Wikipedia talk:WikiProject Mathematics/Archive/2006/Apr

Parametric coords

Hi all. I saw there wasn't any article on parametric coords. I am willing to create one, if needed. However, since it might be the same thing as curvilinear coordinates, I've just put in a redirect for now. I've asked the question on Talk:Curvilinear coordinates, but so far nobody can tell me if they are identical, or just related, topics. Please take a look and post your conclusions at that talk page. StuRat 21:24, 1 April 2006 (UTC)

If someone does write the article, please don't use that name, but spell "coordinates" out in full. Ryan Reich 22:14, 1 April 2006 (UTC)

Absolutely. I do like to add redirects from short names to full names, though. This allows users to enter shorter words like "coords", "lab", "gym", etc., which are both more convenient and less likely to contain spelling errors. StuRat 02:31, 2 April 2006 (UTC)

Parametric coordinates really require a parameterisation, for example a parameterised curve or surface. For that reason I've now made parametric coords redirect to parametric equation. --Salix alba (talk) 09:40, 2 April 2006 (UTC)

Yes, but not all parametric equations describe a parametric curve or surface. Therefore I feel that an article specific to this application of parametric equations is justified. StuRat 02:29, 3 April 2006 (UTC)

Direct logic

Could someone take a look at Direct logic? I see some potential problems with this, given who the author is. —Ruud 16:01, 2 April 2006 (UTC)

IMHO, it looks like this is original research and doesn't belong. How does one tag an article to indicate as much?Lunch 18:42, 3 April 2006 (UTC)

Petition on WAREL's talk page

For background, see Wikipedia talk:WikiProject Mathematics#Statistics on User:WAREL several sections above.

Fresh out of his most recent 48 hours block, WAREL/DYLAN has been engaging in edit wars at field (mathematics) and division ring, moving, incorrectly, interwiki links from the former to the latter, see WAREL's contribs and DYLAN's contribs.

I wrote a petition on the top of his talk page asking him to stop revert wars, as this has been going for too long. If you are familiar with WAREL's edit warrior activity, and think that it's a bad thing, you may help by signing the petition. I doubt WAREL/DYLAN will learn anything from it, but it may give more legitimacy to future attempts at blocking him for disruption. Oleg Alexandrov (talk) 17:46, 3 April 2006 (UTC)

I've tried to figure out what this editor's motivation could possibly be, and my current working hypothesis is that he's engaged in a "destructive testing" experiment to figure out exactly how much it's possible to get away with before drawing blocks/RfC/permanent ban. Otherwise it's hard to understand why he keeps pushing just inside the edge of written rules, trying to get trivial changes kept, ones it's hard to believe he thinks would make any real difference.

Is it time to think about bringing the experiment to a successful conclusion? --Trovatore 21:06, 3 April 2006 (UTC)

Guys, make it an RfC. It's what that is for. Charles Matthews 21:35, 3 April 2006 (UTC)

I am currently editing Wikipedia:Requests for comment/WAREL -lethe ^{talk +} 22:30, 3 April 2006 (UTC)

I guess the RfC has to be certified by other people, so anyone who cares to, certify it. -lethe ^{talk +} 22:55, 3 April 2006 (UTC)

Great, thanks! I guess the RfC has been certified, I see a lot of names there. I now unblocked WAREL so that he can comment in the RfC. Oleg Alexandrov (talk) 00:04, 4 April 2006 (UTC)

DYLAN and finite fields

While I am not sure on what to do about the current dispute at field (mathematics), which is centered on the use of "field" at the Japanese Wikipedia, DYLAN LENNON now claims that a finite division ring is not the same as a finite field, and removed the interwiki link from our "finite field" to the Japanese "finite division ring". Comments welcome at talk:finite field. Oleg Alexandrov (talk) 18:57, 6 April 2006 (UTC)

My Muddle

I have frequently had an unpleasant experience when looking up mathematical terms in Wpedia. I go to the article I want and, reading the definition of the term, I encounter another term I don't understand. If there is a link connected to the term I open a new tab to find the definition of the second term. In reading the second definition I find the need to look up a third, then a forth, fifth, sixth. I am soon swamped by "hanging" definitions. But, not infrequently, a term is used without any attempt to define it. Do mathematicians write these articles only to communicate with other mathematicians? Surely an encyclopedia is meant to educate people about things they don't already know. Too Old 00:19, 7 April 2006 (UTC)

This is more or less of a problem depending on the topic in question and how much effort has been spent on writing it. If you mention it here, or on the discussion page of the relevant article, it's more likely to get fixed. Dmharvey 00:25, 7 April 2006 (UTC)

Hmm...I sometimes find that some calculus-related articles make more sense on Wikipedia than Wikibooks — Ilyanep (Talk) 00:38, 7 April 2006 (UTC)

Wikipedia is not meant to teach you the background knowledge you need. Wikipedia is an encyclopedia, not a collection of tutorials. If you want that, try Wikibooks. Dysprosia 00:40, 7 April 2006 (UTC)

Yes, it is good to keep things accessible, that means having relevant links to all concepts encountered. That of course does not mean it is Wikipedia's fault if you start reading an article about a term you don't know only to run into links to other terms you don't know. Wikipedia is (and should be) after all a loose collection of essays, not a course (and even for a course, you have prerequisites :) Oleg Alexandrov (talk) 01:08, 7 April 2006 (UTC)

An encyclopedia should not be of use only to a specialist, like a physician's medical database. An encyclopedia is, IMHO, meant to be a resource for the generally well-educated layperson, who might need the occasional definition, but definitely should not need a tutorial to understand an article. The background you speak of should not have to be extensive prior knowledge of the subject. When I consult, for example, the article on steel, I find an extensive treatment of the subject, occasionally having to find a definition, but not having to undertake a course in metallurgy in order to understand the article. When I go to look up a definition in that article, I need not go further and further afield in order to understand the definition. Too Old 01:37, 7 April 2006 (UTC)

An encyclopedia is a reference work, a collection of facts that are explained well and do not attempt to excessively mollycoddle the reader. You are comparing apples and oranges with your example of steel there -- mathematics, as well as certain other fields, are necessarily reliant on your accumulation of prior knowledge. A more apt analogy is expecting to understand an article on quantum spin. That article does not and should not teach you the basics of physics before launching into the actual article content, but it can give some motivation and make some simple insightful analogies. Dysprosia 01:52, 7 April 2006 (UTC)

I would like to dispute you on one point without arguing with the intent. The argument that "math is special" because it is more structured (or more rigorous, or constantly evolving, or any other argument I've seen used at various times) is very silly and I don't think it's good here. There are a lot of topics that can be covered with only elementary background. What do I mean by elementary? Well, read steel carefully and see what it assumes: right off the bat it talks about alloys, various chemical elements, technical ideas like "ductility" and "tensile strength", and the notion of atoms. All fundamental ideas in chemistry and physics. Too Old seems to have had no problem with these, yet I don't feel that this corpus of prerequisites is any larger than asking people to know calculus or Euclidean geometry. But I don't know that this was his problem, since he never said which articles he's found too technical.

I guess my point is that I feel like "math is hard" pulls too much weight around here even (especially!) when spoken by mathematicians. A reasonable article should assume the reader's knowledge of terms which form a language of discourse for the subject, so that each sentence need not be interrupted with definitions and qualifications, but anything that (in the context of the discursive standard) could be taken as technical should be explained. Rather than telling Too Old to go off and get an education, we should at least extract some productive information from his complaints and see what sort of stylistic changes might be needed around here. Ryan Reich 03:03, 7 April 2006 (UTC)

The companion matrix article, for instance, assumes you know what a polynomial is (and knowing what a polynomial is requires its prerequisites), knowing what a matrix is and the necessary basic matrix algebra necessary, plus a little more advanced matrix theory such as the characteristic polynomial is, diagonalizability, plus if you'd like to get through the rest of the article, assumes you know some basic field theory and linear algebra. There are articles and areas of mathematics with much worse prerequisites than that -- there are a lot of extremely deep areas, just pick something that is right near the bottom of that "depth". Mathematics does build on prior knowledge and decreeing this fact as "silly" doesn't quite make much sense.

No one is telling Too Old to "go off and get an education", though one should not blame the article for one's gaps in knowledge. Of course, a bad article can and does exist where it explains the concepts in an illucid way, and that of course should be fixed, but an article should not aim to teach the reader prior knowledge -- that responsibility is up to the reader, not the reference work. Dysprosia 03:43, 7 April 2006 (UTC)

My complaint was that the claim that math has special depths of prerequisites is silly. Go look at any science; they're just as bad. In particular, the use of this claim in this context, namely in response to someone who was almost certainly referring to articles that an amateur might be interested in reading, is silly, since such articles can without doubt be disposed of without using advanced concepts (of course, later in the article advanced ideas may arise. That has never been part of this discussion, though). In particular, I was not claiming that all math can be done at an elementary level (actually, I think I made allowances for the opposite). The example you give simply supports my contention that a common language be established at the start of the article. What might not be a good idea, in this particular case, would be for the article to introduce the theory of companion matrices in the context of modules over a PID, since it can be done more simply. This is the sort of distinction I'm making, yet I'll bet some people (I might be one of them, depending on my mood) will argue that the article should talk about companion matrices this way, since it's "more correct". That argument only works if it doesn't sacrifice clarity. Ryan Reich 04:12, 7 April 2006 (UTC)

I don't understand why you make the claim because I never did claim myself that math has "special depths of prerequisites" -- I said "mathematics, as well as certain other fields", and made special note that physics is just as bad. Otherwise I think we may be in violent agreement. Dysprosia 04:37, 7 April 2006 (UTC)

Oleg, you've absolutely hit the nail on the head. Dysprosia 01:52, 7 April 2006 (UTC)

Two sources of difficulty are obvious: (1) the structure of the subject, and (2) how it's presented. It is a fact of life that knowledge is a web, not linearly structured in dependency. Knowledge of A supports understanding of B, but also knowledge of B supports understanding of A. A writer of a text must work hard to order the presentation linearly, and at best achieve only partial success. Often a text read a second time will make more sense, because the additional context is available. A writer of a web article has no control over order of access. The only option is to include definitions, not just link to them; but taken too far, these intrusions become an obstacle themselves. Instead, some people use popups to get a quick look at a linked definition without opening a tab (or a window, in an antiquated browser). --KSmrq^T 01:24, 7 April 2006 (UTC)

Pop-ups are life savers (well okay time-savers) — Ilyanep (Talk) 01:31, 7 April 2006 (UTC)

We don't write our articles solely for mathematicians; we endeavor to make them as readable as possible. Accessibility is definitely a consideration for us. But only one of many, so sometimes an article is not as accessible as we might like. If you think the articles need help, then you know what to do. This is a wiki, be bold, edit. Complaining about the quality of some difficult work done for free by volunteers in their spare time is not going to win you any friends. -lethe ^{talk +} 01:57, 7 April 2006 (UTC)

For the record Talk:Hilbert_space#The_Layperson, Talk:Calabi-Yau manifold, Talk:Lie_group#is_this_useful.3F, some more examples of people with the exact same complaint. Happens a lot, I guess. If there were some magical way to easily write mathematics articles that were easy to learn, I would employ it in my writing. -lethe ^{talk +} 04:00, 7 April 2006 (UTC)

Per Ryan Reich, please make the complains specific. There are reasonable complaints, and there are unreasonable ones. :) Oleg Alexandrov (talk) 03:13, 7 April 2006 (UTC)

Well, it seems that I am not alone. But, people, I did not mean to attack your virtue. There was a suggestion that I should "be bold, edit". Were I 30 or 40 years younger, and had the resources, I might take up the serious study of mathematics. I then might find a way to rewrite some of these articles to make them more accessible. But, life is too short... I have had my say. I leave you now to play The Glass Bead Game among yourselves. If you have any thing to say to me I shall be happy to read it on my talk page, or you may email me. Too Old 07:11, 7 April 2006 (UTC)

Sorry, but sciences just aren't for everyone; you have to have a certain basic knowledge to be able to understand more complicated concepts in mathematics, physics, and so on. There's only so much we can do about that. —Nightstallion (?) ^{Seen this already?} 14:51, 7 April 2006 (UTC)

I think Too Old has a valid criticism, frequently repeated. The coverage of mathematics is often at too high a level, organisation of articles is confusing, core topics like Algebra are woefully inadaquate. Yes we have done good work todate, our coverage is extensive, but there is still a long way to go.

I propose creating Wikipedia:WikiProject Mathematics/Essential articles where we can identify which are the most important mathematics articles, assess then for quality and also mathematical level required. An example we could follow is Wikipedia:WikiProject Computer and video games/Essential articles which nicely organises that fields core material. This would also fit in with the Articles for the Wikipedia 1.0 project discussed above.

Is anyone interested in helping on this? --Salix alba (talk) 23:09, 8 April 2006 (UTC)

WAREL/DYLAN indef blocked

Well, the RfC and all our pleas seem to have no effect on his behavior. I blocked both accounts indefinitely, and wrote a note at Wikipedia:Administrators' noticeboard/Incidents#Indef block of WAREL/DYLAN LENNON.

This will generate serious questioning, as we are talking about an indefinite block, no less, so your comments there are appreciated, to make the case that this is a community-backed decision. Oleg Alexandrov (talk) 17:49, 7 April 2006 (UTC)

formal laurent series

Should formal Laurent series redirect to Laurent series (as it currently does) or to formal power series (my preference)? Dmharvey 18:20, 7 April 2006 (UTC)

I think formal power series is better, especially since the doubly infinite Laurent series cannot be treated formally (with rare exceptions). — Arthur Rubin | (talk) 18:52, 7 April 2006 (UTC)

Maybe the section on formal laurent series in the article Laurent series should be merged into the corresponding section of formal power series. -lethe ^{talk +} 18:54, 7 April 2006 (UTC)

Done. Dmharvey 17:03, 9 April 2006 (UTC)

references: multiple page numbers for same book

I've been trying out the new cite.php tool, i.e. with the <ref> and </references> tags. See for example quasi-finite field. But it looks a bit silly there, because I have two different page numbers for the same book. Does anyone know a slicker way to handle this? Dmharvey 18:22, 7 April 2006 (UTC)

David, I've made an edit at quasi-finite field, to suggest another way of handling your situation. However, I don't really like the look of the cite tool, I prefer the rf/ent templates, so I've also made a second edit using the rf/ent templates, to see if you like the way they look better. Paul August ☎ 21:49, 7 April 2006 (UTC)

I gotta admit I don't like any of the options very much. What I really want is something like LaTeX's \cite command, i.e. each reference gets e.g. a number or sequence of letters, and then you can specify the page number inline. So for example it would read like "according to [Se, p.198] you can do ..., or you can see later on [Se, p.204] suggests blah blah blah", and then in the references it just has one item, "[Se] Serre, Jean-Pierre, Local fields, etc". But it doesn't look like any of the automated mechanisms allow one to do this. Dmharvey 02:27, 8 April 2006 (UTC)

Solicit help organizing topics relating to approximation theory

I have recently created some material in the approximation theory page, relating to polynomial approximations to special functions. This is related to function approximation, Chebyshev polynomials, and polynomial interpolation, but in ways that I'm not clear about. I'm not an expert in the taxonomy of this area of mathematics, only in the specific things about which I wrote. In particular, I know that there is a field of interpolating polynomials through given data points, and that Chebyshev polynomials (and their roots) are involved in this. I can't believe that "approximation theory" is just about Remes' algorithm or use of Fourier/Chebyshev analysis to make optimal polynomials. So this whole area may be somewhat messed up, and my material might be in the wrong place. Would someone who knows his/her way around in this area be willing to take a look and move things around?

William Ackerman 00:40, 8 April 2006 (UTC)

Copies of long essay on multiple talk pages

User:BenCawaling has added apparently identical copies of a 2,500 word essay titled "About the incomplete totality of the infinite set of prime numbers" to the following talk pages:

Talk:Riemann hypothesis

Talk:Gödel's incompleteness theorems

Talk:Cantor's theorem

Talk:Cantor's diagonal argument

Talk:Bijection

Talk:Prime number

Talk:Fermat's last theorem

I don't think that Wikipedia is the right place for this diatribe, and we certainly don't need multiple copies of it - but as it's all on talk pages, I don't know what policy or guideline could be quoted in support of removing it. Does anyone have an opinion on what should be done about this (if anything) ? —Preceding unsigned comment added by Gandalf61 (talk • contribs) 11:41, April 8, 2006

I think we should remove it as a kind of spam. Paul August ☎ 15:36, 8 April 2006 (UTC)

Replace all but one of them with a link to the remaining one? Or replace all with a link to his userspace? -lethe ^{talk +} 15:37, 8 April 2006 (UTC)

I suppose any of these things would be OK, but there's a risk that it would constitute paying him too much attention. At least he's been good enough to confine his ramblings to a single section on each talk page, and as far as I've seen no one's bothered to respond. If it stays that way, maybe he'll get bored and go away, and the screeds will eventually pass harmlessly into archives. Of course if he were to start editing article pages, or injecting irrelevancies into other discussions on talk pages, then action might have to be taken. --Trovatore 18:32, 8 April 2006 (UTC)

You are right about the unnecessary multiple copies of some of my discussion text. I have just downloaded Wikipedia's "How to edit a page" and would make the deletions and links to one in "Prime number" article talk page. For now, you may do as you please with my "contributions".

You are wrong about no one's responding --- countless with positive reactions do in my Yahoo e-Mail address (I intentionally include it because, just like David Petry's last comments "As I see the situation now" in his "Controversy over Cantor's theory" article, the majority of Wikipedian administrators and editors are Cantiorian fanatics who (loking at their user pages (where there are any) are not at all mathematically qualified to discuss these stuff and whose best response is bad-name-calling (just read the next 3 messages) or appeal to their or their idolized "authoritative knowledge" but not actually refuting the arguments proferred even though they cite only elementary mathematics understandable by even honor high school students. The Yahoo e-Mail messages that I received confirms to me that Wikipedia articles are widely read by mostly amateur mathematicians or stidents. I was hoping to give them alternative understanding of the most controversial issues in modern mathematics to discuss with their professors.—Preceding unsigned comment added by BenCawaling (talk • contribs)

A better idea would have been to actually contribute to the creation or update of an article, instead of spamming multiple pages. By the way, thanks for insinuating that we are nothing but name-callers, then accusing us of being "Cantorian fanatics". Isopropyl 03:21, 14 April 2006 (UTC)

Crank spam. Delete. Charles Matthews 18:39, 8 April 2006 (UTC)

Agreed; delete. Talk pages are explicitly devoted to discussions about the article itself. --KSmrq^T 22:05, 8 April 2006 (UTC)

Agreed; crank spam. There is lots of that in talk pages in violation of the stated purpose of talk pages, unfortunately. However, in most cases enforcing this policy is probably a pain. In this case there's so much of it that it should all be deleted. So I guess the message to crank spammers is this: if you have something cranky to say, keep it short.--CSTAR 22:34, 8 April 2006 (UTC)

I have moved this essay to User:BenCawaling/Essay and replaced each copy on an article talk page with a link to its new location. Gandalf61 08:46, 14 April 2006 (UTC)

WAREL is back

This is getting interesting: two socks at the same time: [1] [2]. And an anonymous edit: [3]. Oleg Alexandrov (talk) 19:57, 8 April 2006 (UTC)

How sure do we have to be that these are him before we permban the socks? That's my inclination. -lethe ^{talk +} 20:32, 8 April 2006 (UTC)

I was under the impression that on-sight permabanning of socks was reserved to Willy on Wheels-level offenders. Isopropyl 20:40, 8 April 2006 (UTC)

Oleg, just do it. We'll pick up the pieces later. We can always apologize to anyone blocked by mistake; it's not like any huge permanent damage is done. --Trovatore 20:50, 8 April 2006 (UTC)

Oh, and by the way, this last incident should more than justify restoring the permanent ban on WAREL. --Trovatore 20:52, 8 April 2006 (UTC)

Someone made the comment that WAREL isn't learning anything from these repeated blocks. I think that if we keep unblocking him and he continues along the same path, we're the ones who aren't learning anything. Those who are about to block, we salute you. Isopropyl 21:25, 8 April 2006 (UTC)

I banned 64.213.188.94 (talk · contribs) indefinitely. -lethe ^{talk +} 22:33, 8 April 2006 (UTC)

I asked Lethe to shorten the block for a day, as IP addresses can be shared, unlike user names. On the more general problem, I start thinking that WAREL may actually not only be a highly arrogant user but also have some kind of compulsive disorder. In the worst case scenario he will play a cat and mouse game making new accounts just as we block them. No easy solution in sight. Oleg Alexandrov (talk) 00:25, 9 April 2006 (UTC)

Interesting common line of thought there. I almost posted a comment that when the permanent ban is put into place, a suggestion to seek psychiatric help should be posted on his user page. That would make it clear we have WAREL's interest at heart. On a practical matter, what IP addresses have the named accounts used by WAREL had? Elroch 00:56, 9 April 2006 (UTC)

Looking through the "contributions" of 64.213.188.94, from day one I see lots of silly vandalism and trolling of the worst sort, interspersed by occasional relatively lucid postings on the very mathematics subjects WAREL and DYLAN LENNON like to post, such as Perfect number and Masahiko Fujiwara. I also see some fascination[4][5][6][7] with one Doyle Farr, apparently a black student at Franklin Pierce College. Whether shared IP or not, I can't say that a permanent ban would be a big loss to Wikipedia. Lambiam^Talk 04:04, 9 April 2006 (UTC)

I don't think this anecdotal evidence makes a very strong case that the next person who tries to edit from that IP won't be a legitimate, good-faith contributor. Let's keep our responses targeted. OTOH I think immediate permanent blocks should be imposed on User:DEWEY and User:KOJIN and future recognizable sockpuppets as they appear. If we make a mistake it can always be corrected. --Trovatore 16:28, 9 April 2006 (UTC)

Length of an "arc" or of a "curve"?

At Talk: Length of an arc I added a comment arguing that the title ought to be Length of a curve (presently a redirect to Length of an arc). Please discuss there if you care (one way or another). Lambiam^Talk 03:18, 9 April 2006 (UTC)

{numbers}

Number systems in mathematics.
Basic
$\mathbb {N} \subset \mathbb {Z} \subset \mathbb {Q} \subset \mathbb {R} \subset \mathbb {C}$ Natural numbers $\mathbb {N}$ Negative numbers Integers $\mathbb {Z}$ Rational numbers $\mathbb {Q}$ Irrational numbers Real numbers $\mathbb {R}$ Imaginary numbers Complex numbers $\mathbb {C}$ Algebraic numbers Transcendental numbers Transfinite numbers Split-complex numbers $\mathbb {R} ^{1,1}$
Complex extensions
Bicomplex numbers Hypercomplex numbers Quaternions $\mathbb {H}$ Octonions Sedenions Superreal numbers Hyperreal numbers Surreal numbers
Others
Nominal numbers Serial numbers Ordinal numbers Cardinal numbers Prime numbers p-adic numbers Constructible numbers Computable numbers Integer sequences Mathematical constants Large numbers Pi π = 3.141592654... e = 2.718281828... Imaginary unit $i^{2}=-1$ Infinity ∞

Here is the {{numbers}} template. Today is the second instance when somebody felt templated to insert it in all the articles linked in there (first time was a while ago). I feel this is the case when being in Category:Numbers is enough for these articles, and the gain given by this template in all articles is not offset by the huge size of the template and the distraction it causes on the page. Comments? Oleg Alexandrov (talk) 04:01, 10 April 2006 (UTC)

The template is certainly sort of obtrusive visually. On the other hand these are all articles aimed at a pretty elementary audience. Maybe it is useful for them to have this reminder of how the various sets of numbers fit together. Could we find some of them to ask? --Trovatore 07:39, 10 April 2006 (UTC)

This is an absurd template. How many times and places do we need to know about, say sedenions? Perhaps if the template limited itself to the basics it might be justifiable. --KSmrq^T 08:41, 10 April 2006 (UTC)

I agree. It's absurd. I'm very skeptical as to its utility even for the "elementary audience" Mike mentions. I would think an appropriately placed link to number systems or whatever would be better; I think we all know how to keep a brower window or tab open :-) --C S (Talk) 08:49, 10 April 2006 (UTC)

This is the sort of thing I made {{otherarticles}} for. Septentrionalis 22:31, 10 April 2006 (UTC)

Neusis again

I'm a bit miffed that my original post on this topic seems to have been blown by without comment. I'm not an expert and I really don't know the answer.

Please see Jim Loy's angle trisection page. He shows a few methods using forbidden tools; I call your attention to the so-called tomahawk and to the movable, marked carpenter's square. Is the use of these tools not equivalent to neusis? John Reid 01:57, 11 April 2006 (UTC)

Maybe it's just that no-one here knows the answer. Dmharvey 02:23, 11 April 2006 (UTC)

A curious fact of life in posting to forums like this is the extreme differences in volumes of responses questions can provoke, differences which sometimes seem to be independent of the merit of the questions. The answer to your question requires technical study of the tools in question. The general situation is that we know compass-and-straightedge constructions only allow solutions to linear and quadratic equations; the additional tools allow solutions to broader classes of equations such as cubics. This much every serious mathematician knows. However, it may not be obvious which additional classes any particular tool admits. For example, we know a number of different tools that can be shown sufficient to solve cubics (hence permit trisection); but that does not mean they are equivalent in power. So my short answer to your question is, "I don't know." If everyone who does not know the answer to a question posts a statement to that effect, we are overwhelmed with useless noise; therefore the convention is that only those who know (or, sigh, think they know) post — which in this case may be none of our regular readers. After a respectful amount of time with no response, it is acceptable to ask a followup question. A good followup: "Is there a problem with my question?" :-D --KSmrq^T 03:34, 11 April 2006 (UTC)

I believe the movable square is equivalent to neusis; I think, but am less certain, that the tomahawk is. I have no proof of either right now, which is why I haven't posted. Septentrionalis 03:55, 11 April 2006 (UTC)

(rolling eyes) Oh, that I should have asked mathematicians for opinions! "What color is that tree?" "It might appear to be some shade of green on the side that was visible at the time of obseveration." ;-) It really would be informative to hear a number of expert users say "I don't know."

It's okay. For the immediate, ugly, practical purpose of editing the project, it's enough that I think both are cases of neusis, Pmanderson suspects it, and nobody yet is ready to say they're not. That's enough information for me to proceed with my rounds. If an expert has more information later, well, we'll change it. Thank you. John Reid 18:22, 12 April 2006 (UTC)

Edit war over Jaina "mathematics"

Before I continue the edit war which has developed between "Jagged 85" and myself (with some others), I would like to bring the case to our community. Jagged 85 has been adding (what I consider) irrelevant material to several articles in the "Cardinal numbers" category (and I think elsewhere as well). I removed it once. Now he has put it back. This inspite of the fact that there is an already existing article on Indian mathematics to which he has been adding. See Talk:Cardinal number for more information. In my opinion, he is just cluttering up these articles and making them hard to read. There are no mathematical theorems or hard facts in his writing, just attempts to grab credit for the Jaina. JRSpriggs 03:20, 11 April 2006 (UTC)

Yeah, this is a bit of an ongoing problem, and not just about the Jains, but about ancient Indian mathematics in general. Jag, and maybe a couple of others, repeatedly make "anti-Eurocentric" claims that strike me as having a political axe to grind. See especially Kerala school#Possible transmission of Keralese mathematics to Europe, which consists mostly of speculation that European mathematicians could have learned of these claimed precedents and thus may not really have made their discoveries independently. Now, he does have lots of sources; my guess is that they have a political agenda as well, but that's speculation on my part, given that I haven't seen the sources. --Trovatore 04:03, 11 April 2006 (UTC)

A political agenda won't surprise me. I recall the dispute at Arabic numerals, which was moved to Hindu-Arabic numerals and back in total 12 times hist, and see also Talk:Arabic numerals. That not meaning to say that I have anything against India or its great contributions. Oleg Alexandrov (talk) 04:34, 11 April 2006 (UTC)

Long, long, long, long, LONG "stub" articles!

Please look at:

Template:Algebra-stub

I've deleted the "stub" notice from a few dozen of these. Please help. Click on one. If it's too long to be called a "stub", deleted the {{algebra-stub}} notice. Start at the bottom, since I started from the top, so the ones NOW near the top have been dealt with. Some are AMAZINGLY long articles, and are called "stubs". Others are fairly short and could use more material but are clearly too long to be called stubs.

Then we can go on to "geometry-stub", etc., etc., etc., etc.......... Michael Hardy 03:09, 12 April 2006 (UTC)

I've checked every article in the category [8]. --MarSch 11:59, 12 April 2006 (UTC)

Weisstein reliability (or not)

Debate is getting a bit heated at Wikipedia:Articles for deletion/Radical integer and Wikipedia talk:Articles for deletion/Radical integer, with one contributor arguing that it's not within our purview as editors, even if experts, to judge the reliability of anything written in Weisstein's encyclopedia, unless some other source directly contradicts it.

That idea strikes me as a recipe for disaster. Weisstein's work has so much overlap with our project, and is so full of idiosyncracies, that we have to view with caution any article on which he's the only source. If our hands are tied on this, the quality of WP math articles is at risk. Please come and state your views. --Trovatore 21:34, 13 April 2006 (UTC)

I think you're right, as knowledgable editors, we have to use some discretion about what sources are allowable for original material to be included; otherwise we will have to allow all kinds of crackpot material. However, I don't really see a need to take a hardline stance about Weisstein. We can also use our discretion about what of his meanderings should be allowed, which is why I haven't really entered into that debate. -lethe ^{talk +} 00:12, 14 April 2006 (UTC)

Oh, of course. I'm not saying we should automatically reject material just because it comes from him. I'm just saying it needs extra scrutiny when it comes only from him. More scrutiny than might be required with regard to sole-source material from a recognized specialist in whatever the subject matter is. --Trovatore 01:06, 14 April 2006 (UTC)

Well then we're in complete agreement. -lethe ^{talk +} 01:10, 14 April 2006 (UTC)

Also agree (on both points).--CSTAR 02:23, 14 April 2006 (UTC)

Soni's theorem

Has a trivial subject and I could not find any google hits. Should it stay? Oleg Alexandrov (talk) 04:10, 14 April 2006 (UTC)

I'd say no. --Trovatore 04:14, 14 April 2006 (UTC)

I couldn't find anything about it either --MarSch 11:47, 14 April 2006 (UTC)

I would say this article is a strong keep. It has been refined by another user, and I believe the content is much clearer now. This theorem is not trivial, it is like the Trivial Inequality (I don't know if non-mathematicians will understand that reference, so I will explain). This theorem is useful by itself, and not at all obvious. However, when combined with other things, such as De Moivre's, this can be incredibly useful. It should not be deleted for any reason. perhaps a more experienced mathematician can refine it... Mysmartmouth

I nominated it for deletion using the WP:PROD process. So, if nobody objects in 6 days, it will get speedy deleted. Oleg Alexandrov (talk) 20:42, 14 April 2006 (UTC)

Deprodded by author, listed on AfD by me. --Trovatore 23:01, 14 April 2006 (UTC)

Please add your comments to the AFD page.--C S (Talk) 23:30, 14 April 2006 (UTC)

Help with matrix groups

I've been working on the matrix group page and need some help with the content. In particular I'm trying to summarize the types of classical groups but don't have the necessary background to do so. Some of the changes involve generalizing the definitions on other pages (such as unitary group) to arbitrary fields as well as possibly adding some pages (such as projective special orthogonal group).

I've put a summary of the changes I think would be helpful on Talk:Matrix_group. TooMuchMath 05:00, 14 April 2006 (UTC)

Update: The page is starting to come along, however we now have some redlinks if anyone wants to take a shot at them:

• projective special unitary group
• projective symplectic group
• general symplectic group
• projective orthogonal group
• projective special orthogonal group

TooMuchMath 17:39, 21 April 2006 (UTC)

Well as you can see the links are no longer red and the classical groups portion of the page is looking pretty good. More contributions are welcome, of course! TooMuchMath 22:52, 24 April 2006 (UTC)

The links have become redirects, but have the target articles added the necessary discussions? For example, "projective special orthogonal group" redirects to "orthogonal group", but that article says nothing specific to support the redirect. --KSmrq^T 23:09, 24 April 2006 (UTC)

references for basic topics

Since we seem to be discussing references/sourcing so much recently.... can I ask what is the deal with references for all of our articles on more basic topics? For example, none of the following articles have any book/journal references: irreducible polynomial, normal subgroup, null space, vector space, affine scheme, group (mathematics), symmetric group, function composition. And there are plenty more, they're very easy to find. For such articles, sourcing would have two primary purposes: (1) historical information about where the concept first appeared, possibly in nascent form (this is hard because it involves genuine historical research), and (2) pedagogical, i.e. "where you can learn more about this idea". The second one is obviously problematic because in some cases there are many thousands of textbooks that cover the relevant material. On the other hand, sometimes I feel like there are some double standards going on in the background: for topics which all of us here know are important and standard, we don't require any sourcing, but things like "radical integer" make sparks fly.... Dmharvey 12:20, 14 April 2006 (UTC)

I certainly think that for basic subjects, referencing one or more modern textbooks on the subject would be really useful. For example, something like "An introduction for Undergraduates is given by 'Algebra' Splodgett and Madeup (Cambridge 2003). A textbook more suitable for postgraduates is 'Introduction to Algebra' Spurious and Fictitious (Springer Verlag 1998)." (I pick on Algebra because I was recently looking at [Elementary Algebra] and that has poor references (though I didn't know of a good one to use myself). There's no way that a wikipedia page, no matter how good, can teach a basic mathematical topic and therefore a textbook reference (and some insight into what level of student it would suit) would be very helpful. I realise this could possibly cause issues with people recommending their own books or particular favourite texts. --Richard Clegg 14:10, 14 April 2006 (UTC)

There are double standards and double standards; I think this double standard is absolutely rational and legitimate. I am unembarrassed to say I think we should have that double standard. Just the same, the point is well taken: While not as essential for topics we know about than those we don't, sourcing is still useful and the article isn't really complete until it's provided. --Trovatore 19:34, 14 April 2006 (UTC)

Well, sure, we should source things properly. If they aren't, then we shouldn't include it. On the other hand, we often give editors the benefit of the doubt. If there are no sources for something, then if the creator of the article is a known, respected contributor, not known for randomly inserting crazy crap into Wikipedia, then we give him/her time to find a source. I think it's perfectly fine to rely on the trust built among known contributors. In this case, it was a respected contributor Henrygb who had created the article, even giving a source. However, in this case, another respected contributor questioned the source, as upon investigation the source cited a mailing list which is not available for view and other searches through the usual methods, Google, MathSciNet, etc., were unable to find the term "radical integer". In this case, it's not applying a double standard to ask, "Should we allow this material?" It's natural and perfectly fine to engage in discussion, even amongst contributors who hold a great deal of trust for each other. Such discussion acts as a "reality check", making sure we don't get carried away and making sure we ultimately uphold the standards.

Even when the editor is an anon, we often give the benefit of the doubt, investigating how common the terminology is and whether the results are mentioned in some well-known resources. I'm even amazed at the lengths people sometimes take to investigate rather dubious-sounding claims, in the interest of completeness and fairness.

So I would say there is no double standard here. We often allow anyone to edit and insert material without citing, as if we didn't, we wouldn't gain a lot of content. On the other hand, to make sure we don't allow the crap to build up, we rely on trust of known contributors and also our expertise, e.g. "hey, this guy says some cubics can't be solved by radicals; that's not what I learned in undergrad algebra!" Eventually, though, we should be adding sources, and indeed some people are clearly going through articles and added citations where needed. So it's not accurate to say we don't require sources for some articles. --C S (Talk) 20:18, 14 April 2006 (UTC)

Let's not mix apples and oranges. Sources for mainstream mathematical content act as enrichment, "See also". The content is not in dispute, perhaps with a few lunatic exceptions. Many of the algebra topics, for example, could cite Mac Lane and Birkhoff's Algebra (ISBN 0023743107), or van der Waerden, Moderne Algebra (ISBN 0387974245), or Artin's Algebra (ISBN 0130047635), or numerous other texts; and they should. In other cases, we have questions of proof, or notation, or history, or who-knows-what. It is not practical to referee every article like a journal paper, and even then many assertions are accepted without proof. We concentrate our demand for references on statements that raise suspicion. In principle, we should be able to defend "1+1=2", but in practice that level of citation would be absurd. --KSmrq^T 22:41, 14 April 2006 (UTC)

I would agree with KSmq. The rules for when a reference is not required (as I remember from high school) is if the information is "widely known" (which in high school meant that it was avaliable in three or more sources). "Moscow is the capital of Russia" would not need a citation for this reason. Even when we do run into problems with conflicting definitions ("St. Petersburg is the capital of Russia" was true for a time) citations aren't strictly required if both definitions are or have been widely used. In fact a discussion of the historical (or motivational) reasons for differing definitions is often more useful than a citation in these cases. A citation is required only when a definition is obscure. Aside from the academic integrity motivations for proper citation, this is particularly important on Wikipedia to ensure the "no original research" policy as well as to weed out the junk science. That said, a good reference or two can enrich the content substatially, so even for widely known topics it would be a good idea to add references. TooMuchMath 18:16, 15 April 2006 (UTC)

That's nicely put. This is the "rational double standard" I was advocating above. However I wouldn't formalize the "three sources" standard; I think the appropriate test is more whether an ordinarily prepared worker in the specialty would know the facts asserted. --Trovatore 19:26, 15 April 2006 (UTC)

OK, I agree with the bulk of what everyone's saying here, certainly I agree with the "rational double standard". I intended my comment to focus more on the educational usefulness of Wikipedia, rather than its veracity. In fact, if I had more time available now, I would consider trying to organise a "let's find book/pagenumber references for all those unreferenced basic topics articles" project, for the sole purpose of assisting those who are using Wikipedia as part of their mathematics studies. It's getting to a point now where an undergraduate and even a graduate student (like myself) can profitably use Wikipedia as their first stop when looking stuff up, and it would be incredibly helpful to have more pointers to denser sources of information. Unfortunately I don't have the time now. (nudge nudge wink wink) Dmharvey 19:47, 15 April 2006 (UTC)

This is a problem I have encountered when ever I nominate maths articles for Good Article status - they very often comment on teh lack of sources. The trouble is that many of the common topics (groups, vectors etc.) are written entirely of own knowledge, which means the source is out own knowledge hence the lack of physical references. That said, I think we should always list *some* references, if only to provide a place for readers to verify the info or find out more. Don't forget it says under any edit box that "Content must not violate any copyright and must be verifiable". Any book which know contains infomation for the article in question is suitable. Putting the article name in Amazon's search box often provides something suitable. (Although the references I list tend to come from the reading list for my uni's maths course). Tompw 20:01, 15 April 2006 (UTC)

PDE Surfaces

Copied from Talk:Mathematics --Salix alba (talk) 14:18, 15 April 2006 (UTC)

This seemed like the best place to get people's attention about the article PDE Surfaces, written by Zer0 cache. I suspect that it's promoting research, but I can't be sure. It would be appreciated if other editors can check this out. I've also left a small query at PDE surfaces talk page. MP (talk) 11:28, 11 April 2006 (UTC)

it seems fully referenced... hmm I guess Salix Alba fixed it already. --MarSch 17:43, 15 April 2006 (UTC)

Hm, what about the naming? I've already downcased it, but it didn't occur to me at the time that it would probably be more standard to move it to PDE surface, assuming there is such a thing as a PDE surface that makes sense in isolation from other PDE surfaces. On the other hand, if it's the description of a method rather than a kind of mathematical object, should it perhaps be method of PDE surfaces? --Trovatore 17:48, 15 April 2006 (UTC)

mathematics for AID

mathematics is curerntly going very well on Wikipedia:Article Improvement Drive. Maybe you want to vote for it --MarSch 18:13, 15 April 2006 (UTC)

debate over external link at Talk: Serge Lang

There's an extremely heated debate going on the talk page for Serge Lang between two editors, User: Revolver and User: Pjacobi. The issue is whether an external link to an article on the AIDS wiki (which was written by Revolver) should be allowed. I've just made my thoughts known there, and I also noticed that an RFC had been filed, but no comments had been made here (which is requested on the RFC page). --C S (Talk) 04:18, 17 April 2006 (UTC)

Theorem 1

I nominated Theorem 1 for deletion. I tried using {{prod}} first but its author disagreed. Comments welcome. Oleg Alexandrov (talk) 03:55, 18 April 2006 (UTC)

Delete. The author says "There is a list, and this is #1." I'm not aware of any cosmic list of theorems. Now it does have something of a place of distinction -- postulate #4 of book 1 of Euclid's elements. But it isn't "theorem #1". Will there be a theorem #2? William Ackerman 17:16, 18 April 2006 (UTC)

There is no point in commenting here. To find the discussion, go to the article in question, and follow the link at the top of the page. --Trovatore 17:17, 18 April 2006 (UTC)

NPOV dispute at geostatistics, kriging, and spatial dependence

There is an NPOV dispute at the above articles: we need expert advice from statistician(s), especially those familiar with spatial statistics.

Briefly: User:JanWMerks claims that geostatistics is a scientific fraud, and has repeatedly edited these related articles to reflect that POV. Myself, User:Antandrus, and others were trying to point out Wikipedia rules, such as WP:NPOV, WP:VERIFY, and WP:NOR. Much edit warring ensued.

Now, the dispute (at spatial dependence) is over whether the F-test is a valid statistical test for spatial dependence. Also: several references (at geostatistics and kriging) are being used to support the claim that kriging is invalid, and I don't have easy access to a good library to check these references.

I hope that someone is willing to research the claims of invalidity better than I can, or perhaps simply provide a third opinion about the dispute.

Please feel free to visit Talk:Geostatistics, Talk:Kriging, and Talk:Spatial dependence to help out. Thanks!

-- hike395 17:40, 22 April 2006 (UTC)

cron vs hedron

I wonder if these two Greek suffixes mean the same or almost the same thing. Then, the following redirects may make sense:

• Great dirhombicosidodecacron --------> Great dirhombicosidodecahedron
• Great dodecahemicosacron --------> Great dodecahemicosahedron
• Great dodecahemidodecacron --------> Great dodecahemidodecahedron
• Great icosihemidodecacron --------> Great icosihemidodecahedron
• Small dodecahemicosacron --------> Small dodecahemicosahedron
• Small dodecahemidodecacron --------> Small dodecahemidodecahedron
• Small icosihemidodecacron --------> Small icosihemidodecahedron

I stumbled into them at the Missing science project, and don't know what to do about them. Thanks. Oleg Alexandrov (talk) 18:55, 22 April 2006 (UTC)

I think the ones on the left are duals of the ones on the right or something. They should be given seperate articles. -- 127.*.*.1 20:33, 22 April 2006 (UTC)

Indeed the coverage of dual is week at the moment. I've mentioned this on Talk:Polyhedron. --Salix alba (talk) 22:39, 22 April 2006 (UTC)

Delete "Category:Continuum theory"?

This category called "Category:Continuum theory" is a subcategory of "Set theory" and of "General topology", but it contains no articles. Should it be deleted? How can I propose it for deletion? JRSpriggs 07:20, 26 April 2006 (UTC)

Wikipedia:Categories for deletion explains the deletion process. It might be applicable for speedy deletion. --Salix alba (talk) 07:34, 26 April 2006 (UTC)

Yup, WP:CSD says that empty categories can be speedied. I'm going to do it. This category defines a continuum as a compact connected metric space, which isn't right. The real line is not compact. -lethe ^{talk +} 07:56, 26 April 2006 (UTC)

Continuum has more than one meaning in mathematics. In continuum theory, which is related to dynamical systems, continuum does indeed mean what the category said. Perfectly cromulent articles which would have belonged in this category include pseudo-arc, indecomposable continuum and solenoid (mathematics). —Blotwell 14:49, 26 April 2006 (UTC)

Well, if the category had a correct definition, and also there are articles which could live in it, then the deletion was inappropriate. I will now undelete, and promise to be more careful when speedying things in the future. Thank you. -lethe ^{talk +} 20:34, 26 April 2006 (UTC)

Help requested at hyperbolic 3-manifold

An editor insists on removing red links as "cleanup". I think the participants here realize the importance of red links to this project (and Wikipedia in general). I'm puzzled why anyone would insist on removing them, but this editor has been quite stubborn, insisting that the articles *must* be created before links to them can be included in this article. --C S (Talk) 00:41, 28 April 2006 (UTC)

I've made some comment's at the user's talk page (User talk:PHDrillSergeant); hopefully, this should be enough. --C S (Talk) 01:01, 28 April 2006 (UTC)

Edward R. Dewey

A stock market "analyst" who sold a correspondence course on "cycle analysis".[9] This link includes a table of contents which I think makes clear how trivial Dewey's "system" is; please comment on Wikipedia:Articles for deletion/Edward R. Dewey. Septentrionalis 19:13, 28 April 2006 (UTC)

Should Radical integer be deleted?

A newly created article Radical integer has been listed for deletion. Should it be kept or deleted? Note that the article resolves a long-standing redlink in Algebraic integer listed on Wikipedia:Missing_science_topics/Maths8. Weigh in. Lambiam^Talk 17:50, 9 April 2006 (UTC)

I'm the one who listed it for deletion, because the given source (MathWorld) looked hinky and in a quick search I couldn't find the term clearly and independently attested. I'm not a number theorist, so if it's not something one of Eric Weisstein's buddies just made up one day, by all means say so. --Trovatore 17:59, 9 April 2006 (UTC)

Someone somewhere has got to have a short name for Algrebraic integer expressible by radicals, but this doesn't seem to be it. Septentrionalis 22:33, 10 April 2006 (UTC)

Radical extension, extension by radicals, or (most common, I think) pure extension is standard, and radical number I think I've seen. Radical integer is logical and has a MathWorld article to go with it, which speaks in its favor. It seems to me that all of this should be discussed somewhere in an article on solvable extensions, but I can't find any such article. Should I write one? I don't want people deleting it if I do. Gene Ward Smith 21:25, 13 May 2006 (UTC)

Let me summarize the history as I see it:

1. The article radical integer was sourced only to MathWorld and all the Google hits seemed to trace back there. So I nominated it for deletion as one of Eric Weisstein's neologisms (as you'll have gathered, I don't think the existence of a MathWorld article speaks particularly well in favor of it; it's not a strike against it per se, but certainly not enough support for an article by itself).
2. During the discussion it emerged that there was more than a not-so-interesting definition involved, but rather an actual putative theorem, which (if true) goes as follows: Consider all numbers that can be expressed by starting with the naturals and closing under addition, multiplication, subtraction, division, and extraction of natural-number roots. Intersect that class with the algebraic integers. Then any number in the intersection can be expressed by starting with the naturals and closing under the previous operations, without division.
3. That theorem, if it is one (which I think it probably is), is very interesting, and clearly justifies the creation of a term for an element of the class. Unfortunately at the current time the theorem cannot be sourced, except to MathWorld, which IMO is not reliable. Moreover I think it's a reasonable principle that sources for putative theorems ought to point the reader to an actual proof, and the MathWorld source does not do that. --Trovatore 17:26, 25 May 2006 (UTC)

It might be posible to get a better source, the theorem was discussed on the math-fun mailing list, which I presume is on the web somewhere. In an email to me Rich Schroeppel said he would try to dig up the archive when the tax season was over. If anyone is interested this would be great to follow through. --Salix alba (talk) 17:35, 25 May 2006 (UTC)

Oh, one more small point: What I said about "sourced only to MathWorld" is not strictly true; I'm including Weisstein's encyclopedia of math as part of MathWorld. With that addendum it's true. --Trovatore 17:35, 25 May 2006 (UTC)

• It seems to me if I understand the claim that Schroeppel's theorem is too trivial to use as a reason for an article. If μ is an algebraic integer, then it has a monic polynomial, and expressing it as a root expresses it without division. Expanding on that, the ring of integers in any number field has an integral basis; it can be written as c₁ μ₁ + ... + c_n μ_n, where the c's are ordinary integers and the μs are algebraic integers in the field, so in terms of this basis everything in the ring of integers is precisely everything which can be expressed without division.

• So, what exactly is the statement of this theorem? Gene Ward Smith 19:47, 25 May 2006 (UTC)

I think I've already stated it exactly; here's the example that came up as to why it's not trivial. The golden ratio is a root of x²−x−1=0, so it's an algebraic integer. It's also obtainable from the naturals by iterating the operations listed, including division, as

${\frac {1+{\sqrt {5}}}{2}}$

However it's not immediately obvious that you can get it from the naturals by iterating the operations not including division. But you can. It's

${\sqrt[{3}]{2+{\sqrt {5}}}}$

(Thanks to Lambiam for that representation.) Unless I've misunderstood it, the argument you give does not prove this. --Trovatore 19:55, 25 May 2006 (UTC)

Here's a sketch of an almost-proof. "Almost" because I'm left with a denominator of at most 2.

Let S be those numbers obtainable from the natural numbers by addition, subtraction, multiplication, division, positive integer roots. (I want to call this the maximal radical extension of Q, but I'm slightly concerned about roots of unity. Never mind.) Let R be the "radical integers", i.e those numbers obtainable from naturals by addition, subtraction, multiplication, and positive integer roots (but not allowing division). First I claim that any x in S is of the form y/d for some y in R and some integer d. This is done by induction on the structure of x. Clearly addition, subtraction, multiplication pose no problems. Integer roots also fine (i.e. $(y/d)^{1/n}=y^{1/n}d^{(n-1)/n}/d)$). Division is slightly more troublesome, you need some kind of "rationalising the denominator" trick.

So now suppose we have x = y/d as above, and suppose further that x is an algebraic integer; we want to prove that x is itself a radical integer. Let K = Q(y), and let O be the ring of integers of K, so x is in O. As Gene pointed out above, O has a finite Z-basis, and the basis elements are polynomials in y with coefficients in Q, so for a large enough integer m we find that mO consists entirely of radical integers. Split m into a product of powers of prime ideals in O, say $m=\prod _{P}P^{r_{P}}$. By looking at the rings $O/P^{r_{P}}$, we can find some large integer n such that xⁿ is congruent to either 0 or 1 modulo each $P^{r_{P}}$. Then $x^{2n}-x^{n}$ is in mO, so is a radical integer, say z. Then we have $x=\left({\frac {1\pm {\sqrt {z}}}{2}}\right)^{1/n}={\frac {2^{(n-1)/n}(1+{\sqrt {z}})^{1/n}}{2}}$, which is a radical integer possibly divided by 2.

Anyone buy that? Getting rid of that last 2 seems a little problematic. Dmharvey 00:26, 26 May 2006 (UTC)

Oh yeah, by the way you can apply that proof to the golden ratio case quite easily. We already have $x={\frac {1+{\sqrt {5}}}{2}}$ presented in the right form. Let O be the ring of integers of $\mathbf {Q} ({\sqrt {5}})$. Then the ideal (2) is inert in O because the polynomial $x^{2}-x-1$ is irreducible mod 2. So the quotient O/2 is GF(4), so cubes of anything nonzero are congruent to 1. So $x^{3}-1$ is in 2O, so is a radical integer. And indeed $\left({\frac {1+{\sqrt {5}}}{2}}\right)^{3}-1=(1+{\sqrt {5}})$ is twice an algebraic integer, so must be a radical integer, which is I suppose where Lambian's formula comes from :-) Dmharvey 00:33, 26 May 2006 (UTC)

OK, here's the rest of the proof to handle that annoying factor of 2. You need to treat the residue characteristic 2 a little carefully.

Again suppose x = y/d where x is an algebraic integer. Let $\theta =(1+{\sqrt {5}})/2$ be the golden ratio. Consider the extension $K=\mathbf {Q} (y,\theta )$, let O be its ring of integers. Again we can find some m so that mO consists entirely of radical integers. Consider all prime ideals P of O of residual characteristic 2, suppose their multiplicites in m are given by r_P. Take some high power of x, call it x₂, which is = 0 or 1 modulo each $P^{r_{P}}$. Then x₂ + θ is not in any $P$, because θ is not 0 or 1 modulo 2 (i.e. neither θ nor θ−1 is twice an algebraic integer). So some high power of x₂+θ, let's call it x₃, is congruent to 1 modulo every $P^{r_{P}}$. Then x₃−1 is = 0 modulo every $P^{r_{P}}$. Now consider all the other primes Q of various other residue characteristics, which have multiplicities $r_{Q}$ in m. Then some high power of x₃−1, let's call it x₄, is either 0 or 1 modulo each $Q^{r_{Q}}$, and is still 0 modulo every $P^{r_{P}}$. Now look at x₄+1; it's either 1 or 2 modulo each $Q^{r_{Q}}$, and it's 1 modulo each $P^{r_{P}}$. Since the residue characteristics of the Q are not 2, some high power of x₄+1, say x₅, is 1 modulo all of the $Q^{r_{Q}}$ and all of the $P^{r_{P}}$. So x₅−1 is in mO, and therefore a radical integer. If you unroll your way through x₅, x₄, x₃, x₂, back to x itself, you get that x is a radical integer. Whew! Dmharvey 02:48, 26 May 2006 (UTC)

Applause. Now get that published in the Journal of Number Theory and we can write an article about it :) --Lambiam^Talk 16:21, 26 May 2006 (UTC)

Update on the lists of missing math topics

The lists at Wikipedia:Missing science topics#Mathematics now contain entries from MathWorld, Springer Encyclopaedia of Mathematics, Charles Matthews' maths lists (thanks Charles!), St Andrew's, and PlanetMath. There are 15465 redlinks and 9700 bluelinks (in separate lists), which is a progress of 38.55% towards eliminating the redlinks. For many redlinks it is likely that the information exists on Wikipedia but under a different name, so creating redirects is a good way to advance that project forward. The harvest is great and the workmen are few[10] (since it's Easter today :) Oleg Alexandrov (talk) 22:21, 16 April 2006 (UTC)

And I finally got permission from Springer to use their lists in our project. Oleg Alexandrov (talk) 03:25, 25 April 2006 (UTC)

Really? That's very generous of them, I didn't think they would. I think mathworld wasn't willing. Neat! -lethe ^{talk +} 03:32, 25 April 2006 (UTC)

If Mathworld was not willing, how come the Wikipedia:Missing science topics was created to start with? Before I got there, all the math entries from there were copied from MathWorld, all the way to incomplete entries, like Archimedean Spiral Inv.... Oleg Alexandrov (talk) 03:37, 25 April 2006 (UTC)

I seem to recall a discussion here on the wikiproject talk page, where someone created a carbon copy of the mathworld index of topics, and someone emailed them, and they indicated that it was indeed a violation of their copyright. In fact, my recollection is that you were in this converation, though I could be mistaken. Anyway, I don't know where the content of Wikipedia:Missing science topics comes from, but unless I'm misremembering something, to have their index is a copyright violation. I guess I should see if I can find that old conversation. -lethe ^{talk +} 07:37, 1 May 2006 (UTC)

That's really good news. I'm not so surprised though, that Springer was willing but MathWorld not. There are people at Springer that are truly committed to what they're doing and I've seen Springer do things that strictly speaking, they did not need to do. --C S (Talk) 07:27, 1 May 2006 (UTC)

listing variable names after formulas

I wonder what people think of these multiply-indented lists to define all the variables that appear in a formula. An example is found here. It is claimed that this format is somewhat standard here at wikipedia and is found in hundreds of articles, but I've never seen it, and furthermore don't really like it, I prefer instead a regularly indented paragraph of text. What are your opinions of this format? -lethe ^{talk +} 00:52, 22 April 2006 (UTC)

It takes too much space. -- 127.*.*.1 03:26, 22 April 2006 (UTC)

Yes, that is quite an unfortunate presentation style. A simple paragraph of explanation would be much better.  — merge 08:07, 22 April 2006 (UTC)

From a dyslexic point of view I have problems parsing large blocks of text and tend to find lists easier to read. I had a play about with a more compact format using tables. Compare

---

The Schrödinger equation is:	i		the imaginary unit,
	t		time,
$H(t)\left|\psi (t)\right\rangle =i\hbar {\partial \over \partial t}\left|\psi (t)\right\rangle \qquad$	${\partial \over \partial t}$		the partial derivative with respect to t,
	$\hbar$		reduced Planck's constant (Planck's constant divided by 2π),
	$\psi (t)$
	H(t)		the Hamiltonian - a self-adjoint operator acting on the state space.

---

The Schrödinger equation is:

$H(t)\left|\psi (t)\right\rangle =i\hbar {\partial \over \partial t}\left|\psi (t)\right\rangle \qquad$   

where i is the imaginary unit, t is time, ${\partial \over \partial t}$ is the partial derivative with respect to t, $\hbar$ is the reduced Planck's constant (Planck's constant divided by 2π), $\psi (t)$ is ...., H(t) is the Hamiltonian - a self-adjoint operator acting on the state space.

---

--Salix alba (talk) 09:27, 22 April 2006 (UTC)

If a list seems necessary, why not use a list?

The Schrödinger equation is:

$H(t)\left|\psi (t)\right\rangle =i\hbar {\partial \over \partial t}\left|\psi (t)\right\rangle \qquad$,

where:

• i is the imaginary unit
• t is time
• ${\partial \over \partial t}$ is the partial derivative with respect to t
• $\hbar$ is the reduced Planck's constant (Planck's constant divided by 2π)
• $\psi (t)$ is ....
• and H(t) is the Hamiltonian - a self-adjoint operator acting on the state space.

---

 — merge 09:42, 22 April 2006 (UTC)

I wonder if those explanations of the symbols make this equation any more comprehensible to someone not familiar with the notation. If you don't know what the symbol is for partial differentiation then IMO it is very likely that you don't know what partial differentiation is and the same goes for the imaginary unit.--MarSch 09:55, 24 April 2006 (UTC)

I don't think it's necessary to explain certain things, such as the imaginary unit, time, or the partial derivative. Articles assume some basic knowledge, so we should rely on this (however, we should clearly attempt to make the number of assumptions as smallest as sensibly possible). Dysprosia 10:05, 24 April 2006 (UTC)

The Schrödinger equation is:

$H(t)\left|\psi (t)\right\rangle =i\hbar {\partial \over \partial t}\left|\psi (t)\right\rangle \qquad$

where H is the Hamiltonian, ψ is the state and t is time,

but even better is probably

A physical system with Hamiltonian H and initial state vector ψ₀ can be described at time t by the state vector ψ(t) which is a solution of the initial condition ψ(0) = ψ₀ and the differential equation called the Schrodinger equation

$H(t)\psi (t)=i\hbar {\partial \over \partial t}\psi (t)$

--MarSch 10:09, 24 April 2006 (UTC)

I'm in favor of lists for equations. The main reason is that I don't like to read the whole article - and lists of variables show a clear spot where I can find all the information I need. This is of course provided that its written properly. If the variables in the equation are fully clear, then theres no need. However, in the case of the schrodinger equation, almost none of the variables and symbols are familiar to most people. Also, most always, all variables do need description. Leaving out variables leaves the equation incomplete, and even a reader who assumes the right meaning might question himself, and end up having to double check the formula somewhere else. Stuff like simple operators probably don't need explaining, but I've found a good compromise in that respect to define the derivative of something rather than the dervative operator (for example: "dp/dt is the instantaneous rate of change of the momentum").

Another main consideration is consistancy. If equations are written in 5 or more different forms, users will have a harder time sorting through the formats to find what they need. Almost always, variables are written below the equation, and when they're not - I find it difficult to follow. The list format makes it easy to find the perhaps one or two variables you don't know, and refer back to it without losing your place.

We as editors should consider that wikipedia isn't only used by people wanting an in depth overview of a subject, but may also want a quick reference. Articles that distinguish different parts of the article (like equations, subject headers, examples vs generalities) are much easier to read and use. The faster a reader can find the information they are looking for is (in my opinion) far more important than making the page compact. Fresheneesz 07:25, 2 May 2006 (UTC)

AFD - How to get the prime factors of a number

I have nominated How to get the prime factors of a number for deletion. Comments welcome. -- Meni Rosenfeld (talk) 16:46, 26 April 2006 (UTC)

It seems like useful information, although it could be better written. Is this info in some other article? If not, maybe the article should stand. PAR 16:58, 26 April 2006 (UTC)

Please take comments on the merits to the AfD page. --Trovatore 17:04, 26 April 2006 (UTC)

Deleted. -lethe ^{talk +} 05:17, 1 May 2006 (UTC)