborate libraries for computational geometry which also fit the definition.
• The GNU Multi-Precision Library is another example.

David Eppstein presumably is invoking the decidability of quantifier elimination for a real closed field, which relates to Tarski's axiomatization of the reals but for a first-order theory. More concretely, this is about George Collins’ seminal work in cylindrical algebraic decomposition for semi-algebraic sets. (I would love to have Wikipedia links for the preceding sentence, but we have none of the relevant articles!) In order to have polynomial-time algorithms for arithmetic, we may restrict our attention to real roots of univariate polynomials with rational (or integer) coefficients, Q[x]; these are the real algebraic numbers. Otherwise, the time required can be far from practical. However, this theory does not allow us to introduce an arbitrary assortment of fancy functions beyond basic arithmetic.

Yet within a computer algebra system we can surely know that 4 tan⁻¹ 1 is exactly π, or that e^iπ is exactly −1. Furthermore, we can do a wide variety of calculations and comparisons with π, more than enough for most practical purposes.

In contrast, using IEEE floating-point as our standard, we cannot express 0.1 accurately! The problem is that the radix-2 expansion repeats periodically. Compare this to √2, which happens to have a periodic regular continued fraction. Or compare to e, whose continued fraction merely requires an arithmetic progression.

The moral is, if we are too sloppy to define our terms, we're sunk. But I repeat myself. --KSmrq^T 15:19, 18 October 2006 (UTC)

Hamiltonian, anyone?

If your expertise allows you to contribute in a meaningful way to articles involving Hamiltonians and their applications, please take a look at Wikipedia talk:WikiProject Physics#Hamiltonian articles.  --Lambiam^Talk 01:35, 17 October 2006 (UTC)

Constructibility

In Talk:Borel algebra the following question is proposed by User:Leocat:

Can someone tell me how to construct an isomorphism between such Polish spaces as the unit ball in L^2[0,1] and the real line with the natural topology?

Now by Kuratowski's theorem, both objects are uncountable polish spaces and hence Borel isomorphic, so "there exists" an isomorphism. My guess is that this isomorphism is constructible, but I don't know enough about constructive mathematics to know for sure.

If anybody knows the answer to this question, you can post it there.--CSTAR 02:30, 19 October 2006 (UTC)

Well, it depends on what you mean by "constructive". There's no single agreed definition of that term. (By the way, be careful of substituting "constructible" for "constructive"; "constructible" has another constellation of meanings.)

Here's one partial answer: The arguments I know for the existence of such an isomorphism certainly use excluded middle. Basically you show that there's a Borel injection from Cantor space into any Polish space, and you show there's a Borel injection from any Polish space into Baire space, and you show there's a Borel injection from Baire space into Cantor space, and then you chase around the triangle using the Schroeder-Bernstein construction. It's the last part that uses excluded middle; you have to distinguish whether a point is or is not in the range of an injection, and without using excluded middle, it's going to be tough to prove that it either is or isn't. --Trovatore 03:47, 19 October 2006 (UTC)

Another empty category

There are currently no articles or subcategories in Category:Infinity paradoxes which is a subcategory of Category:Infinity. Possibly related articles are in Category:Paradoxes of naive set theory which is in Category:Basic concepts in infinite set theory which is in Category:Infinity. Does anyone want to put something in the empty category or shall we delete it? JRSpriggs 08:17, 16 October 2006 (UTC)

I say nominate for deletion. Category:Mathematics paradoxes is a reasonable upper bound, and the Category:Paradoxes of naive set theory was deliberately created to sort out those relevant to infinite cardinality. Charles Matthews 13:09, 16 October 2006 (UTC)

If I understand the rules correctly, I can add {{db-catempty}} to the category on 20 October 2006. Will that result in it being deleted? Or must I also list it somewhere? JRSpriggs 05:55, 17 October 2006 (UTC)

No, just speedy it. It's not like deleting an empty category is a big deal; if someone wants to recreate it, it takes all of five seconds. Melchoir 06:29, 17 October 2006 (UTC)

Although I have suggested (on this page) deleting a category once before, I have never gone thru the process myself. As I understand it, I would have to persuade an administrator to delete it. Do I just ask one, like User talk:Oleg Alexandrov or User talk:Arthur Rubin? JRSpriggs 07:59, 17 October 2006 (UTC)

{{db-catempty}} is actually a a speedy tag. Basically just put it on the page and wait. If no one objects it will go. WP:CSD explains more. --Salix alba (talk) 08:24, 17 October 2006 (UTC)

Apparently, someone beat me to the punch and deleted it already. I was going to add the template tonight. JRSpriggs 02:08, 20 October 2006 (UTC)

Eigendecomposition

I've added "eigendecomposition" as a synonym for "spectral decomposition" in the spectral theorem article: I'm almost completely sure that's right, but my maths is a bit rusty these days -- could someone more up-to-date double-check this, please? -- The Anome 11:59, 20 October 2006 (UTC)

Aaagh: Google says 84K of hits for eigendecomposition. That's already far too many ... Charles Matthews 15:43, 20 October 2006 (UTC)

{{Maths rating}}

Do people think it would be a good idea if I had MetsBot tag all pages in Category:Mathematics with {{Maths rating|class=|importance=}}? —Mets501 (talk) 01:15, 15 October 2006 (UTC)

Could you give some background? What would be the advantage of doing that? -- Jitse Niesen (talk) 03:13, 15 October 2006 (UTC)

Eh? How can a bot give meaningful ratings? And, for all of mathematics, how can you? If the ratings are not meaningful, they shouldn't be added. This kind of useless busywork would light up every page on our watch lists, which strikes me as a spectacularly bad idea.

But I'll tell you what a bot could do that would be an interesting exercise, if you want to crawl over all the mathematics pages. Use one of the mechanical tests of readability, such as SMOG, both on the article as a whole and on the intro alone. Report back what you find. We could improve the overall quality of our writing by having short lists of easy-to-read and hard-to-read articles. Of course, better still would be to go beyond that, to teach good writing. But that a bot cannot do. --KSmrq^T 07:35, 15 October 2006 (UTC)

I'm not sure tagging all pages will be a good idea, its something like 10,000 pages most of which will probably stay unrated. For me the real use in the maths rating is identifying and grading the most important articles, I guess about 500 articles. There is some good work a bot could do. Currently only about half the articles listed in subpages of Wikipedia:WikiProject Mathematics/Wikipedia 1.0 have a rating tag, so taging these pages would help. Further as we move away from these hand compiled lists to automated lists like Wikipedia:Version 1.0 Editorial Team/Mathematics articles by quality the shear number of articles will be problematic. Hence a bot could use the field tag of the template to assemble lists for each field of mathematics.

Reply to Jitse. The mathematics article rating is part of a wider project grading much of wikipedia, WP:1.0. There are 135 participating project. The aim of WP:1.0 is to make a CD with the best of wikipedia for which they need wikiprojects to identify their best and most important articles. Grading will also help identify the better mathematics articles, and promote them to GA/FA status, find week spots in our coverage. Overall grading ties with Jimbo's talk at wikimania that we have to start changing the focus from quantity to quality. --Salix alba (talk) 08:45, 15 October 2006 (UTC)

According to Portal:maths, there are over 14,000 maths articles. I'm not sure if this is based on articles in Category:Mathematics, or List of mathematics articles, but either way, the number includes a lot of articles that are only tangentally connected wih maths. A lot would probably come under the scoep of other wikiprojects, and for that reaosn alone, it is not worth tagging every single article. IOne of the main reasons for the tagging is to try and help prioritise efforts, by highlighting important articles that need improving.

Related note: Do people think it is worth having a list (either on the wikiproject main page or a subpage) of high-importance stubs and top-importance start-class articles? (There are now no top-class stubs :-) ). Tompw 10:07, 15 October 2006 (UTC)

Tompw 10:07, 15 October 2006 (UTC)

The number 14,000 is based on all the math articles listed in the list of mathematics articles. It is true that some of them are only somewhat mathematical, as this is a general purpose encyclopedia and the distinction between what is true math and what is math-related can be blurry.

I agree with Tompw's arguments above about not tagging all math articles by a bot. Oleg Alexandrov (talk) 16:11, 15 October 2006 (UTC)

OK, no problem. I was doing it for other wikiprojects who requested it, so I figured I'd ask here. —Mets501 (talk) 19:18, 21 October 2006 (UTC)

Powers

Any consensus on the policy on fractional powers? We write the squareroot sign for powers of one half, but what about cube roots? Do we put the squareroot with the 3 above, or do we put ^1/3? And the others? yandman 09:57, 19 October 2006 (UTC)

Any reason not to use <math>\sqrt[3]{n}</math>? —David Eppstein 15:05, 19 October 2006 (UTC)

Where do we draw the line? ${\sqrt[{20}]{n}}$ looks a bit silly to me. yandman 15:31, 19 October 2006 (UTC)

Single digits or single letters only seems like a reasonable rule of thumb to me. —David Eppstein 15:44, 19 October 2006 (UTC)

(Edit conflict). Well, I think it's better than $n^{\frac {1}{20}}$, personally. However, $n^{\frac {3}{20}}$ looks better than ${\sqrt[{\frac {20}{3}}]{n}}$. So, I would be inclined to say use the "root" notation when the root is an interger, and use the "exponent" notation otherwise. Whatever the ourcome of this discussion, I think it (the outcome) should be added to Wikipedia:Manual of Style (mathematics). Tompw 15:56, 19 October 2006 (UTC)

The integer root rule works badly for formulas like O(n^1/32,582,658). As usual, it's an area where common sense and rules of thumb may be more appropriate than strict guidelines... —David Eppstein 16:04, 19 October 2006 (UTC)

I have to say, I don't think I have ever seen the notation ${\sqrt[{3}]{n}}$ in a book above introductory college textbooks. In journals it is very common to use the superscript even for square roots when it would simplify notation. (e.g. a lot of people prefer

${\frac {4\pi ^{6}A^{1/2}g_{s}^{2}}{\Gamma (1/4)n}}$

to

${\frac {4\pi ^{6}{\sqrt {A}}g_{s}^{2}}{\Gamma (1/4)n}}$,

and for long formulae you would definitely use parentheses and an exponent instead of a very large square root sign.) Using an exponent has the added benefit that simple formulae with exponents will not render to .png for people (such as myself) who have their math tags set to render to text for simple formulae. –Joke 00:05, 21 October 2006 (UTC)

One I recently edited here was

$c={\sqrt[{3}]{\frac {2\pi ^{2}}{3}}}\approx 1.874.$

in no-three-in-line problem. You could inline it as π^2/3(2/3)^1/3 (or some variation of the same with frac instead of slashes) but I think all the /3's make it confusing, and using the cube root sign makes it very clear visually that everything in the expression has a fractional exponent. On the other hand, I prefer your first formula to your second because the fractional exponent is formatted more similarly to all the other exponents. —David Eppstein 00:14, 21 October 2006 (UTC)

One more advanced instance of radicals that I've seen is in field theory. It is, of course, common to write $\mathbb {Q} ({\sqrt {2}})$ to denote the field obtained by adjoining a number whose square is 2. Also common, though, is to write $\mathbb {Q} ({\sqrt[{3}]{2}})$ to denote the field obtained by adjoining a number whose cube is 2. It would be improper to write $\mathbb {Q} (2^{\frac {1}{3}})$, both because of convention, and because the exponential notation (for whatever reason, possibly convention) suggests a sort of deterministic choice, especially when its argument (i.e. 2) is real. $\mathbb {Q} ({\sqrt[{3}]{2}})$ is an abstract field, and could just as easily be $\mathbb {Q} (2^{\frac {1}{3}}e^{\frac {2\pi i}{3}})$, where now I've deliberately used the exponential notation to single out particular complex numbers. Worse, of course, and not only in the context of field theory, is the fact that the power functions are of course not one-to-one, so that their inverses are multi-valued, and so using fractional powers only makes sense in the presence of a convention as to the specification of a particular value (like when we take square roots of positive real numbers).

However, since this doesn't seem to be a discussion of whether to use one symbol or the other but rather when, I would say that it's as much a matter of audience as of aesthetics. Certainly the radicals should be avoided for roots which consist of more than a single character or for all but diminutive radicands (i.e. ${\sqrt[{2}]{2}},{\sqrt[{5}]{n}},{\sqrt[{n}]{m}}$, but not ${\sqrt[{20}]{2,535,099,102,664}}$) but on the other hand, in articles which are expected to see traffic by novices, radicals may be preferred. Fractional powers constitute a mild form of mathematical jargon and certainly represent a reasonably sophisticated idea that, say, students below college might not be comfortable with. Conversely, of course, in professional-level articles, we should probably avoid radicals unless (as in field theory) their use is conventional.

Ryan Reich 21:32, 21 October 2006 (UTC)

I definitely agree. Out of habit I might have used the formula

$c=\left[{\frac {2\pi ^{2}}{3}}\right]^{1/3}\approx 1.874,$

but I think either looks great, especially compared to the inline formula you produced. –Joke 00:35, 21 October 2006 (UTC)

Note: it is generally a good idea to use linear notation in sub- and superscripts ($x^{a/b}$, not $x^{\frac {a}{b}}$). Particularly when the formulas are rendered in low resolution as they are here. Fredrik Johansson 22:45, 21 October 2006 (UTC)

Use of the radical forces texvc to produce a PNG, which looks bad inline. Using wiki markup, we can write x^a⁄_b. --KSmrq^T 23:59, 21 October 2006 (UTC)

English composition

Put it before them briefly so they will read it, clearly so they will appreciate it, picturesquely so they will remember it and, above all, accurately so they will be guided by its light.
— attributed to Joseph Pulitzer

Wikipedia mathematics editors are brilliant and well-educated, naturally. Yet many have never studied the art of readable writing, especially for the general public. I’d like to offer a few suggestions. With your approval, they may later find their way into our Manual of Style.

I begin by quoting two well-known mathematicians.

The first rule of style is to have something to say. The second rule of style is to control yourself when, by chance, you have two things to say; say first one, then the other, not both at the same time.
— George Pólya

[T]he problem is to communicate an idea. To do so, and to do it clearly, you must have something to say, and you must have someone to say it to, you must organize what you want to say, and you must arrange it in the order you want it said in, you must write it, rewrite it, and re-rewrite it several times, and you must be willing to think hard about and work hard on mechanical details such as diction, notation, and punctuation. That’s all there is to it.
— Paul Halmos

When I give a lecture or write a paper, I consider myself lucky if I can convey one idea clearly, so that my audience pays attention, understands, remembers, and is inspired. This is more difficult than it sounds! Both mathematicians quoted above agree. Thus the heart of good technical writing is our first guideline:

• Know precisely what you want to say.

Halmos next says to know your audience, and again I agree; yet for Wikipedia the audience can include university faculty, the general public, and youngsters. Readability studies suggest several ways to help. Two basic guidelines, with broad empirical support, are:

• Avoid long sentences with complicated structure.
• Avoid unfamiliar words with many syllables.

And more technically,

• Minimize adjectives, adverbs, and passive verbs.

These studies also emphasize the value of structure, as do both our mathematicians. Structure occurs on three levels: sentence, paragraph, and article. All three should be clear, logical, and memorable. And I have just illustrated the next suggestion:

• Use twos and threes for organization.

Examples of twos include if–then and either–or. More generally, balanced structure and parallel structure help the reader. This is less useful at the paragraph level; but we can suggest the following.

• Give each paragraph a clear topic, preferably in its first or last sentence.

At the article level, the order and content of sections should never leave the reader disoriented. Work for a natural flow, a sense of inevitability. We want readers to know where they’ve been and where they’re going.

Pay particular attention to the introduction, especially the first paragraph. The first sentence should both engage readers, and orient them to what is to come. It need not summarize the article.

All of the suggestions so far apply to any kind of writing. I have a few personal touchstones for mathematics. It is natural to include theorems and proofs, but I also try to incorporate:

• Motivation
• Intuition
  ———
• Examples
• Counterexamples
  ———
• Pictures
• Connections

Finally, I do my best to sneak in a little humor. Some may damn this as “unencyclopedic”, but the best teachers have always done so. We all know, when we’re honest with ourselves, that when we laugh, we learn. With that in mind, I end with another quotation.

I hope that posterity will judge me kindly, not only as to the things which I have explained, but also to those which I have intentionally omitted so as to leave to others the pleasure of discovery.
— René Descartes

Perhaps another time I can add links to writing resources. Meanwhile, take what you can of value from these suggestions, and help make Wikipedia better. --KSmrq^T 16:04, 19 October 2006 (UTC)

Sour comment: you know when Samuel Johnson said that if you were particularly proud of a piece of writing, you should cross it out? Here on WP you needn't bother. Someone else will surely edit it out for you. Charles Matthews 16:20, 19 October 2006 (UTC)

That's partly what motivated me to write this. I'm hoping to elevate the awareness of editors, both in their own writing and in critiquing others. I have no illusions that all those who read this handful of suggestions will become great technical writers overnight, or perhaps ever. Still, it may begin to help. Halmos himself said, “The ability to communicate effectively, the power to be intelligible, is congenital, I believe, or, in any event, it is so early acquired that by the time someone reads my wisdom on the subject he is likely to be invariant under it.” Yet he tried. Perhaps those drawn to improve Wikipedia will also wish to improve themselves, and maybe they can. We can hope. --KSmrq^T 19:11, 19 October 2006 (UTC)

"Minimize adjectives, adverbs, and passive verbs.". Umm... no. Without adjectives and adverbs, a sentence contains only nouns and verbs, which would make it less readable. Maybe what you meant was "avoid excessive adjectives and adverbs", which is something I completely agree with. (This is not the same as minimisation. Any sentence can have *all* its adverbs and adjectives removed - the ultimate in minimisation - and remain grammatically correct.)

Also, what is wrong with the passive voice? I use the passive voice occasionally, whenever I feel that the object of a sentence is the important part, rather than the subject. I hope I don't come across as overly-critical here, as I agree with the broad thrust of your comments.

"Always have a quotation handy; it saves original thought". Tompw 22:13, 20 October 2006 (UTC)

This is Wikipedia; original thought is prohibited. ;-)

Readability studies disagree with your objections. Here is one survey you may find enlightening. I also refer you to Strunk & White's acclaimed guide, The Elements of Style. Among their guidelines are these, supporting the one in question.

• Use the active voice.
• Write with nouns and verbs.
• Avoid the use of qualifiers.
• Avoid fancy words.

Those who have been force-fed an excess of Strunk & White may appreciate Lanham's amusing Style: An Anti-Textbook (ISBN 978-0-300-01720-5).

Your objection shows you think about how you write. English is a second language for many of our editors; yet even our native-speakers will not become good writers unless they, too, begin to think about their writing. --KSmrq^T 11:58, 21 October 2006 (UTC)

Simenon apparently used to draft his books by locking himself in a room for 72 hours, to get a draft. When he had recovered from that, he went through crossing out all the adjectives and adverbs he could find ... Charles Matthews 15:13, 22 October 2006 (UTC)

Sounds painful. I think that providing people think about what they write, don't write in the same way they speak, and read through what they have written, then few stylistic problems will crop up. (Also, British English and American English do have different styles, and I'm British. I know US manuals on style seem to regard the passive voice as an abomination. The UK and US are two nations divided by a common language...) Tompw 16:06, 22 October 2006 (UTC)

This is not a question of taste, but of readability. If you want to write as readably as possible, you must train yourself to use active voice. That is what readability studies tell us, whether we like it or not. Lest we think only Yanks and Brits have something to say, I quote a German author and a French author, both of some stature:

A writer is somebody for whom writing is more difficult than it is for other people.— Thomas Mann

Those who write clearly have readers; those who write obscurely have commentators.— Albert Camus

While I would not ask James Joyce to write like Ernest Hemingway, I’ll wager The Old Man and the Sea gets read cover-to-cover more often than Ulysses. --KSmrq^T 05:07, 23 October 2006 (UTC)

General Comment about Math articles from a non-mathematician

I think your readership might be better served by providing more background explanation and examples of advanced math concepts designed for a lay audience than your current pages do. Since Wolfram Mathworld already does an excellent job of rigorous textbook style explanations with all of the relevant equations why not just link to them for this content and give Wikipedia readers a simplified plain English version with some real-world applications (along with the graphs suggested above, and perhaps historical development and relevance and maybe some nice pictures of engineering applications etc.) to get them started? --—The preceding unsigned comment was added by 67.174.240.33 (talk) 22 October, 2006

It is probably true that a lot of math articles could be made a lot more accessible than they are to lay audiences. But being accessible to the extent the material allows is not the same as lobotomizing all technical or rigorous content. And I think it's often possible to do a lot better than mathworld in terms of depth and rigor and correctness, and to have content in a single place that's useful for readers at all levels. —David Eppstein 01:25, 23 October 2006 (UTC)

I hope wikipedia is strong enough to be self-contained and not to rely on third party's stuff. --Beaumont (@) 09:10, 23 October 2006 (UTC)

Several points. I'm all for history. MathWorld was invented, basically, to promote the kind of mathematics where formulae are central. It has then branched out. We on the other hand have always taken the whole range of mathematics as our remit. Some doesn't have obvious engineering aspects. In other cases, for example cryptography, we have _both_ the mathematical articles on finite fields, say, _and_ articles dedicated to cryptographic applications. Charles Matthews 09:18, 23 October 2006 (UTC)

Yeah, there is room on Wikipedia for all kinds of articles at all kinds of levels. But indeed, making articles more acessible is a great goal. Adding a more elementary intro, putting a picture here and there, making more connections between math and physics or other applications are very good things, and we are aware of that. Oleg Alexandrov (talk) 14:47, 23 October 2006 (UTC)

I'm aware of a number of articles where the introductory material has been made harder, in some supposed trade-off with accuracy or a more 'professional' feel. It would be interesing to compile a list where the intro is unnecessarily off-putting, and where the article also ought to be of general interest. Charles Matthews 16:03, 23 October 2006 (UTC)

I would really request that any such edits which complicates introductions be reported here. I think there is a consensus over here that introductions must be kept as simple as possible, and we definintely don't want people obfuscating introductions. Oleg Alexandrov (talk) 03:26, 24 October 2006 (UTC)

You mean, like the "articles that are too technical" list here? —David Eppstein 16:37, 23 October 2006 (UTC)

That page is a long list of whinges. I took one at random: D-separation. The list says 'needs more context'. It's obvious when you look at it that it's a technical thing about Bayesian networks, and sometimes technical stuff is irreducible. No, not what I meant. I meant examples of the ratchet at work, where the user-friendly sentences get shredded because some expert decides they are holding up the parade. Charles Matthews 16:47, 23 October 2006 (UTC)

In our defence, writing an intro that is accessible but still correct in all important respects is not as easy as you might think. Look at what an anon editor has created recently in Trigonometry (the Overview section) to see an example of how not to do it. Gandalf61 16:16, 23 October 2006 (UTC)

So long as Wikipedia let's anyone edit, we will have the burden of reverting and explaining why. How many editors have read WP:MSM, which advises writing broadly accessible intros? I also think we could benefit from providing a simple readability measurement tool, as many of today's word processors do. It could help take discussions out of the realm of opinion and stylistic preferences, making them more quantitative. We are fighting a tradition of professional writing that is often unreadable, and we can hardly blame people for imitating what they have seen, attempting to "sound professional". Ironic that, since empirical evidence suggests that more readable papers are more influential.

I don't trust the automatic tools enough to make them a straight-jacket requirement. I would not say, "The intro must be written at a 9th grade reading level." For one thing, there are aspects of readability that cannot be captured by counting words and syllables. Still, if an edit changes a passage from 10th grade to 16th, we can use such a measure to help train the writer.

Train we must, perpetually, if Wikipedia wishes to be a professional quality encyclopedia. As the readability improves across all our articles, it will set an example that may help. However, even that can never substitute for awareness and deliberate attention to the features that make for readability. --KSmrq^T 17:58, 23 October 2006 (UTC)

The article titled uses of trigonometry, which I originated and which is still mostly my material, is an example of the sort of thing requested here. On the other hand, some of the statistics articles tell you what a concept is used for without ever saying what it is. Those would be greatly improved by more technical material. Michael Hardy 20:33, 23 October 2006 (UTC)

One problem I see in intros is that scientists/mathematicians like to start right off with "the most general case", which often involves a complicated formula. Sometime later they reduce that down to the common formula which everybody uses. For ease of reading, the simple case, with a real world example, should appear first, and the general case/derivation should be at the end. For example, I worked on the weighted mean article, and added an example, but it still has the technical "gobbledygook" (like the discussion of variance) up front, which makes this seemingly simple topic seem complicated. (I just moved some of the complex portion to the end, but I'm worried that this edit will be reverted.) StuRat 03:49, 24 October 2006 (UTC)

Yes, each new editor must be "re-educated". It may help to repeatedly cite WP:MSM. Here is a relevant excerpt:

---

Suggested structure of a mathematics article

Probably the hardest part of writing a mathematical article (actually, any article) is the difficulty of addressing the level of mathematical knowledge on the part of the reader. For example, when writing about a field, do we assume that the reader already knows group theory? A general approach is to start simple, then move toward more abstract and technical statements as the article proceeds.

Article introduction

The article should start with an introductory paragraph (or two), which describes the subject in general terms. Name the field(s) of mathematics this concept belongs to and describe the mathematical context in which the term appears. Write the article title in bold. Include the historical motivation, provide some names and dates, etc. Here is an example.

In topology and related branches of mathematics, a continuous function is, loosely speaking, a function from one topological space to another which preserves open sets. Originally, the idea of continuity was a generalization of the informal idea of smoothness, or lack of discontinuity. The first statement of the idea of continuity was by Euler in 1784, relating to plane curves. Other mathematicians, including Bolzano and Cauchy, then refined and extended the idea of continuity. Continuous functions are the raison d'être of topology itself.

It is a good idea to also have an informal introduction to the topic, without rigor, suitable for a high school student or a first-year undergraduate, as appropriate. For example,

In the case of real numbers, a continuous function corresponds to a graph that you can draw without lifting your pen from the paper; that is, without any gaps or jumps.

The informal introduction should clearly state that it is informal, and that it is only stated to introduce the formal and correct approach. If a physical or geometric analogy or diagram will help, use one: many of the readers may be non-mathematical scientists.

It is quite helpful to have a section for motivation or applications, which can illuminate the use of the mathematical idea and its connections to other areas of mathematics.

---

We could improve the manual (how many readers will understand raison d'être?), but the message seems clear enough: First inform and engage the general reader, then dive into the technical details.

This does address Michael Hardy's point, somewhat. We do not omit technical details, we merely postpone them. In fact, WP:MSM is explicit:

---

There should be an exact definition, in mathematical terms; often in a Definition(s) section, for example:

Let S and T be topological spaces, and let f be a function from S to T. Then f is called continuous if, for every open set O in T, the preimage f ⁻¹(O) is an open set in S.

---

I'm uncomfortable with linking "if" to if and only if and linking "for every", and with omitting links for topological space and open set; and not every mathematical topic demands or admits a definition. Quibbles aside, the call for content is clear. We don't want to be an auto mechanic who is courteous and friendly, but who never does the job. --KSmrq^T 13:22, 24 October 2006 (UTC)

The point about postponing technical details rather than omitting them is well made. In response to StuRat, however, I must point out that we are writing an encyclopedia, not a textbook. It is appropriate to start with an informal introduction which covers in informal terms even the general cases. JPD (talk) 14:01, 24 October 2006 (UTC)

To chime in... from what I've seen, most of the mathematics articles do not even have an introduction that would be accessible to a non-math-major. I don't think it has to be this way, although I appreciate the difficulty of explaining these concepts to the layperson. As an example, I was just looking at the Measure (mathematics) article, and this is definitely something that can be understood intuitively, but while the first sentence mentions "size" and "volume", it does not explore these concrete concepts and launches straight into abstraction, even within that sentence. Overall, the collection of mathematics articles seems like an excellent survey of modern mathematics, and perhaps useful for jogging your memory if you've forgotten some detail, but it is not functional as general encyclopedia content. The places where it really seem silly are where a very fundamental concept is explained, something that any mathematician MUST know, and yet it is explained using language and notation that only a mathematician well-versed in that particular subfield could understand. —The preceding unsigned comment was added by 65.95.229.253 (talk • contribs) 1 November 2006 .

Citation guidelines proposal

Since the discussions seem to have abated for some time now, I am asking the Mathematics and Physics WikiProjects if they support the new citation guidelines that I (and others) have devised. The point of the guidelines is to establish an appropriate, sensible standard for referencing articles in our fields so that we are less likely to run into objections (such as those that have come up recently) when we try to write technical articles that others then tell us are impropoerly sourced. I think these guidelines are now well thought out enough that they can be added to the main pages of the two WikiProjects and perhaps linked from WP:CITE. I should also note that they seem to have attracted some encouragement from outside the WikiProjects, on their talk page, mine, and on WP:CITE.

One outstanding issue is where to move the page. I don't have any great ideas. Wikipedia:WikiProjects Mathematics and Physics/Citation guidelines is too cumbersome. We could just leave it under physics as Wikipedia:WikiProject Physics/Citation guidelines or be BOLD and put it at Wikipedia:Scientific citation guidelines (presumably this would mean we would have to engage with the rest of the community to ensure there is consensus). I submit we should go with Wikipedia:WikiProject Physics/Citation guidelines and once we have consensus here go to Wikipedia:WikiProject Biology and Wikipedia:WikiProject Chemistry (and wherever else seems appropriate) to solicit their opinions, and then move it out of the physics WikiProject. We could even eventually go ask the wider Wikipedia community what they think at WP:CITE but I think that should be left as a longer term project. –Joke 22:14, 16 October 2006 (UTC)

Since there doesn't seem to be any objection to this proposal, I have gone ahead and moved it to Wikipedia:Scientific citation guidelines and added links on the pages of the relevant WikiProjects and on WP:CITE. –Joke 03:52, 26 October 2006 (UTC)

Support

1. I already offered my support on the talk page of WikiProject Physics, but also with my mathematician's hat on I support this.  --Lambiam^Talk 01:28, 17 October 2006 (UTC)
2. I like this proposal and support any step that moves it forward to wider acceptance. —David Eppstein 01:58, 17 October 2006 (UTC)
3. CMummert 02:55, 18 October 2006 (UTC)
4. I've also left a more detailed comment on the guidelines talkpage. --Salix alba (talk) 07:30, 18 October 2006 (UTC)
5. Support - excellent draft guideline - clearly written, pragmatic, comprehensive without becoming verbose. Gandalf61 08:10, 18 October 2006 (UTC)
6. This seems the best way to proceed. I would suggest also posting at Wikipedia:WikiProject Science. Tompw 15:13, 18 October 2006 (UTC)

Object

Neutral/Comment

1. I generally support it, but I find the statement "articles that link to [eponymous articles] may choose not to cite the original papers, depending on the context" too vague. I would prefer if such cases were handled just like links from a summmary to a sub-article. This would reduce the "dense referencing" and facilitate maintenance, since the sub-article is the best place to discuss and maintain attribution. — Sebastian (talk) 05:35, 19 October 2006 (UTC)
2. I agree with the text. I questioned some details on the talk page. The only problem I have is that I'm not convinced that it's a good idea to have separate citation guidelines. My impression is that most Wikipedia editors would agree with it, but that the so-called inline citation squad, having strong opinions on this topic, are very vocal at WP:CITE and (for some reason I don't quite fathom) at WP:GA. However, they are not in the maths or physics WikiProjects (or if they are, they haven't come out of the closet yet). -- Jitse Niesen (talk) 14:55, 21 October 2006 (UTC)

Project directory

Hello. The WikiProject Council has recently updated the Wikipedia:WikiProject Council/Directory. This new directory includes a variety of categories and subcategories which will, with luck, potentially draw new members to the projects who are interested in those specific subjects. Please review the directory and make any changes to the entries for your project that you see fit. There is also a directory of portals, at User:B2T2/Portal, listing all the existing portals. Feel free to add any of them to the portals or comments section of your entries in the directory. The three columns regarding assessment, peer review, and collaboration are included in the directory for both the use of the projects themselves and for that of others. Having such departments will allow a project to more quickly and easily identify its most important articles and its articles in greatest need of improvement. If you have not already done so, please consider whether your project would benefit from having departments which deal in these matters. It is my hope that all the changes to the directory can be finished by the first of next month. Please feel free to make any changes you see fit to the entries for your project before then. If you should have any questions regarding this matter, please do not hesitate to contact me. Thank you. B2T2 00:20, 26 October 2006 (UTC)

mathematician-stub

The various mathematician-stub templates are currently being discussed at Wikipedia:Stub types for deletion/Log/2006/October/19 Affected templates {{mathbiostub}}, {{mathbio-stub}}, {{math-bio-stub}}, {{mathematician-stub}}. --Salix alba (talk) 11:32, 26 October 2006 (UTC)

Name of theorem?

I was fiddling with some formulas, and seem to have stumbled over the following theorem: given any topological space X and any homomorphism $g:X\to X$, there exists a measure $\mu$ such that it is preserved by the pushforward $g_{*}\mu =\mu$ (aka the direct image functor on the category of measurable spaces(?)); equivalently, there is always a measure such that g is a measure-preserving map, and furthermore, this measure is unique. This theorem is little more than a fancy-pants version of the Frobenius-Perron theorem, and the measure is more or less the Haar measure. I was wondering if this theorem has a name? Is it in textbooks? Or is it supposed to be a nameless corollary of the theorem that defines the Haar measure? Thanks. linas 03:35, 21 October 2006 (UTC)

I find uniqueness hard to believe. JRSpriggs 06:40, 21 October 2006 (UTC)

I question existence, since Haar measure depends on having a group structure. --KSmrq^T 12:29, 21 October 2006 (UTC)

Existence is true if X is a compact space, in which case the measure μ can be taken to be a probability measure. This is just the compactness of the space of Borel probability measures in the weak* topology and the fact the group of integers Z is amenable (actually this is equivalent to a fixed point theorem for continuous affine mappings on compact convex sets. See Dunford Schwartz, although I don't have it in front of me so I don't know the exact formulation.) However, in general uniqueness is false even for compact X and imposing the additional requirement that the measure μ is a probability measure. Uniqueness is a special property called unique ergodicity. For non-compact X, existence is also false without some additional assumption on X.--CSTAR 16:08, 21 October 2006 (UTC)

Thank you CSTAR, this pointer is just what I needed. (My X was indeed compact, and my g ergodic. I'm not sure what other additional errors assumptions I might have accidentally made along the way.) KSmrq, I'm looking at dynamical systems, so the hand-waving physics argument for existence is that physical systems always have a ground state, and, for systems in thermodynamic equilibrium (i.e. ergodic), so that all symmetries are broken, the ground state is unique. I'm grappling with general formulations, but this is new territory to me. I assume "Dunford Schwartz" is the book "Linear Operators" from 1958. I presume newer books on operator theory will have similar content. linas 22:17, 21 October 2006 (UTC)

Dunford and Schwartz vols 1 and 2 (vol 3 is much less interesting), though dated, are unsurpassed as general references in functional analysis.--CSTAR 22:30, 21 October 2006 (UTC)

Someone creted an artcle just today, for at least half of what I was looking for: the Krylov-Bogolyubov theorem. linas 23:48, 26 October 2006 (UTC)

Article count?

Is there any way to obtain a count of how many articles are in the Mathematics category or any of the categories beneath it, that is, articles that are in the scope of this project? What about other science projects such as Physics, Chemistry, etc.? CMummert 16:43, 26 October 2006 (UTC)

User:Jitse's bot says its 14953 which is updated daily. Its dificult to give an exact answer as it all depends by what you mean by a mathematics article. --Salix alba (talk) 17:36, 26 October 2006 (UTC)

Thanks. The goal I has was to get a relative sense of the sizes of the various projects. Obviously article counts don't tell the whole story, but they do give interesting numbers to compare the different projects. Is it true the Jitse's bot runs with regular user permissions (no SQL queries or anything like that)? If so, I might someday try writing a script to count the articles. CMummert 17:48, 26 October 2006 (UTC)

What you can do is download a database dump, parse that to find the links table and play around with that to your hearts content without bothering the servers (avoid importing into MySQL as it take forever). I guess there are about 1000 maths categories so querying that does impose some load. Theres lots of other ways to do queries meta:toolserver and http://en.wikipedia.org/w/query.php are both options. --Salix alba (talk) 19:49, 26 October 2006 (UTC)

It's kind of easier to figure that mathematics is 1% of enWP and then you count using the Main Page. (The proportion has been dropping, but slowly ...) Charles Matthews 21:27, 26 October 2006 (UTC)

Unfortunately, the category system here is sometimes surprising. For instance, Lute is in Category:Musical instruments is in Category:Music is in Category:Sound is in Category:Waves is in Category:Differential equations is in Category:Differential calculus is in Category:Calculus is in Category:Mathematical analysis is in Category:Mathematics. For this reason, User:Oleg Alexandrov maintains list of mathematics categories, which lists the categories that are considered mathematics.

There is also a bot called User:Pearle which does something similar to Wikipedia:WikiProject Mathematics/Current activity, but I don't quite know what it does or how it works. -- Jitse Niesen (talk) 02:54, 27 October 2006 (UTC)

And the line between math and nonmath can be blurry indeed. A few days ago my bot added the article Robert Byrd about the US senator to the list of mathematics articles because the guy has been put in the Category:Mathematics education reform. Gosh. Oleg Alexandrov (talk) 03:19, 27 October 2006 (UTC)

There is a shorter path for Lute. Category:Differential equations is in Category:Equations is in Category:Mathematics. JRSpriggs 09:15, 27 October 2006 (UTC)

Erdős number tags

Apart from the fact that I think it's annoying to be told Atiyah has Erdős number 4, as if this was on the same level as a Fields Medal: I think we should point out clearly that any information here should be verifiable. Apart from a complete list of collaborators of Erdős, it is going to be hard to verify numbers at all; certainly the only assertion you'd responsibly get is ≤ 3 and so on. Charles Matthews 19:01, 20 October 2006 (UTC)

Mea culpa; I supported keeping the categories. But I see no reason to mention the number in the text. I believe we can verify 1 and 2 easily, and larger numbers with more difficulty. Not that I'm volunteering to do it! Note date and location of birth can also be hard to track down, and we often manage that anyway. Shall we say every Erdős number tag should be accompanied by a certificate of authenticity on the talk page? That puts the burden on those who wish to add these categories. --KSmrq^T 19:32, 20 October 2006 (UTC)

Cats should only be added if the reason is obvious when looking at the article (and I suppose the talk page). Note the hard part, unless we link to an Erdős number site, is verifying that Atiyah is not EN 3...Septentrionalis 19:38, 20 October 2006 (UTC)

It would be very difficult to present a complete certificate of authenticity for an Erdős number >2; the best you could do would be to present a certificate of the authenticity of an upper bound. How do you prove that someone's Erdős number is really 4, and not 3? -- Dominus 12:28, 29 October 2006 (UTC)

Well, exactly. We have the choice of taking down the EN3 tag wherever it appears, and asking on the Talk page for such a certificate. I'd favour that. There is the perfectly good point that tracking all collaborations of EN1 mathematicians is hard, of EN2 mathematicians is ridiculous, and from then on it becomes plain daft. I vote we get a bit more lawyerish about this. Charles Matthews 12:35, 29 October 2006 (UTC)

For numbers one and two, one can look at the Erdős number project data, and for greater numbers (with the appropriate subscription?) you can use MathSciNet, assuming all the relevant pubs are in their database (a reasonable assumption for mathematicians, not so much for other kinds of scientist). So I don't see the difficulty of finding verifiable data as being much of an obstacle. —David Eppstein 20:21, 20 October 2006 (UTC)

PS Atiyah should be 3 not 4, according to MathSciNet:

Michael Francis Atiyah   	 coauthored with   	 Laurel A. Smith   	 MR0343269 (49 #8013)
Laurel A. Smith 	coauthored with 	Persi W. Diaconis 	MR0954495 (89m:60163)
Persi W. Diaconis 	coauthored with 	Paul Erdös1 	MR2126886 (2005m:60011)

—David Eppstein 20:22, 20 October 2006 (UTC)

Questions is mathscinet a reliable source? It can provide an upper bound on the Erdős number, but not necessarily the exact EN. Also it becomes on the bounds of original research to use the database, as its not a traditional publication. I know some of the people adding these cats are using mathscinet for their info (see my talk page). Still despite these reservations if we ate going to have the numbers its better to get the most accurate number possible. I like KSmrq's solution, maybe we should workup a policy on how to handle these. These cats are going to become an annoying waste of time.--Salix alba (talk) 21:20, 20 October 2006 (UTC)

It's original research to enter two names on a web query form and report the result of that form? It does take some checking afterwards to make sure the papers it returns are real joint publications, but the chain it gives you is readily verifiable, often without further need of their database. —David Eppstein 22:03, 20 October 2006 (UTC)

I guess that Archimedes must have been a lousy mathematician, because he did not have an Erdős number (sarcasm). JRSpriggs 06:38, 21 October 2006 (UTC)

The problem with MathSciNet is that it is not just a web query form. I mean accesibility. Well, one may pay for a subscription; as far as I can understand $2226 will do. I found nothing about such commercial databases in WP:VER policy. Do we really consider it verifiable? I guess we do not. So, inserting info about Erdos number would require a chain of publications as indicated above. As for reliability, MathSciNet should be considered on the top; it is likely to give you the best (often exact) easily verifiable result. Erdos number caracteristic seems to be interesting and notable enough to be mentioned in the bios, at least for EN<=5 mathematicians (and it is not considered as a coeficient related to notability of this mathematician!). Essentially, I agree with David. --Beaumont (@) 09:50, 21 October 2006 (UTC)

The strongest evidence that Archimedes, Euler, and Gauss were not great mathematicians is that none of them won a Fields Medal. (Tongue firmly in cheek.) :D

Relax, no one is obliged to research and incorporate an Erdős number category for any mathematician. It has not yet joined “use massive numbers of inline citations” as a criterion for Good or Featured articles.

For those who want to add these categories, the most verifiable “certificate of authenticity” would be the chain of publications. It is irrelevant whether MathSciNet or some other method is used to assist in finding the chain. I would recommend affixing any such certificate near the top of the talk page, to make it easy to find. --KSmrq^T 12:24, 21 October 2006 (UTC)

Re paying for the service: instead, you could walk into the library of most public universities and use the computers there. —David Eppstein 15:29, 21 October 2006 (UTC)

Errr ... you assuming we are all in the USA, or something? I think those who add such a category do owe us a list of intermediate people, and the best way is to add it to the page itself, by the category, and commented out. Charles Matthews 19:02, 21 October 2006 (UTC)

Err, there are no university libraries in other countries? Or (like some private ones in the US) they don't let you in without some kind of affiliation? In any case I agree that it's appropriate to provide a chain of intermediates; when the EN is mentioned in the text, it would be appropriate to do so there, but your suggestion of commented out next to the cat makes sense too. The few times I've changed these recently I've put the chain in the edit summary, but I guess that's not as easy to find. —David Eppstein 19:09, 21 October 2006 (UTC)

0.999...

Briefly browsing the archives suggests that this has not been discussed here before (and correct me if I am wrong). It seems like a good idea to bring it up now, seeing that said article has recently been the main page featured article and all.

Long ago, KSmrq has rewritten the article (which was then named Proof that 0.999... = 1) to look something like this (I'll refer to that as the "old" version). It stayed in that form for quite a while, until this edit, where Melchoir has begun a massive rewrite, ultimately resulting in something like this (I'll refer to that as the "new" version). In the meantime, the article has been, with overwhelming support, moved to the new title 0.999... to more faithfully represent its new (and old) content (as can be seen in this archive).

KSmrq has strongly opposed the move and the rewrite, and very frequently criticizes the new version and the editors who have worked on it. Needless to say, I have the greatest admiration for KSmrq's opinion, but happen to personally disagree with him on this matter (I accept some parts of the criticism, though, and believe these should be worked on on a case-by-case basis). I also got the impression that there are not many other editors who agree with him. In my opinion, while the fact that this article has become featured in its current incarnation obviously proves nothing, it supports this impression.

I therefore invite everyone here to share your opinions on the matter, with hope to finally settle this matter once and for all. I'll emphasize that it is not necessarily my wish to see consensus supporting the new version (which, again, is more to my taste), but rather to see consensus supporting some version, and having the article become as good as it can be as a result.

Those with some extra time on their hands could also skim through the extremely numerous reactions to the article (in Talk:0.999... and Talk:0.999.../Arguments) from the last two days, and see if they give them any ideas for possible changes to improve the article.

Since Talk:0.999... is a mess right now, I suggest that replies are made on this page. -- Meni Rosenfeld (talk) 16:42, 26 October 2006 (UTC)

Well, the feeling I get most strongly from the reactions is this: We have to figure out a way to get readers who doubt the validity of digit manipulations to skip the 0.999...#Digit manipulation section, or at the very least not get stuck on it. In general, the sections should better describe their relationships to each other. At the same time, it would be useful to create new articles, or improve existing ones, to describe the foundations of decimal arithmetic for all those skeptics.

In general, I'm thrilled to discuss problems on a case-by-case basis. There's a very indirect lesson from the FAC; some of the supporters praised it for having great writing. While that's certainly a welcome sentiment, it isn't ultimately any more helpful than KSmrq blasting the article for having terrible writing. We should focus on specific, actionable issues if we want to understand each other, let alone generate progress and consensus. Melchoir 19:16, 26 October 2006 (UTC)

We should just redirect this page to 1 (number), you know. Merge or not? Charles Matthews 09:29, 27 October 2006 (UTC)

Seems the mailing list discussion was right: you do need tags like <irony>.Charles Matthews

Heh, I often use <sarcasm> tags just to be sure - it is often too easy to get confused about the intention of others. Sorry for misunderstanding. Any other thoughts, though? -- Meni Rosenfeld (talk) 17:01, 27 October 2006 (UTC)

0.9999... should redirect to 0.999.... Oh, it does. Well, scope for ... Charles Matthews 18:49, 27 October 2006 (UTC)

Are you really saying that there is nothing in this article which a general reader might want to know, or benefit from knowing? Obviously, I disagree, and I trust many others will, too. -- Meni Rosenfeld (talk) 10:12, 27 October 2006 (UTC)

My opinion is that its best to do nothing and move on. We have a slightly kooky feature article, which explains a frequently asked question about the reals. Redirecting to 1 (number) is just silly, as the article is actually about any decimal ending in 999... A merge is even sillier as it would give far to much attention to just one aspect of 1.

There plently else we could be doing, Addition is I feel close to FA status, Derivative and Integral could take some work to secure their GA status and Gottfried Leibniz needs some seriuos work to sort out an unusual citation system. --Salix alba (talk) 11:31, 27 October 2006 (UTC)

If this article should be merged at all, the target should be Recurring decimal. - Fredrik Johansson 11:49, 27 October 2006 (UTC)

Please forgive me if I say a few words, but not few enough.

When BradBeattie created the article (appropriately named Proof that 0.999... equals 1) on 2005-05-06, it was a sad little stub that evolved over the next weeks into a minor service article focused on the proof. Starting on 2005-10-27, I (KSmrq) began to work it over to more effectively confront the issues raised in the thousands of posts on the topic scattered around the web. A few other users helped with tweaks and vandalism reversion, of course. (We even got a visit by WAREL, lucky us.) Inevitably, on 2006-03-26, someone felt compelled to insert a pathetic infinite sum proof, which I had deliberated avoided for reasons I detailed at various times on the talk pages. That was the beginning of an accelerating downward slide. Concern for the readers who needed the article was shoved aside as more and more and more pet proofs and passions were stuffed in. I used the talk pages at great length to explain why that was counterproductive. Then, stunningly, on 2006-06-29, Melchoir began slapping on OR tags, adamantly rebuffing everyone who visited the talk page to nudge him out of such extremism. As the end of summer approached and sensible editors took vacations, Melchoir launched an all-out assault, beginning on 2006-08-23 and continuing with twenty or more edits a day. After making a few protests that drew retaliatory threats, I wrote it off as a bad investment of my time and took the article off my watch list.

Today the article has

• a few meaningless pictures
• section after rambling section arranged in no particular order
• explanations of no benefit to those who really need them
• topics better left to their own articles (such as Construction of real numbers)
• a blizzard of 63 (!) odd, redundant in-line citations, including this series:

  27. Griffiths & Hilton §24.2 "Sequences" p.386

  28. Griffiths & Hilton pp.388, 393

  29. Griffiths & Hilton pp.395

  30. Griffiths & Hilton pp.viii, 395

• a total of 49 (!) references of dubious utility

This article in its present state does not represent the best of our mathematics community, nor the best of Wikipedia. To the contrary, I find it an embarrassment to both.

I believe it was helpful to have a small service article on the proof, and when Melchoir goaded a naive editor into nominating the article for deletion (before taking it over), large numbers of other mathematics editors agreed with that view. I think it would be helpful to recreate a small article under the original “Proof…” title, with Melchoir prohibited from editing it. Then this abomination can drift into well-deserved oblivion.

Honestly, this is a minor backwater of mathematics. I am happy to have played a pivotal role in moving the proofs away from endless ineffective parroting of "geometric series" and the like, at least temporarily. I am happy to have raised awareness of the role of standard real numbers. I am not happy with what has happened since. I am unwilling to engage in more fruitless debates with Melchoir (or his surrogates). I will not participate in a revert war. And, frankly, I'm inclined never to see this topic ever again, a view I suspect is widely shared!

I am more concerned with the bigger questions implicit in this debacle. However, I have already exhausted my patience, and likely yours as well, so I'll stop here. --KSmrq^T 19:23, 27 October 2006 (UTC)

MediaWiki talk:Common.css#span.texhtml

I've mentioned this before, but I want to get it implemented now. See MediaWiki talk:Common.css#span.texhtml. —Mets501 (talk) 21:48, 28 October 2006 (UTC)

Yes, you've suggested it before. And then, as now, the answer is that you can make it happen in your own personal style sheet, called monobook.css. (See Help:User style or Wikipedia:Help desk.) There is no point in wasting our time again, and certainly not developers' time, with this. The new STIX fonts will be serif fonts, and we'd like to switch over to blahtex as soon as possible. --KSmrq^T 22:58, 28 October 2006 (UTC)