Wikipedia talk:WikiProject Mathematics/Archive/2005/Sep-Oct

Games and determinacy

There's some fairly good work on WP about determinacy, but it's a bit haphazard. The axiom of determinacy article doesn't explain very clearly what a game or a strategy, or in particular a winning strategy, is. Winning strategy itself tries to be all things to all people. See my remarks in Talk:Axiom of determinacy and Talk:Winning strategy#Organizational questions for some thoughts with no clear conclusions, but I think a good starting place for trying to get the (nonexistent) category into better shape.

A couple of things of which I recently became aware have given me a little more sense of urgency about this. There's a Wikipedia:WikiProject Game theory, and they added winning strategy to it, which may be appropriate if that article should be ceded to the game theorists, and another written for the determinacy theorists (I'm thinking of writing a Game (set theory) article to subsume a whole bunch of these things, and change links from other articles to it). See my remarks in User talk:Kzollman#Game theory wikiproject.

Also there's apparently a category, Category:Combinatorial game theory, which deals with John Horton Conway type games.

I think this needs to be sorted out before it becomes an irretrievable mess. Would anyone be willing to work on a Wikipedia:WikiProject Determinacy?

---

On further reflection, I think the central article of the Determinacy category should just be called Determinacy. It's a much more general topic than Axiom of determinacy, which currently serves the purpose of a central reference point. You can see an outline at User:Trovatore/Sandbox/Determinacy. --Trovatore 01:45, 2 September 2005 (UTC)

So the article is far from finished, but there's enough there to put it in article space I think, and I've done so. --Trovatore 04:33, 2 September 2005 (UTC)

Axioms of an equation

I like the intent of this new stub, but I think this material really belongs in Elementary algebra. In a sense, the material is already there, but Elementary algebra seems to already assume that the reader is familiar with the semantics of "=". In other words, Elementary algebra is not quite as elementary as it could be. The new article Axioms of an equation appears to be attempting to fill the gap for, say, late primary or early secondary school students, by explaining more explicitly how to work with "=". Dmharvey File:User dmharvey sig.png Talk 02:57, 3 September 2005 (UTC)

We have equals sign and equality (mathematics), and various other pages on equations, no doubt. The Axioms page should really be re-styled as an easy introduction to those topics. Charles Matthews 09:00, 3 September 2005 (UTC)

Any quantity can be added to both sides. Some equations came from physics, and you can not add joules to meters. For algebraic equations, I would rephrase it to something like "validity of equation holds if you add same thing to both sides". Besides what's about adding two equations?(Igny)

Well, getting picky about that, any dimensionless quantity can be added to both sides of an equation in dimensionless form. But in algebra everything is dimensionless anyway. Adding two equations, ie add A = B and C = D to get A + C = B + D, should follow in two steps A + C = B + C and 'substituting equals for equals'. Charles Matthews 19:43, 3 September 2005 (UTC)

You can also raise both sides to a power, apply the logarithm on both sides, take the square root on both sides (be careful with the signs though)... this article isn't very complete, or could just be summed up in one line. --R.Koot 19:47, 3 September 2005 (UTC)

Hehe, which I've just done, but this stuff should really be merged somewhere. --MarSch 10:27, 5 September 2005 (UTC)

This discussion is already archived, but I want to report that I've merged the article into Equation. Melchoir 00:18, 27 November 2005 (UTC)

Length of a stub

Exactly how long should an article be before it stops being considered a stub? I removed [Digamma function]] and earlier (before Linas's major edit) Harmonic number from Category:Mathematics stubs, but I am not currently sure if articles such as Omega constant are still to be considered stubs or not. Scythe33 01:57, 4 September 2005 (UTC)

The criteria for "math-stubbiness" have baffled me for some time. I don't think it should purely be a question of length - I think the question of whether anything more can be said about the subject should be a criterion as well. But this inevitably becomes subjective. For example, I don't think quartic should be classified as a stub, even though it is very short. It defines the word in question and gives links to quartic equation and quartic function - I struggle to see what else could be added to make it non-stubby. But that is just my opinion. Does anyone have any objective criteria for determining stubbiness ? Gandalf61 10:25, September 4, 2005 (UTC)

Opinions differ (as always). I think that stubs are articles for which it is immediately obvious that they are missing something. An article with just a definition is a stub, an article with more than a definition probably not, an article with definition and some discussion on why this concept is important is never a stub. Some examples: Digamma function and Harmonic number were not stubs when Scythe33 removed the message and Omega constant is not a stub either; on the other hand Peetre's inequality, Egon Pearson and Cauchy surface are stubs. I consider Artin reciprocity and cylindrification as boundary cases; if forced to decide, I'd classify only the second as a stub. Of course, there are exceptions: quartic is not a stub because I consider it as a disambiguation page. You can use {{expansion}} for articles which are not stubs but still need expansion; you'd probably also need to specify what needs to be added. This is all just my opinion of course; I just had a discussion with an editor of a very different opinion. See also Wikipedia:Stub#Identifying a stub. And of course, don't start a fight about whether an article is a stub. -- Jitse Niesen (talk) 12:05, 4 September 2005 (UTC)

Category:Mathematics in India

I just discovered this new category as a subcategory in Category:Mathematics. While I have nothing against Indian mathematics, I wonder if it is wise to have such a category. Next thing we know is Category:Mathematics in United States followed by 100-200 more subcategories in Category:Mathematics. What do people think of this? Oleg Alexandrov 23:16, 5 September 2005 (UTC)

So my main objection to this category is this nonsense notion that an article shouldn't be both in a category and in a subcategory of that category. Following that ridiculous guideline, which it should be a high priority to delete ASAP, if an article is placed in Category:Mathematics in India, it ought to be removed from Category:Mathematics, and that would be silly. But the silly thing is the guideline, not the category. --Trovatore 05:32, 6 September 2005 (UTC)

Perhaps it would be better titled "Indian mathematics" instead of "Mathematics in India"; there may be use to put stuff like Vedic stuff in there. Dysprosia 08:46, 6 September 2005 (UTC)

I can imagine having a category for history of mathematics in India for Vedic stuff, and having this as subcategory of Category:History of mathematics. I struggle to see why present-day mathematics in India should be put in a separate category. Oleg's problem can be resolved by collecting Category:Mathematics in India, Category:Mathematics in United States, &c in something like Category:Mathematics by country. By the way, I quite like the guideline Trovatore mentions. -- Jitse Niesen (talk) 12:46, 6 September 2005 (UTC)

It seems to me that, if B is a subcategory of A, you may put an article in B for reasons involving a small piece of the article. If the rest of the article would by itself qualify as category A, then the article should stay in category A, otherwise not.

A slightly different issue is that a reader may be interested in seeing all articles in a category without having to know which subcategory to look in. If I browse Category:Mathematicians it's reasonable to expect to see John von Neumann without having to know that he was Hungarian or American or what century he worked in. --Trovatore 15:10, 6 September 2005 (UTC)Septentrionalis

The reason for the rule is that only 200 articles will be visible in a single category; Septentrionalis

Well, that should be changed. Let's get a feature request in. --Trovatore 22:07, 6 September 2005 (UTC)

Having tried to find things in large cats, I oppose the existence of larger ones. A cat of the thousand great mathematicians would be very slow to load and, by me, almost useless. Septentrionalis 22:23, 6 September 2005 (UTC)

The user interface needs some thought, to be sure. Possibly when a cat comes up very large, there should be some sort of page where the user decides what to do about it (view only subcats, split up by first letter, etc). But the classification question shouldn't be decided primarily by this sort of technical issue, much of which will change as servers get better, more users get broadband, etc. --Trovatore 22:32, 6 September 2005 (UTC)

and there are (thoughout history) a good many mathematicians even of v. Neumann's quality. Therefore Category:mathematicians includes by reference Category:American mathematicians Category:Hungarian mathematicians and Category:Game theorists and v. Neumann should be in all three of them.. Septentrionalis 21:46, 6 September 2005 (UTC)

As I see it, it is a guideline and not a hard rule, thus one may disregard it if one has a good reason. The first case mentioned by Trovatore could be a good reason; I'm less convinced by the second case. -- Jitse Niesen (talk) 22:18, 6 September 2005 (UTC)

Sure, I understand that it's not a hard rule. The problem is that too many editors follow it when they shouldn't. This is the reason, when I created Category:Determinacy, that I didn't make it a subcategory of Category:Set theory, even though it logically should be. I didn't want articles disappearing from the latter category just because they had some relevance to the former. --Trovatore 22:20, 6 September 2005 (UTC)

I asked the creator of this category to comment about it. Oleg Alexandrov 22:29, 6 September 2005 (UTC)

• I appreciate that this is a rather odd category. I created it to clear the main menu in Category:India - something which has already been done for the United States and United Kingdom, and should be done for all countries (the problem with clearing most articles from a national category, but leaving a few awkward cases is that it highlights a few minor articles, whereas if any articles are to be left in the main national menus, they should be the most important). I don't mind what you do with this category, so long as you don't put the contents directly into the main India category. CalJW 22:32, 6 September 2005 (UTC)

I see. I would support renaming this to Category:Indian mathematics (per Dysprosia). I will post this on CfD today. Oleg Alexandrov 15:14, 7 September 2005 (UTC)

I posted this for deletion or renaming at Wikipedia:Categories for_deletion/Log/2005_September 7#Category:Mathematics in_India. I myself voted to delete it as I don't see any special need for such a category. Oleg Alexandrov 19:26, 7 September 2005 (UTC)

Table of Lie algebras & groups

I am vaguely thinking of starting an insane and hopeless task, and that is to create a page listing low-dimensional, non-supersymmetric Lie groups and algebras, thier properties, isomorphisms, topologies, etc. I despair, because this seems like a collossal project trying to describe a hopelessly tangled web of inter-relationships. I was irked because what I really wanted was a list of (examples of) infranil manifolds. Any suggestions on how to minimize the pain and maximize the gain? linas 15:19, 6 September 2005 (UTC)

There is a start to this project at the list of simple Lie groups; this still needs some work in filling in the properties of these groups. This will not help much if you want to know about nilpotent groups. R.e.b. 20:31, 6 September 2005 (UTC)

There is also table of Lie groups which I somehow blindly didn't see at first. linas 04:37, 7 September 2005 (UTC)

10000 math articles

The drinks are on me!

According to Wikipedia:WikiProject Mathematics/Current activity there are now 10029 mathematics articles and mathematician biographies. Now, around 500 of them are redirects, a bunch are arguably more physics or related than math, and a rather good chunck are stubs. Still, this is something of a milestone.

This also makes me think (again) that with so many articles, there is just not enough manpower to even check articles for vandalism and style, not to talk about the mathematical correctness and if articles are coherent rather than just a bunch of text put together by different contributors.

This is probably a good moment to think of where we are, and wonder what the future will hold. Oleg Alexandrov 22:59, 6 September 2005 (UTC)

Well, so far the pessimists have been wrong - badly wrong - about WP in general. It's bigger, and it's better, and articles are generally longer and better written. And more people come to look, and some stay to help. About the only thing that gets worse is the proliferation of tags (including unresolved clean-up). Charles Matthews 16:23, 8 September 2005 (UTC)

I think we should raise a glass in celebration. Paul August ☎ 16:54, September 8, 2005 (UTC)

Indeed! An excellent idea! A bit of celebration is in order. Cheers! linas 23:45, 9 September 2005 (UTC)

I am glad to see that Wikipedia is exceeding my previous expectations. When it came to joining this project, the choice was between here and Planetmath. I chose to work here, primarily for the reason of having all of the information in one place, instead of scattered across multiple sites with conflicting standards. What if there were separate sites "PlanetLinguistics", "PlanetZoology", "PlanetBotany", etc? I personally cannot tolerate this kind of fragmentation. I hope that people on Planetmath begin to feel the same way, and move their work over to this site to avoid duplication of effort. By the way, maybe with 10,000 articles we now have the leverage to ask for some tools to create commutative diagrams on Wikipedia (again: I mean the kind you can edit along with the rest of the article, not just uploading images). Wishful thinking ;-) - Gauge 21:32, 9 September 2005 (UTC)

What did the non-abelian dalek say? Charles Matthews 21:42, 9 September 2005 (UTC)

(Umm, did Charles have a little bit too much to drink?) linas 23:45, 9 September 2005 (UTC)

What did the non-Abelian Dalek say? linas 23:47, 9 September 2005 (UTC)

He says: "DOES - NOT - COMMUTE … DOES - NOT - COMMUTE" Paul August ☎ 00:00, September 10, 2005 (UTC)

Have we sunk so low? (And shouldn't that be K9? Daleks are organic.)

• Q: What is purple and commutes?
• A: An abelian grape.
• (As told by non-mathematician) Q: What is purple and travels to work?

Hey, I didn't start this! Cheers indeed! --KSmrq^T 23:57, 13 September 2005 (UTC)

Gauge, are you aware of our PlanetMath Exchange project? Paul August ☎ 23:17, September 9, 2005 (UTC)

I am aware of the PlanetMath Exchange. You can guess in which direction I prefer to port articles. Btw: What do you call a commutative semigroup?

A: A carpool. :-) - Gauge 02:14, 14 September 2005 (UTC)

If you start copying articles from Wikipedia to PlanetMath, you will get a commutative diagram. Oleg Alexandrov 02:26, 14 September 2005 (UTC)

That reminds me I forgot to comment on Gauge's idea of a commutative diagram tool. I've yet to contribute in any significant way to the category theory articles, (ostensibly one of my areas of expertise) because I can't work up the gumption to create those diagrams by hand. I would really love such a tool. Paul August ☎ 03:20, 14 September 2005 (UTC)

What happens when you get kidnapped by the mathematical mafia? Dmharvey File:User dmharvey sig.png Talk 02:24, 14 September 2005 (UTC)

I give up. What does happen? Paul August ☎ 15:44, 14 September 2005 (UTC)

They make you an offer you can't understand. Dmharvey File:User dmharvey sig.png Talk 22:37, 18 September 2005 (UTC)

Why are fields immoral? --Trovatore 23:05, 18 September 2005 (UTC)

lemma moved to lemma (mathematics)

The article lemma was moved to lemma (mathematics), with the former being made into a disamibig. I disagree with the move, as the absolute majority of pages linking there are about the mathematical term. And even if one agrees with the move, one needs to disambiguate the links, and having them point to the correct destination. I asked the person who did the move to comment here. Other opinions welcome. Oleg Alexandrov 21:58, 8 September 2005 (UTC)

It should be moved back. This should be a case of "primary disabiguation". The primary meaning is the mathematical one. Paul August ☎ 00:26, September 9, 2005 (UTC)

I agree - the mathematical meaning is likely to remain primary. Charles Matthews 07:08, 9 September 2005 (UTC)

I think we should maybe tread a little lightly. It's true that a large majority of the links are mathematical, but that could reflect the vigor of the mathematics project, our 10k articles and all that. If it's an important term for linguists, maybe they should get equal time in the dab page. (Like Alice, I only said "if"--I don't know enough linguistics to know how important a term it is.) --Trovatore 03:16, 9 September 2005 (UTC)

And the OED has another set of definitions entirely: ranging for "motto" to "basic definition" in lexicography. Go comment on that talk page, but we should not be rash. Septentrionalis 03:46, 9 September 2005 (UTC)

As the editor who moved the article, my main concern was to fix the lemma page that looked like this at the time. So the main purpose was to create a disambig page. I decided to move the page because (as others here have already pointed out) experts in other disciplines link to lemma with the same confidence that they know what it means. If that article is a {{disamig}} page, that will be noticed and fixed by Wikipedia:Disambiguation pages with links (because internal links should not go to dab pages). — That said, I anticipated that some might not agree with the move I made, so I created direct links to lemma (linguistics), but didn't fix articles to point to lemma (mathematics). In other words, it's easily undone if you don't like it, but please bear in mind that the WikiProject Mathematics may be a tad biased, and it's going to be more expensive to fix if you wait until the other disciplines realize that they've been had :-). Algae 06:27, 9 September 2005 (UTC)

I think it is probably better this way. --MarSch 11:12, 9 September 2005 (UTC)

The best solution is to have the mathematical sense as the main article, and use a disambiguation on that page (ie. See Lemma (disambiguation) for other uses). The mathematical sense is far more commonly used than the linguistics sense. Dysprosia 11:45, 9 September 2005 (UTC)

Dysprosia's solution is in line with the official policy: Wikipedia:Disambiguation#Page naming. Oleg Alexandrov 15:22, 9 September 2005 (UTC)

Well, that's assuming that the mathematical meaning really is the primary one. Is it? It's certainly my primary meaning, but then I'm a mathematician. I think we should hear from some linguists about how much they really use the term. --Trovatore 16:01, 9 September 2005 (UTC)

By the way, I suggest that this discussion (that is, all the above text) be moved to, and continued at, Talk:Lemma. That's a better place for people to find it in the future, and it's "neutral ground" so to speak. --Trovatore 16:41, 9 September 2005 (UTC)

Copied to Talk:Lemma

This discussion should follow.Septentrionalis 17:24, 9 September 2005 (UTC)

Connected, connectivity, etc.

For several months, I have been doing occasional clean-up work on the pages related to connectedness, connectivity, etc. Things are still a little messy, but I am not sure what to do about some issues. In particular:

• The word "connected" has similar meanings in many fields of mathematics. Thus we have connected space, connected graph, and connected category. Do we want to consider "connected" as a mathematical term, independent of what field it is used in? Currently, there is a link to connected from List of mathematical topics (C). I consider this link to be somewhat inappropriate, since connected is a disambig that also points to nonmathematical usages. Should there be a page called "Connected (mathematics)"?
• "Connectivity" is a slippery word. I have heard a number of mathematicians use it as a synonym for "connectedness". In graph theory, of course, it has a very precise meaning; thus, we have connectivity (graph theory). In some semi-mathematical fields, like cellular automata, image processing, and robotics, it seems to be used in the sense of how cells arranged in a grid are considered to be adjacent to each other. Thus, automata researchers might speak of "4 connectivity" (I guess). The word is used in the article Image processing, and I think this is what it means there, but I am not sure. In any case, there is no good place for that link to go; currently, it goes to connected. What should we do about this? Should there be a page about this meaning of the word, and if so, what should it be called? Maybe "Connectivity (grid)"? Is there a better word than "grid"? I have heard of "lattice connectivity". Is this the same thing?

— Nowhither 00:01, 9 September 2005 (UTC)

In image processing on a square grid, a pixel is connected North, South, East, West (4-connected) to its neighbors. Many algorithms, such as flood fill (propagating a color to neighbors), offer the optional inclusion of the diagonal neighbors NE, SE, SW, NW (8-connected). --KSmrq^T 03:38, 2005 September 9 (UTC)

Connectedness should be developed, since we prefer nouns. Connectivity can imply things about the topology. Charles Matthews 07:11, 9 September 2005 (UTC)

Good point about "connectedness". On the other hand, I think there is still a need for the connected page to be a general disambiguation, since there are pages that would not fit well with "connectedness", for example, Connected (album).

So, how about this scheme:

• Connectedness will be an article, pitched at a relatively non-technical audience, giving an overview of mathematical uses of the word. It will refer to the more technical articles connected space, connected sum, connected graph, and connected category. At the top will be an italic note pointing at connected for non-mathematical usage.

• Connected will stay much as it is now: a general (mathematical & non-mathematical) diambig. It will include links to connected space, connected graph, etc., just as it does now, and it will also link to connectedness.

Connectivity is still a sticky issue. User:Kku has just made it a disambig, with the former content at connectivity (computer science). I agree that this is an improvement, but I am not sure if it is optimal.

I still think there needs to be an article about the definition of connectivity as it is used in image processing, cellular automata (?), and possibly robotics, parallel computing, etc. But I still do not know what to call it, or which of these fields use the same definition.

— Nowhither 00:30, 10 September 2005 (UTC)

News flash: I wrote the connectedness article. See New "connectedness" article, below. — Nowhither 03:13, 12 September 2005 (UTC)

Omega?

Do we have a specific math article on Omega? The specific one that states that mathematics can't be strung together and that discoveries are just luck? It also states that its goal is to try and find the halting possibility of a computer when faced with an infinite answer.

Omega doesn't "say" that; it's just a number. But Wikipedia does have an article on it: Chaitin's constant. — Nowhither 00:11, 10 September 2005 (UTC)

Math in the dock

See Wikipedia:Village_pump (miscellaneous)#Riemann_zeta_function. Oleg Alexandrov 03:56, 11 September 2005 (UTC)

At analytic continuation, some decent diagrams would help. For example of overlapping circles, showing how analytic continuation by re-expanding a power series can gain a fingernail-shaped area of definition. Charles Matthews 06:30, 11 September 2005 (UTC)

This kind of discussion gets my goat. It's absolutely ridiculous that people without prior experience in a field read an article about a topic in that field and then complain that it's the article's fault that they don't understand it. I know little to nothing about quantum mechanics or geology for example, but I wouldn't complain if I didn't understand the spin (physics) article or the Quantum Hall effect article. Wikipedia articles are not self-contained instructional works. Sure, an article can try and explain as much as reasonably possible for someone with some assumed knowledge, but the important fact remains that Wikipedia is a reference work and not an instructional work (compare Wikibooks). This is doubly inappropriate for mathematics works, where the very nature of the topic depends on having assumed knowledge to understand deeper and more complex work. Dysprosia 07:40, 11 September 2005 (UTC)

I'm not exactly fond of the comment or commentator. There aren't many mathematical articles where the exposition is perfect; nor is the coverage anything like complete in 'core' topics (whatever those are). So the chances are that matters can be improved. Charles Matthews 08:26, 11 September 2005 (UTC)

Oh, absolutely, I'm not disagreeing that pages can be improved -- many of the math articles could do with improvement from what I've seen, but it's the sort of "I don't understand the article, so it must be a bad article" attitude that irritates me. Dysprosia 09:00, 11 September 2005 (UTC)

As one of the laypeople who responded to that "survey", I'd like to chip in. Please understand that I mean this as constructive criticism and not as bashing or saying that you guys are going about things in the wrong way -- on the contrary: I'm impressed that we've got such thorough coverage of these topics in the first place.

Of course not every math article is going to be 100% comprehensible to the layperson. On the other hand, it is possible for every math article to make clear to the layperson why its subject is important. Not everyone who reads that article will be a mathematician. A large number will presumably be people who were reading about something else that mentioned the Riemann Zeta Function and want to get at least a basic sense of why the Riemann Zeta Function is such a big deal.

I've got a 4-year college degree, including two years of math: so probably a stronger math background than 90% of Americans -- and I still get lost in the first two sentences of most math articles on Wikipedia. Anyone in this wikiproject knows more math than I, and that's necessary for this project to be possible. On the other hand, it may make it more difficult to see things from the perspective of someone who doesn't already have a firm grasp of the concepts you're discussing.

If a layperson doesn't understand an article, it doesn't mean it's a bad article. It may, however, be an indicator that there are areas of the articel that could still be improved. I think it would be possible to improve the comprehensibility of many of the math and science articles on this encyclopedia. If I knew anything about the subjects, I'd work on it myself -- as it is, I'd be happy to give any assistance I can to anyone in this wikiproject who is interested in attempting to do so. -- Avocado 14:54, September 11, 2005 (UTC)

I think both Charles, Avocado, and Dysprosia have very good points. A great many math articles are written for an audience which knows at least as much as the person writing the article. In many cases there is no motivation, no intuitive explanation, no gradual development from easy to complex, no pictures, no examples, and the list can go on. If one would teach in college with the same attitude, one would get quickly fired (well, ideally :)

However, there is only that far one can go in making a topic acessible. For example consider the meromorphic function article, which now has a {{technical}} template slapped upon. If you know anything about the complex plane and about functions, you should understand from the examples and the picture that a meromorphic function is roughly a fraction of two functions, with the denominator going bad every now and then. However, if you say that you don't understand the statement:

In complex analysis, a meromorphic function on an open subset D of the complex plane is a function that is holomorphic on all D except a set of isolated points, which are poles for the function.

then that's your fault. You cannot possibly understand meromorphic functions unless you know what holomorphic functions and poles are. Oleg Alexandrov 17:30, 11 September 2005 (UTC)

"A meromorphic function is roughly a fraction of two functions, with the denominator going bad every now and then."

I understand that that phrase is probably an oversimplification and not 100% accurate, but it makes it a million times more clear to me what a meromorphic function is, even without my knowing much of anything about the complex plane. A few more plain-english explanations might be helpful. I don't need to understand meromorphic functions any more than I need to understand the internal workings of my cellphone's AC adapter, but having an idea of what they are or what makes them interesting is possible. -- Avocado 17:54, September 11, 2005 (UTC)

suggestion

Please note that there are now 10,000 math articles on WP (making it as large as Wolfram's mathworld, it seems), and that maybe 80% of these articles require at least a math major, and many require considerable post-graduate studies. Its impossible to make these 80% understandable to non-mathematicians; even math professors trained in one field might not understand articles written in another field. So what can we do?

I suggest a new category, Category:Overview of mathematics, that would contain articles from any branch of math, but with the requirement that these articles be comprehensible (and enjoyable) by anyone with no more than a year or two of college math education. For example, what's knot theory and why would anyone care? How about soap bubbles as minimal surfaces? Of course chaos belongs there, as does gravity, and something along the lines of Riemann zeta revealed. Furthermore, these articles could be written as "educational trampolines", starting at the most basic level, e.g. torus, and rocketing the reader into very advanced topics (the torus opens the door to things like Albanese variety) if the reader is diligent enough. In some sense, Category:Overview of mathematics would be the math version of "featured articles", with the bar set maybe only a little bit lower. linas 17:39, 11 September 2005 (UTC)

(Corollary: "too technical" labels will be unceremoniously stripped from articles that are not in Category:Overview of mathematics, e.g. the meromorphic function article.) linas 17:48, 11 September 2005 (UTC)

It sounds good to me. I do think we should be careful that this solution not become a way to remove all pressures to add intuition and motivation, though. In my own case, I know that my Prewellordering article is guilty of the offenses Oleg mentions, particularly the Prewellordering property section.

The other side of that is that it is better to have something than nothing, I think. Prewellordering needs to be motivated, but for me at the moment finishing the Determinacy article is a higher priority, and I do have non-Wikipedia tasks as well. In the mean time I think it is better that there be an unmotivated article on the prewellordering property than none at all. --Trovatore 18:00, 11 September 2005 (UTC)

In theory it would be possible for a high school student to learn linear algebra from the articles on wikipedia, in practice this wouldn;t work, because s/he wouldn't know were to start and in what order to read the articles. So we could create an article called learning linear algebra. On the articles we could slap some prerequisites such as linear algebra and comples analysis which link to those articles. (Unsigned comment by User:R.Koot 18:02, 11 September 2005)

No. Wikipedia is a reference work, not an educational one. Learning mathematics from an encyclopedia would be extremely difficult, because the encyclopedia material is not geared for learning, it is geared to be a reference work. Wikibooks is for educational material. Dysprosia 23:20, 11 September 2005 (UTC)

I can find nothing above with which I disagree ;-) Per Euclid, There is no royal road. But we need to keep trying to make the road as short and smooth as possible. Paul August ☎ 18:53, September 11, 2005 (UTC)

Having math overview articles aimed somewhat lower than the normal math articles is a good idea. My suggested "connectedness" article (see "Connected, connectivity, etc." above) could be one of these. However, I must agree with Dysprosia, that educational works belong in Wikibooks. In fact, the linear algebra tutorial suggested by R.Koot has already been started there; see wikibooks:Linear algebra. — Nowhither 00:31, 12 September 2005 (UTC)

I may as well throw in my 2 cents: I have been developing an idea that certain topics in mathematics have a certain intrinsic minimum complexity which cannot be reduced in any exposition. In this sense, one can either present the material as simply as possible while retaining accurate content, or lose accuracy for the sake of readability. I agree with Linas that the current Riemann zeta function article may in fact be too simple rather than not simple enough; an accurate description of the zeta function and its properties is complicated business, no matter how you present it. I tend to write articles as reference works aimed at graduate students and researchers. I recommend (to those who are interested) the creation of an article Riemann zeta function (overview) or something similar for those who want a less technical exposition. There is certainly room for both perspectives (research-oriented and pedagogical).

Also some nitpicks that I have with the current article:

1. The Easier proof for the layperson section really belongs in another article if we are to make this article the more technical one. The technical proof is shorter and more elegant.
2. The "Importance of the zeros" section needs elaboration and appears in an odd place (before "basic properties"?). It should be moved further down into the article.
3. I wonder if the physics applications of the Riemann zeta should have its own separate article? I have a feeling that there are enough applications just in physics to warrant such an article...
4. If this article does become the more technical one, we should place a warning at the top pointing readers to the "easier" version as well.

- Gauge 02:34, 12 September 2005 (UTC)

So what's the plan?

I like Linas' suggestion at least in principle (with the caveat that it not become an excuse to avoid adding motivation to articles). I'd suggest further that there be a uniform naming scheme for the simpler articles, say Foo (introduction) or Foo (elementary) for the beginners' version of Foo. But it does seem like something of an "unfunded mandate"; I'm not personally volunteering to produce these articles for the hundreds if not thousands of topics that'd need them. Any further thoughts? I hate to see the matter just dropped, without a clear decision. --Trovatore 20:13, 13 September 2005 (UTC)

One more idea

As a less radical measure, how about updating just the introductions of some of the math articles to be more accessible. For instance, something to the effect of:

The Riemann Zeta Function is a mathematical function discovered by Whatever-his-first-name-is Riemann in 1822. It is important in number theory because it demonstrates some property of prime numbers, as was proven in 1903 by whoever.

< template of some sort >

What follows is a technical discussion of the properties of the Riemann Zeta Function. This discussion assumes familiarity with meromorphic functions, the Euler Product Formula, basic forcing, and whatever else.

< / end template >

-- Avocado 21:29, 13 September 2005 (UTC)

It's all a question of perspective

From the back-jacket information for Itay Neeman's book on The Determinacy of Long Games, which I will likely cite:

The book is largely self-contained. Only graduate level knowledge of modern techniques in large cardinals and basic forcing is assumed.

--Trovatore 18:41, 11 September 2005 (UTC)

That's a good one! Only very basic forcing is assumed, right? As far as I am concerned it means that I will have no clue whatsoever about the very first section in the book. :) Oleg Alexandrov 23:04, 11 September 2005 (UTC)

That's cute. FWIW, I know a Ph.D. student who did his dissertation on forcing. Apparently the first question at his defence was, "So, what's 'forcing'?" He said he immediately knew he was going to pass. — Nowhither 03:00, 12 September 2005 (UTC)

New "connectedness" article

As suggested above in a couple of places, I have written a new article: connectedness. This is supposed to be an overview of mathematical uses of the term (and similar words), written at a somewhat lower level than most mathematical articles. I would be interested in hearing what people think about:

• Is this a good article to have?
• Is it written at a low/high enough level?
• Should there be other similar articles?

By the way, I also put a note linking to the new article in connected, which is a general (non-mathematical) disambig. And I removed "connected" from the List of mathematical topics (C) and replaced it with "connectedness". And ... I'm still wondering what to do with connectivity.

— Nowhither 03:12, 12 September 2005 (UTC)

Looks useful to me; but, like most readers at this page, I cannot tell what it would look like to a non-mathematician. You should take this question to the Village Pump, or, despite the fact you actually want cmments, WP:RfC

Was Bertrand Russell Welsh?

And, speaking of RfC, one of the topics there is:

Was Bertrand Russell Welsh and does he belong in Welsh Wikipedia:categories? (He was born in Monmouthshire, and lived there until his parents died - when he was four.)

I'm not making this up; if anyone has an opinion on the matter (I did) do go share it with Talk:Bertrand Russell; maybe we can drown out the various contending nationalisms. Septentrionalis 22:46, 12 September 2005 (UTC)

How important is a list of publications?

Currently, List of publications in mathematics has at the bottom 31 mathematics categories. Some explanation for that is here. The whole thing seeems to be an effort by APH as part of Wikipedia:WikiProject Science pearls. I truly doubt that there is any article under the wiki Sun so important as to be included in that many categories. Oleg Alexandrov 06:24, 13 September 2005 (UTC)

I agree; this is an inherently PoV effort to make a list do the work of a category. Unmaintainable, controversial, naturally incomplete - and if completed, useless. AfD? Septentrionalis 03:28, 14 September 2005 (UTC)

AfD, seems a bit drastic. I don't think I could support that. Lists have several well discussed advantages over categories, for example they can be annotated, as this one is. (By the way just out of curiosity, a show of hands, how many people know that VfD has been renamed?) Paul August ☎ 04:49, 14 September 2005 (UTC)

I don't want that artilcle deleted either, just put in two to three relevant categories and link to it from other places. Oleg Alexandrov 04:56, 14 September 2005 (UTC)

I know what you are implying when mentioning AfD. I agree with renaming the VfD but I think the decision was taken very fast and without public consultation. Uncle G, can you clarify us in here? (Uncle G's bot did the move.) Oleg Alexandrov 04:56, 14 September 2005 (UTC)

I sort of agree with Paul the list could be valuable. Right now IMO it's overly weighted to publications of historical importance; what's really more needed is a bibliography of reference works and textbooks. Maybe with BibTeX entries too? That'd be great.

On the other hand the book reviews that make up much of the content could be problematic. I just wrote one today for Kunen's set theory book, but it occurs to me that a book review is almost on its face original research, or at least original journalism. Still, WP has lots of 'em. --Trovatore 04:58, 14 September 2005 (UTC)

I'd like to respond to the ideas above. First, I'd like to point out that I also think that the use of a list is problematic. I see it as an initial phase before creating an article for every publication and connecting them using categories (See more details at the project description). Note that in the next phase the problem that bothers Oleg will be solved too. An article about logic won't be in the topology category. The description of the publication shouldn't be an original research. Most of the times, something quite similar to the publication abstract will do. BibTeX entries is a great idea. APH 05:37, 14 September 2005 (UTC)

Isn't there a larger issue here? What we have on List of publications in mathematics, especially near the bottom, is a list of papers. But mathematical research papers are being published at a rate of something like 100 per day (rough estimate — and that's only the ones that make it into Math Reviews). It is ridiculous to expect to sort through these and point out those that ought to be listed, whether in a big list, as separate articles in a category, or whatever. The problem with this page is not misuse of categories, or anything like that, but that it is aimed at an impossible task, the magnitude of which boggles the mind. The page very badly needs a more focused purpose. — Nowhither 01:16, 16 September 2005 (UTC)

Science pearls

Hello, Please notice this project. I hope that the List of publications in mathematics, List of publications in statistics and List of publications in computer science will be adopted by the mathematics project. Thanks,APH 06:48, 13 September 2005 (UTC)

Converse

It seems to me that the article on logical converse is incomplete. It has the schoolbook definition of the converse, which is that the converse of a statement of the form (A → B) is the statement (B → A). But I think that "converse", as the term is used by mathematicians, is actually a more subtle and complex concept. I've put some simple examples at Talk:Converse (logic).

I think that if we actually look at examples, we'll find all sorts of different forms that the converse can take, and that this information should be incorporated into the Converse article.

I hope people will assist me in this. -- Dominus 13:32, 14 September 2005 (UTC)

Boolean algebra, redux

Once again someone has been trying to rewrite the Boolean algebra article based on the preconception that it's about the logical calculus sometimes called "Boolean algebra". I'm afraid I got into a mini-editwar with him; he got tired of it and went to write his own article called Boolean algebra (basic concepts). I think he wants to rename Boolean algebra to Boolean algebra (complex theory).

I think there should be two articles, but I see dark clouds on the horizon with this editor. He doesn't show any signs of wanting to believe me that a Boolean algebra is something like a group or ring, rather than a "complex" version of what he thinks of as "Boolean algebra" as a mass noun. I'm worried that he'll try to incorporate material about the algebraic-structure notion into his "basic" article, which will only confuse the issue. I could use some help here, guys.... --Trovatore 21:26, 14 September 2005 (UTC)

At the risk of being contrary, the first sentence of Boolean algebra suggests to me that it would rather be in an article called Boolean algebras.Hv

Well, see, here you run into a Wikipedia convention. All such articles have singular titles. There's an article called orthogonal polynomials, but that's only because there's no such thing as an "orthogonal polynomial" in isolation. --Trovatore 23:51, 14 September 2005 (UTC)

Certainly the current link to Binary numeral system is a poor substitute for an article that would talk about the (singular) Boolean algebra that high school mathematicians and computer scientists have to deal with. Hv 23:47, 14 September 2005 (UTC)

Yes, that's true; that article needs to be written. If we could only agree on what it should be called.... --Trovatore 23:51, 14 September 2005 (UTC)

My five cents (yeah there's been some inflation): if we have a decent article on Boolean algebra as envisaged by StuRat et al (i.e. currently named "basic concepts"), then that should get primary status as Boolean algebra, simply because it's the one more likely to be searched for by a general audience; and there should be a dab notice on that pointing to something like Boolean algebra (algebraic structure). Dmharvey File:User dmharvey sig.png Talk 23:57, 14 September 2005 (UTC)

Hm, wouldn't be the solution if I were God. But if it keeps this problem from recurring I s'pose I can live with it. Still leaves open the question of what should really go in the article, though. How is it different from propositional calculus? Just by adding Boolean search terms & such? --Trovatore 01:07, 15 September 2005 (UTC)

I think the solution is to merge Boolean algebra (basic concepts) into Boolean logic; the latter is not very good, and is just shy of being a stub. Septentrionalis 14:48, 15 September 2005 (UTC)

I don't think that's a natural fit. Boolean logic is about a correction to Aristotelean logic, which was overly complicated because it didn't allow propositions to be vacuously true. So it doesn't really make sense to talk about Boolean logic except when you also talk about Aristotelean logic, and we have no need to to that for this subject. --Trovatore 15:00, 15 September 2005 (UTC)

I think both things are and should be called "Boolean algebra" with at least one being of the form "Boolean algebra ( … )". I suggest that we set aside for the moment which, if either, should simply be called "Boolean algebra". Let's assume for the moment that both articles need parenthetical disambiguation, and try to decide what they should be.

• For the 6-tuple one (A, +, ·, ~, 0, 1) should it be:

• mathematical structure?
• algebraic structure?

I'm not completely happy with this one because I also (perhaps not alltogether correctly) think of this structure as an order theoretic, a set theoretic and a logical structure as well.

• structure?
• object?

• For the the article about, in DmHarvey words, " the art of manipulating truth values and logical connectives", should it be:

• methodology?
• logic?

Of the two I guess I like this one best.

(By the way this looks like a good online reference for this article.)

Paul August ☎ 22:02, 15 September 2005 (UTC)

Yeah, I also have noticed the problem with "algebraic structure"; e.g. one of the properties of BA's that should be addressed in the article is completeness, which is not definable algebraically. OTOH that's a bit of a nit; it's not as though anyone would object to addressing completeness in an article called "Boolean algebra (algebraic structure)". I agree "logic" is better than "methodology" for the other concept but I'm not entirely happy with it. --Trovatore 23:13, 15 September 2005 (UTC)

How about cutting the Gordian knot (for the first concept) with Boolean algebra (structure)? --Trovatore 18:58, 18 September 2005 (UTC)

Wow this is hard. I don't like Boolean algebra (structure) because "structure" is too vague -- it sounds like it means "structural aspects of Boolean algebra", like Economy of China (structure). I liked one of the earlier suggestions: Boolean algebras, although this might be against WP naming conventions (???). Perhaps Boolean algebra (mathematical entity) or Boolean algebra (set with operations)? Arrgggh. Dmharvey File:User dmharvey sig.png Talk 19:48, 18 September 2005 (UTC)

The situation's not that bad--we don't have to go suggesting spiritual emanations, which is what "entity" makes me think of. I'm ok with either "mathematical structure" or "algebraic structure". I just thought maybe it could be made less wordy and more inclusive by dropping the adjective. --Trovatore 19:57, 18 September 2005 (UTC)

I like the "Boolean algebras" name. In cases where the singular has come to mean one thing and the plural something entirely different (maybe "datum" and "data" or "Earth" and "earths" would be good examples), I think it should be permissable to use a plural name. StuRat 20:00, 18 September 2005 (UTC)

I see that one of Paul's suggestions I overlooked was Boolean algebra (object). That's not bad, though I think I still prefer "mathematical structure". I don't like the plural because it (1) suggests that these things are somehow "alternative versions of Boolean algebra" and (2) is not in line with the naming given to other structures, like Group (mathematics). --Trovatore 20:07, 18 September 2005 (UTC)

If we are to use strictly singular, shouldn't that have been Group (mathematic) ? StuRat 20:31, 18 September 2005 (UTC)

Perhaps Boolean algebra (mathematical object)?. Dmharvey File:User dmharvey sig.png Talk 22:36, 18 September 2005 (UTC)

I could live with that. I prefer "mathematical structure", though. --Trovatore 23:13, 18 September 2005 (UTC)

Yep, "mathematical structure" works for me too. Dmharvey File:User dmharvey sig.png Talk 23:22, 18 September 2005 (UTC)

Indicial calculus

Indicial Calculus claims that it is "the calculus used to extract root indices of order x, where x is an element of a Galois splitting field for a given polynomial equation $P$ of ductivity $D[P,0]=0$." Does this ring a bell to somebody? The reference to "Little Bride Bonnie (1859-1941), a German mathematician known for early work in group theory" made me suspicious, and a quick search on MathSciNet and Google didn't yield any results. -- Jitse Niesen (talk) 21:18, 15 September 2005 (UTC)

The intro, as phrased, is nonsense: whatever a root index is, its order shoulc be an ordinal, not an element of a Galois field. Constructing a cube of side e (next paragraph) is trivially equivalent to constructing a segment of length e. I've never heard of ductivity, either. Septentrionalis 01:21, 16 September 2005 (UTC)

A mathematician Little Bride Bonnie is mentioned there. From what I know, Bonnie is a girl's name. Equivalently then, the name of this German mathematician is Little Bride Mary if you wish. BJAODN. Oleg Alexandrov 02:06, 16 September 2005 (UTC)

No paper by Hinkle is in Jahrbuch über der Fortschritte der Mathematik for 1899-1901. Hoax. AfD, IMO. Septentrionalis 05:00, 16 September 2005 (UTC)

Bonnie (also spelled bonny) means pretty, as in "my bonnie lass" and brides are often referred to as bonnie (search Google for "bonnie bride" or "bonny bride"). Paul August ☎ 05:47, 16 September 2005 (UTC)

I did some digging and posted my impressions on the talk page. Especially, the index calculus algorithm is frequently cited in cryptography. Given the existence of that page, even if Indicial Calculus is meant to be legitimate its page should not exist. --KSmrq^T 11:49, 16 September 2005 (UTC)

I decided to replace the article by a redirect to cyclic group, which is where index calculus also redirects to (KSmrq found this out, thanks). Saves a trip to AfD. -- Jitse Niesen (talk) 14:39, 16 September 2005 (UTC)

List of mathworld's math articles

See discussion at Wikipedia talk:Requested articles/mathematics#MathWorld?. Comments welcome. Oleg Alexandrov 03:20, 16 September 2005 (UTC)

Is a high school math teacher who got a prize for undergraduate paper notable enough?

... We will find out. Wikipedia:Articles for deletion/Mark Schmitt. Oleg Alexandrov 02:01, 17 September 2005 (UTC)

Note for Lie algebra specialists

Anybody heard of the "corank" of a Lie algebra? An anon replaced "rank" with "corank" at Affine Lie algebra, and I don't know if that's correct or not. Oleg Alexandrov 16:06, 18 September 2005 (UTC)

I'm watching that one, I think that's rigt, that's what makes it affine. But not sure; I was going to read on the topic (quantum groups) this summer, but got distracted. Maybe next summer. Its a pretty advanced topic, mostly just string theorists live there. linas 04:41, 20 September 2005 (UTC)

The "corank" here refers to the generalized Cartan matrix, the dimension of its null space. However, neither choice seems to agree with the definition already in place at the end of the Kac-Moody algebra page. The symmetric factor of the matrix is there required to be positive semidefinite, which does not place such a stringent restriction on either rank or corank. Even knowing almost nothing about the topics it appears that something is amiss. If someone wants to dig further, a standard reference book seems to be Victor G. Kac's Infinite-Dimensional Lie Algebras, 3/e, CUP 1990, ISBN 0521372151 (paperback: ISBN 0521466938). Or ask your friendly neighborhood string theorist. --KSmrq^T 06:53, 20 September 2005 (UTC)

Check those links

Just a reminder that when you've guessed the name of an article you're linking to, and it comes up blue and you save your edit, it's worth clicking through to those links and seeing if they say something sensible and relevant to the meaning you have in mind.

I happened across a page called complete Boolean algebra that had some trivial nonsense in it, nothing to do with CBAs, yet it was linked to from complete lattice.

Another possibility is that the link from "complete lattice" was originally red, and then someone came along and filled in the incorrect "complete Boolean algebra" page. To protect against this sort of thing, click through to your redlinks and add them to your watchlist (yes, this works). --Trovatore 17:32, 19 September 2005 (UTC)

One can also check Wikipedia:WikiProject Mathematics/Current activity for incoming stuff. Oleg Alexandrov 04:35, 20 September 2005 (UTC)

What is an Isometry?

Our articles Isometry and Metric space have different definitions of isometry. The former requires an isometry to be onto, the latter does not. There is a discussion at Talk:Metric_space#Isometry, about which is more standard, and what we should do about it. Please share your thoughts there. Thanks Paul August ☎ 16:38, 22 September 2005 (UTC)

Unicode in math articles

The bot User talk:Curpsbot-unicodify has started crawling the math pages and converting html greek characters, such as γ, into glyphs that are hard to work with (although they render the same way). I don't think this is a good idea for math formulas and math expressions, although I support it for the other cases (people/place names, etc.) I'd like to see some sort of majority consensus developed on this, for or against, at User talk:Curpsbot-unicodify. linas 14:56, 24 September 2005 (UTC)

Sorry, I don't see the problem, can you please elaborate?

You aren't forced to enter Unicode characters, you can still use the HTML entities, if you don't have keyboard access to the special characters. And the Curpsbot-converted characters look in the edit field the same as both style of characters look in the article.

Pjacobi 17:53, 24 September 2005 (UTC)

That's a WYSIWAG approach--"what you see is all you get". For mathematics it's better to preserve the meaning of symbols in the source code, not just their appearance. HTML doesn't really do that very well, but it's better than Unicode. --Trovatore 18:04, 24 September 2005 (UTC)

WYSIWYG: Screen readers for the blind, last I checked, handled &gamma; a lot better than unicode. Nahaj 18:16, 24 September 2005 (UTC)

I added a comment to the effect that if we had replaced such strings in the editable code as "&gamma;" by the more accurate "<math>\gamma</math>", then there wouldn't be a problem. -- Arthur Rubin 21:40, 24 September 2005 (UTC)

If screen readers really do have trouble with unicode, then I will oppose conversion to it. - Gauge 00:09, 25 September 2005 (UTC)

As I understand it, it isn't Unicode per say that is the problem... It is a matter of how many characters (of the many thousands) have speakable names listed in the screen reader's tables. Someone should check this... my information is a few years old. Nahaj 01:40, 25 September 2005 (UTC)

The age of my information may be moot. Many handicapped folk are running older software for financial reasons. Nahaj 21:38, 30 September 2005 (UTC)

First of all, the bot has not started systematically crawling the math pages. It only happened to crawl the Wess-Zumino-Witten model article because that was on a list of requested articles sent to me by User:Beland, and he only wanted that article processed because it contained two spaces instead of one in a [[Riemann  sphere]] link (the bot also does this, although its main function is Unicode conversion). The bot is mostly concentrating on eastern European pages and such at the moment (for instance, see this edit to Russian grammar).

For the time being, I have edited the bot code to skip any page that contains a <math> tag. It might revisit them later with a flag set to avoid processing Greek letters. In the long run, however, you might be better off to use <math>\gamma</math> instead of &gamma; as Arthur Rubin suggests, because the visual appearance of $\gamma$ and γ is usually quite different, and if you're arguing that the visual appearance of γ is confusing in the editor window then it's surely equally confusing in the reader window (displayed browser page). Or perhaps even more confusing, since readers are sometimes less sophisticated than editors and the two different-looking gammas might be mistaken for different symbols.

By the way, I presume you folks know that &epsilon; &phi; (ε,φ) are not the same things as \epsilon \phi ($\epsilon ,\phi$ or ε,ϕ)? According to the TeX book and Unicode.org respectively, the latter are supposed to be "lunar" epsilon and "unbroken-circle" phi with bar extending above the circle, although the glyphs used in various fonts may render them identically (as seems to be the case under Windows XP, for instance). See [1] and compare U+03B5 vs. U+03F5 and U+03C6 vs. U+03D5. This is another argument against using HTML entities when TeX math symbols are intended. -- Curps 20:21, 25 September 2005 (UTC)

PS, also, &asymp; and \asymp refer to entirely unrelated symbols (a naming issue), although the <math> tag doesn't seem to recognize \asymp.

Warning: ϕ (the unicode &#x3d5) does not display, at least on this computer, although all the rest of Curps' post does, including \phi. (Neat trick with the &amp; though.) Also, the <math> epsilon and the unicode epsilon(&#x3b5;) are not identical; the latter is almost identical to &epsilon. (This is a library machine using Windows, so I can't comment on what else it's doing.) Septentrionalis 01:06, 26 September 2005 (UTC)

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 [2]. --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)

I agree that having the formula right there is better than having to follow links to read the missing symbols, but still think that's infinitely better than just having boxes with no links at all. The underline problem is a good pt, but I think they are usually blue underlines to distinguish them from regular black text, so that might help some. Another idea is to have a pic of the entire formula, not just each symbol in the formula. StuRat 05:15, 22 November 2005 (UTC)

As my preferences are configured, they show the underline. And mine are pretty default except that I added MathML when possible, which I don't think affects this issue. It's probably not a good idea to assume people won't see the underlines. --Trovatore 05:20, 22 November 2005 (UTC)

And are they blue underlines that can be distinguished from regular black text ? StuRat 05:24, 22 November 2005 (UTC)

The underlines are blue, but so are the characters. It is not obvious that they are not part of the symbol. --Trovatore 13:42, 22 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. [3]), although the names of the symbols seem to suggest that the bar should be at the side of the normal subgroup ([4], [5]). 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)

I feel quite bad with Boolean related articles. It appears that the special case of algebraic structures with 2 elements makes everything unclear: you may define a boolean ring, a boolean algebra (which should assume scalar multiplication, even with scalar in {0,1}), post algebra (there you use $\oplus$ (i.e. XOR, i.e. + modulo 2) instead of $<\cup$ thus building a field), boolean logic axioms, order on 0 and 1, aso. From there you can extend to boolean polynomial algebra, boolean logic, boolean lattices, and if you choose + mod 2, you can go to vector fields and end into algebraic graph theory. All of these things are, in my personal opinion, different as the "main" property which is used in an algebraic structure are niether the particular elements or operations which are used, but the axiomatic which is assumed; even if the elements and the operations are the same, the mathematical context is given by the axiomatic, which will usually allow more general reasonning. pom 18:27, 26 November 2005 (UTC)