Wikipedia talk:WikiProject Mathematics

For older discussion, see /Archive1, /Archive2, /Archive3, /Archive4(TeX), /Archive5, /spoof edits alert (past hoaxes), /Archive6, /Archive7, /Archive8, /Archive9, /Archive10, /Archive11, /Archive12

Commuting diagrams?

What are the prospects for commuting diagrams in TeX on WP? Most pages that have them seem to have custom-generated PNG's. My attempts to create a native diagram result only in ugliness:

${\begin{matrix}K&{\begin{matrix}1_{K}\\\longrightarrow \end{matrix}}&K\\\downarrow ^{\eta _{A}}&\,&\eta _{B}\downarrow \\A&{\begin{matrix}f\\\longrightarrow \end{matrix}}&B\end{matrix}}$

and a triangle:

${\begin{matrix}&&K&&\\&\swarrow ^{\eta _{A}}&\,&\eta _{B}\searrow &\\A&&{\begin{matrix}f\\\longrightarrow \end{matrix}}&&B\end{matrix}}$

The markup is complicated too ... Any better way of doing this? linas 00:01, 26 September 2005 (UTC)

Yes, it would be nice if the powers that be included some diagram package into the wiki math code. I generate PNG's using a program called textogif and just upload them. It is fairly fast and painless once you have it all set up. Check out my page on Wikimedia Commons. I have some minimal set of instructions there. -- Fropuff 16:26, 26 September 2005 (UTC)

I thought one can use xypics to create diagrams. This is a LaTeX package. So, all needed is for the Wiki TeX dialect to support this package. I also wish that Wiki TeX also supported the amsart package, as when we copy articles from PlanetMath as part of the WP:PMEX project, often many TeX symbols are not recognized. Oleg Alexandrov 17:36, 26 September 2005 (UTC)

Merging manifold and manifold/rewrite

The article manifold has been rewritten at manifold/rewrite. Manifold/rewrite has had around 225 edits since June 19 when Jitse started it as a text in his sandbox to offer some constructive suggestions to the arguments at talk:manifold. Now the rewritten article looks nice and needs to be merge into manifold, which itself underwent around 58 edits since June 19. The big question is, how to merge them? One can merge the edit histories, see Wikipedia:How to fix cut and paste moves, but it could be a mess. The only other choice is I think to give up on the history of one of the two articles. What should be the right decision? Let us discuss this at talk:manifold/rewrite. Oleg Alexandrov 04:27, 26 September 2005 (UTC)

Comments requested on new proposed math stub names

See Wikipedia:WikiProject_Stub_sorting/Proposals#More_Math_stubs. Oleg Alexandrov 00:51, 27 September 2005 (UTC)

Controversy over the birthday paradox article

At Talk:Birthday paradox it is being proposed to delete from the article the section on Paul Halmos' view of the matter. That is the only section that takes the reader beyond the stage that any freshman who thinks the problem through would figure out. It's a fairly short section. Three Wikipedian support deletion; only I have opposed it. Would mathematicians please comment at Talk:Birthday paradox? Michael Hardy 22:41, 2 October 2005 (UTC)

Oh: It's the part labeled "long, windy, not needed". Michael Hardy 22:42, 2 October 2005 (UTC)

... and now I've changed the title of that section of that long talk page, to make it easier to find. Michael Hardy 22:44, 2 October 2005 (UTC)

New article on anti-Cantor newsgroup participants

Dave Petry (I'm 99% sure it's he) has started a new article called Controversy over Cantor's Theory. Dave's been showing up from time to time on sci.math and sci.logic for some years with variations on this theme--set theory is "mythological" and has nothing to do with "reality" as defined by things that can be observed on a computer. He's not stupid or crazy, just wrong; it's sort of amusing how he says (on the article's talk page)

This article is an attempt to give an overview of the more sensible views on this topic

because the less sensible views are those of certain individuals at least one of whom has a WP article about him (Archimedes Plutonium).

Anyway the project itself is perhaps worthwhile; I don't see anything wrong with having an article about philosophical views hostile to the use of set theory in mathematics, and how they have evolved, if indeed they have, as a result of the "computer age". This particular article in its current form, though, is very much OR and very POV. I hope others will take a look at it and figure out how to fix it or whether it's worth fixing; I really should be working on that paper.... --Trovatore 04:12, 3 October 2005 (UTC)

Well, it's rambling, unsourced, POV and apparently quite ignorant of work in areas such as domain theory that do argue for replacements of set theory for purposes of theoretical computer science. Move to criticisms of set theory, and cut down by about 80%, I'd say. Charles Matthews 21:36, 5 October 2005 (UTC)

The point of the article is to document the debate that has been taking place on Usenet over the past decade and a half at least, and to show that the current debate is really not much different from the debate from the early part of the twentieth century, except that the computer revolution does give people a new way of thinking about mathematics. As I point out in the article, the current anti-Cantorians are not pure mathematicians mostly, but rather people who have applied mathematics. I don't think you guys (Mike Oliver and Charles Mathews) understand what the debate is all about, and hence you guys are not really qualified to judge the article. It is "unsourced" currently, as it is still a work in progess. If you want to add a link to domain theory, that would be just fine -Dave Petry 5 October 2005

Let me add some comments especially directed to Mike. First, we know that quite a few very talented mathematicians have objected to Cantor's Theory. The names Kronecker, Poincare, Brouwer, Weyl, and Bishop usually are mentioned in this regard. Would you say that those guys are just plain "wrong". Are they more wrong or less wrong than me, and why. But furthermore, do you think those guys would say that the article I wrote is "original research". Although I have given the subject a slightly different perspective (invoking computers), I think those earlier mathematicians would recognize almost everything I have written as being very close to their own ideas. 24.18.232.215 03:01, 6 October 2005 (UTC)

OK, there's two separate points here, correctness vs original research; let's keep them separate.

Correctness: I actually agree with you about the applicability of the scientific method to mathematics. I think you're wrong that the appliction of the method militates against set theory. In fact, set theory makes refutable predictions in a Popperian sense, and they have thus far all been confirmed. And they can be formulated in terms of the computational world you discuss. I suspect that you may have a prejudice that a scientific approach requires restricting attention to the physical world.

Historical figures: All those you mention have made important contributions. That doesn't mean they weren't wrong about some things too, and I think they were. (Kronecker's a separate case; I tend to think of him as actually a bad person, for his persecution of Cantor, but it could be that my view of this is filtered through Cantor's depression and paranoia, plus (as I point out at every opportunity) I'm not much of a historian.

Original research: Let's be very clear that this part of the discussion has nothing to do with the merits of your ideas. The fact is that they appear to be your own personal observations. Even the language you attribute to the "anti-Cantorians" is in many cases almost identical to your own newsgroup essays. Yes, I think all the historical figures you mention would call your page "original research", once they understood the Wikipedia definition of the phrase. Hint: Just because it's OR here, doesn't mean a journal couldn't reject it for not being original. See WP:NOR for more information. --Trovatore 03:45, 6 October 2005 (UTC)

On this topic, you are not an expert. You don't understand the views of those you disagree with. I hope you don't succeed in keeping my article out of the wikipedia.

Have you read the WP:NOR correctly? Fortunately, Wikipedia isn't about who is/isn't an expert, but rather about who can give some source to backup his claims. And no, USENET is not a reliable source of mathematical knowledge. Samohyl Jan 14:32, 6 October 2005 (UTC)

We can have an article about criticisms of set theory, as we have one about criticisms of Wal-Mart. It must conform to WP's standards, that's all. Charles Matthews 21:03, 6 October 2005 (UTC)

For the historical "anti-Cantorian" arguments, I can easily give sources, and I intend to(the article is not finished). Part of the purpose of the article is to document the Usenet debate about Cantor's Theory, and to show the similarity of that debate with the historical criticisms of set theory. It would be a stretch to say that showing the similarity of the arguments is "original research". And likewise, the Usenet is most definitely a reliable source for knowledge of the debate taking place on Usenet. I understand why the wikipedia doesn't allow original research, but I don't think the intent is to keep articles like mine out. I absolutely do not accept Charles Matthew's butchering of my article, and eventually I plan to revert to a previous article.

Certainly there are other controversial topics in wikipedia, for example, Matthews mentions criticisms of Wal-Mart. So how does wikipedia stop "combatants" from sabatoging each other's articles? 66.14.95.197 23:31, 6 October 2005 (UTC)

In wikipedia, no single editor owns or possesses an article, thus the possessive in the phrase "each other's articles" makes no sense. With very few exceptions, every editor has equal rights to edit any article, however they see fit. It is the miracle of Wikipedia that this works, but it does. Paul August ☎ 15:50, 7 October 2005 (UTC)

Butchering is silly talk (like it says below the box, If you do not want your writing to be edited mercilessly and redistributed at will, do not submit it). I cleaned it up to conform with our style. Freely-made comments about what I don't understand are also silly, as are threats to revert. Feel free to add back anything specific. I doubt you'll get much sympathy. Charles Matthews 07:06, 7 October 2005 (UTC)

I missed this thread first time around, but I noticed Charles Matthews say:

work in areas such as domain theory that do argue for replacements of set theory for purposes of theoretical computer science

This isn't quite right: domain theory (and especially synthetic domain theory) wants to build better mathematical structures for doing Tarski-style interpretations of programs into, but in turn the foundations of domain theory are regular set theory. It might be better to call it a better interface onto set theory than a rival to set theory. Martin-Loef's type theory is an example of an actual rival to set theory, which is, again, peddled mostly by theoretical computer scientists.

I agree with Charles M's objection though. The section of that article called "recent attacks" has as its most recent commentator Hermann Weyl! In the mathematicians section, Kline is not objecting to set theory as a mathematical structure, but to its role in mathematical education, in particular the air of unreality refers to the lack of good intuition a certain kind of emphasis on farmalism and foundations can lack (caveat: I don't recognise this particular passage of Kline, but I've read a lot of Kline and I know his hobby horses).

Having said that, I think that if we find the right home for this, there might be a nice article that can be grown for it. I don't like "criticisms", I'll make a proposal for alternative name candidates at Talk:Controversy over Cantor's Theory --- Charles Stewart 15:24, 13 October 2005 (UTC)

Khayyam-Pascal's triangle

Paskal's triangle has been moved to Khayyam-Pascal's triangle. It is claimed there now that the latter is the internationally recognized name. Discussion is welcome at Talk:Khayyam-Pascal's triangle. Oleg Alexandrov 21:35, 5 October 2005 (UTC)

Oh, just move back. We use the common name. The history can be dealt with in the article. This is the standard way. Charles Matthews 21:38, 5 October 2005 (UTC)

Your wish is my command, so I moved it back. -- Jinn Niesen (talk) 23:16, 5 October 2005 (UTC)

Category:Article proofs

This category has some proofs, as subpages. It seems to be at odds with two widely held views, one that there should be no subpages (Christoffel symbols/Proofs is a subpage to Christoffel symbols), and that the proofs should not be on separate pages. Also, wonder I, why is this separate from Category:Proofs. I myself would suggest the proofs in there, together with the mother category, be deleted. Wonder what other opinions are. Oleg Alexandrov 00:16, 6 October 2005 (UTC)

Are you proposing that articles in Category:Proofs like Cantor's diagonal argument and Proof that e is irrational be deleted, or just the ones in Category:Article proofs? I would disagree with the first statement, while I have no strong opinion on the second statement. Furthermore, nobody reacted when it was asked whether these subpages are allowed at Wikipedia talk:Subpages#Special dispensation for mathematical proofs several months ago, so one could argue that the prohibition on subpages does not apply here. -- Jitse Niesen (talk) 22:00, 6 October 2005 (UTC)

No, I don't suggest deleting all the proofs on Wikipedia outright. Just the subpages in Category:Article proofs. Oleg Alexandrov (talk) 23:06, 6 October 2005 (UTC)

Making them into full, self-sufficient, articles called, for example, Proofs of the Bianchi identities, would seem to be less wasteful; but I agree they should not stay where and as they are. Septentrionalis 02:57, 7 October 2005 (UTC)

Subpages bad. Articles like a hypothetical Bianchi identities (proofs) stand or fall by their general interest (Fermat's Last Theorem (proof) would obviously be OK). I agree that the Category:Proofs should be for pages about proof and types of proof, not pages giving specific proofs. Perhaps a list of 'sample' proofs for the latter? Charles Matthews 07:02, 7 October 2005 (UTC)

How about putting back those proofs into the articles? --MarSch 15:01, 7 October 2005 (UTC)

I don't want to lose these proofs, I think they are valuable. I don't see the problem in having them on a subpage. Can someone explain the harm in that? If we don't want them there, or in the article, or in a seperate article of their own, then we could always put them on the talk page, but I would be strongly opposed to just deleting that content. Paul August ☎ 15:20, 7 October 2005 (UTC)

Putting the proofs back into articles is out of question. Proofs are typically technical, do not add much to understanding the concepts in the article, and interrrupt the flow of the article. Let us not forget that we are dealing with encyclopedic essays here, oriented towards the general public.

Keeping them as subpages is not good either. There is no hierarchy on Wikipedia; each article should be able to stand on its own. I would argue that the only option beside deleting the proofs is keeping them on their own standalone page.

Now, are proofs that much worth it, besides some classical proofs? Proof articles will be visited more seldom than others, and will be harder to fact check, which raises the spectrum of some obscure articles with more errors than others. Oleg Alexandrov (talk) 18:09, 7 October 2005 (UTC)

I suggest deferring a decision for at least several years. WP has the potential of being more than just encyclopaedic, although this potential is years away. Math books are quite useful in that they provide (non-notable) proofs for their theorems. Although WP is still far away from being detailed at a level equal to that of a book, I think it would be a mistake to declare as policy that WP must ever become as detailed as a book. As to obscure articles with errors, I don't think the way to eliminate errors is to eliminate obscure articles. linas 00:52, 14 October 2005 (UTC)

Note that Proof of angular momentum is an excellent example: its crudy, haphazard and weak, yet has had a half-dozen editors and is translated into four languages!! People seem to like this stuff, and I don't think it should be banned on principle.

Also, some articles cite too many references (in my opinion), and I would like to see, in such cases, that the references (and footnotes) are banished to a subpage.

Think of "proofs" as something that is less formal than a real article, but more formal than a talk page. linas 01:02, 14 October 2005 (UTC)

The {style} template

The {{style}} template pops up every now and then at Wikipedia:Manual of Style (mathematics) and is there now. I would argue that it is unnecessary. Its only purpose is for a user to hop from manual of style to manual of style, but for people who actually use a particular manual of style, like our math manual, the links to the manual of style about writing China-related articles, how to write footnotes, etc, are not be helpful. I would argue that a link to the Wikipedia:Manual of Style on top of our manual of style should be enough. From there, one can access any other style manual if one wishes so. Wonder what people think. Oleg Alexandrov (talk) 04:12, 7 October 2005 (UTC)

Harmless; and if we remove it, it will be back. Why bother? Septentrionalis 20:03, 7 October 2005 (UTC) (And it makes the page look a little more "official", which can hardly hurt.)

Wikipedia: Make technical articles accessible

I posted a note on this guideline's talk page proposing a change in this policy (Wikipedia talk:Make technical articles accessible). --- Charles Stewart 02:22, 8 October 2005 (UTC)

Please vote on list of lists, a featured list candidate

Please vote at Wikipedia:Featured list candidates/List of lists of mathematical topics. Otherwise, the issue may be decided by (from the looks of it at this time) people who never heard of mathematics until they saw this nomination. Michael Hardy 03:35, 13 October 2005 (UTC)

Wikitextbooks or www.yourbooksucks.com

I am attending an AMS sectional conference this weekend, and once again listening to everyone complain about how badly math is taught in the US, how lousy all the grade school textbooks are (except the Singapore textbooks), and how the three big textbook publishers are so powerful that nobody has a ghost of a chance of making things better.

Naturally, I thought of Wiki.

What I propose is a series of articles on mathematics written at the grade school level, so students and teachers who actually care about mathematics can have at least one source to which to turn.

I'm going to start at Grade school mathematics and take it from there.

Want to help?

Rick Norwood 22:46, 15 October 2005 (UTC)

I would like to help, but think a problem needs to be addressed first: stability. A book written by committee, and constantly changing, will be as bad as what's out there now. We would need to have one committed person in charge, who could review potential contributions from many authors and decide which to include as is, which to include with changes, and which to reject. This is rather "anti-wiki" so may not work here. That said, I suppose we could write many articles within the current structure with the goal of copying them and making them uniform, outside the wiki structure, to make a textbook, at some future date. StuRat 23:24, 15 October 2005 (UTC)

Agree w/StuRat on this point. I'm finding that WP articles tend to be "average" and not "excellent" because the excellent material in WP tends to get edited to oblivion. For a reference, such as WP, that's fine. For a textbook, which you learn from, "average" is not good enough. A better model is the Linux kernel, where an authoritarian few act as gatekeepers to contributions. linas 19:12, 16 October 2005 (UTC)

The first task, I would think, would be to come up with an ordered list of topics to be covered, by age group. A grade school book should have lots of colorful illustrations, so having a graphic artist on the staff would sure be a good idea. StuRat 23:31, 15 October 2005 (UTC)

Also, you should set up a project page for this, so discussion can take place there. StuRat 23:32, 15 October 2005 (UTC)

We have Wikibooks, with a few mathematics texts there already. See http://en.wikibooks.org . Educational material should go there and not in Wikipedia. Dysprosia 00:44, 16 October 2005 (UTC)

Agree with Dysprosia. Wikipedia is for reference, it is a collection of encyclopedic essays. I am getting weary of people trying to use Wikipedia to fix the wrongs of the world. Oleg Alexandrov (talk) 03:53, 17 October 2005 (UTC)

Yes, please support wikibooks. Charles Matthews 09:23, 17 October 2005 (UTC)

Reminder: Wikipedia:WikiProject Physics !

Just in case there are still Quantum and GR types lurking here, who haven't yet found Wikipedia:WikiProject Physics ... well, now you know: there's a physics project as well. Add your name to the list, and visit the talk page as well: I'm sure the topics are as lively and maybe more argumentative than those here! linas 00:28, 18 October 2005 (UTC)

Mathematical characters usage

As most readers here know, Dmharvey is working on a MathML solution for Wikipedia, called Blahtex. A perennial problem in mathematics is the large number of potential characters, and the MathML spec defines quite a large list. For your viewing pleasure, I have made a page where you can try to see many of them in your browser. (The list does not include all the fraktur, script, and blackboard-bold characters, some of which are in a higher Unicode plane.) Using a Gecko-based browser (from the Mozilla Foundation) and the Code2000 font, I see excellent coverage. That's a Good Thing, because the STIX fonts have had their projected release pushed back to mid-2006. In light of evolving developments, the question here is, what do we do now in editing articles?

Because Wikipedia has switched to UTF-8, it directly accepts any Unicode character. We can also use HTML named entities, and character entities. Come MathML, readers must be prepared to cope with these. Meanwhile, the processing of <math> allows a limited subset, producing either an image or HTML markup. (The subset does not include the full set of LaTeX characters, much less the complete range of MathML characters.) Finally, outside of the <math> tags we can use images of characters.

Folks writing in other scripts, from Cyrillic to Devanāgarī to IPA to Hangul and others, seem unapologetic about the need for their kind of characters in their kind of article. With the advent of MathML presentation it will become extremely awkward and ugly to use the image crutch; we need our characters, too.

How many people are going to scream if I start writing the cross product properly as A⨯B (using U+2a2f, &Cross;) instead of A×B (using U+00d7, &times;)? That's silly, right; who needs the fancy character? But I've also gotten curses for using the semidirect product, N⋉H (using U+22c9, ⋉), which LaTeX calls "\ltimes" but <math> does not allow. (Especially annoying, the complainant thought a picture of &rtimes; was a fine substitute, even though it's the wrong character and precludes <math>!)

I will scream, because it shows up as a little square, like any other unreadable character. Please don't. Septentrionalis 18:40, 26 October 2005 (UTC)

Did you mean Cross or ltimes? Either way, one down, how many left to go? (By the way, your browser can read the character fine; it can't display it with your present setup.) Unfortunately, unless folks respond here an editor has no way to know which characters display for you as missing character boxes. I might be using FreeBSD and Firefox and Free UCS Outline Fonts, someone else might be using Mac OS X and Safari and default system fonts, and you might be using Win98SE and IE5 and Lucida Sans Unicode. Some kind of documented guidance could benefit everyone. That could be a list of safe characters, and/or suggestions for browser/font configurations to help in filling the boxes. --KSmrq^T 20:40, 26 October 2005 (UTC)

So, are all characters fair game as numeric entities? As UTF-8? (Clearly not as <math>!) If not, which do we exclude, why do we exclude them, how do we substitute (in all contexts), and what do we do when MathML arrives? --KSmrq^T 13:33, 18 October 2005 (UTC)

When using special characters, they should be properly displayed for, say, 90% of all readers. Thus at least IE should display them properly, and not just in one of its font settings. Otherwise it is better to use LateX, or if a symbol is not available, an image.--Patrick 13:28, 20 October 2005 (UTC)

Somewhat related was the discussion at Wikipedia talk:WikiProject Mathematics/Archive12#Unicode in math articles. There people objected against unicode but for different reasons.

With Firefox on Windows XP, I can't see one of the characters KSmirq wrote above, the one with U+2a2f, there is only a question mark in there. I guess it sounds reasonable that one not use the more exotic unicode characters, but rather TeX. Of course, TeX has the problem that the restricted Wikipedia dialect does not have all the symbols, but at least once the Wiki TeX parser agrees to generate a formula, it will be visible to everybody. Oleg Alexandrov (talk) 13:39, 20 October 2005 (UTC)

The archived discussion was about replacing numeric entities with UTF-8, which is related, but logically distinct. Using no UTF-8 beyond ASCII, an article can still use &2a2f; — which may not display as hoped. It is unrealistic to ask each editor to personally test special characters on all available OS/browser/font/config variations. Yet nowhere can I find any guide to what LaTeX constructions <math> tags support (including, but not limited to, characters); and nowhere can I find a guide to which characters are "safe" and which are not. Is my only resort trial and error, to try to use a character and see if the Wikipedia software or some other editor rejects it? Does that mean all mathematics must be written in ASCII?! That's an extreme example, but then where do we draw the line? Are all HTML 4.01 entities safe? Is any character in, say, Arial safe? Does Microsoft dictate through IE on WinXP? (If so, how are MacOS and BSD users to know what's safe?) And, again, MathML is looming (I hope!). --KSmrq^T 16:04, 20 October 2005 (UTC)

I did not say you should use plain ASCII for math formulas. :) And, I think the issue is not with people using XP or BSD, rather, the browser might not have all the fonts installed.

I guess the rule of thumb should be that if you suspect a given Unicode character might cause problems, you better you TeX instead, if TeX supports that symbol. But ultimately math display on the web sucks no matter what you use. Oleg Alexandrov (talk) 00:54, 21 October 2005 (UTC)

FWIW, I now have three browsers at my disposal; IE 6, Netscape 7.2, and Opera 8.5. None of then see 2a2f, while all except IE see 22c9. Arthur Rubin (talk) 14:04, 23 October 2005 (UTC)

That sounds about right. Your report, however, omits needed details, since what you see depends on OS+fonts+browser+config. For example, try installing the Code2000 font and see what you get. In regards to suspecting a problem, why would anyone not using IE/Win think a character they can see might be troublesome? I'm sure we all agree that mathematicians are the brightest and best-looking people on the planet, but that does not equate to web or wiki expertise! :-D —KSmrq^T 21:24, 23 October 2005 (UTC)

I'm running mac OS 10.4.2, with no additional fonts installed. On both Safari 2.0 and Firefox 1.0.6, I'm missing a large proportion of those characters. I haven't counted -- maybe missing 30% or so, especially towards the second half. Dmharvey File:User dmharvey sig.png Talk 00:03, 24 October 2005 (UTC)

That makes sense. Some of the MathML entities are composites, such as a relation overlayed by a negation (e.g., solidus), but otherwise I listed them in numeric order. The higher code blocks are likely to be more esoteric, and less well covered by standard fonts. Without the Code2000 font I get coverage like yours; it would therefore be interesting to know if adding that font completes your coverage. I hesitate to ask you to compare IE5/Mac [1]. --KSmrq^T 02:56, 24 October 2005 (UTC)

An approach I've taken is to provide links to bitmap images for characters which don't display on every browser. That way, at a minimum, users can click on a link to see characters like  ∈,  ∉, ∅,  ⊆,  ⊂,  ⊇, and ⊃; if they don't display on that user's browser. StuRat 00:12, 1 November 2005 (UTC)

That is a nice service, but $\notin$ and $\varnothing$ can better be displayed as image directly, they give most problems.--Patrick 07:44, 1 November 2005 (UTC)

I'm guessing you mean the fewest problems ? StuRat 08:35, 1 November 2005 (UTC)

I mean, they are the symbols which give the most problems if they are not displayed as TeX image but coded with &notin; and &empty;.--Patrick 00:56, 3 November 2005 (UTC)

Sorry to take so long to respond; busy elsewhere. This is a creative idea, but hampered by two crippling drawbacks. The first is that seeing a formula with boxes on one page, and individual symbols separately, adds up to an unreadable formula. The second is unintentional creation of a mistaken symbol, which came up in a different context when the suggestion was made that a formula could link to explanations of its operators. This happens because many browsers are configured to underline links. Two examples:

• "2+2=4"
• "For all primes p>2, p is odd."

Obviously, "+" and ">" aren't special characters (so everyone can appreciate the examples, which look like "±" and "≥"); but the general danger should be clear. --KSmrq^T 03:07, 3 November 2005 (UTC)

Semidirect product symbol

The common notation of a semidirect product seems to be G = N File:Rtimes2.png H, with the normal subgroup at the left, while the symbol is a cross with a vertical bar at the right (see e.g. [2]), although the names of the symbols seem to suggest that the bar should be at the side of the normal subgroup ([3], [4]). Have other people any thoughts?--Patrick 13:37, 20 October 2005 (UTC)

Perhaps it would be better to redirect such a specific discussion to Talk:Semidirect product? --KSmrq^T 19:23, 20 October 2005 (UTC)

move of manifold/rewrite/*

The main article was moved, but the two subpages weren't. differentiable manifold, topological manifold redirect there. Admin privileges probably needed, since I couldn't do it. --MarSch 11:14, 20 October 2005 (UTC)

I will take care of this now. Oleg Alexandrov (talk) 11:20, 20 October 2005 (UTC)

Done. I also merged their edit history with the corresponding ancient redirects created by Toby Bartels in 2002 or so. Oleg Alexandrov (talk) 11:27, 20 October 2005 (UTC)

Thanks --MarSch 11:37, 20 October 2005 (UTC)

Live preview

This is not about math, but might be helpful to the fellow mathematician. I found a very userful tool in my opinion, Pilaf's Live Preview at Wikipedia:Tools#Alternative_previews. It allows one to do instant preview, without waiting for seconds or more after hitting the "Preview" buttion. It works by some javascript magic, and is just as easy to install as pasting several lines of text into a file and doing a reload of your preferences (control-shift-r for Mozilla, Ctrl-F5 in IE, and F5 in Opera). I already love this tool. :) Oleg Alexandrov (talk) 12:51, 25 October 2005 (UTC)

Note that it does not do LaTeX formulas, and does not show redlinks as red (one needs to check with the server for things like that), so the good old preview is still needed, but it can still cut the number of times one needs to use the usual Preview button. Oleg Alexandrov (talk) 14:02, 25 October 2005 (UTC)

Classification

Hey! In a case of absent mindedness, you forgot to classify the numbers. I searched a lot. If already present, I apologize. --Davy Jones 02:50, 26 October 2005 (UTC)

who's you and what numbers are you talking about? --MarSch 09:29, 26 October 2005 (UTC)

Firstly, I am persuing my bachelors degree in engineering. secondly, I mean the classification of numbers into Real numbers and Imaginary Numbers and their subdivisions. this willl clear the basics of numbers for the novice. --Electron Kid 00:14, 27 October 2005 (UTC)

Still don't understand what it means to classify a number. linas 00:24, 27 October 2005 (UTC)

Please note the plural numbers. Its like : numbers have been classified as Real numbers and complex numbers. complex numbers are further classified as complex and imaginary. Real numbers are further classified as rational and irrational. Rational numbers = fractions + integers. Integers = (negative numbers) + (Whole numbers). Whole numbers = 0 + (natural numbers). Further, a different symbol is used to represent each set. I thought of adding a page, if not already present. --Electron Kid 01:00, 27 October 2005 (UTC)

I really wouldn't recommend adding such a page. I would guess it would show up on AfD very quickly. You might take a look at the number article and seeing if you want to add a section there; it mentions various sorts of numbers, but not in that sort of hierarchy.

By the way, 0 is a natural number for lots of mathematicians, including me; the locution "whole numbers" is almost never used except in high school math texts, or perhaps in some informal contexts. --Trovatore 01:10, 27 October 2005 (UTC)

I find the discussion at number page to explain very well what kinds of numbers are out there. Oleg Alexandrov (talk) 02:55, 27 October 2005 (UTC)

Yeah, number already covers all of this. (Anyway, electron kid, I don't think your classification of "numbers" into "real" and "complex" does much justice to all the other wonderfully wacky kinds of "numbers" that mathematicians have thought up... p-adic numbers, ordinal numbers, etc etc) Dmharvey File:User dmharvey sig.png Talk 03:23, 27 October 2005 (UTC)

Differentiating Functions on AfD

The article Differentiating Functions is on AfD (doesn't show up in the Current Activity page because it's not in any math category). The article is very badly written, though one editor seems to think it's more accessible than Calculus with polynomials, which I find hard to credit.--Trovatore 05:52, 28 October 2005 (UTC)

What's the current activity page? -Lethe | Talk 06:15, 28 October 2005 (UTC)

Wikipedia:WikiProject Mathematics/Current activity --Trovatore 06:23, 28 October 2005 (UTC)

Boolean algebra

Without some support on Boolean algebra, I think I may just merge it into Boolean logic, take the flak and pick up the pieces later. It is clear that making it a purist page meets continuing resistance. I don't do edit wars. Charles Matthews 21:40, 28 October 2005 (UTC)

Look, I don't care what the articles are called, within reason. But there needs to be a page on the algebraic structure. I've already expressed a willingness to have it called Boolean algebra (algebraic structure), with Boolean algebra itself containing the content now in Boolean logic. I see no reason that latter page (whatever it's called) should even refer to the algebraic structure, except maybe a line or two about related topics.

It occurs to me that the page on the algebraic structure might be made more accessible with a picture of the eight-element BA (its Hasse diagram, say, with the bottom node black, the next three red,green,blue, the next three yellow,magenta,cyan, the top one white, and explanation of how the \land and \lor correspond to following lines on the graph). Anything to make it clear that we're interested in the structure itself, not just the corresponding logic. I'm not very good with making such pictures--anyone want to draw it up? --Trovatore 22:07, 28 October 2005 (UTC)

I agree with Trovatore on this one. Merging the two articles won't help, but will lead to continuous edit wars between you guys and the general public, both of whom want different things from the article. StuRat 22:50, 28 October 2005 (UTC)

Looking at both Boolean algebra and Boolean logic, neither one clearly says "theory" or "application" — not in so many words, and not in the content. In my experience, that's usually a false dichotomy; but if that's what's intended, say so emphatically. Meanwhile, I've rewritten the opening of Boolean algebra (which had lapsed into nonsense), and said a few words on its talk page. Hope it helps; and good luck. --KSmrq^T 03:03, 29 October 2005 (UTC)

No, that's absolutely not the intended distinction (at least, not my intended distinction; certainly other contributors may have different opinions). The distinction I have in mind is between the algebraic structure (currently at Boolean algebra), and the propositions that are true in those structures (currently at Boolean logic). So for example "How many elements has the Boolean algebra B?" is a perfectly sensible question, whereas "How many elements has Boolean algebra (i.e. Boolean logic)?" is complete nonsense. --Trovatore 03:12, 29 October 2005 (UTC)

The difference in emphasis isn't strictly application vs. theory, although the Boolean logic article certainly has more application text and the Boolean algebra article has more theory. The Boolean logic article could be described as "the theory and application of the common subsets of Boolean algebra which apply to real-world applications". StuRat 03:18, 29 October 2005 (UTC)

I've done a little research on this, and the split over the articles is typical of mathematical encyclopedias (the Soviet one has algebra of logic + Boolean algebra, the Japanese some sections on symbolic logic + Boolean algebra). So it is not actually eccentric to divide it the way it currently is. That being said, I've heard nothing that convinces me there are two separate subjects, any more than discrete mathematics is disjoint from logic or computing applications. Charles Matthews 06:39, 29 October 2005 (UTC)

I think there is nothing at Boolean logic which shouldn't be at Boolean algebra and I dislike extremely how half of the article is doing set theory. Please go ahead and merge them Charles. --MarSch 12:42, 1 November 2005 (UTC)

As I said before...Merging the two articles won't help, but will lead to continuous edit wars between you guys and the general public, both of whom want different things from the article. StuRat 19:14, 1 November 2005 (UTC)

Wikibook proposal

Since the purpose of the article originally started by StuRat was in part didactic, how about farming it out as a wikibook? There is still the historical question of the relation of Boole's algebra to the different entity called Boolean algebra to be sorted out, and yet another new article housed at BL might be the best place to do this. The new article can then comment on the non-mathematical aspects of cultural usage that originalyy prompted StuRat to write his text, and the genuinely encyclopediac contribution of the BL article can still be accomodated in the BA article. --- Charles Stewart 18:57, 1 November 2005 (UTC)

I have no objection to there being a WikiBook on either, or both, the current Boolean logic content and the current Boolean algebra content. However, if this is to be used as a justification for deleting either article, in whole or in part, from WikiPedia, I am strongly opposed to that. StuRat 19:07, 1 November 2005 (UTC)

The new article would not be based on your article, but it would be non-PhD-level and it would document what non-algebraists get out of the mathematics. I don't think that a compelling case for en.wikipedia to host an introduction to BAs for people who don't want to learn algebra has ever been made, if that is the deletion that my proposal makes that you object to. --- Charles Stewart 19:11, 1 November 2005 (UTC)

The basics of set theory are taught well before algebra in school. For example, an episode of the PBS kids (ages 7-11) math show Cyberchase contained an introduction to set theory including Venn diagrams. Any assumption that elementary set theory, and the Boolean logic operations based on it, requires advanced algebra, is therefore faulty. StuRat 19:40, 1 November 2005 (UTC)

I don't see the relevance of your remark to mine. --- Charles Stewart 20:17, 1 November 2005 (UTC)

I was responding to the statement "I don't think that a compelling case for en.wikipedia to host an introduction to BAs for people who don't want to learn algebra has ever been made...", which seems to be saying that a knowledge of algebra should be required to understand the introduction sections. My point is that the introductory level material can be made without the use of algebra, and that such material can be added later. StuRat 20:55, 1 November 2005 (UTC)

I made no such claim. WP articles on topics of broad interest should be accessible, even if the article should contain material that is not generally accessible. Wikibooks is the place for tutorials, see WP:NOT, point 8 of Wikipedia is not an indiscriminate collection of information, which is what "an introduction to BAs for people who don't want to learn algebra" would be. What is at stake in hosting such an introduction here rather than there? I see no point of principle at play here besides the one about following policy. --- Charles Stewart 15:38, 2 November 2005 (UTC)

Your statement that "WP articles on topics of broad interest should be accessible..." seems to imply that you don't think that we should have the goal of making all articles accessible. I disagree, and think that all articles should be made accessible to the broadest audience possible. Removing info from Wikipedia makes it considerable less likely to be found and thus less accessible. StuRat 15:56, 2 November 2005 (UTC)

I believe that there are articles for which it is not very important to spend much time thinking about the general reader, but instead most effort should be directed at the specialist. As you are aware, I've been citing analytic continuation as an example of this for some time. --- Charles Stewart 19:12, 2 November 2005 (UTC)

I don't think suggesting a wikibook is helpful. What is in wikibooks and what is here is in no way related.--MarSch 18:31, 2 November 2005 (UTC)

Are you disputing the policy? Are you aware that both WP and Wikibooks are both hosted by and reflect the values of the Wikimedia Foundation? --- Charles Stewart 19:12, 2 November 2005 (UTC)

I believe MarSch means the same thing as me, that while adding a WikiBook on any topic is a worthy goal, to use that as a justification for deleting material from WikiPedia, if that is your intent, is not at all helpful. StuRat 20:00, 2 November 2005 (UTC)

Issues with the real numbers

See Talk:Mathematical analysis#Mathematical.2FReal Analysis. A fellow is having problems with the modern defintion of real numbers (among other things). He/she says "infinitesimals exist". My reply would be that the real numbers are defined by axioms, and it follows from those axioms that there are no infinitesimals. It would be good however to have more in-depth comments than that on that talk page. Oleg Alexandrov (talk) 11:22, 29 October 2005 (UTC)

I would take the reals to be defined in terms of other things rather than axiomatized, but the answer comes out the same: "this is what we're talking about; talk about whatever you like, but don't call it the reals". At a cursory glance it looks like you're arguing with a crank over there. The best way to do that is not to; since he seems to have given up, I'd just let it go. --Trovatore 19:49, 1 November 2005 (UTC)

Infinitessimals exist, John Conway does a marvelous and fun construction in "On Numbers and Games". Although they exist in between real numbers, they're not exactly "numbers" themselves, though. I've always wondered if its possible to do some sort of calculus with them, e.g. treat them as some sort of fiber bundle or something over the reals, and get something other than trivial results. No idea. linas 16:04, 3 November 2005 (UTC)

WHat about non-standard analysis? --MarSch 16:57, 3 November 2005 (UTC)

and Non-standard calculus? --MarSch 17:06, 3 November 2005 (UTC)

J.H. Conway's surreals and NSA's hyperreals are both interesting structures (or classes of structures in the case of the hyperreals; there are nonisomorphic structures that fit the description). But they aren't the reals. Considerations involving them may tell us things about the reals, but they aren't the reals. Sorry to use baby talk; I imagine that both of you know these things--I'm just listing the points that can't be fudged when presenting the material to naive readers, or when having a discussion with a crank (if the latter is adjudged necessary). --Trovatore 17:10, 3 November 2005 (UTC)

The infinitesimals are not real, and they are not imaginary either. Gosh, what's left then? Oleg Alexandrov (talk) 17:45, 3 November 2005 (UTC)

My professor in introductory calculus would occasionally refer to indeterminate forms, infinities, and infinitesimals as "Christmas trees". Actually quite a good way to stop you from carelessly using them as regular numbers. Fredrik | talk 18:01, 3 November 2005 (UTC)

It's worth amplifying on non-standard analysis, though I think the original discussion was at a much lower level of sophistication. Suppose we lay out a system of axioms for the reals, then look around for possible models that satisfy those axioms. A standard model includes just what we expect and no more. A non-standard model — which supports the same set of theorems — can exist and have extra goodies like infinities and infinitesimals. To put the extra goodies to work requires careful distinctions. Another tactic is to use topos theory and the different logics that allows. In this way we get a somewhat different version of infinitesimals such as those discussed in smooth infinitesimal analysis [5] (PDF). A limited number of mathematicians enjoy these foundational games; many more seem to take the attitude "go away, we're trying to get work done here". But then, I remember hearing some insist that category theory was a waste of time, on the one hand; and I've seen topos logic [6] (PDF) [7] [8] put to serious work in the semantics of programming languages, on the other hand. I feel it's a delicate topic, because while I'm in the camp that enjoys foundational explorations, I'm painfully aware that most of the people who raise questions on Wikipedia about infinities and infinitesimals are clueless cranks. Too often the cranks are able to get some leverage because of loose writing, acceptable for informal mathematical discussion but not careful enough to stave off false interpretations. It's a difficult discipline, should one choose to accept it. For thousands of years mathematics progressed with stronger intuition than foundation, and I suspect that even though we're taught we should respect foundations today, many still just pay lip service. And for good reason: if we have to dot every "i" and cross every "t" any time we speak, we'll be tongue-tied. --KSmrq^T 20:31, 3 November 2005 (UTC)

Parameterize

During the travails of my spellbot, I got the following comment:

It turns out that both "parameterize" and "parametrize" (the bot's spelling) are very common; M-W lists both. I learned the first version somewhere back in the mists of time and only found out just now of this variant. I was actually surprised to see that in many of my books also use the second version, and I never noticed... (incidentally the bot also corrected a "parameterise" to "parametrise", too. Yay for bots that also know British spelling :-) Choni 13:06, 29 October 2005 (UTC)

Makes me really wonder, is it indeed correct/widespread to use "parameterize" (one extra "e") as synonymous with "parametrize"? I never encountered the former, even though it would make sense as it all comes from "parameter". Thanks. Oleg Alexandrov (talk) 13:15, 29 October 2005 (UTC)

I am only familiar with the former version. It seems more natural, being closer to the root word, as well. StuRat 23:55, 31 October 2005 (UTC)

American Heritage seems happy with both, nodding slightly towards including the "e". That agrees with my practice when writing or proofreading: either is fine. It might be nice if an article was at least self-consistent, but frankly I doubt many readers would notice. In contrast, "parametric" does not allow an extra "e". --KSmrq^T 00:11, 1 November 2005 (UTC)

Of the four permutations, the only one that looks really wrong to me is "parametrise". I think british and american speakers actually pronounce the word slightly differently. (I'm an Australian speaker.) Reminds me of aluminium vs aluminum. Dmharvey File:User dmharvey sig.png Talk 00:14, 1 November 2005 (UTC)

I think aluminium is what is used in most languages. Therefore I prefer to use it also in English. --MarSch 12:45, 1 November 2005 (UTC)

The situation is a bit different, because in the case of Aluminium, there is actually an international standard that specifies the official name as "Aluminium", and not "Aluminum". See for example IUPAC Periodic Table of the Elements, which says: '“Aluminum” and “cesium” are commonly used alternative spellings for “aluminium” and “caesium.”'. As an American, I find this annoying, but that's the way it goes. -- Dominus 15:49, 1 November 2005 (UTC)

Hey that's good :) Now we only need to get rid of potassium and call it Kalium instead.--MarSch 17:07, 1 November 2005 (UTC)

Sure, but then we need to find a way to extract it from kale, instead of potash. 17:58, 1 November 2005 (UTC)

Americans don't get annoyed; we effect regime change. I can say that now that I'm in Canada. Then again the Canadians might not know I'm joking. --Trovatore 20:28, 1 November 2005 (UTC)

Yea, you might get kicked "oot". StuRat 20:46, 1 November 2005 (UTC)

Let's get back on task, eh? For what it's worth, I've met people (including myself) who insist it should be spelled "parametrize" (or "parametrise" if you live across the pond). I'm not sure how often I've run into the latter, though. - Gauge 03:45, 10 November 2005 (UTC)

Hilbert problems

The Hilbert problems page is seeing some development, which is only right and proper. It is also raising numerous issues, in respect of what a 'solved' problem is. This is an opportunity, to do better than other Web treatments (few of the historians really have all the background to write with authority on all 23). The words 'worms', 'can' and 'of' come to mind.

I wonder whether the laudable effort to get a table summary of it all on the page hasn't had its day. It is hard to write enough in a table entry, since some of the problems have several 'ply' in them. I also think that where [[Hilbert's n-th problem]] is now a redirect, we really need to have the buffer of a separate page. For example, Hilbert's fifth problem used to redirect to Lie group, but it seems clearer not to have arguments about what a Lie group is, and what the Fifth Problem was, on the same page.

Please come and help. This page missed Featured Article status over the summer, but has already been much expanded. Charles Matthews 09:49, 3 November 2005 (UTC)

Help wanted at rotation

See talk:rotation#Request for comment. Oleg Alexandrov (talk) 00:58, 6 November 2005 (UTC)

proofs of quadratic reciprocity

If anyone's feeling energetic, I started an article on Proofs of quadratic reciprocity. Sadly, it was a bigger job than I foresaw, and I've had enough for now. It needs several things done to it; see Talk:Proofs of quadratic reciprocity for my opinion on this. Thanks! I should go back to writing blahtex and existing in the real world now... Dmharvey File:User dmharvey sig.png Talk 03:11, 6 November 2005 (UTC)

I've intervened to link to Gaussian period to use indirection on the quadratic field. IMO this can be an interesting page, but mainly to send the reader to other parts of the site. Charles Matthews 11:17, 6 November 2005 (UTC)

Category:Professors

Wikipedia:Categories for deletion/Log/2005 October 30 - the classification of academics needs a big clean-up. Please come and vote. Charles Matthews 11:56, 6 November 2005 (UTC)

Articles listed at AFD

• Dragan conjecture (AfD discussion)

Unfortunately, the automation makes it difficult to manually add articles such as this to the current activity list. Uncle G 00:53, 10 November 2005 (UTC)

• • Done (by placing {{math-stub}} in the article). It should be picked up, eventually. Arthur Rubin (talk) 01:14, 10 November 2005 (UTC)

Exclusive nor

See the talk page. Has anyone else heard of this, outside of MathWorld? Arthur Rubin (talk) 01:14, 10 November 2005 (UTC)

It would seem more logical to me to call this thing NXOR, per the suggestion at the talk page. XOR is probably a more familiar operation than NOR, and it is much easier to figure out what NXOR means: XOR goes 1 only on different inputs, so NXOR must go 1 only on the equal inputs. With XNOR one would probably have to draw a truth table. I checked that it is also equivalent to XAND, but people probably aren't used to working with XAND (I wasn't until I thought about it a bit). - Gauge 04:23, 10 November 2005 (UTC)

If it is true only on the same inputs (both true or both false), wouldn't the simplest and most logical name be SAME ? StuRat 11:46, 10 November 2005 (UTC)