# Jan 2008

## Mathematical proof

The first paragraph of mathematical proof sounds a bit strange to me. It says:

In mathematics, a proof is a demonstration that, assuming certain axioms and rules of inference, some statement is necessarily true.

I don't think that this has ever been a standard definition of "mathematical proof". For example Euclids' proof that there are infinitely many primes couldn't be expressed in the "axiom->theorem" form until Peano axiomatized arithmetic, and have been called "a proof" for centuries (and we can find many other proofs that didn't have the "axiom->theorem" form until Zermelo&C. axiomatized set theory or Robinson axiomatized Non-Standard Analysis).

Moreover: Why a proof of the irrationality of e should be "a demonstration that assuming certain axioms and rules of inference e is necessarily irrational" and not just "a demonstration that e is irrational"? If there is no problem with using vague expressions like "demonstration" we can assert directly the second one. The first seems to express a formalistic point of view.

In virtually all branches of mathematics, the assumed axioms are ZFC (Zermelo–Fraenkel set theory, with the axiom of choice), unless indicated otherwise. ZFC formalizes mathematical intuition about set theory, and set theory suffices to describe contemporary algebra and analysis.

This seems arbitrary:

1. "Assumed" by whom? Do we mean that there is an implicit and eventually unconscious assumption?
2. "Unless indicated otherwise" according to which convention? Synthetic geometry or visual geometric proofs of algebraic equalities surely are far away from ZFC but nobody feel the necessity to specify this.
3. Why ZFC and not NBG or New Foundations?
4. The majority of mathematicians make proofs without ever knowing exactly what ZFC (NBG or whatsoever) is and having no idea of how the ZFC axioms would work in their proof

What do you think?

--Pokipsy76 (talk) 08:04, 2 January 2008 (UTC)

I agree that the definition sounds more like a definition of proof in the sense of proof theory in mathematical logic, which is a way of formalizing within mathematics of what mathematicians have been doing for ages. There is an unfortunate ambiguity of the term "axiom" that does not help here; the term can mean:
1. a proposition that is considered to be self-evident or in any case accepted as being true, even if (or because) it cannot be proved (for example, the axiom of infinity);
2. a property that is part of the defining characteristics of some abstract mathematical structure, such as the commutativity of addition in a field (mathematics).
(To some extent these meanings may overlap, but they have a different status; in particular, it is (marginally) conceivable that someone could convincingly disprove the axiom of choice by showing it contradicts something that is evidently true; whereas the idea of disproving the commutativity of addition in fields is meaningless.) So it may be better to start with a definition that also works for Euclid, and for that matter for proofs as performed in practice by diligent students of elementary algebra, and later make it clear that there may be different views on what constitutes a valid proof, and connect that to the foundations of mathematics and axiomatic set theory, and also to proof theory.  --Lambiam 13:42, 2 January 2008 (UTC)
Informal mathematics does not use ZFC because the mathematicians are intending to use it. Rather, ZFC is a formalization of the methods which (it has been found that) mathematicians use informally. JRSpriggs (talk) 03:52, 3 January 2008 (UTC)
Yeah, that's true, to an extent. But the key word is "a"; it's not any sort of precise demarcation of methods that mathematicians use informally. You can make a case for both stronger and weaker systems as formalizations of informal mathematical methods. (I don't think you can make a very good case for NF in that role, though.)
I agree with Pokipsy and Lambiam about the defects of the text as it stands. --Trovatore (talk) 05:07, 3 January 2008 (UTC)
Ok, so we first have a general notion of (not completely formalized) proof and than (later) we have many atempt to formalize the notion of "proof" in formal systems that mimic a lot of branches of mathematics. My point is that the voice about "mathematical proof" (in general) should firstly define the former and more common and general notion of proof before addressing the latter formalized one.--Pokipsy76 (talk) 08:13, 3 January 2008 (UTC)
In proofs, when not explicitly stated, implicitly there are only those axioms which are necessary for the proof. I'd bet that many or most mathematicians could found their proofs explicitly if someone requested such a thing. Tparameter (talk) 15:50, 3 January 2008 (UTC)
(Responding to your first sentence) there's a rough convention to that effect, yes. It's not philosophically well-justified though, nor does it always apply (for example in some contexts set theorists may use large cardinals without explicitly mentioning that their existence is assumed). It's more of a time-saving linguistic convention than any sort of hard-and-fast rule, and still less is it revelatory of the essential nature of proof. --Trovatore (talk) 18:20, 3 January 2008 (UTC)
Oh, wait a minute, I may have misinterpreted you -- I thought you were using the word those in reference to ZFC. Maybe you were saying that a proof is implicitly from the minimum collection of axioms necessary to make that particular proof go through? That's also a possible interpretation, I suppose, though in a lot of cases different readers could interpret differently which axioms were being used. --Trovatore (talk) 19:25, 3 January 2008 (UTC)
I mean that the implicit axioms are the minimum necessary. I had a prof who would sometimes point out fundamental axioms that were required for this or that - but, I always take a proof to implicitly include a fundamental set of mathematical foundations. Of course, logically, it would be the smallest collection needed. Tparameter (talk) 19:52, 3 January 2008 (UTC)
"The minimum necessary" is not likely to be well-defined. --Trovatore (talk) 19:56, 3 January 2008 (UTC)
Wouldn't it always be 1, trivially? Not to be too stupid, but if we're talking about all possible sets of axioms, you want to prove X is in the theory of some set of axioms, the most obvious minimal choice would be {X}. That or perhaps {} for a tautology. --Cheeser1 (talk) 06:20, 4 January 2008 (UTC)
It's contextual. We cite the premises that are helpful in the context. If I give a talk about complex analysis to electrical engineers, I should say something like "i is the square root of minus one"-- because they use j instead, as 'i' is inductance. If we had to define every symbol we use in every context, we would never get to stating our results, would we? Then, common usage evolves with time. It used to be typical for ZF to be presumed, and ZFC to be mentioned when AX was needed; now I think ZFC is presumed. It only matters when there is ambiguity, then we are obliged to be more specific and expansive. Even mathematical language is imperfect. Pete St.John (talk) 19:39, 3 January 2008 (UTC)
Certainly, to the extent mathematical proofs are taken to be axiomatic proofs at all, the collection of axioms used is context-dependent. The issue here is that mathematical proofs are not necessarily proofs in a well-specified axiomatic system, in the first place. That's where the article under discussion falls short; it takes a formalist account of mathematical proof and presents it too uncritically. --Trovatore (talk) 19:45, 3 January 2008 (UTC)
I agree with this assessment. If I had access to my books, I'd check, but I vaguely recall a passage from an introductory logic book (Enderton probably, it's the one I used in a class) explaining that logic (the mathematical variety, that is) is not an attempt to do other parts of math more thoroughly, but to formally (symbolically, mathematically, rigorously, choose your word) study deduction, proof, etc. It's not necessary or required framework for other mathematics - if ZFC was never formulated, I don't think some guy studying numerical solutions to PDEs would fret over the rigor of his assuming the axiom of choice. Things like this are meta-mathematics. Of course, mathematical logic is useful in its own right (not to mention applications like nonstandard analysis), but some piece of math is significantly related to logic, or when conclusions have particular deductive nuances, logic comes up because it's relevant - the axiom of choice does matter, as logicians can tell us, but it does come up in others' work on its own. That's not because ZFC (or take your pick) underlies the work of all mathematicians, but because things like ZFC are constructed precisely to study the deductions and proofs that other mathematicians are already doing. The idea of "mathematical proof" isn't precisely defined, as far as I've ever seen. To me, it is (vaguely) a demonstration that something is true (in the appropriate mathematical context) based on the applicable standards of rigor. What those contexts and standards are, that is (and has always been) completely local to the field of study, level of work, type of audience, etc. --Cheeser1 (talk) 20:05, 3 January 2008 (UTC)
of course anyone can make a mistake, but any correct proof is also a correct proof in a formal system, when every premise is a theorem in that system. All the premises I ever make are theorems in ZF. Unless I make a mistake :-) so I expect to be able (when pressed) to extend every proof to one which is correct in ZF. (It just happens I've never needed AX in my work.) Right? Pete St.John (talk) 20:18, 3 January 2008 (UTC)
That's the formalist view. In my view, that account of proof is inadequate and fails to account for either the history of proof or the actuality of proof in mathematical practice. While it is probably true that, with sufficient effort, you can use one of your informal proofs as an outline around which to construct a formal derivation in ZFC, the process is not entirely trivial, and along the way you will be making some rather arbitrary choices -- that is, there won't be a single canonical ZFC derivation that corresponds to your informal proof, but rather quite a number of different derivations. So it's difficult to defend the idea that the ZFC derivation is the real thing and your informal proof is just a shorthand for it. It's more like your informal proof is the real thing, and the ZFC derivation is an analogue that's easier to study as a mathematical object in its own right.
(Just BTW, the usual abbreviation for the axiom of choice is AC, not AX -- the first time I thought you might just have hit the wrong key, but then you repeated it.) --Trovatore (talk) 20:41, 3 January 2008 (UTC)
re: AX, yeah, that must be old; for awhile we were writing "X" for Chi to abreviate "ch", and theta for "th", as in "4 <chi> map <theta>" for "four color map theorem" (since "color" in greek is "chroma"). I guess we were just too cool for school ...I mean, for sXool :-) Pete St.John (talk) 22:16, 3 January 2008 (UTC)
We still do that - a coloring of some object (e.g. a graph) is a function from the set making up part of that object (e.g. edges) onto a set of colors, and it's canonically (universally?) denoted Χ. I (and others that I know) frequently write things like mono-Χ instead of monochromatic. On the other hand, I've never seen it substituted for "ch" in general like that. --Cheeser1 (talk) 22:27, 3 January 2008 (UTC)
Isn't the reason we accept theorems the fact that we know that they're built from the ground up, and a path can be found back to the founding axioms? Tparameter (talk) 21:21, 3 January 2008 (UTC)
That's one view. As I say, I think that's an inadequate account. --Trovatore (talk) 21:24, 3 January 2008 (UTC)
Regarding the article, I definitely defer to your expertise. Regarding your comment - I'm curious, why do we accept theorems, or am I wrong in that assumption in the first place? Are theorems still debatable? Tparameter (talk) 23:10, 3 January 2008 (UTC)
Theorems are accepted because it's the work we do, and the results that we're interested in. If a proof meets the standards of rigor (ie it has been reviewed or verified, in some way), then we accept the result as valid. Not because it is a fundamental truth of the world (or of ZFC), but because it is a meaningful result and that's what we want. Mathematics is philosophy - theorems are debatable because they rely on assumptions and structures that we've thought up. All mathematical structures are "debatable" in some way - why have numbers like we do? Surely, there are compelling reasons and motivations for doing it the standard way, but structures in mathematics are entirely invented (at least for the purposes of analyzing them mathematically). And with mathematical logic we've done the same thing to proofs themselves - a proof becomes a mathematical object, as do axioms, statements, rules of inference, etc. These things become mathematical structures, and are invented and "debatable" like anything else. --Cheeser1 (talk) 00:56, 4 January 2008 (UTC)
Hmmm. Good answer. But, I guess we see things differently. The way I understand it, we shake hands and agree on the definitions and axioms, and from that point, the theorems we develop are absolutely true, given our agreement. This is the basis of mathematics (logic), as far as I know it. Tparameter (talk) 01:13, 4 January 2008 (UTC)
Well, as I say, that's the formalist view, more or less. From a realist viewpoint, the axioms themselves could be true or false, and a "mistake" might consist not in an error of logic, but in using an axiom that happens to be false.
There's no point in trying to settle such issues here--the point is that the article needs to avoid presenting one particular conception of proof as though it were accepted by the entire community, which it's not. --Trovatore (talk) 02:08, 4 January 2008 (UTC)
In addition to what Trovatore says - with which I agree, formal derivations are much more than trivial to distill from any usual mathematical work - I would point out that deduction itself is open to study. It's not as though logic is devoted to theorems and axioms, and how they just fall out of one another - what constitutes a valid deduction is open to interpretation (although again, there is a general convention in most contexts as to what is appropriate). What constitutes a "legal step" is just as much in question, even if there is a greater or wider consensus on the appropriate convention (I don't know if there is, I'm not that familiar with this stuff, but it seems as though something like modus ponens is probably more universally accepted than something like AC). And of course, it's very important to recognize and define rules of inference (even if they are agreed upon or considered trivial or obvious) because in logic, you're studying these deductions as mathematical structures - you can't just say "well MP works because it's logical." You must (explicitly) have a rule that says the formulas A and A→B imply the formula B, whereas most mathematicians make such a trivial deduction without taking the time to explicitly or formally say so. --Cheeser1 (talk) 21:12, 3 January 2008 (UTC)

## Tacit extension on AfD

Tacit extension is a stub article on mathematical logic which, if legitimate, certainly does not say enough; it doesn't really make clear what the concept is. So:

The edit history is interesting, User:Jon Awbrey had some beef with wikipedia and started a discussion on wikipediareview [1] inviting others to blank this page (and several other). This led to a revert war and subsequent page protection. It may be worth examining the other articles mentioned

## Boolean logic is back

Boolean logic in computer science has been moved back to Boolean logic. It has been zigzagging a bit lately: [2].  --Lambiam 15:34, 4 January 2008 (UTC)

I could see two articles, "Boolean Logic" and "Boolean Logic in Computer Science", making sense, just because of my respect-for/ fear-of the vast scope. An example of an item in the latter might be the use of XOR for fast, reversible varying-key encryption. Implementing boolean logic with electrical and electronic elements. A world of stuff. Historical items about Ada Lovelace reading George Boole. Pete St.John (talk) 19:16, 4 January 2008 (UTC)
The current situation is clearly unsatisfactory, mainly because "Boolean algebra" is the common name for the topic being discussed (and unfortunately for a quite distinct one as well). But I doubt a separate "computer science" article is the way to go -- Lambiam is right that the proliferation of articles is out of hand. Discussion at talk:Boolean logic#Move/merge -- still unsatisfactory. --Trovatore (talk) 19:29, 4 January 2008 (UTC)

## Population genetics on the "current activity" page?

Oleg, do articles in Category:Population genetics show up on the "current activity" page? One could say that this is not mathematics per se and that maybe the fact that an article belongs in that category doesn't always mean that it's mathematical. But nearly all of the articles in that category are on something in mathematics that is known almost only to those who apply mathematics to biology. Michael Hardy (talk) 23:45, 30 December 2007 (UTC)

I'd argue that population genetics is a bit too far from math to show up in the list of mathematics articles, and consequently, in the current math activity page, but I am open to views to the contrary. (BTW, I did not add the information theory categories to the bot list, as agreed earlier, will do so soon.) Oleg Alexandrov (talk) 07:32, 6 January 2008 (UTC)

## Relation composition

Looking at occurrences of the search term "tacit extension" I was led to our Relation composition article. What a complete and total mess! This is a phenomenal example of "mathematics made difficult". Is there something salvageable in there? Any reason not to change this into a redirect to Composition of relations?  --Lambiam 09:32, 4 January 2008 (UTC)

I support the merge. There's no need for two articles on the same concept, and this particular article is a model of how to make a simple concept obscure. — Carl (CBM · talk) 13:28, 4 January 2008 (UTC)
I agree. It's too bad about all the misdirected effort, but there doesn't seem to be anything worth keeping. (Except perhaps the idea to explain composition in terms of bipartite graphs.) --Hans Adler (talk) 22:57, 5 January 2008 (UTC)

## Mathematics Equation

Hi all I am currently working on an Article Process Management (Computing) and I am having trouble with an equation that I want to put in as I cant get the format correct is there a tag or something that you use for such equations thanks in advance. BigDunc (talk) 08:46, 7 January 2008 (UTC)

I would suggest starting by reading Wikipedia:Manual of Style (mathematics)#Typesetting of mathematical formulas. --Cheeser1 (talk) 08:57, 7 January 2008 (UTC)
I will thanks for the pointer. BigDunc (talk) 12:18, 7 January 2008 (UTC)

## Stevan Pilipović

Stevan Pilipović has been nominated for deletion - after originally being CSD'd as non-notable. I have no idea about the notability of this mathematician; comments are welcome here. Mostlyharmless (talk) 23:12, 8 January 2008 (UTC)

## HTML markup for composition

Various ways are in use for denoting the round symbol for composition using HTML markup:

roman o
f o g; R o S.
small roman o
f o g; R o S.
degree sign
f ° g; R ° S.

None of these looks particularly good to me. The degree-sign solution is really ugly on the Mac OS X platform, as the little circle is kissing the f and shying away from the g, leaving a huge gap. I tend to prefer the small roman o, but recently, in an article where I used that, another editor changed it to degree signs. Is there any reason why I should not use small o's? Which is preferable in general?  --Lambiam 15:26, 7 January 2008 (UTC)

Perhaps this gadget f○g  ? It's very big on older Firefox browsers, though. Jakob.scholbach (talk) 16:25, 7 January 2008 (UTC)
What about U+2218 "RING OPERATOR"? fg; RS. –Henning Makholm 16:27, 7 January 2008 (UTC)
I was going to suggest that, but it doesn't display well for me. Perhaps at home, where I use the STIX fonts, it will work. Ryan Reich (talk) 16:36, 7 January 2008 (UTC)
When I see them in my browser (Camino, a Firefox derivative, on a Mac), Jakob's circle is too big and Henning's is too small and too high. The Roman o is much closer to the right size and placement, and much more reliable, I think. —David Eppstein (talk) 16:37, 7 January 2008 (UTC)
Henning's ring looks perfect to me (Firefox on Win32), but the small Roman o works just fine. In no case should the degree symbol be used. CRGreathouse (t | c) 19:19, 7 January 2008 (UTC)
For some reason what I see for Henning's ring is like a degree sign in size, but placed even higher, and with a huge blank area to the right of it. I just tried it in Safari, and get the same result, but Jakob's circle looks much better in that browser. —David Eppstein (talk) 19:41, 7 January 2008 (UTC)
Henning's circle works for me with the STIX fonts; previously it was as CRGreathouse said, more like the degree sign. Jacob's circle is too big for me (and not on an old version of Firefox!) and although Lambiam's small 'o' looks good here (but a little uncentered vertically), at work, in Firefox on a Mac, it was ugly. This is one of those problems that is going to go away when Real Fonts are available; until then, I support the lower-case 'o' solution (either of Lambiam's first two is acceptable). Ryan Reich (talk) 19:58, 7 January 2008 (UTC)
"Real Fonts"? CRGreathouse (t | c) 14:17, 8 January 2008 (UTC)
That was Tongue-In-Cheek for "fonts that do what I want", which in this particular instance is display mathematical characters. I haven't heard that Real was releasing a font set :) Ryan Reich (talk) 13:33, 9 January 2008 (UTC)

## Project Proposal

It was recommended that I ask my question here. If I have an idea for a mathematics project where can I purpose it? The Isiah (talk) 13:42, 8 January 2008 (UTC)

Here is a good place. Jakob.scholbach (talk) 14:05, 8 January 2008 (UTC)

My idea was this what if we create an index of theorems and their proofs. In such a way as that a mathematician can place a alphanumeric code on a paper that would refer to a proof found on wikipedia. An example: lets say that we have a proof of Pythagoreans theorem call it PP112 and I am a mathematician and I need that theorem to prove something else I could write "based on PP112 we can say....". The benefit of this system is that we can have a complete listing of every theorem in existence in an easily referenced way. An index of theorems with their proofs. The alphanumerics code could also give a hint about how what type of proof strategy was used like direct, by induction etc. as well as what type of theorem it is geometry, number theory, etc. Hope this seems like a good idea. The Isiah (talk) 11:44, 9 January 2008 (UTC)

Every theorem in existence? This would be far too much, and would not be suitable for Wikipedia. Wikipedia is an encyclopedia, and what you are proposing is that an encyclopedia contain virtually everything ever published in Mathematics. There are millions of journal articles, books, unpublished papers, etc that this would include. It is impossible. Furthermore, Wikipedia is not an academically reliable source - you've got it backwards. We rely on and cite academic works - not the other way around. And this idea would be impractical because Wikipedia constantly changes. Any proof we have is subject to change, deletion, etc. and frankly, proofs we present here could reasonably (and legally) be reproduced elsewhere. Finally, there are already standard ways to cite Wikipedia that work just as well. Sorry if I'm "shooting down" your idea, but it doesn't seem like something appropriate to Wikipedia. What you suggest is essentially to transfer the entire body of mathematical knowledge onto Wikipedia, but only to provide a new way to do what standard citations do for us already. --Cheeser1 (talk) 11:51, 9 January 2008 (UTC)
Interesting idea. As Cheeser1 points out, Wikipedia isn't the place for that -- but have you looked at Metamath, which does want to standardize and collect mathematical theorems? CRGreathouse (t | c) 17:29, 9 January 2008 (UTC)
Looking at that, Mizar is probably closer to what he wants. Septentrionalis PMAnderson 00:25, 10 January 2008 (UTC)

## Mathematical induction

I made a remak in the talk page about the intro but nobody considered the issue, so now I'm coming here.

In the intro of mathematical induction I read:

Indeed, the validity of mathematical induction is logically equivalent to the well-ordering principle.

what is it referring to? We have a section "proof or reformulation of mathematical induction" where it is shown that MI can be proven assuming WOP and some other axioms, but this is something different from "logical equivalence". Shouldn't this be fixed in some way?--Pokipsy76 (talk) 17:35, 8 January 2008 (UTC)

I've simply removed this questionable sentence. It does only make sense to proclaim logical equivalence of two sentences if the logic is given in which these sentences are formulae, which is not the case here. In some logics they are equivalent, in some other logics they are not.  --Lambiam 16:04, 9 January 2008 (UTC)

## (Incomplete) Summary of Joint Math Meeting "Wiki Math" session

(organized by Bill Casselman and David Austin)

### CS's report

#### Articles viewed (with summary of Casselman and/or Austin comments)

Penrose tiling: overview of the article's development - article created with figure, additional figure violating parallelogram rule added, later fix of caption explaining figure violates parallelogram rule, eventual fix of the complete condition for Penrose tiling, removal of Richert claim. Casselman [David A, not me: Bill C] then attempted to demonstrate how to edit Wikipedia by editing a statement (which he disputed) that "Penrose tiling" usually refers to two special Penrose tilings with extra symmetry. But he ran into an edit conflict, so moved on. [Again from Bill C: I thought he recovered very well; it must have been one of the audience who made the change! after all.]

Floer homology: issues regarding readability of technical articles, made some quick comments about talk page discussion

Division by zero: briefly explained how this article had clearly been significantly improved upon, "don't know if Wikipedia needs an article like this" but said the article indicates quality on Wikipedia gets significantly better over time

Archimedes (and FAs in general): horrible article, not professionally written, many inaccuracies (explained how the historians of mathematics at the JMM had expressed their dissatisfaction with history of mathematics articles on Wikipedia), not enough about mathematical contributions

#### Closing points

1) Casselman had clearly prepared some material on who edits Wikipedia. One slide, for example, (briefly flashed), showed a list of contributors, probably ranked by contributions. But he chose to skip this, and early on, he made some comment like "it's interesting to see who the primary contributors are but I won't talk about that" or something to that effect. I wonder if Arcfrk's comments had an effect here. At the end, he expressed the opinion that real name usage was the way to go, "...it raises the level of discourse much more quickly to a mature level."

2) Casselman and Austin both seemed very knowledgable about how Wikipedia functioned, for example, comments on !votes as "the participants don't vote...it ends up being determined by committee somehow. I wish I knew more of how it worked." Interestingly, some very pragmatic advice on how to start editing Wikipedia was given. The first step, according to them, is to avoid editing popular topics. Pick a little worked-upon topic and work on it extensively before moving on to more major topics.

3) They expressed a desire to set up something where the AMS could help mathematicians learn to contribute to Wikipedia, possibly utilizing WikiProject Mathematics.

4) One criticism I heard of the presentation (and one that occurred to me also) is that the abstract suggested the issue of disputes over mathematics articles would be investigated in some depth, but this did not occur, only some brief comments on "too many cooks". There are a variety of interesting ways disputes arise over math articles (usually because of the "cooks" issue) but none of this was shown. I know a number of people were disappointed by this. [Bill C sez: we ran out of time, sorry about that. Why didn't you ask questions at the end? In my talk I raised the topic that someone had brougt to my attention, a Computer Science guy who was investigating how consensus was formed on Wikipdia. Does anybody know about this?]

1) Casselman commented upon how Sanger advocated an "expert" approach while Wales advocated "anarchy". It didn't seem to me he was aware of Jimbo's somewhat nuanced position on authority and credentials, per the whole Essjay controversy and his subsequent proposal to authenticate people's credentials.

2) WikiProject Mathematics and the Math MoS was discussed at several points. The MoS was commented upon favorably, but the Project got a bit of a black eye. Namely, Casselman (or was it Austin?) showed the ratings table and started discussing the math FAs. His general conclusion (as mentioned above) is they had a lot of problems and were certainly far from the standard he expected from the FA criteria. For example, he commented upon the many footnotes which do not actually act to make the article more reliable. He did not mention (probably because he was unaware) [Bill C: yes, unaware. Not mentioned in the ratings themselves, where FA lies on top of A class.] any of the controversy about math FAs and the friction between FAC/FAR editors and Project members (particularly about this whole footnote issue). He also did not mention the A class articles, which was set up to avoid FAC and some here may consider more representative of the best math articles on Wikipedia than the FAs.

[I left a message on Casselman and Austin's talk pages linking this discussion.] --C S (talk) 19:57, 9 January 2008 (UTC)

### WPM Discussion

I see, á propos, that nobody commented on the FAR of Gauss, except me, briefly. There's a case for ignoring FA completely; but if we do, we should cease to note it in the project statistics, and we should probably lobby for another way to pick front page articles. Septentrionalis PMAnderson 23:10, 9 January 2008 (UTC)

(independent comment: ec) Many many thanks for reporting so carefully on this here, C S. I am particularly interested in the comments about ratings. One thing I would emphasise is that these are primarily a tool for editors not for readers, which is why they are placed on talk pages.

However, FA is a bit of an exception, because of the high profile and the little star these articles get. In this regard, we all know that it is quite difficult to get maths articles listed as FA, because of all the WP:MoS and inline citation hoops, but I have also found it surprising that it takes quite a bit of work to delist an FA whose content quality is poor. My main experience was with Galileo, an article that utterly failed to address his mathematical contribution. To list this as FAR, I was expected to make a serious attempt to fix the problems, which I am not qualified to do, so I ignored it. Eventually, after some weeks and disagreements, it was delisted. I suspect it would be a lot of work to delist (say) Archimedes for inadequate coverage of his huge contribution to mathematics. I don't have any conclusion to make here. Does anyone else? Geometry guy 23:20, 9 January 2008 (UTC)

Yes, thank you very much for reporting on the WikiMath section. A few follow-up questions:

• Can we get more people who attended the session (and took notes) comment on it? Perhaps, they can provide more details on presentation and the relative importance of the issues discussed.
• Does anyone have more specific information on the concerns of the historians of mathematics about its treatment on Wikipedia? Even knowing the names of the people who care about these issues would be helpful (in my opinion, the quality of historical aspects of mathematics articles is of several orders of magnitude worse than the quality of their mathematical aspects – look no further than Linear algebra). Can they be induced to participate in the project, or at least provide "quality control" type of feedback?
• Would the text of Casselman's presentation be made available?

Arcfrk (talk) 00:40, 10 January 2008 (UTC)

## Status of the project

I think it's a good time of year to reflect on the status of the project. What articles did you feel were success stories in 2007? Are there any articles or processes that should be given more emphasis in 2008? What's the status of mathematics on Wikipedia at the end of 2007? — Carl (CBM · talk) 14:09, 26 December 2007 (UTC)

The more advanced topics have reasonable to good coverage, and most articles are in decent shape – although many could still bear a more elementary and explanatory introduction, and better motivation and examples. On the negative side, I think much of the rather basic stuff does not get much attention (or perhaps relatively more attention from less informed editors) and is often not in very good shape, sometimes even embarrassingly bad. This applies both to elementary concepts (for example System of equations) and to fundamental concepts (for example Definition and Defined and undefined). It tends to get worse when the topic involves logic; try to understand from our articles what the distinction is between the Law of excluded middle and the Principle of bivalence.
In general, we have done well in terms of working together to improve the encyclopedia. It is a pity the cooperation of the week|month won't take off and stay in flight; perhaps we should move to the cooperation of the year. The proliferation of Boolean algebra articles, with the Boolean algebra (logic) article starting with "Boolean algebra (or Boolean logic) is a ..." while Boolean logic itself redirects to the ill-named Boolean logic in computer science, is not a showcase of how the famous Wikipedia consensus process works. (Strangely enough, Boolean Logic redirects to Boolean algebra (logic), and so do Boolean algebra (basic concepts), Logic design, Logic function, and Elementary Boolean algebra. And then there are separate articles titled Boolean function, Boolean-valued function, Finitary Boolean function Finitary boolean function and Truth function. I'm sure I am forgetting some, but it should be clear this is somewhat of a mess.)  --Lambiam 15:22, 26 December 2007 (UTC)
What I forgot is Propositional formula, which has considerable overlap in content with Boolean logic in computer science.  --Lambiam 21:59, 29 December 2007 (UTC)
I agree with Lambiam, that the more elementary articles often need more work to get them into decent shape. For example probability, circumference, group (mathematics), Galois group. Some of the collaborations of the month (integral and homotopy groups of spheres) were a success. However, at a certain (high-level) point everybody seemed to be content and it didn't improve that much anymore. An idea: given such an article. How about contacting external expert reviewers, i.e. mathematicians working in the respective field? One could take somebody who is already cited in the references section of the article (and still alive...). Their review could stimulate further improvement. Jakob.scholbach (talk) 20:15, 26 December 2007 (UTC)
I have in fact several times suggested a phased approach that would start with a peer review: User talk:Meekohi#MCOTW procedure and Wikipedia talk:WikiProject Mathematics/Archive 24#Wikipedia:Mathematics Collaboration of the Week. This will allow more people to participate; I think it will be helpful to also get input from mathematicians who are not experts on the topic, since they can more easily spot unwarranted assumptions about what the reader knows already, and also more readily identify how accessible the exposition is. The next phase may help by setting a target for improvement, and also by getting people engaged.  --Lambiam 21:25, 26 December 2007 (UTC)

### Most articles too technical

According to the section of the WikiProject page, "some issues to think about":

I find there are many incomprehensible Wikipedia articles on mathematics, physics and related subjects, which is unfortunate, given the importance of mathematical thinking in being able to gain a deeper understanding of many useful subjects, ranging from economics to technology. Bear in mind that those who are able to understand the technical concepts are those who have the least need to look them up in a general encyclopædia!

However, adding a prominent link to relevant articles is not enough, as it may lead readers on a wild-hyperlink-chase, if you will: they find a concept they don't understand, so they click on it, only to be sent to another article that assumes a level of mathematical knowedge they don't have. Rather, the default should be to:

1. add a link to table of mathematical symbols, and
2. include a step-by-step explanation of any concept deeper than the meaning of the symbols themselves.

By the way, I oppose the use of "trampoline" articles for any but the broadest of topics, such as, perhaps calculus. As far as I know, most print encyclopædias don't use them, unless you count the articles in Micropædia, which aren't really trampoline articles anyway.

Finally I wish to suggest that WikiProject general audience be revived. 69.140.159.215 (talk) 03:42, 10 January 2008 (UTC)

This is a tricky subject and I have to choose my words carefully. It is very true that a great many articles suffer from not being as readable as they could be, and this is a serious flaw. All of us who work on technical articles need to keep it in mind and do what we can to alleviate it.
However it is not realistic to think that articles on highly esoteric topics will ever be accessible to readers without a solid grounding in the field. If you want to understand the Stone–Čech compactification, the article will be a great resource for that -- if you first have a firm understanding of the basic notions of general topology. If you don't, it's hopeless. You first have to go and learn them. Wikipedia is not a textbook and can't teach them to you (though with sufficient effort, you can perhaps teach them to yourself, using Wikipedia). --Trovatore (talk) 19:59, 10 January 2008 (UTC)
I concur. We have to remember the difference between a reference book/website and an instructional book/website. --Cheeser1 (talk) 20:30, 10 January 2008 (UTC)

### Wiki Math at JMM

On a related subject, the Joint Math Meetings in San Diego will feature the AMS Special Presentation Wiki Math, organized by Bill Casselman, Tuesday January 8, 2008, 2:15 p.m.–4:15 p.m. The abstract sounds very intriguing, and I think that the Math Project should send its deputies (incognito?) to check it out. Arcfrk (talk) 15:58, 26 December 2007 (UTC)

Curiously, I can't find this mentioned on the AMS web pages on the Joint Mathematics Meetings, but you can find the abstract in the November issue of the Notices on page 1228, and online (as a PDF document) here.  --Lambiam 17:19, 26 December 2007 (UTC)
Sure, the more the merrier. Both David Austin and I will be happy to let anybody speak. Tuesday 2:15 - ? (BUT I want to go to Terry Tao's talk at 4:00), in the large lecture hall Convention Center 6AB (last minute change 'cause that's the only room with an Internet connection). But why incognito? I'll ask that again - why incognito?--Bill Casselman (talk) 20:56, 3 January 2008 (UTC)
Some people register and contribute under their real name; others prefer to contribute under a nickname pseudonym. Do you want to force them to reveal their identity? Arcfrk (talk) 04:35, 4 January 2008 (UTC)
According to the official schedule (and I know of no announcement to the contrary), Tao's talk is on Sunday at 11:10. "Wiki math" is also listed at 9-10:55 on Tuesday. As for "incognito", some people just like wearing masks and silly costumes. I personally will be dressed in a monkey suit and a black diamond-studded masquerade ball mask. --C S (talk) 06:00, 6 January 2008 (UTC)
Re "...monkey suit and a black diamond-studded masquerade ball mask.": that is very pimp. Mct mht (talk) 11:58, 10 January 2008 (UTC)
Corrections: While Tao's talk already happened at the time I said, "Wiki Math" was indeed moved to 2:15 as Casselman said. So the time listed (in the correction handout I got) is 2:15, Tuesday, 6AB. But Casselman will need to find a new excuse to leave early. Also, I will forgo the monkey suit. --C S (talk) 06:17, 7 January 2008 (UTC)
Actually, I'm a bit chagrined to note that Tao does have another talk at 4pm. The Wiki Math thing will start soon..I suggest watching for Casselman-incited vandalism. He seems a bit of a prankster. In particular I recommend watching for edits to articles like Langlands program. --C S (talk) 21:25, 8 January 2008 (UTC)
I'll take a look since I will be there (unless I have to do something during that time). If they say something too erroneous, perhaps I will try and make a correction. --C S (talk) 02:53, 27 December 2007 (UTC)

## Top page views for mathematics articles

Hi all, finally some data for page view of Wikipedia articles is available [3]. So I thought I'd use that to see what the most popular mathematics articles are. For the first twelve hour of December 10 2007 the most view articles were:

1. Standard deviation 5039
2. Pi 3533
3. Normal distribution 2971
4. Golden ratio 2588
5. Game theory 2331
6. Entropy 2320
7. Definition 2262
8. Fibonacci number 2207
9. Physics 2150
10. Statistics 2026
11. Quantum mechanics 2021
12. Quadratic equation 2004
13. Portal:Mathematics 1977
14. Prime number 1964
15. Nash equilibrium 1841
16. Derivative 1818
17. Variance 1811
18. Chaos theory 1742
19. Newton's laws of motion 1729
20. Mathematics 1729

you can see a more extensive listing at User:Salix alba/One day of mathematics page views, and more detail day by day listings of individual articles at [4]. --Salix alba (talk) 14:00, 4 January 2008 (UTC)

Dismayed to see standard deviation and normal distribution topping the list, I did some computations and arrived at what might generously be termed some cynical statistics. The above pages fall into four very broad and perhaps stereotyped academic subjects:
1. Mathematics "proper" (19847 views)
2. Statistics and economics (16019 views, of which Nash equilibrium and game theory are economics)
3. Physics (8220 views)
4. Wikipedia (1977 views)
The only article whose subject here may not be obvious is chaos theory, which I deemed to be "mathematics proper". I could be wrong. The largest subject (to my relief) was in fact mathematics proper. However, it falls into three broad and even more stereotyped subcategories:
1. Popular subjects (10292 views)
2. "Real" math (4004 views)
3. "Easy" math (3822 views)
4. Mathematics itself (1729 views)
The hit count for mathematics is oddly appropriate. It's also not fair to put it on the list separately, and maybe it should be in "popular". Popular math otherwise comprises pi, golden ratio, Fibonacci number, and prime number. I have generously deigned to place chaos theory with definition in "real" math, despite my suspicions about the affiliations of its patrons, which leaves quadratic equation and derivative for "easy" math, whose popularity I suspect to be due to people under 19 and people who regard the topics with relieved nostalgia. But then, we are not a textbook, so I should hardly expect otherwise. Ryan Reich (talk) 18:05, 4 January 2008 (UTC)
Does raise an interesting question -- why are standard deviation and variance separate articles? Should they be merged? --Trovatore (talk) 19:43, 4 January 2008 (UTC)
Standard deviation appears to be much less technical, which may be a good thing. Septentrionalis PMAnderson 21:30, 7 January 2008 (UTC)
It may be a good thing to have articles at different levels (I'm kind of conflicted about that), but does it really make sense to differentiate between "standard deviation" and "variance" based on the difficulty of the exposition? --Trovatore (talk) 21:38, 7 January 2008 (UTC)
I'm conflicted about Trovatore's question. The obvious answer is No; the inobvious side of the issue is: We will always have links to both, and some of our readers will be thrown by clicking on standard deviation and ending up at variance, or conversely. Also, since they go different directions, merging them will either mean losing stuff or ending up with a very long article. Septentrionalis PMAnderson 21:45, 7 January 2008 (UTC)
Isn't "variance" the more general term? So, we say "ANOVA", "analysis of variance" instead of "Analysis of Standard Deviations". It makes sense to me if the more general or abstract terms get more technical detail than the more familiar corresponding terms, e.g. "Lebesgue Measure" vs "integral" and "number theory" vs "arithmetic". As long as they point to each other, the reader looking for either more or less technical detail can find it. Pete St.John (talk) 22:10, 7 January 2008 (UTC)
No, it isn't clear to me that "variance" is the more general term. If it is, there's no mention of it at variance -- it's always the square of the standard deviation and has no more or less information than the standard deviation. The covariance matrix is more general, of course, but it isn't called the "variance" as far as I know. "Analysis of variance" is a term of art and doesn't tell us that much about the usage of "variance" in isolation; I think the latter is always just the one number. --Trovatore (talk) 17:11, 8 January 2008 (UTC)
Another little linguistic point: I think the reason it's "analysis of variance" is that "analysis" is being used here in the sense of "breaking apart" -- the sum-square-difference is broken down into a linear sum of pieces attributed to the various factors. That wouldn't work with standard deviations. --Trovatore (talk) 17:36, 8 January 2008 (UTC)
You could take this as a justification for the difference between the two. While the mathematical relationship is simple they are functionally different serving different roles. Standard deviation is a measure of spread whilst variance is nicer to work with.for more sophisticated analysis. As you point out the variance article could do with some expansion with summary style sections on Analysis of variance and Covariance. (Of course both concepts leave a lot to be desired being heavily affected by outliers Robust statistics is the way to go!) --Salix alba (talk) 01:11, 9 January 2008 (UTC)

### Portal:Mathematics

One thing I did note was that Portal:Mathematics gets a quite a high number of page views, more than the Mathematics page. I guess this is because it is linked from the Main page. As such it serves as an important route into the mathematics articles, yet does not seem to get much attention. --Salix alba (talk) 12:20, 10 January 2008 (UTC)

## funny article

List of scientific theories and laws. AfD? Mct mht (talk) 11:56, 10 January 2008 (UTC)

Redirect to a portal? It will be unmanageably long as a statement of all theories now held valid. Septentrionalis PMAnderson 19:34, 10 January 2008 (UTC)
Someone has marked it as in the middle of revamping. I would say let that get finished and take a look. I'm concerned that the list doesn't have a clear defining property - it seems too vague. --Cheeser1 (talk) 19:44, 10 January 2008 (UTC)

## Peer review help

Would some mathematicians give their opinion at Wikipedia:Peer review/Force? Thanks a 10^6. ScienceApologist (talk) 18:20, 11 January 2008 (UTC)

## Help on parametric math

I would appreciate some help in this discussion (as well as the two sections below it). There's a dispute over whether three parameters can be mapped to a geometric solid. SharkD (talk) 03:57, 14 January 2008 (UTC)

## Collatz conjecture

Please take a look to the edits by an unregistered user who cutted a lot of things, I don't understand them quite well and I am a little skeptic.--Pokipsy76 (talk) 17:23, 9 January 2008 (UTC)

I don't know enough about what this new user is trying to say to figure it out, but there was a substantial change in content here that I'm not sure is legitimate. Could someone with a little more expertise, or at least a better understanding of the context, take a look? --Cheeser1 (talk) 20:08, 9 January 2008 (UTC)
I've never heard of the Collatz Conjecture. It might help if someone who's read it abstracted the subject matter; does it require an algebraist, a group theorist, a non-abelian group theorist...? If it involves ennumerative combinatorics drop a note on my user page. But no Infinitary Combinatorics, those guys are nuts :-) Pete St.John (talk) 21:46, 9 January 2008 (UTC)
It is mostly elementary math: a bit of number theory and dynamical systems, and probably some combinatorics, yes. Geometry guy 21:59, 9 January 2008 (UTC)
To be fair, it's not easy to say exactly "what kind of math this is" since this is unsolved, and for all we know, it might be solved by Fourier analysis 10 years from now. But just by looking at it, it seems to be number theoretic (the content in question seems to be number theoretic at first glance, which I suppose is the more germane consideration). --Cheeser1 (talk) 22:03, 9 January 2008 (UTC)
Having skimmed over it, I'd say "unsolved conjectures in elementary number theory" which yeah, can be arbitrarily difficult and involve any imaginable technology. It looks like quite a bit could be trimmed as OR, there seems a dearth of references. I think it's more of an editorial issue (keeping up with overeager grad student who doesn't have an account) than a math issue (no problem following the logic in "optimization", at least in the earlier version, but maybe no reason to?). Pete St.John (talk) 22:42, 9 January 2008 (UTC)
I always discuss the Collatz Conjecture when I lecture in Algorithms or Automata (upper division computer science courses). You can write a very simple program (the one given in the article) that halts for all inputs if and only if the Collatz conjecture is true, for example. This is the main importance of the Collatz Conjecture to me, since it illustrates that it can be extremely difficult to decide whether an extremely simple program halts. Vegasprof (talk) 10:23, 15 January 2008 (UTC)

## Deego & mathematical software

User:Deego seems to have decided that most or all of the articles about mathematical software read like advertising and is flinging around frivolous advert & notability tags. I have reverted some, but he is restoring tags when I (and others) revert. Can an admin familiar with this general class of article please have a look at his recent contributions? --Pleasantville (talk) 16:59, 10 January 2008 (UTC)

The articles include such sentences as Mathsoft Engineering and Education, Inc., the company that sells those popular products was is just one division of what used to be MathSoft. Popular is the sort of language WP:PEACOCK was written to discourage, and I would not be vastly surprised to find the whole sentence, before the incomplete correction, in promotional literature. Septentrionalis PMAnderson 20:42, 10 January 2008 (UTC)
I would like to point out that:
1. Pleasantville clearly seems to have a commercial interest or relationship with wolfram research.
2. He was initially very concerned with my advert tags to each of wolfram's minor products.
3. He has consistently dodged the question and refused to identify his relationship with that company.
4. Subsequently, he's started looking up my edit history, and undoing my changes to other promotional material for other companies, perhaps to appear more credible.
5. He called my advert tags "frivolous" which alone betrays his strong interest in Wolfram.
6. He simply undid my "frivolous" changes, without following protocol of bothering to discuss or following protocol.
7. He resorted to a lot of ad-hominem attacks on me at various places. Only now have I questioned his personal behavior.
8. Mathworks'-related pages clearly look like promotional material.
9. Just to cite one example, here is one page: http://en.wikipedia.org/wiki/MathModelica_System_Designer ;
10. it is full of weasel words like "professional",
11. it looks like promotional material,
12. is hardly notable.
13. As I said, there are more such pages related to Wolfram research.
14. It would be weird if we created a wikipedia page for every add-on package related to GNU Octave, for example.
15. The sheer number of pages related to minor products from Wolfram research on wikipedia makes one wonder if this whole phenomenon does not look like promotion.
16. I suggest that Pleasantville disclose his commercial relationship with mathworks.
17. I also request that he and more generally, others with relationship with mathworks, refrain from editing mathworks pages, to avoid conflict of interest.
18. Wikipedia is an encyclopaedia, not a place for commercial interests to do PR.
sincerely, Deego (talk) 21:59, 10 January 2008 (UTC)
For someone who knows so much about User:Pleasantville, it surprises me that you didn't notice that she's a woman. Stop hurling about these accusations, or do it civilly through the proper channels (eg WP:COIN). That is, if you can substantiate your claims. --Cheeser1 (talk) 22:10, 10 January 2008 (UTC)
Ok, http://www.kathryncramer.com/about.html - "She is an Internet Consultant (read: promotional writer) for Wolfram Research, Inc. in the Scientific Information Group. She lives in Pleasantville, New York." It is sad that PR people from companies make it to wikipedia and spoil the whole process, while even refusing to disclose their identities. Deego (talk) 22:13, 10 January 2008 (UTC)
I'll try a dialog at the Talk pages. I have prior good experience with Pleasantville regarding the Wolfram pages, but I agree with Deego that the overall tone of some of these articles is more positive than I would write myself. My sense is that neither wants to paint with too broad a brush. Pete St.John (talk) 22:46, 10 January 2008 (UTC)
I have now flagged this and other violations by User:Pleasantville (including an article on herself on wikipedia!) at WP:COIN. I don't have time to fight people with commercial interests, so I am hoping someone who reads this will take this up, and hopefully, some admins will do something about it. I am most likely signing off. Deego (talk) 22:49, 10 January 2008 (UTC)

Dear all,

Uninterested third party here. I have looked at User:Pleasantville, and overall she seems to be a constructive Wikipedia editor. I also see on User:Pleasantville that she does work for Wolfram, and so hopefully I think it's best to be mindful of WP:COI and the guidelines on external links and promotional material (see, e.g., [5], [6], [7], [8]).

I cannot say anything about User:Deego.

Sincerely,

Loisel (talk) 22:55, 10 January 2008 (UTC)

Here is just one example of COI on her own page: http://en.wikipedia.org/w/index.php?title=Kathryn_Cramer&diff=103478188&oldid=103390946 There are many others. Also, a lot of contributions on that page come from IP addresses. Deego (talk) 23:00, 10 January 2008 (UTC)
Wow! Maybe I should do this. WP:AB [9]. Loisel (talk) 23:02, 10 January 2008 (UTC)
The above was a very incorrect characterization of my behavior: "plastering everything written by her with tags". First, when I added advert tags, I didn't even know of a user:Pleasantville. Second, I added them following just the right protocol - I added them to articles that read like PR. Third, It's funny, at the COI page that you just suggested, your fellow friends are advising that the proper protocol is to rather do what I had done to begin with - address individual problematic pages. Deego (talk) 05:40, 11 January 2008 (UTC)
Anyhow, I haven't made any further flagging of advert or any edits since then, rather entering into a discussion here, and flagging COI. Since edits seemed to lead to edit wars, and I am not a fan of them, I have stopped making them. Deego (talk) 06:17, 11 January 2008 (UTC)

I was going to stay out of this, but I did just notice while browsing Wikipedia that Deego has been insistent on tagging the The Geometry Center article with a notability tag. This seems highly misguided, especially after a link to a Science article about the Center was added. The original WP article perhaps didn't do such a good job of establishing "notability", although certainly anybody that read the article carefully would not have tagged it. But the Science article gives good context, e.g. Center was first NSF Science and Technology Center, involvement of several Fields Medalists, early Web involvement (one of first 100 websites). I expect Deego mistakenly tagged some other articles too. --C S (talk) 04:59, 13 January 2008 (UTC)

I've been trying to find some more reliable sources to help establish the notability of the Geometry Center, but I've had a hard time getting meaningful results out of google. There is a problem with many mathematical organisations in that these tend not to attract much mention in the mainstream press, but those in the field can appreciate their notability. If anyone has a copy of the science article I'd like to see it but alas I don't have a subscription so can't get it from the website. --Salix alba (talk) 15:30, 13 January 2008 (UTC)
The Science article is distinctly more negative than ours: the first paragraph is Was the cause professional jealousy, loss of key personnel, shifting priorities, the lack of community support, or a breakdown in communication with National Science Foundation (NSF) managers? Observers disagree on what killed the first Science and Technology Center (STC) at the University of Minnesota, created in 1991. But its demise provides a cautionary tale. Only one other center in the program's history has been terminated early, and that death was due to technical problems in trying to apply magnetic resonance technology to basic biology. If the second sentence means it was the first STC anywhere, that would be notability; but I doubt it. Septentrionalis PMAnderson 23:25, 13 January 2008 (UTC)
A quick look at Google News Archives suggests that it was mentioned fairly often in the press in the early-mid 90s. Also, there are a fair number of mentions accessible via the Amazon Search Inside This Book program, though I haven't sifted through. --Pleasantville (talk) 23:33, 15 January 2008 (UTC)

## Rollback ability

I have learned that the ability to rollback edits, which is used to revert vandalism more easily, can now be granted to non-admin users. Unlike the undo operation, rollback does not require entering an edit summary and can be done from the user contributions page. It should be used only to revert edits that are clearly vandalism, but does make this more convenient. At the moment, any admin can enable the rollback ability for any user (I don't understand the process by which this was determined). If you are interested, please ask me or another admin on this list. — Carl (CBM · talk) 21:27, 14 January 2008 (UTC)

## Greenwaldian Theorem

Is this similar or based on anything real, or is it basically just a one-off joke limited to Futurama: Bender's Big Score? A google search reveals 23 hits and a google news and books search gets zilch, so it doesn't appear to be a "real" theorem. I'm sorry if it's a stupid question, but I never was any good at math... -- Scorpion0422 01:20, 15 January 2008 (UTC)

It doesn't seem real to me. Way too in-universe to be presented as the "Greenwaldian Theorem." We don't do articles for every single joke in every single TV show, and that's what this seems like to me. --Cheeser1 (talk) 01:26, 15 January 2008 (UTC)
Okay thanks, that's what I thought. In the DVD, she explained it as if it was a real thing, so I thought I'd double check here. -- Scorpion0422 01:31, 15 January 2008 (UTC)
According to the Law of cosines (spherical), "... the spherical Pythagorean theorem reads ${\displaystyle \cos(c)=\cos(a)\cos(b)\,}$" when the angle between sides a and b is a right angle. To the fourth order, this gives 1 - c^2/2 + c^4/24 = (1 - a^2/2 + a^4/24)*(1 - b^2/2 + b^4/24) = 1 - a^2/2 + a^4/24 - b^2/2 + a^2b^2/4 + b^4/24. Thus we get 12c^2 - c^4 = 12a^2 + 12b^2 - a^4 - 6a^2b^2 - b^4. Replacing c^4 by (c^2)^2 = (a^2 + b^2)^2 = a^4 + 2a^2b^2 + b^4, we get 12c^2 = 12a^2 + 12b^2 - 4a^2b^2. Thus c^2 = a^2 + b^2 - a^2b^2/3 < a^2 + b^2. So the "Greenwaldian theorem" is true for small right triangles on a sphere. JRSpriggs (talk) 05:22, 15 January 2008 (UTC)
Or more generally on any surface of positive curvature, I believe. Algebraist 07:38, 15 January 2008 (UTC)

## Category:Abel Prize laureates at CfD

Category:Abel Prize laureates has been nominated for deletion. 132.205.44.5 (talk) 23:13, 15 January 2008 (UTC)

## random math article?

Is it possible to jump to a random math article (just like Special:Random, but restricted to math articles)? Jakob.scholbach (talk) 18:35, 17 January 2008 (UTC)

This is one way. -- Meni Rosenfeld (talk) 19:40, 17 January 2008 (UTC)
I am probably displaying my ignorance of the modern Internet, but is it possible for Jitse to provide that PHP file for download, so I could (say) put a link to it on my machine as a bookmark and not have to pass through his school's server? This would make it rather faster. Ryan Reich (talk) 02:30, 18 January 2008 (UTC)
I believe you need some php-server to display php-files on your local machine, say. Jakob.scholbach (talk) 08:21, 18 January 2008 (UTC)
That's basically correct. Besides, you would also need another file on my computer which contains the names of all the articles and is read from the PHP file. That other file is updated daily. -- Jitse Niesen (talk) 15:21, 18 January 2008 (UTC)
I guess I'm not yet so ignorant that I don't know when to ask the question. That's what I thought the answer would be. Thanks. Ryan Reich (talk) 16:11, 18 January 2008 (UTC)

## Category:Metalogic

There is a discussion going on whether the newly split-off Category:Metalogic should be merged back into Category:Logic.  --Lambiam 10:25, 18 January 2008 (UTC)

## Grounded relation on AfD

The article Grounded relation has been proposed for deletion.  --Lambiam 05:38, 19 January 2008 (UTC)

## "Ultra power" etc.

New user Ultra.Power has recently created three almost identical articles: Ultra power, Ultra Exponential Function and Infra Logarithm Function, and added links to them to other mathematics articles and lists. These articles appear to be describing a non-standard, non-notable, single sourced version of the tetration operation. I first saw Infra Logarithm Function on Wikipedia:WikiProject Mathematics/Current activity (other articles were not categorised) and added a prod tag. User:Utcursch quickly removed the prod tag with an edit comment "notable for mathematicians". Are these functions notable under these names and notation ? I haven't come across them in this guise before - I would say that the "ultra power" function is called hyperpower or tetration - and the articles do not seem to be saying anything that is not already covered by the tetration article. Views ? Gandalf61 (talk) 10:58, 12 January 2008 (UTC)

In my expert opinion, the function described in Ultra Exponential Function is equivalent in all respects to the "linear approximation" section of tetration. Also, Bromer, Wassel, Rubstov, and Romerio have set the tone for "super" as the standard prefix for tetration, not "ultra". AJRobbins (talk) 11:45, 19 January 2008 (UTC)
After some tidying up by User:RHaworth, all three pages now redirect to ultra exponential function, and I have changed links to bypass redirects, so at least the cloning of articles has been resolved - but I still think that ultra exponential function says nothing that is not already in tetration, apart from introducing non-standard terminology and notation. Gandalf61 (talk) 16:32, 12 January 2008 (UTC)
I believe I have seen ultra used for tetration in print, although I have not done a search to find it; so non-standard may be a touch strong. Littlewood also wrote of "towers" before any of the current literature, and IIRC he had defintion for fraction tower heights. Merging may be in order. Septentrionalis PMAnderson 16:44, 12 January 2008 (UTC)
I think I have never heard of these terms in such a context. I am, however, very familiar with ultraproducts and their special case ultrapowers, as used in universal algebra and model theory. The result of a search with Google Scholar was quite interesting: On the first couple of pages "ultra power" only appears in the sense that I know as well as in non-mathematical contexts (related to electric power). Ultrapower was already a redirect to ultraproduct. The same is now true for ultra power and ultra product.
As to notability of this tetration-related terminology, I think the following Google Scholar search results speak for themselves: [13], [14] and [15]. Therefore I decided not to add a disambiguation note to ultraproduct at this point. But I am of course not fundamentally opposed to that if it turns out that more than one author is using this term. --Hans Adler (talk) 16:57, 12 January 2008 (UTC)
I don't know the journal in which Hooshmand's paper appeared, but it seems to be legitimate (as it is reviewed in Mathematical Reviews and Zentralblatt). I can't read the paper from home (or even the references), but the abstract cites 3 previous works: Euler, Baker and Rippon, and MacDonnell. It turns out that searches for "hyperpower"/"hyper power" in connection with Baker and Rippon, or MacDonnell, are successful, and searches for "ultrapower"/"ultra power" are not. (Apart from Hooshmand's paper.) Based on this I think the "ultra" terminology for tetration clearly fails WP:N. (WP:COI and especially WP:BITE also seem to be relevant.) --Hans Adler (talk) 17:36, 12 January 2008 (UTC)
I hope it is considered fair use to list the Hooshmand paper's references here. They are:
• Euler, L., 1777, De formulis exponentialibus replicatus. Acta Academiac Petropolitenae, 1, 38--60.
• Macdonnell, J., 1989, Some critical points on the hyperpower function $^{n}x=x^{x}$. International Journal of Mathematical Education in Science and Technology, 20(2), 297--305. MR0994348 (90d:26003)
• Baker, I.N. and Rippon, P.J., 1983, Convergence of infinite exponentials. Annales Academiac Scentiarium Fennicae. Mathematika. Series AI, 8, 179--186. MR0698845 (85g:30039)
It is beginning to sound as though Hooshmand's usage of the term 'ultra power' is his own coinage. EdJohnston (talk) 18:05, 12 January 2008 (UTC)
Per this discussion, I {{prod}}ed this one, also. (It should also be noted that the infra logarithm almost certainly only exists (and is not unique) for 1 < a, not for 0 < a < 1.) As I noted in the {{prod}} notice, the question of the infra logarithm (to the base e) has been discussed for quite a while. It's the notation that I, also, object to. — Arthur Rubin | (talk) 18:56, 12 January 2008 (UTC)
Hooshmand defines it for a < 1. He has a proof of uniqueness under a convexity condition for a > 1, but leaves uniqueness for a < 1 as an unsolved problem. Septentrionalis PMAnderson 22:54, 13 January 2008 (UTC)

What this article calls the "infra logarithm function" is common in algorithm analysis, with the notation ${\displaystyle \scriptstyle \log ^{*}n}$ (pronounced log-star). I agree that the nomenclature in that article appears to be a neologism, though. —David Eppstein (talk) 20:50, 12 January 2008 (UTC)

FWIW, the Wikipedia article on that is at Iterated logarithm. CRGreathouse (t | c) 23:52, 12 January 2008 (UTC)

It would be a shame to outright delete these articles, destroying this misplaced but interesting contribution from a talented user. A merge would be better, given the nice explanations and examples given in the articles. Is there a deletion discussion ongoing? Tparameter (talk) 02:58, 13 January 2008 (UTC)

This would be better than the {{prod}}s, which UltraPower has taken out. Septentrionalis PMAnderson 22:57, 13 January 2008 (UTC)
Clearly ultra power should redirect to ultrapower. However if it can be established that the "tetration" sense has some currency in the literature, then a dablink could be placed at the top of ultrapower.
This is an orthogonal question to the question of what is to be done with the content. I haven't looked at the content but I can't see any plausible reason it would need to be deleted from the history (which is what article deletion would do), whether it's good or bad. If it's good, then yes, it could be merged somewhere, taking care to preserve attribution for GFDL purposes. --Trovatore (talk) 23:03, 13 January 2008 (UTC)
Concerning the content, I am a bit skeptical. Unless the tetration article gets it wrong, Hooshmand's paper uses not only non-standard terminology but also non-standard notation. This often indicates that a paper is fundamentally flawed, as the author did not know about the state of the art. Tetration states that the question of a canonical extension to non-integer hyper-exponents is an area of ongoing research. Ultra exponential function seems to claim that Hooshmand's paper contains the solution for this problem, but that for integer values the second derivative does not exist. This does not sound convincing at all. And I don't see how ultra exponential function explains the basics better than tetration does. --Hans Adler (talk) 23:20, 13 January 2008 (UTC)
The purported "main theorem" in ultra exponential function is obviously false. If a>e, then you can take any smooth concave function g: [-1,0]->[0,1] such that g(-1)=0, g(0)=1, g'(0)=(lna)²g'(-1), and trivially extend it to an f that satisfies all the given conditions. A lot of different g's are possible - for example, choose g'(-1) strictly between 1/ln²a and 1; draw lines of appropriate slopes trough (-1,0) and (0,1) until they intersect; smoothen out the intersection with an appropriate piece of a parabola. Thus it cannot be true that the conditions in the "theorem" determine f uniquely. –Henning Makholm 00:03, 14 January 2008 (UTC)
The second derivative (of the quasi-exponential function) does not exist at the integers because the first derivative is discontinuous. It seems clear that Hooshmand made up his own extention of the obvious tower, but it probably should still have a paragraph in the tetration article. Septentrionalis PMAnderson 23:27, 13 January 2008 (UTC)
I'm not sure why we should fear the loss of a misplaced but interesting contribution. It might be interesting as mathematics, but WP is not intended to be a home for original research. There is also a concern about abuse of terminology, which is most easily cured by keeping the redirect of ultra power to ultrapower. You wouldn't be able to save Hooshmand's contribution without also accepting his abuse of terminology. Could you restate the material in his versions in terms of tetration? If you did so, how would it be cited? If you cite his externally-published papers, you would have to restate their conclusions using the term 'tetration' instead of 'ultra power'. Surely this would be WP:SYN, unless you could somehow claim it was merely a change of definitions. EdJohnston (talk) 23:32, 13 January 2008 (UTC)
Tetration only has a consensus definition for integer values; it has at least two common notations, and several rare one. Mentioning Hooshmand's extension to real values should be no problem; I doubt the others cited were all originally published in the same notation either. Septentrionalis PMAnderson 23:42, 13 January 2008 (UTC)
(edit conflict) I don't think this would violate WP:SYN. Rephrasing is allowed; it is even required for copyright reasons. And using a different term which has exactly the same definition is just the mathematical equivalent to using a synonym. I see no harm in mentioning Hooshmand's paper in the tetration article (without any details), but I am not exactly keen on that either. --Hans Adler (talk) 23:49, 13 January 2008 (UTC)
I agree with the crytics by PMAnderson. I dislike the definition of tetration as well as definition of Ultra exponential function. Please define them on the complex plane (or explain why they cannot be defined for complex arguments) and then we analyze, are the definitions equivalent or not. For example, is it possible to express tetration in terms of functions of a single argument? dima (talk) 02:52, 14 January 2008 (UTC)
There isn't a unique continuation of integer tetration to real numbers or complex numbers, and though I've read some proposed continuations (Galidakis?) so far there's nothing definitive like an analogue of the Bohr–Mollerup theorem. CRGreathouse (t | c) 04:40, 14 January 2008 (UTC)
RE: "It might be interesting as mathematics, but WP is not intended to be a home for original research". I thought original research applied to wikipedia editors, not published research. Sorry, but what to what original research are you referring? Tparameter (talk) 16:52, 19 January 2008 (UTC)

## "Stevens' theorem?"

In irrational number, someone has added this:

The numbers exp r, cos r, and tan r are irrational for every rational ${\displaystyle r\neq 0\,}$.

They've cited an item published in that year. But it seems likely that the proposition is far far older than that. Perhaps what was published was a new proof of an old theorem. Does someone here know the facts? Michael Hardy (talk) 06:17, 19 January 2008 (UTC)

As stated, it is an immediate corollary of the Lindemann-Weierstrass theorem (1885). –Henning Makholm 19:32, 19 January 2008 (UTC)
The result is mentioned without the theorem name at http://mathworld.wolfram.com/IrrationalNumber.html. The name "Stevens's theorem" was added by the notorious 218.133.184.93 (block log). PrimeHunter (talk) 06:36, 19 January 2008 (UTC)
I removed the "theorem" text altogether, the user in question has a two-year pattern of introducing questionable information (whether with or without citations). I blocked him too, for edit warring at Parity (mathematics). Oleg Alexandrov (talk) 17:28, 19 January 2008 (UTC)
I can't believe he was still trying to insert that result into Parity, as if it falls within the scope of the article. There are thousands (millions?) of results in number theory that mention parity, odds, evens, etc. They don't all belong in there. --Cheeser1 (talk) 19:16, 19 January 2008 (UTC)

## Real or complex?

The article titled Euler's formula says:

Euler's formula states that, for any real number x,
${\displaystyle e^{ix}=\cos(x)+i\sin(x)\!}$

If it had said "complex number" rather than "real number", the identity would of course still be correct. The question is whether that statement ought to be called "Euler's formula"? Michael Hardy (talk) 17:07, 19 January 2008 (UTC)

Rudin's Real and Complex analysis is a fairly well known reference and suggests the real version is called Euler's identity (pg 2), but I found something that might be a little more useful to us. In a book by Moskowitz (A Course in Complex Analysis in One Variable, pg 7), he states the complex version ${\displaystyle e^{iz}=\cos(z)+i\sin(z)\!}$ and follows with "In particular, taking z real .. we get Euler's relation. Sometimes ${\displaystyle e^{iz}=\cos(z)+i\sin(z)\!}$ itself is called Euler's relation."
So maybe we can say either is acceptable and use the Moskowitz book as a reference? Ben (talk) 17:43, 19 January 2008 (UTC)
Does anyone know what Euler himself stated (I don't know whether he allowed complex arguments for trig functions)? Algebraist 18:29, 19 January 2008 (UTC)
If Euler's formula tells us how to do it for real x, why would the natural extension of the formula to all of C be called anything but "Euler's formula" too? It's the same formula, with a larger set of arguments. --Cheeser1 (talk) 19:13, 19 January 2008 (UTC)
I don't think he is explicit about it, but the argument in the presentation of the formula, for which Euler uses the letter v, is the result of multiplying an infinitesimal angle z with an infinite multiple n so as to get a finite value v (so nz = v), and the context suggests Euler is not considering complex-valued angles here.
Wouldn't it be sufficient to remark in the article that the equation holds equally for arbitrary complex-valued x, without entering into a consideration of whether it then should still be named "Euler's formula"?  --Lambiam 19:27, 19 January 2008 (UTC)
True, an easy work-around would be to say "Euler's formula says ____. It also holds for complex arguments." Or something like that. --Cheeser1 (talk) 19:34, 19 January 2008 (UTC)
Does that clear it up for any readers that ask themselves the same question Michael did though? Ben (talk) 19:41, 19 January 2008 (UTC)
Probably not, but then, is it the task of an encyclopedia to tell people what ought to be?  --Lambiam 01:04, 20 January 2008 (UTC)
No. But we should make it clear that Euler's formula does not only refer to the real version (that is, authors refer to the complex version as Euler's formula too), which we can do now per the ref I gave above. Isn't that all Michael wanted to clear up? Ben (talk) 01:38, 20 January 2008 (UTC)

(outdent, edit conflict) I don't think the question asked was what people ought to say, but what the encyclopedia ought to claim as truth. FWIW I think we can safely describe the complex-z version as "Euler's formula", irrespective of whether Euler himself considered complex z's. (One source for this usage is Ian Stewart and David Tall: Complex Analysis, Cambridge University Press 1983, p. 85). It seems to be generally accepted that named theorems may be restated in newer terminology, or even generalized to new settings, without losing their name. For example, you can use Euclid's algorithm in domains that Euclid had never heard of (and would have considered grievous fallacies of concept if he had); or pick up a selection of algebra texts and marvel at the variety of propositions billed as the Nullstellensatz. –Henning Makholm 01:42, 20 January 2008 (UTC)

Moreover, I think it is perfectly OK, and perhaps even good style, for an encyclopedia to be ambiguous in such cases. (So long as the fact that some people use the term in one way and some in another is not notable, which should rarely be the case.) --Hans Adler (talk) 01:58, 20 January 2008 (UTC)

## Organization question

Why doesn't Category:List-Class mathematics articles exist? Nousernameslefttalk and matrix? 02:10, 20 January 2008 (UTC)

Can you explain why it should? It looks like a naming scheme that I have never come across. --Hans Adler (talk) 02:13, 20 January 2008 (UTC)
There is Category:Mathematics-related lists. Is that what you were after? Ben (talk) 02:19, 20 January 2008 (UTC)
Yes. But when you enter {{ maths rating | class = list }} it has a link to Category:List-Class mathematics articles instead of the latter. Thanks for the clarification. Nousernameslefttalk and matrix? 04:00, 20 January 2008 (UTC)
It's an historical relic, I believe. When the WP 1.0 ratings were originally set up, some people thought it would be good to have a quality rating for all sorts of pages - lists, disambig pages, etc. But there isn't any reason to use those in the math project. The list of mathematics articles is automatically made without talk page tags, so we can limit the use of talk page tags to articles. — Carl (CBM · talk) 05:55, 20 January 2008 (UTC)

## Category:Leslie Fox Prize for Numerical Analysis winners nominated for deletion

This seems to be part of a pattern of categories of prize winners nominated for deletion [16]

Does anyone know what is going on here? It seems someone called User:Lquilter has some kind of mass deletion of categories campaign using some spurious criterion called "over categorization by award". Is there such a concept? Has it been agreed somewhere as a principle? I think we need to look at what is happening here and nip it in the bud before we everything including Category:Fields Medalists. Billlion (talk) 09:01, 17 January 2008 (UTC)

fixed username. Algebraist 14:33, 17 January 2008 (UTC)
There are a lot of unnecessary categories so people like Lquilter are going through them. See WP:OC which was linked by somebody in the Abel Prize discussion. I don't understand why we have certain categories and not others -- it's very inconsistent. But I think most of these categories should be deleted, including Abel Prize Laureates, Fields Medalists, Fox Prize, etc. They don't serve a function, as far as I can tell. For example, I would prefer looking at the Fields Medal article rather than the category. --C S (talk) 17:55, 17 January 2008 (UTC)
This seems to be similar to the Erdos Numbers categories (which were deleted despite consensus to keep). There seems to be an editorial philosophy that hasn't (so far as I know) been enunciated in a way that makes sense to me (or any math contributors). So I think this will be a recurring problem until someone figures out how to explain what they want and why, so we can address it. Pete St.John (talk) 19:48, 17 January 2008 (UTC)
C S, if categories don't serve a function, then why keep any of them? Pete St.John (talk) 19:51, 17 January 2008 (UTC)
I didn't say categories in general don't serve a purpose. But yes, I agree, ones without a purpose should be deleted. --C S (talk) 21:58, 17 January 2008 (UTC)
Of course. So now if you point out some categories that do serve a purpose, the rest of us can try and figure out what that category has that this category lacks, which would be a clue to understanding the PoV of the editors who advocate deleting (seemingly any) categories. Right now I don't have a clue. So please help. Pete St.John (talk) 22:10, 17 January 2008 (UTC)
I don't know what group "the rest of us" is, but let me try and clarify things. Certainly Category: Riemannian geometry and Category: number theory are examples of categories I expect everyone would want to keep. There is a clear use as a navigational aid. Editors like Lquilter have spent quite a bit of time explaining their rationale, which seems to at least partially involve function as navigation. I expect all the folks urging listify do not see any use, as I said, for the categories such as Fox prize winners.
It's interesting that you bring up the Erdos number cats. There are some similarities. When those cats were first created, it was pointed, by Charles Matthews and some others, that the (existent) lists were just superior: the chain of connections can be shown and is the chief source of interest. Another similarity: most people don't really care if these categories are deleted. --C S (talk) 23:27, 17 January 2008 (UTC)
Categories serve the purpose of automatically compiling lists of articles that have something in common - such that people who got a certain prize. What's wrong about that? Application of the "write once" principle. That would imply existence of stub entries whose only purpose would be to provide listing within a category. I think I tried to do some of those but they tend to get killed. Heard about the concept of database, anyone? It's the manually compiled lists that should be killed, as they will be always out of date. Jmath666 (talk) 01:30, 26 January 2008 (UTC)
"Most people don't really care if these categories are deleted" is a really bad argument for deleting anything on Wikipedia, because there are very few articles or other objects on Wikipedia for which it's true that most do care. It's more important whether the people who actually see and pay attention to the category links care about these ones. Also, I don't understand why it is necessary to hammer categories into a shape that is only fit for a single purpose, navigation. Wouldn't it be better to allow them to have other functions as well? —David Eppstein (talk) 00:02, 18 January 2008 (UTC)
Yes, that would indeed be a bad argument. I certainly hope nobody has made it. If you're wondering about my comment above, take that as my way of suggesting that perhaps project editors' efforts are better spent elsewhere. My attempts to figure out what's going on with the category business has only led me to the conclusion there are better uses of time. But of course everyone is free to do as they wish....although I note there have been several defunct attempts recently at creating interest in improving the quality encyclopedia articles. By the way, I meant "most mathematics editors don't really care...", and if not they, then who? --C S (talk) 00:12, 18 January 2008 (UTC)
Indeed, editors like that have spent a good deal of time explaining their rationale; mostly, frankly, by citing themselves, explaining, etc. Be that as it may, it was never to my satisfaction; so I'm glad you are willing to take this up. What about the Number Theory category is more useful to navigation than the Erdos Number category? Thanks Pete St.John (talk) 23:51, 17 January 2008 (UTC)
I think that's the wrong question to ask. How else can we navigate the number theory articles? There are ways like lists of certain subtopics, but certainly the cat is there simply because we can't think of anything better. There is an obvious improvement on the Erdos Number category, which is to create a list which would have the additional info that many mathematicians find interesting about Erdos numbers, e.g. the names of the collaborators. --C S (talk) 00:35, 18 January 2008 (UTC)
I still don't see any definitive explanation of what makes or breaks a category. And by "rest of us" I think Pete is referring to people who aren't actively contributing to CfDs on a regular basis (at first glance, there are 10-20 people whose contributions make up what appears to be the vast majority of all CfD discussions - for better or worse). --Cheeser1 (talk) 23:54, 17 January 2008 (UTC)

See also User_talk:Billlion#categories vs. lists where I reply to a query by User:Lquilter. It be interested in people's opinion over the value of categories in database searches.Billlion (talk) 01:32, 18 January 2008 (UTC)

### going forward

• Dear math people who are upset about CFD nominations relating to math: You might consider participating more regularly at WP:CFD to get a sense of what happens there on a regular basis, and not just on math topics. It might help avoid feelings of persecution, and it would certainly help the project-based vote stacking that happens when a math issue comes up. That's not helpful for the overall project, because it's much better that we have consistent treatment across the various disciplines and subjects. If you think CFD currently leans too delete-happy, then regular participation by category-keepers could shift the balance. On the other hand, if you, like me, participate for a while and over time find yourselves becoming more parsimonious with your ideas of what are appropriate categories, then you will perhaps be happier when math-related categories come up for discussion. Either way you can help categorization practice become more consistent across Wikipedia.
Right now, in response to people complaining about the math-related awards CFD nominations, there is a discussion at WP:OCAT about developing better examples and language for WP:OCAT#Award winners. Since a number of math project-related folks expressed strong opinions of various sorts (including calling me a "deletionist", which is pretty funny if you knew me) I'd really like to invite you to participate in that discussion to help improve WP's categorization guidelines. It can perhaps help us to develop a more robust consensus about these guidelines and practices.
Cheers, Lquilter (talk) 21:17, 21 January 2008 (UTC)

## Set spherical coordinates straight?

In the Spherical coordinate system, there are three quantities that define a coordinate: distance from the origin, azimuth, and zenith (collatitude).

The symbols used for these quantities has historically been inconsistent, and worse, in Wikipedia it is internally inconsistent. Compare:

Main problem is azimuth and zenith. Some use ${\displaystyle \phi }$ and ${\displaystyle \theta }$, others ${\displaystyle \theta }$ and ${\displaystyle \phi }$. This catches my attention because I have a homework assignment that I'm working on now, and I was terribly confused. The literature in general is confusing because different sources follow different conventions, but Wikipedia is especially tragic because it's self inconsistent.

So I suggest we unify things. I'd be happy to scavenge every trace of inconsistency and fix it myself. But I thought I'd discuss first. I suggest that we go with Wolfram's convention [17]. It's nice because:

• Using ${\displaystyle r}$ instead of ${\displaystyle \rho }$ prevents confusion with density. My assignment now is fluid mechanics, I need ${\displaystyle \rho }$ for this.
• Using ${\displaystyle \theta }$ for azimuth, because this way the definition is identical to what you see in cylindrical coordinates.
• Using ${\displaystyle \phi }$ for zenith, because that's what's left.
• Ordering them ${\displaystyle r}$, ${\displaystyle \theta }$, ${\displaystyle \phi }$, because again this follows cylindrical coordinates.

Main problem is confusing ${\displaystyle \theta }$ and ${\displaystyle \phi }$. Yesterday was the first time I worked in spherical coordinates. In cylindrical coordinates, ${\displaystyle \theta }$ is azimuth, and I found it really confusing that some sources use this for zenith in spherical coordinates. Why in the world would it be the opposite of cylindrical coordinates? Makes about as much sense as an extremely poisonous frog driving a motorboat. I'm mentioning this so that you see the point of view of someone who's just stumbled on the topic...

Let's get a consensus so I'll get to work. —Preceding unsigned comment added by Ben pcc (talkcontribs) 21:32, 21 January 2008 (UTC)

I've no immediate opinion on the desirability of imposing internal consistency here, but for what it's worth, the MathWorld notation is also the first choice in the article Spherical coordinates at PlanetMath.org. I note that all articles clearly explain that different conventions exist.  --Lambiam 02:33, 22 January 2008 (UTC)
I think it's a good idea to settle on one convention. See Wikipedia:WikiProject Mathematics/Conventions. On a related note, I'd like to invite you to have a look at Talk:Laplace operator (towards the bottom) where someone else brought the same thing up earlier today. Silly rabbit (talk) 02:38, 22 January 2008 (UTC)
Consistency is good, all other things being equal. The question is whether all things are equal. There are several claims in the various articles that one set of variables are physicists' coordinates and another one is mathematicians'. If that is correct (rather than just single editors extrapolating from small random selections of math/physics texts), it may be unrealistic to achieve and preserve global consistency.
Yes, but I'm concerned with mathematics articles. Also, while some say "physics vs math", I've also seen "American vs European". I don't think were you come from or what you study should affect practicality. I don't believe consistency could be preserved, but could increasing consistency do anything but help? -Ben pcc (talk) 03:55, 22 January 2008 (UTC)
Apart from the choice of variable letters, there is also a choice of zero point for the "latitude" coordinate. I was surprised to see "distance from the pole" being presented as the standard choice; I'm much more used to seeing systems where the "equator" has coordinate 0 and the poles have coordinate ±π/2. No convention is good for all applications here (it seems to depend on whether one is interested in the local geometry of the sphere, or in its global symmetries), but perhaps if we're discussing standardization anyway, we should settle on different symbols for the two coordinates? –Henning Makholm 03:13, 22 January 2008 (UTC)
There is no question about the zero point. In mathematics, we use colattitude (distance from the pole), in geography we use latittude (distance from equator). I've never seen an exception. It's also very straightforward to go from one to the other. -Ben pcc (talk) 03:55, 22 January 2008 (UTC)
I think you are using "azimuth" when you should be saying "longitude". Also "zenith distance" is not the same as the correct "colatitude". "Longitude" and "colatitude" refer to the coordinate system of the whole (the Earth, star, or other central body which is at the origin). "Azimuth" is the horizontal (as seen locally) angle from north. "Zenith distance" is the angle from the zenith (straight up from wherever you are). These two terminologies are the same only when you are at the north pole.
It is impractical to reserve any greek letter for a single purpose across all Wikipedia articles. There are not nearly enough letters for that. Just try to be unique within an article and clearly define what you mean. JRSpriggs (talk) 03:34, 22 January 2008 (UTC)
I'm not suggesting any letter be reserved, I never implied that (I use ${\displaystyle \theta }$ for contact angle on a daily basis). I'm suggesting consistency within a topic. Apparently I'm not the only one confused.-Ben pcc (talk) 03:55, 22 January 2008 (UTC)

Coincidentally, just today I've seen a remark in an undergraduate level textbook on differential geometry to the effect that the use of phi and theta for spherical coordinates in this book is the opposite of the convention adapted by many authors of calculus textbooks. Arcfrk (talk) 04:55, 22 January 2008 (UTC)

Actually, I don't agree that mathematics always uses colatitude. Furthermore, the equations if you use "latitude" have better symmetry, IMHO. — Arthur Rubin | (talk) 08:12, 22 January 2008 (UTC)
I've wondered why latitude is not common in math. It does have better symmetry. A component of the gradient is negative, but I can live with that. -Ben pcc (talk) 21:22, 22 January 2008 (UTC)

I don't think you'll ever achieve consistency here. Different people feel too strongly about one convention or another. Personally, I would vote for using θ for the zenith angle and φ for the azimuthal; for two reasons:

• This usage is nearly universal in physics (mostly likely due to the influence of J. D. Jackson's Classical Electrodynamics. Anyone who's suffered through an E&M course with this text is probably set in their ways for life).
• It's an international standard.

I realize that others will (strongly) disagree. I think the most we can hope for is consistency within an article. -- Fropuff (talk) 17:28, 22 January 2008 (UTC)

I agree, and can confirm Arcfrk's comment that this convention is common in differential geometry, where the 2-sphere metric is usually dθ2 + sin2θ dφ2. Geometry guy 18:04, 22 January 2008 (UTC)

Since I am very unlikely to contribute any deep insights myself, here are the most relevant links I have found so far.

From reading these sources I have learned that things are much more complicated than I thought. Apparently, whether someone writes (ρ,φ,θ) or (ρ,θ,φ) is related to the exact definition of φ and θ including handedness. Both the symbols and the order in which they are written vary. --Hans Adler (talk) 19:03, 22 January 2008 (UTC)

The last reference you provide (I recommend everyone interested read this) gives the very good argument that in the context of spherical harmonics nearly everyone uses θ and φ for the zenith and azimuth, respectively. I find it amusing that the reference book CRC Standard Mathematical Tables and Formulae (30th ed.) uses φ and θ for zenith and azimuth when defining spherical coordinates and then reverses their roles later when talking about spherical harmonics. Food for thought. -- Fropuff (talk) 19:44, 22 January 2008 (UTC)

Looking at the flurry of different opinions, I think that this sucks. Mathworld's convention makes more sense and is supported by some people who are easily confused (eg me), but rest of world uses something else. I'm not sure what to do or what can be done.

But one note: it's supposed to be ok as long as things are "clearly defined". In the spherical coordinates it's clearly defined, not usually so anywhere else around here. Usually I have to recognize something like ${\displaystyle \sin(colatitude)}$ and go from there. Put a picture of spheric coordinates in each article? A link to latitude? An explicit statement that "we're going for [or against] the convention in [some source]"? It. Sucks. Terribly. Math isn't supposed to suck like this. That's what metric vs customary is for. This is even worse than ${\displaystyle (-1)^{1/2}=i=j}$. -Ben pcc (talk) 21:22, 22 January 2008 (UTC)

Yes, it sucks. But keep in mind that we are debating something akin to a spelling difference. θ and φ are just letters after all. I don't think that either convention "makes more sense" than the other—it's just a matter of what you are used to. I think, in time, convention will gravitate towards one usage or another, but it's not going to happen anytime soon. In the meantime, it's best to acquaint oneself with both conventions. We should also make sure that any article using spherical coordinates clearly state which angle is the zenith and which is the azimuthal. -- Fropuff (talk) 23:14, 22 January 2008 (UTC)
I agree, whatever happens it'll take time. One thing though: I wasn't used to any convention, I just started working in spheric coords, and got really confused. No one has enforced one or the other onto me. -Ben pcc (talk) 00:39, 23 January 2008 (UTC)
The important point here seems to be that there are pages where the convention used there is not explicitly defined. One thing which could be done is make sub-sections of spherical coordinates for each convention. Other articles could then link to that sub-section. --Salix alba (talk) 14:30, 23 January 2008 (UTC)
Seem like a little bit of an overkill. Actually, in most cases it's easy to determine from context which angle is which. One thing we could do is insist that when listing spherical coordinates in the form (r, θ, φ) that the first argument always be the radial coordinate, the second always the zenith, and the third always the azimuthal. I think many readers, myself included, make this assumption when reading articles. If we clearly state this convention in the spherical coordinates article we should be able to minimize confusion for beginners why still making it easy to use both conventions. -- Fropuff (talk) 17:26, 23 January 2008 (UTC)
It might be sufficient to just be explicit in each first mention; e.g. (r, θ = Zenith, φ) like that? There's no way to be consistent with everything, e.g. "i" for Inductance, ρ for density, etc etc ad nauseam. Pete St.John (talk) 20:06, 23 January 2008 (UTC)
The expression "polar angle" is fairly unambiguous. For example, insert
This article uses φ for the polar angle.
before the first line of the text. Arcfrk (talk) 02:50, 24 January 2008 (UTC)

The word zenith for an angular coordinate is incorrect. Zenith means upwards. This must be corrected. The words "Azimuth" and "Zenith Distance" are specific for horizontal coordinate system and not for general spherical coordinates. Bo Jacoby (talk) 23:37, 23 January 2008 (UTC).

I don't know what you are referring to. The terms zenith angle (or polar angle) and azimuthal angle are the standard names for these angles. Perhaps they have different meanings in astronomy, but that is irrelevant. -- Fropuff (talk) 03:10, 24 January 2008 (UTC)
Just follow the links in Bo's posting and it will (hopefully) become clear what this refers to.  --Lambiam 07:47, 24 January 2008 (UTC)
I did follow those links, but I fail to see any problem. -- Fropuff (talk) 07:55, 24 January 2008 (UTC)
I'm with Fropuff, the usage in physics is universal, and until today, I thought was unambiguous. In honesty, I have seen a lot and have never seen the Wolfram usage, ever, before today. linas (talk) 04:47, 25 January 2008 (UTC)
I was taught to call them lanitude (or colatitude) and longitude. Zenith is new to me; and Zenith does not explain it. This would be the first step. Septentrionalis PMAnderson 05:59, 25 January 2008 (UTC)
• I use θ to be the longitude, because that way the coordinates on the equatorial plane restrict to standard circular coordinates; but I do not expect authors to agree. We have a mathematical conventions page; but readers, as in real life, may just have to adapt to inconsistency. Septentrionalis PMAnderson 06:04, 25 January 2008 (UTC)
Azimuth is an angle, but zenith is originally, and still in most contexts, a direction (and usually observer-dependent). The use of the term for an angle adds to the confusion.  --Lambiam 08:50, 25 January 2008 (UTC)
Yes, but I think zenith angle is fairly clear for "angle measured from the zenith" (assuming one is standing at the origin). But we are getting a little off topic here. -- Fropuff (talk) 18:09, 25 January 2008 (UTC)

## Interpreting integrals

There's a discussion at Talk:Integral regarding whether we should make the multiplication (if we believe there to actually be one) in an integral explicit. That is, should we write

${\displaystyle \int f(x)\,dx}$

or

${\displaystyle \int f(x)\cdot dx.}$

At first blush this seemed straightforward to me: the latter is diverging from standard usage, and even assuming there actually is a multiplication (rather than an anachronistic notational juxtaposition) seemed to be tacitly accepting infinitesimals (and thus going outside the range of definitions of integral discussed on Integral; Riemann, Lebesgue, etc.). Discussion of these points didn't help resolve the issue, and the discussion has now waded into deeper waters than I have the desire or time to get involved in. Perhaps I'm just wrong, or coming at the problem from too narrow a perspective; analysis isn't my field anyway. I would appreciate any input people can provide. -- Leland McInnes (talk) 14:44, 24 January 2008 (UTC)

I don't know about others, but I've never seen a dot or other indication of multiplication between the integrand and the differential. At most, maybe parentheses, eg S(x+4)dx. --Cheeser1 (talk) 15:36, 24 January 2008 (UTC)
A dot is certainly standard notation in the case of a line integral over a vector field (where it stands for a dot product).
For ordinary integrals, it is not uncommon, if the integrand is a fraction with unit numerator, to move the differential into the numerator position, e.g. ${\displaystyle \int {\frac {dx}{1+x^{2}}}}$. And I have seen at least one text consistently write ${\displaystyle \int dx\,f(x)}$. My impression is that standard notation is to notate the differential as if it were a multiplicand. What the question comes down to, then, is whether one would use a dot before Δx when writing down a term in a Riemann approximant sum for the integral. –Henning Makholm 18:52, 24 January 2008 (UTC)
Yes, but using dx in a numerator is a conventional abuse of notation - it can't be used to justify nonconventional abuses. Furthermore, if we're talking about some vector dot product, then maybe we have F(x,y)=<y,x+y> and dr=<dx,dy>. Then after the dot product it's still a standard integral of ydx + (x+y)dy - without dots. --Cheeser1 (talk) 02:53, 25 January 2008 (UTC)

WARNING: Bo Jacoby ahead. --C S (talk) 17:47, 24 January 2008 (UTC)

I see. You encouraged me to do a little further reading with regard to my would be debate partner. It seems that Wikipedia_talk:WikiProject_Mathematics/Archive_16#Problem_editor is relevant here. Thank you. -- Leland McInnes (talk) 18:15, 24 January 2008 (UTC)

If one does a change of variables (uses the chain rule), then

${\displaystyle \int f(x)\cdot dx=\int f(x(t))\cdot {\frac {dx(t)}{dt}}\cdot dt}$

which justifies to me the idea that the integrand is multiplied by the differential. JRSpriggs (talk) 01:44, 25 January 2008 (UTC)

I don't think we should have a discussion here whether it is or is not justified to view this as multiplication. In either case, using an operation symbol in front of dx is completely unconventional, and it is not Wikipedia's role to break new ground in notational conventions, however justifiable and potentially beneficial they may appear to be.  --Lambiam 04:16, 25 January 2008 (UTC)
Which is exactly what we see in this discussion that CS and Leland pointed out. The user who is pushing for the virtually meaningless \cdot apparently makes fusses about weird nonconventinoal and unimportant changes to notation all the time. We should really just stick with convention and not waste our time discussing all this stuff. --Cheeser1 (talk) 20:50, 25 January 2008 (UTC)

## Is TeX simply not working today?

I just spent a half-hour doing some edits on Gershgorin circle theorem that would normally take a minute or two. Five minutes after saving it, I still can't see the article after the edits. TeX seems not to be working today. All I see in the article is the TeX code. I tried previewing it repeatedly while editing, and it never worked. Is this happening to everyone else? Michael Hardy (talk) 14:54, 24 January 2008 (UTC)

It could be a migration issue. I have also noticed that the TeX rendering is sluggish. Silly rabbit (talk) 14:58, 24 January 2008 (UTC)
It isn't displaying for me at all - just a blank space. Septentrionalis PMAnderson 19:05, 24 January 2008 (UTC)
The cause of the problem is described here. — Carl (CBM · talk) 19:57, 24 January 2008 (UTC)
Is this related to Wikipedia:Wikipedia Signpost/2008-01-21/Parser changes? JRSpriggs (talk) 01:35, 25 January 2008 (UTC)

## Logical graphs

Can someone look at logical graphs and tell me if its real or not? It's essentially incomprehensible to me, and is written in such a style as to make me not want to even try to comprehend it. For a while, I confused it with G. Spencer-Brown's Laws of Form, for which I have a personal distaste for, as its shallow, clothed with un-needed cryptic drivel, and is just barely on this side of the distinction of real-vs.-crank math. So, with that prejudice, I was taken aback to find the article on logical graphs, which I can't make heads or tails out of. linas (talk) 04:58, 25 January 2008 (UTC)

Most content produced by Awbrey is written in an obfuscatory manner in which trivialities are presented as deep wisdom, and you never know how much of it is neologisms and original research.  --Lambiam 08:56, 25 January 2008 (UTC)
Yes, well, Pierce seems not only legit but even remarkable, and just skimming his bio page provides a number of interesting surprises. So I have no reason to distrust that he developed some concept of a "logical graph". But the description given in that article had the flavour of obtuse original research.linas (talk) 03:42, 27 January 2008 (UTC)

## Translation from French to English Wikipedia

Hello,

The French Wikipedia article Arithmétique modulaire is (in my opinion) an extremely good article, that I would like to translate into English. The article is much more technical than modular arithmetic on the English Wikipedia. What they did in the French Wikipedia was to have two articles: congruences on the integers (non-technical) and modular arithmetic (technical). I suggest we do something similar here. I just wanted your opinion on this before starting this (rather big) work.

Randomblue (talk) 12:03, 27 January 2008 (UTC)

Wow! I wouldn't call fr:Arithmétique modulaire "more technical" than fr:Congruence sur les entiers. The first was started in August 2007 and became a featured article in October 2007. It's an excellent candidate for translation. The second looks like a typical mathematical article and is (as you say) much closer to modular arithmetic. I see you have done a lot of work on the featured French article. Have you considered merging the other one into it? Was the possibility ever discussed? --Hans Adler (talk) 13:44, 27 January 2008 (UTC)
To answer my own question, I just realised that the smaller article is a "main article" for the bigger one. Yes, that makes a lot of sense. I see no reason why we shouldn't do the same here. --Hans Adler (talk) 13:48, 27 January 2008 (UTC)
Translating articles from other wikis is a great idea. There is a template, {{frenchtrans}}, to put on the bottom of the page to record the original source of the text. I often look at other wikis to get ideas about things; even in languages I don't read, the automatic translation tools are usually good enough to give the idea of the article. — Carl (CBM · talk) 17:37, 27 January 2008 (UTC)

I, on the other hand, think that this is a slippery path. I've seen quite a few minute replicas of Wikipedia articles (usually word-by-word translations from English to another language), with all the biases, errors, and omissions inherent to the original. This horizontal spread of knowledge ("peer-to-peer" type, as opposed to "authority based") is one of significant weaknesses of Wikipedia, especially given the abundance of unreliable information easily available to anyone with a search engine. Additionally, it's impossible, and probably meaningless, to (try to) synchronize articles in different languages. If significant additions or corrections are made to either one, the banner becomes very deceptive (we already have this problem with articles based on Planet Math or Mathworld: if they are edited later, should we keep the acknowledgment of the original source? what is the critical mass of changes that would justify its removal?) These are, of course, general observations; it may very well be justifiable to translate and reuse this particular article. Arcfrk (talk) 05:04, 28 January 2008 (UTC)
… and here are a few specific comments:
• Arithmétique_modulaire is much, much wider in scope than "Modular arithmetic", and the writers make it clear almost from the beginning. It seems to be a general survey article on classical algebraic number theory (approximately, through Dedekind) and its twentieth century applications (primarily, in coding theory and cryptography). In English Wikipedia, it would correspond to a nontechnical version of Algebraic number theory (currently, a stub), but perhaps the most apt title would be The higher arithmetic, after Davenport's famous little book.
• The "historical" part and "mathematical theory", taken together, and the "applications" may have to be split in translation. If you think of the article as a piece of popular writing (and I like it a lot from this point of view!), this would certainly go against its logic. On the other hand, for an article in an encyclopaedia the omission of many important subjects (quite a bit of the nineteenth and most of the twentieth century!) would be unforgivable. Once you start adding them in, the inner logic of the present form of the article can hardly be sustained.
• There are many passages in the beginning which deal with terminological and cultural issues peculiar to French language and culture. It would take a serious effort and some erudition to edit them for use in the English edition of Wikipedia.
• Rather than undertaking the translation, I would recommend, somewhat reluctantly, that anyone interested in the subject consults the French version. As I've pointed out before, the maintenance is a nontrivial problem, and it's reasonable to expect that the French original will be evolving and it will be difficult for us to keep up with it.
Arcfrk (talk) 08:05, 28 January 2008 (UTC)
Those are valid concerns. I think "translation" may be the wrong word for the process, since as you point out there will be a lot of cutting and reworking of the text. The main benefit of starting with a foreign-language Wikipedia article is that we don't have to worry about copyright infringement if a few sentences end up unchanged. The note at the bottom is then used to resolve any issue of plagiarism. It isn't meant to imply that the articles on the different wikis are parallel in content and structure. — Carl (CBM · talk) 13:06, 28 January 2008 (UTC)
I know a bit of French, so I can try to lend a hand if needed. --Cheeser1 (talk) 18:48, 27 January 2008 (UTC)
I speak French, I can help too. I agree with the concerns above, but I think the material in the french article is considerably better than the parallel ones in en.wp, so translating it and merging it into the existing ones will improve the English articles. Jakob.scholbach (talk) 13:43, 28 January 2008 (UTC)

There is a way to move an article from French Wikipedia to English Wikipedia with the edit history intact and translate it and have the translated version's edit history show all edits both before and after the translation. I don't know how it is done. A number of articles I originated got translated into German and appear on German Wikipedia with me as the original author, and if you go back in the edit history you see the article on which I worked is in English. Michael Hardy (talk) 02:32, 29 January 2008 (UTC)

## Boolean algebra task force

I am looking for other editors to participate in a broad task force to organize Wikipedia's articles on Boolean algebra, propositional logic, and related topics. The current organization is quite idiosyncratic, and has been the subject of discussion before. The initial goal of the task force would be to outline the current structure of these articles (the topics covered by each and how they interconnect) and discuss improvements to this organization. If we are successful we will come out with a proposal that can be announced more widely.

Participating in the task force would not require a large time commitment. If you are interested, please look at Wikipedia:WikiProject Logic/Boolean algebra task force and add yourself to the list of editors. The page was created under WikiProject Logic only for convenience. I hope that I will be able to gather editors with a wide range of backgrounds to participate. — Carl (CBM · talk) 13:59, 28 January 2008 (UTC)

## Ferdinand Eisenstein

Hi, I amended the assessment from Stub to Start-Class now that someone has added a decent amount of bio. Hope that's ok. Secret Squïrrel, approx 12:00, 29 January 2008 (Earth Standard Time)

Looks good to me. --Salix alba (talk) 12:22, 29 January 2008 (UTC)

## Reminder of the Philip Greenspun Illustration project

Hi. You may be familiar with the Philip Greenspun Illustration Project. \$20,000 has been donated to pay for the creation of high quality diagrams for Wikipedia and its sister projects.

Requests are currently being taken at m:Philip Greenspun illustration project/Requests and input from members of this project would be very welcome. If you can think of any diagrams (not photos or maps) that would be useful then I encourage you to suggest them at this page. If there is any free content material that would assist in drawing the diagram then it would be great if you could list that, too.

If there are any related (or unrelated) WikiProjects you think might have some suggestions then please pass this request over. Thanks. --Cherry blossom tree 16:54, 29 January 2008 (UTC)

## Extraneous solution

The surprisingly new article titled extraneous solution could use some work. Michael Hardy (talk) 13:50, 17 January 2008 (UTC)

Is that not just words, with standard dictionary definitions, put together? --Cheeser1 (talk) 20:02, 17 January 2008 (UTC)
I'm afraid you've lost me. I don't understand your question at all. Michael Hardy (talk) 03:44, 18 January 2008 (UTC)
I believe Cheeser1 is suggesting that an extraneous solution is nothing but a solution that is extraneous, and as such is not deserving of its own article. CRGreathouse (t | c) 16:06, 18 January 2008 (UTC)
Right. We have an article on cats and an article on purple, but no article purple cats, because purple cats are just cats that are purple. --Cheeser1 (talk) 00:45, 19 January 2008 (UTC)
Some work?! Dr. Hardy, I would normally defer to your expertise - but, holy moly, this article is garbage. The two examples listed in the article would fit better in an article entitled "elementary school misunderstandings about how to do math". Seriously! See article talk page for discussion. I'm thinking deletion, but I don't formally propose such things, and I usually don't support them. But, this is pretty bad. Tparameter (talk) 01:06, 19 January 2008 (UTC)
Looks to me like this is a very special case of what goes on in invalid proof, which is honestly one of the messiest articles I've ever seen. Abusing multivalued functions or nonexistent operations (logs, square roots, "division" by zero, etc) to get more solutions than there should be for something (or, in some instances, concluding that the "right" solution equals the "wrong" solution like 1=0). I've spent some time considering how to clean it up, but have no idea where to even start. --Cheeser1 (talk) 02:07, 19 January 2008 (UTC)
I have heard the term used to describe solutions outside of the domain. For example, imaginary numbers when the domain is defined as being the reals. Then the imaginary solutions would be "extraneous". However, a colleague just told me that the term is also used as a misnomer to describe non-solutions derived with invalid methods, and also almost-solutions not in the domain BECAUSE they result in division by zero - which also happens to be the first example in the article which I criticized. Tparameter (talk) 08:09, 19 January 2008 (UTC)
But the point is, these are simply solutions that are extraneous. I don't know that this is article-worthy. --Cheeser1 (talk) 08:48, 19 January 2008 (UTC)
That's what I thought - but, there is some discussion on the talk page that extraneous solutions are not necessarily solutions in the first place. I've investigated unreliable definitions on the internet that corroborate this definition (to include certain non-solutions). Tparameter (talk) 16:27, 19 January 2008 (UTC)
They are solutions, but just to the wrong equation. A more apt example might be "fat cat" which is an idiom. They are not truly cats (and not necessarily fat). It's still just a dictionary definition. But "extraneous solution" really does mean a solution that is extraneous - to the given equation, or to some equation you get along they way (by using some operation like squaring). --Cheeser1 (talk) 16:35, 21 January 2008 (UTC)
This concept is specifically discussed often enough in modern high school algebra textbooks that it deserves its own article. Extraneous solutions arise naturally in some contexts; for example, when eliminating fractions produces a quadratic equation. I haven't looked at the article yet to say whether it's good but it should exist. Dcoetzee 18:07, 31 January 2008 (UTC)

## Archimedes is on the main page again

Archimedes has made it to the Main Page, there may be some edits to watch for. BTW did we lose the convention for bolding main page articles, they all seem to be bold. --Salix alba (talk) 21:10, 29 January 2008 (UTC)

I noticed that Gauss said the three most impactful mathematicians were Archimides, Newton, and...a guy I'd never heard of. I think the real take-away is that I'd like to understand the broader ramifications of quadratic reciprocity :-) Pete St.John (talk) 22:43, 29 January 2008 (UTC)

That "supposed quote" by Gauss struck a discordant note with me. With a few mouse clicks, it can be traced to a sentence in E.T.Bell (the actual expression used was "epoch making"), and as the regulars will no doubt remember, his assertions should be taken with a pot load of salt. Incidentally, Gauss famously left deeply emerged in thought after Riemann's inaugurational lecture "On the hypotheses which lie at the foundation of geometry". Thus Riemann's insight was so revolutionary that it left Gauss speechless I don't think that an endorsement from Gauss is either necessary or appropriate for the article about Archimedes, though. Arcfrk (talk) 00:46, 30 January 2008 (UTC)

Ir'a in Jacobson's Algebra. This doesn't prevent it from being folk history, of course, but just because Bell said something doesn't prove it's wrong. Septentrionalis PMAnderson 15:59, 30 January 2008 (UTC)
Arcfrk, I've heard as a list of "greatest mathematicians of all time": Archimides, Newton, and Gauss. I wouldn't even want to pick between Gauss and Euler, and I wouldn't know how to meaningfully compare Archimides to Wiles; but it helps to broaden our understanding of history. Gauss isn't just the "de-gauss button on a CRT, if you remember CRTs" guy, and Archimides isn't just the "run-naked-from-a-bathtub" guy; so while the comparisons may not be scientific, I think they have pedagogical utility. And really it's just amazing that Archimides imagined and implemented definite integration so well as he seems to have. Pete St.John (talk) 19:33, 30 January 2008 (UTC)
Isn't it amazing that each of them was also (and maybe, primarily) an applied scientist? Anyway, my point was that a proper place for that saying of Gauss is in a collection of Gauss quotes (that's also where MacTutor puts it). Was there anyone, ever, who did not think that Archimedes was the greatest scientist of antiquity? Arcfrk (talk) 20:26, 30 January 2008 (UTC)
Some of the libraries in antiquity had fewer books than a modern university has undergraduate programs. It's a bit harder to be so eclectic today. But anyway, the quote speaks to the significance of Archimides as a mathematician; you are right, everyone knows he was a great scientist and engineer (he sank a fleet of ships! sorta) but lot's of people don't know, but should, that he was a great mathematician as well. Pete St.John (talk) 20:39, 30 January 2008 (UTC)
That mathematical contributions of Archimedes are not appreciated is a sad story that had started already during his lifetime. But the question is, what is the best way of bringing that out? MacTutor article boldly claims that
The achievements of Archimedes are quite outstanding. He is considered by most historians of mathematics as one of the greatest mathematicians of all time.
If that could be reliably sourced, it would do the job. Arcfrk (talk) 21:06, 30 January 2008 (UTC)
My lecturer's notes have 'easily one of the greatest mathematicians of antiquity, and of all time', but I fear he has never bothered to publish his opinions. If I remember, I'll check a few books for quotes tomorrow. Algebraist 00:35, 31 January 2008 (UTC)
I consider any generally reliable source to be citable, if the fact itself is not questioned; in this case, there is no reason to doubt that Gauss would have considered Archimides a great mathematician, so it is not necessary to scrutinize the published source (Bell). Biographies aren't mathematics and don't have the same standards of rigor, but Bell, like Seutonius, is citable (though historians think of Seutonius as gossipy, sorta the People Magazine of his day, and not a social scientist by modern standards. Did you know that Augustus covered himself with sealskin during rainstorms because he was afraid of being hit by lightning? I would have thought it was because sealskin is waterproof). Pete St.John (talk) 00:51, 31 January 2008 (UTC)
I added the following reference to the one book on history which is within my reach at the moment: Calinger, Ronald (1999). A Contextual History of Mathematics. Prentice-Hall. p. 150. ISBN 0-02-318285-7. Shortly after Euclid, compiler of the definitive textbook, came Archimedes of Saracuse (ca. 287-212 B.C.), the most original and profound mathematician of antiquity. That book also states that Gauss restricts to Archimedes along with Newton the term summus. -- Jitse Niesen (talk) 11:36, 31 January 2008 (UTC)

## Constructible number

It is tempting to use this terminology because of the intuition that it conveys (within a certain context), but is such use widely accepted? The article lists no references. Arcfrk (talk) 09:45, 31 January 2008 (UTC)

I'm fairly certain this book, which is as far as I know a reasonably well-established text on the subject matter, uses such terminology. I could be wrong, I'm no expert on which books or which terminology is commonly used. --Cheeser1 (talk) 09:54, 31 January 2008 (UTC)
See Constructible Number at MathWorld. I've added this and two other references to the article. Gandalf61 (talk) 10:07, 31 January 2008 (UTC)
I believe it is widely used in textbooks on abstract algebra (in the Galois theory section, for instance Hungerford's Abstract Algebra: an introduction). MathSciNet gives two articles with this in the title, both referring to the geometric concept, both research level. I think it is safe to say the term is widely accepted, though perhaps not widely used outside of textbooks and a few articles providing new insights on a problem solved completely in the 19th century. JackSchmidt (talk) 17:47, 31 January 2008 (UTC)

## Explain formula idea

I've suggested an idea at Talk:Second-order_logic#Explain formula idea and given an example there. I thought it would be good if there could be an "Explain formula" link next to complicated formula, that would show/hide an explanation. Perhaps a template could be created for this kind of thing. Any comments on this idea? —Egriffin (talk) 16:29, 31 January 2008 (UTC)

## Proofs

I recall reading somewhere that only one proof of a certain proposition should be in an article, so how does one choose the proof? For example, in the article Simson line. there exists a more elementary proof than the one given. Should I replace it or not? Nousernamesleftcopper, not wood 03:07, 1 February 2008 (UTC)

We have a separate page for discussions of when and how to include proofs in mathematics articles: Wikipedia:WikiProject Mathematics/Proofs. Perhaps it should be turned into a guideline, which then should hopefully also include guidance on when not to include a proof. Examples of articles with many proofs are Pythagorean theorem and 0.999...; you'd almost think there is something fishy with these claims that they should need so many proofs. So a limit of one proof is not a hard and fast rule. But in general, unless there is something particularly illustrative, illuminating or elegant about a particular proof, I'd say: if a proof must be included, keep it as simple as possible (but not more).  --Lambiam 11:27, 1 February 2008 (UTC)

Whether there should be only one or more than one within the article depends on the purpose of inclusion of the proof. With Pythagorean theorem or quadratic reciprocity, the fact that so many different proofs exist is notable. With propositions whose proofs are routine, I'd often want to include only one. Michael Hardy (talk) 15:31, 1 February 2008 (UTC)

## Foundations of statistics

Foundations of statistics has been nomited for deletion. As we've seen happen before, the arguments for deletion go something like this:

"I never heard of 'chemistry'. It sounds like some new religious movement. Delete the article or merge 'chemistry' into 'scientology'."

I think maybe I'll try to start a statistics WikiProject. There's no community and Wikipedia work in that field, even by those who know it well, is so uneven because we lack conventions and the like.

Express opinions on that article here. Michael Hardy (talk) 19:23, 1 February 2008 (UTC)

## Random article link

Inspired by a post at the village pump, I'm wondering if anyone else thinks there ought to be a link to Jitse's random article tool on Portal:Mathematics, as seen on Portal:Middle Earth for example. (And Jitse: would you mind?) Algebraist 23:20, 1 February 2008 (UTC)

I think it's a great idea! Another place where it can be included is the WikiProject Mathematics main page (either in the "toolbox" on the left side or in the "Resources" on the right side). Arcfrk (talk) 23:58, 1 February 2008 (UTC)

## Least squares objectionable rewrite

Petergans, a retired specialist in least squares (among other things), rewrote the article on linear least squares from a more specialized point of view which is harder to understand. Now he wants do the same thing for Gauss-Newton algorithm (a nonlinear least squares algorithm). See Talk:linear least squares and Talk:Gauss-Newton algorithm .

While experts are welcome on Wikipedia, rewriting articles from their point of view and making them not comprihensible to others is I think not good. Can we have a discussion here on that, to keep the conversation in one place and have it be seen by more folks? Oleg Alexandrov (talk) 16:01, 31 January 2008 (UTC)

one place and have it be seen by more folks? Oleg Alexandrov (talk) 16:01, 31 January 2008 (UTC)

Dear Oleg and Petergans,

If I were an external reviewer, I would say that the new article is not ready for prime time.

Aside from Oleg's criticism, I have the additional criticism that the new article inserts statistics into every possible nook and cranny. This obscures the main idea and should have been segregated to its own subsection.

Petergans, wikipedia needs experts like you, but it's a learning process (or at least it was for me). I must say I'm not familiar with all the articles on Wikipedia, but please compare your linear least squares and numerical analysis, integral or Eigenvalue, eigenvector and eigenspace, I think that's the direction we're going as a whole in the Wikipedia math project.

Sincerely,

Loisel (talk) 16:53, 31 January 2008 (UTC)

• I echo Mr. Alexandrov's sentiments and cite the policy Wikipedia:Make technical articles accessible as validation. I remain hopeful that a sustained appeal to the MTAA policy would temper the editor's viewpoint. -- DanielPenfield (talk) 17:02, 31 January 2008 (UTC)
• Least squares should definitely be presented with the statistical motivation. I can find some strictly math sources that do it this way if that would help. However, the current presentation is too immediately steep, as many have noted.
Rather than call this an objectionable rewrite, I think it should be a call for help writing a layman's introduction. There is no need to undo the edits, but there is certainly need to introduce the concepts more gradually. Even the old text was wrapped up in technicalities; they were merely technicalities more familiar to mathematicians (linear algebra and vector calculus, roughly speaking, sophomore level courses). The new material appears a little more advanced at face value, but most of the concepts I picked out were covered in our local sophomore level engineering statistics course.
The material on the normal equations could profitably be moved to its own section. They have nothing to do with the definition or motivation of least squares; they merely motivate a wide variety of other numerical linear algebra which can solve well conditioned least squares problems.
A history section might be very interesting, as Gauss's invention of numerical linear algebra more or less began by solving this statistical problem.
Also, should someone leave a note on Petergans talk page, since the discussion is here, he is mentioned by name, and he is likely not a project member? JackSchmidt (talk) 18:10, 31 January 2008 (UTC)
I left a note for Petergans, inviting him to join this discussion. EdJohnston (talk) 18:33, 31 January 2008 (UTC)
I had posted a note on the three article talk pages at which he announced the rewrites. I agree putting an extra note on his own talk page is good too. Oleg Alexandrov (talk) 18:49, 31 January 2008 (UTC)

Thank you for alerting me to the discussion on this page. Let me explain my motivation for proposing the major project. It stems from the fact that I'm an experimentalist (chemistry), not a mathematician. The earlier linear least squares article would be all but incomprehensible to most chemists, if not others like physicists and biologists. So naturally, I have slanted my draft articles towards the experimentalist, that is, towards the application of least squares methods rather than their purely mathematical basis. Here we have a dilemma. The chemist will not be familiar with specialist mathematical notation, and the mathematician will find the applications aspect difficult!

A second motivation was the apalling lack of consistency in notation across related articles. In particular I feel it is important that both least squares and regression analysis be presented in more or less consistent notation. Otherwise it looks as though they are completely separate topics, which they are not.

Thirdly, the current Gauss-Newton algorithm totally misses the point, that it deals with a sum of squared residuals, as is clearly stated in the lead-in of the introductory article, least squares. There's nothing wrong with the maths, but it's not about the Gauss-Newton method as I know it.

For the moment non-linear least squares resides in User:Petergans/b/sandbox. I will revise it in the light of comments, both here and on talk:least squares or talk:Gauss-Newton algorithm. It can then be moved to its own page, where you guys or any else can tweak it further. The question remains, what to do about Gauss-Newton algorithm, re-write it or over-write it?

1. At present it is likely to be comprehensible only to mathematicians. For instance, it says that J is the Jacobian, but gives no indication as to what partial derivatives it contains. There are other instances of notation which will be obscure to a non-mathematician.
2. The notation is unique, within least squares and regression topics, to this article.
3. As mentioned above, it makes no mention of residuals.
4. It is illogical to describe the line search modification in the article and not the Levenberg-Marquardt modification.

My draft adresses all four of these issues. Petergans (talk) 22:06, 31 January 2008 (UTC)

As far as the linear least squares article is concerned, it is much more likely that the average reader is familiar with some linear algebra and calculus than with statistical data fitting theory.
I suggest you focus on making that article more elementary, for example, by putting back the old first part, and only later start modifying other articles, such as Gauss-Newton algorithm. Oleg Alexandrov (talk) 04:08, 1 February 2008 (UTC)

I am puzzled as to what, exactly, you guys find more difficult about my presentation than about the older one. Is it the use of matrix notation? Is it the reference to experimental data? Is it the inclusion of statistics? Is it too generalized? Regarding statistics, from my perspective the optimal values of the least squares parameters are meaningless without estimates of the associated uncertainties, which indicate how many digits of the value are significant - the experimentalist needs to know both the results and how reliable they are. Petergans (talk) 08:50, 1 February 2008 (UTC)

Petergan's revision looks instantly familiar to me. This is the presentation you will find in a modern statistical text book (I detect a certain flavour of Mardia, Kent and Bibby, Multivariate Analysis here, perhaps a Leeds connection?). It does have the advantage of explicitly mentioning the error functions which the previous version glossed over. Statistical applications is a major application of this technique so it does deserve some treatment. Perhaps what could be done is create a statistical application section with this presentation. As for the technicality Least squares is really the best place for the the layman's introduction. --Salix alba (talk) 10:46, 1 February 2008 (UTC)
As an aside, the german wp has a featured article about least squares. Jakob.scholbach (talk) 14:44, 1 February 2008 (UTC)
(To Petergans.) One should not start the article with statistical data estimation and experimental errors. Start with solving a given overdetermined linear system, and derive the normal equations, which is plain linear algebra and calculus. Only then, as per Salix alba, create a fancy statistical application section describing the origin of of the linear system in fitting experimental data, the issues of weights, variance, etc. I hope I'll get to this myself at some point, you're more than welcome to do this by yourself if you have the time. Oleg Alexandrov (talk) 16:29, 1 February 2008 (UTC)

Oleg has moved the article from my sandbox to non-linear least squares and placed a redirect in User:Petergans/b/sandbox so that I can no longer use it. This is premature and out of order. Will an administrator please restore my sandbox, remove the article non-linear least squares and the redirect in User:Petergans/b/sandbox, so that I can work on the draft in the light of the discussion here, before "publishing" it. Petergans (talk) 00:24, 2 February 2008 (UTC)

I moved it back to User:Petergans/b/sandbox, to give you some more time to work on it before it's "live". But remember that articles don't need to be perfect, or even close, when they are created. — Carl (CBM · talk) 01:52, 2 February 2008 (UTC)
Sorry, I should have asked (I had the impression you were pretty much done with it and that other people liked it, and I was requested to do the move by an editor on my talk page). When you're ready, let us know. Oleg Alexandrov (talk) 04:26, 2 February 2008 (UTC)

### Other language versions

Jakob.scholbach suggested looking at the German version of least squares. I have also looked at the French version. This is how the problem is stated there.

${\displaystyle \chi ^{2}(\theta )=\sum _{i=1}^{N}\left({\frac {y_{i}-f(x_{i};\theta )}{\sigma _{i}}}\right)^{2}=\sum _{i=1}^{N}w_{i}\left(y_{i}-f(x_{i};\theta )\right)^{2}}$
Les quantités ${\displaystyle w_{i}}$, inverses des variances des mesures sont appelés poids des mesures.

(Literal translation) The quantities ${\displaystyle w_{i}}$, the inverses of the variances of the measurements are called the "weights" of the measurements


Both French and German articles are based on the premise that least squares is applied mathematics, and that therefore the physical circumstances of its applications are an integral part of it. Petergans (talk) 09:48, 2 February 2008 (UTC)

## Newton's method

I have found that there are two articles on this topic which slightly contradict each other - Newton's method uses the function and 1st derivative. I was taught this at school as the Newton-Raphson method. Then there is Newton's method in optimization which brings in the 2nd derivatives. Is there a generally agreed way to distinguish between the two methods? I would refer to them as first and second order Newton methods. Petergans (talk) 14:24, 1 February 2008 (UTC)

No, the "second order" Newton method is Halley's method. In optimization, one is looking for the zeros of the gradient, as possible locations of extremal points. So by using Newton's method on the system of first derivatives the Hessian turns up. The order of convergence is still quadratic.--LutzL (talk) 15:20, 1 February 2008 (UTC)
Newton's method is for finding a zero of a function. Newton's method in optimization is for finding an optimum of a function. Applying the latter method to a function f is the same as applying Newton's method to its derivative f'.  --Lambiam 09:20, 2 February 2008 (UTC)

## Accessibility of maths articles

This question has reared its head again at WP:VPP#Mathematics. Algebraist 01:34, 3 February 2008 (UTC)

## Policy on technical terms

Do we have a policy or guideline on the use of technical terms? If not, we should.

I was just looking at finite element method, and it uses two technical terms, "Dirichlet condition" and "displacement condition", to refer to the same thing.

I personally think that, as much as possible, a single article should stick to a single notation, and a single technical term per concept. I think listing other terminologies and notations is a good thing, but I don't think that intermixing terminologies and notations within the article, for no good reason, helps in any way.

So do we have such a policy? Where is it?

Loisel (talk) 04:55, 3 February 2008 (UTC)

I don't know that there's a policy, but it seems to me a matter of good writing, not to be unnecessarily confusing. —David Eppstein (talk) 06:26, 3 February 2008 (UTC)
I'm not as familiar as I should be with the MOS, but I believe terminology switching is frowned upon (in the same way switching BC/BCE or British/US English are not really helpful). --Cheeser1 (talk) 06:32, 3 February 2008 (UTC)

The first paragraph of WP:MOS does provide some guidance on this issue. --Sturm 11:07, 3 February 2008 (UTC)

I think that paragraph refers to consistency across articles, and is given by way of rationale for having a Manual of Style. Nevertheless, the same rationale clearly also applies for consistency within an article being desirable.  --Lambiam 21:39, 3 February 2008 (UTC)
"An overriding principle is that style and formatting should be applied consistently throughout an article, unless there is a good reason to do otherwise". --Sturm 21:46, 3 February 2008 (UTC)
I should have read it more carefully.  --Lambiam 22:25, 3 February 2008 (UTC)

I did not find the term "Dirichlet condition" in Finite element method.  --Lambiam 22:25, 3 February 2008 (UTC)

I guess you're right. It says Dirichlet problem, not Dirichlet condition. Also, thanks for the link to WP:MOS, although I have the feeling that some verbiage that directly addresses notation, symbols and terminology would be more convincing when the issue turns up in an edit war at some point in the future. Loisel (talk) 07:13, 4 February 2008 (UTC)

## Examples

Is there a standard format and location for numerical examples in mathematics articles? Examples seem to be scattered or non-existant. See: Expected_value - 2 in intro; Standard_deviation - 1st section, step by step; variance - no example. If there is no standard, should we make one? --Zojj (t,c) 01:37, 5 February 2008 (UTC)

I guess there is no standard. Examples, pictures, and simple non-technical explanations are of course very encouraged and as early as possible in articles, as they help elucidate matters, especially in math. Oleg Alexandrov (talk) 04:35, 5 February 2008 (UTC)

## Boubaker polynomials refcheck

This article has had a rough start and could use some help. One important part is to improve the references, but this is a big task. An easy first step is to check the provided references to see if they actually support the claims made, and a second is to format the surviving references in a standard fashion. Silly rabbit and I have made some progress on this, but it would be good to have a few more eyes on the project. The topic may be heavily influenced by physics, so those with a dual background would be particularly helpful. As a warning: the original authors may have a WP:COI and may feel they are not being treated WP:CIVILly since their work has been called non-notable and proposed for deletion really quite a few times now. I think this is just an inherent problem with COI edits, and that there has not really been any incivility, but I felt I should warn you about the probable difficulty in finding consensus on the article as a whole. This should not really affect the refcheck, but when you comment on the references, you might want to double check you aren't accidentally insulting someone or otherwise inadvertently inciting something awful. Thanks for any help. JackSchmidt (talk) 05:24, 5 February 2008 (UTC)

## SVD -- primary meaning?

Recently, I noticed that SVD was an article about a sniper rifle, with no reference to any other meanings. When I google search svd, most of the hits on the front page are for Singular value decomposition, a few are for other meanings, and only one (the wikipedia article) is for the rifle.

I moved the rifle article to SVD (rifle) and made SVD a disambiguation page. The creator of the rifle article has since moved SVD (the disambig page) to SVD (disambiguation) and put the rifle article back at SVD with the comment that "google gets enough first page hits to indicate this is a firearm". (Does google tailor your hits based on previous searches?) They did add a link to the disambiguation page at the top, which is good.

Wikipedia:Disambiguation#Primary_topic indicates that when there is a well-known primary meaning or phrase, that topic may be used for the main article with a link to the disambiguation page. Is the rifle really the primary meaning of SVD? Is this worth arguing about? Where would be a good place to have the "extended discussion" that might indicate that there is no primary meaning, and that SVD should be the disambiguation page? -- KathrynLybarger (talk) 06:13, 2 February 2008 (UTC)

I'm not going to comment on the issue you raise. But another more pressing matter is that in the process of moving the pages around, the original page history of SVD was lost. It remained at SVD (rifle), which is now a redirect. An administrator is going to have to fix the problem and re-move the page SVD (rifle) to SVD so that the history is recovered. Any volunteers? Silly rabbit (talk) 06:24, 2 February 2008 (UTC)
I restored the redirect from SVD to the dab page, so that the history now goes with the correct article. No admin powers were needed nor used, though I have them. —David Eppstein (talk) 06:32, 2 February 2008 (UTC)
Thanks! -- KathrynLybarger (talk) 07:10, 2 February 2008 (UTC)
As supporting evidence: SVD matrix: 1.4M Google hits; SVD rifle: 100k Google hits. —David Eppstein (talk) 06:26, 2 February 2008 (UTC)
In my view, it was uncivil of the rifle contributor to claim primacy. If someone writes about "Leonard Carliz (Minor Poet)" then I'm content for a disambig page and renaming my own "...(Mathematician)", we should both just rename our pages, unless the greater significance of one is blatant. To many people I suppose, anything about math is blatantly insignificant :-( Pete St.John (talk) 21:12, 6 February 2008 (UTC)

It seems that Talk:SVD should be moved to Talk:SVD (rifle). But Talk:SVD (rifle) already exists (although it is trivial) so I couldn't move it myself. Some admin should move it, preferably one who has been involved with the other recent moves in this cluster of articles. -- Dominus (talk) 15:27, 7 February 2008 (UTC)

This has already taken place, as attested by the page history. However, some clumsy move attempts were made by User: Koalorka, the editor who thought the rifle ought to be the primary meaning, leaving a bit of a muddle. The necessary repairs and redirects have been made. --Sturm 15:56, 7 February 2008 (UTC)
It seems that the talk page history was also lost, but during a much earlier move [18]. Silly rabbit (talk) 17:30, 7 February 2008 (UTC)
The original talk page was at Talk:Dragunov Sniper Rifle – again, a move handled by a clumsy copy-and-paste. I think I'll be having a word with Kolorka. --Sturm 19:04, 7 February 2008 (UTC)
If it helps, he was warned before in Nov 2007. The warning had a neat link I hadn't seen before to a backlog of such moves. It is also a neat diff because of the QINU bug. JackSchmidt (talk) 20:21, 7 February 2008 (UTC)

## Warren Goldfarb

Today I stubbed out an article about logician Warren Goldfarb of Harvard University. It was later tagged for speedy deletion since it did not sufficiently establish Goldfarb's notability.

I have contested the deletion: I believe Goldfarb is notable, although I agree that I did not establish this in the stub article. But before I put more effort into it, I would like feedback from members of this community: is Warren Goldfarb sufficiently notable to merit a Wikipedia article?

Thanks for any feedback you can provide.

-- Dominus (talk) 01:14, 7 February 2008 (UTC)

Ask User:Gregbard for an opinion. His list of papers doesn't suggest that he works in a field of logic where I understand notability. — Arthur Rubin | (talk) 01:24, 7 February 2008 (UTC)
The relevant guideline, WP:PROF, is very vague. I'm also not familiar with the philosophy side of logic. My impression is that there is a good chance the article would last at AFD, since there are at least two things that the article can say: he has a named professorship, and he was a co-editor of Goedel's collected works, a very important publication. — Carl (CBM · talk) 01:52, 7 February 2008 (UTC)
I know little of such logic, but I would concur that these two points clearly demonstrate notability per WP:PROF (and don't seem to require specific knowledge of this field). --Cheeser1 (talk) 02:27, 7 February 2008 (UTC)
The named professorship at Harvard by itself is strong evidence to me that he's notable enough for an article, and I'd hope that (after I've added a line naming the chair to the article) it would be safe from speedy. It seems likely that this is what DGG meant by "obviously not a speedy". —David Eppstein (talk) 02:17, 7 February 2008 (UTC)

Thanks all, and especially to DGG, who removed the speedy tag, and to David Eppstein, because I was completely unaware of Goldfarb's significance as an openly gay professor and his founding of the Harvard Gay and Lesbian Caucus.

Several people mentioned his named chair as being evidence of notability. I was not aware that this was important. Can someone briefly explain its significance?

Thanks again, -- Dominus (talk) 06:15, 7 February 2008 (UTC)

Named professorships are typically considered prestigious and competitive. Those who receive them are well established in their field, with a long history of strong research. A named professorship would be mentioned in a formal introduction, like an award the person has won. — Carl (CBM · talk) 13:00, 7 February 2008 (UTC)
It is, as far as I am concerned, an award. It's like a named scholarship or a named award, only it's attached to your job, instead of your financial aid or some big certificate or whatever. --Cheeser1 (talk) 20:57, 7 February 2008 (UTC)

## An issue in the definition of Decidability (logic)

I'd like to draw your attention to an issue in the definition of Decidability (logic), namely whether that definition should be based on the imprecise notion of "effective method", or the precise notion of "recursive computability". See Talk:Decidability (logic)#Precise and imprecise definitions.  --Lambiam 16:32, 8 February 2008 (UTC)

## Selection of articles for offline releases

We at WP:1.0 are currently testing a bot for selecting articles for offline release, based on a balance of importance and quality. You are familiar with the quality scale, but we are also trying assess article importance. We want to develop a good algorithm that uses a four-component formula involving WikiProject assessment (Top/High/Mid/Low), no. of hits, no. of links-in and no. of interlanguage (interwiki) links. We now have some test results for Maths (scroll down to reach Maths), and we'd really appreciate feedback on the various algorithms. The first is a simple addition of weighted components, but the other two use a logarithmic function (which is more valid mathematically?!). Which algorithm works best - sort2, sort3 or sort4? We want to see that the listed articles are ordered from the highest importance-quality to the lowest; which list looks to be giving the most sensible ordering? Many thanks, Walkerma (talk) 22:17, 8 February 2008 (UTC)

## Political issue

As much as I prefer to ignore wikipolitics to the extent possible, there's a question that may interest some here at Wikipedia talk:Manual of Style#Proposal. --Trovatore (talk) 03:10, 7 February 2008 (UTC)

I completely agree with you there. I don't even understand what this sort of "enforcement" would do to help build the encyclopedia. --Cheeser1 (talk) 04:15, 7 February 2008 (UTC)
I notice people getting very stressed over at WT:MOS, but due to my ignorance I don't perceive the relevance to math articles. Can anyone familiar with past formatting issues of math articles give examples of conflict with WP:MOS? The Talk page of the math-specific MOS is a surprisingly quiet place, so I don't know where the controversies are hiding out. (There have been issues in the past with FA and GA reviews of math articles, but I didn't know that formatting and style was the problem). EdJohnston (talk) 04:42, 7 February 2008 (UTC)
I don't think there has ever been a conflict between the people at WP:MOS and people from this WikiProject. -- Jitse Niesen (talk) 22:10, 7 February 2008 (UTC)

(←) I remember a while back there were some issues with the GA process, particularly regarding the formatting and use of inline citations; this was a motivation for the scientific citation guideline. But Geometry guy assures me this has gotten better.

I think it's important to remember that the project itself doesn't have a voice; individual editors do. If a large number of editors here all feel strongly about something, they will speak up about it, but I attribute this to their own personalities as much as anything else. Unfortunately, it can come across as "math vs. everyone else", which is a perception I think everyone should be careful not to cultivate. — Carl (CBM · talk) 22:23, 7 February 2008 (UTC)

Thanks Carl: I agree very much with this last comment. In my (1 year) experience, the main conflicts with GA have been some bad GAR discussions last spring, and a bit of trouble with GA "sweeps". The issue with GAR discussions was aggravated by multiple drive-by "Delist. Not enough inlines" recommendations. This really has changed. I've not seen such a recommendation since at least September (and probably not since early summer last year). Also, the citation requirements for GAs have been changed to emphasise the cases where citations are really required by WP:V, so actually the Scientific citation guidelines are in some ways stronger than the general GA requirements. (Caveat: this is not yet typically reflected on the ground.)
Good. Congratulations on the good work. Septentrionalis PMAnderson 19:11, 11 February 2008 (UTC)
As for this particular issue, one problem was that the proposal, as phrased, had the following consequence: if WP:MoS and WP:MSM contradicted each other, then WP:MoS would prevail. This flies in the face of a lot of Wikipedia policy, and had the potential to cause a great deal of trouble. I think this has been recognised, and discussion is moving towards ideas that would address inconsistency problems without centralizing power. Geometry guy 23:00, 7 February 2008 (UTC)
The push here is that MOS (and all its subpages, no matter how obscure or bizarre) are treated as mandatory at FA even when they are phrased as recommendations, so there is a movement to gather up these Roolz where they can be found. This is one of FA's many problems, about which I should really write an essay. Septentrionalis PMAnderson 19:11, 11 February 2008 (UTC)

### Mathematics manual of style

I looked at WP:MOSMATH this morning, and I realized that it doesn't actually contain much advice about editorial style. It does contain a small amount, but mostly it gives advice about how to structure and write a WP mathematics article. Compare it to the real manual of style to see the difference. Both have specific purposes. I think it would be reasonable to do some combination of the following:

This would eliminate any confusion about the role of MOSMATH as advice about how to write good math articles on Wikipedia, rather than advice about how to punctuate those articles. Thoughts? — Carl (CBM · talk) 16:00, 8 February 2008 (UTC)

What about all this stuff on how to write maths in wikicode, the section Typesetting of mathematical formulas? -- Jitse Niesen (talk) 17:21, 8 February 2008 (UTC)
I don't see much point in renaming it. As Jitse points out, all the typesetting stuff is very much a style issue. -- Fropuff (talk) 18:52, 8 February 2008 (UTC)
It's been a long time since I thought about typesetting maths as a style issue, but I do recognize that it is often considered one (the Chicago manual spends time on it for example), so I see Jitse's point. — Carl (CBM · talk) 19:03, 8 February 2008 (UTC)
Maybe we could have both kinds of page? Geometry guy 19:36, 8 February 2008 (UTC)
Again, I don't really see the point of splitting off some of the material. Its convenient to have it all in one place. Are there any real disadvantages to doing so, or are we just trying to find a problem to fit a solution? -- Fropuff (talk) 20:08, 8 February 2008 (UTC)

Here are a few things that are sorely lacking from the Mathematics Manual of Style:

1. Discussion of the most common formats for bibliographical references. I've recently spent several hours navigating less than perfect explanations scattered around various template pages, and came out without full understanding of how they work, let alone, which ones are most helpful to use in a specific situation. (One annoying bug that I wasn't able to figure out: in a reference with multiple authors that uses "cite" template, it seems impossible to wikilink authors that who are not the main author.) This can also include links to various bibliographical databases that were discussed in this talk page over the past year.
2. Description of the basic templates and advise on when and where to use them. Some examples: "main", "otheruses", "seealso", "math-stub" and its refinements.
3. Suggestions on the optimal length of the article, the lead, and the individual sections. Also, when should the article be forked?
4. Any guidance on figures and tables. Where to place them, how many, how large, which templates to use. Certain things just don't work well on all platforms, so it would be helpful to collect the wisdom gained from successful and unsuccessful experiments rather than to leave the editors guessing.

It would also be helpful to comment on duplication of material in the "main" article and the corresponding sections elsewhere. This is part of a much wider consistency issue that is very, very challenging, but in some limited contexts, we can try to reign it in. It seems to be quite common practise to edit the section "History of algebraic widgets" of "Algebraic widgetology" to the extent that it becomes much more expansive than the corresponding "main" article, or sometimes, directly conradicts to the corresponding "main" entry. Conversely, some editors dump material from the "main" article into the sections of other articles, without first checking that it's correct. Frequently, it results in lowering the quality of the subsection (which could have been written later and/or by more expert editor). Arcfrk (talk) 01:55, 9 February 2008 (UTC)

Many of these issues are in no way specific to mathematics.  --Lambiam 18:29, 9 February 2008 (UTC)
As for the reference citations. The "citation" template is very versatile and covers books, news, journal papers. It also provides good structure to neatly use (and wikilink) several authors:
{{Citation | last1=Arthur | first1=James | last2=Bombieri | first2=Enrico | author2-link=Enrico Bombieri | last3=Chandrasekharan | first3=Komaravolu | last4=Hirzebruch | first4=Friedrich | author4-link=Friedrich Hirzebruch | last5=Prasad | first5=Gopal | last6=Serre | first6=Jean-Pierre | author6-link=Jean-Pierre Serre | last7=Springer | first7=Tonny A. | last8=Tits | first8=Jacques | title=Armand Borel (1923--2003) | mr= 2046057| year=2004 | journal=[[Notices of the American Mathematical Society]] | issn=0002-9920 | volume=51 | issue=5 | pages=498–524}}
gives
There are also special cases, like {{cite journal}} and {{cite book}}. All they do is supply formatting, so I find easier to format the reference by hand than do all the cutting and pasting to get the template to do it for me; but tastes vary. They are not required, last I saw, by any version of MOS. Septentrionalis PMAnderson 19:00, 11 February 2008 (UTC)

Arcfrk's issues probably should not be discussed at WP:MOSMATH unless we have reason to differ from other articles, which we may. (Links to other guidelines make sense.) They should be covered, at least by cross-reference, at WP:MOS; at least #3 (headers and so forth) is covered in some detail. Septentrionalis PMAnderson 19:04, 11 February 2008 (UTC)

## Least squares: implementation of proposal

This is a courtesy posting. Please post your particular comments on individual articles on their repective discussion pages. I suggest that comments relating to more than one article be posted on talk: least squares. Please also note request to delete Weighted least squares

which contain more technical details, but it has sufficient detail to stand on its own.

In addition Gauss-Newton algorithm has been revised. The earlier article contained a serious error regarding the validity of setting second derivatives to zero. Points to notice include:

• Adoption of a standard notation in all four articles mentioned above. This makes for easy cross-referencing. The notation also agrees with many of the articles on regression
• New navigation template
• Weighted least squares should be deleted. The first section is adequately covered in Linear least squares and Non-linear least squares. The second section (Linear Algebraic Derivation) is rubbish.

This completes the fist phase of restructuring of the topic of least squares analysis. From now on I envisage only minor revision of related articles. This note is being posted an all four talk pages. Petergans (talk) 10:23, 8 February 2008 (UTC)

How do you folks feel when you labor making more accessible an article written by a stubborn specialist and adding a pretty picture, only to have that specialist working separately on his own fork in his sandbox then overwriting your work without discussion ('cause his version "is better")? Oleg Alexandrov (talk) 15:41, 8 February 2008 (UTC)
I too think there was a lot to be said for Oleg's version/s compared to this, and I am strongly tempted to edit the article back to something much closer to it, when I have some more time. Jheald (talk) 20:24, 8 February 2008 (UTC)

Weighted least squares is now on AfD.--Salix alba (talk) 19:42, 11 February 2008 (UTC)

## collaboration on Riemann surface?

I wanted to ask whether people are interested in collaborating on the Riemann surface article, similarly to the collaboration on homotopy groups of spheres initiated by Geometryguy some months ago. The current article is in a decent start-up-shape, but I'm sure there is ample opportunity to improve and enhance it. Jakob.scholbach (talk) 11:37, 11 February 2008 (UTC)

## Aceromath deletion

I nominated Aceromath for deletion; it is an article on a software program, and Oleg correctly recatted as software, but the author of the article has reverted; so our program may miss it. This looks like a newbie, a one-man company looking for free advertising, so we should delete but not bite. Septentrionalis PMAnderson 18:57, 11 February 2008 (UTC)

I'm going to leave a note about constructive contributions vs. contributions made as the representative of a corporation (per WP:UN and WP:COI). Actually, I just did. Hopefully I've done what I can to keep this person from being chased off of the 'pedia, even if the account itself seems to have serious issues. --Cheeser1 (talk) 19:08, 11 February 2008 (UTC)
For reference, this is also interesting: User:Thenetcentinell. --Cheeser1 (talk) 19:12, 11 February 2008 (UTC)
That's why I deduce a one-man company. Septentrionalis PMAnderson 19:13, 11 February 2008 (UTC)
I concur, but since that's a bit of a gray area, I don't think reporting him for a WP:UN-block would be appropriate. However, I MfD'd his autobiography/userpage/vanispamcruftisement. --Cheeser1 (talk) 19:49, 11 February 2008 (UTC)

## Gauss's lemma (Riemannian geometry)

A week ago Zadigus (talk · contribs) produced an article in French called "Lemme de Gauss" which turned out to be about Gauss's lemma (Riemannian geometry), previously a redlink from the DAB page Gauss's Lemma. I have moved it to the English title, and have also done a translation from the French to the best of my ability, which is currently in my user-space here, the main article being (mostly) still the original French for comparison. I would welcome any comments and improvements; in a few days, unless there are objections, I plan to move the translation into the main article, and fix the links from the article Exponential map to point to it. JohnCD (talk) 22:40, 12 February 2008 (UTC)

No offense, but it reads like a cliche differential geometry textbook, too many formulas. WP:NOT#TEXTBOOK may be relevant. Arcfrk (talk) 03:49, 13 February 2008 (UTC)

## Comments wanted on Logarithm

Currently the Logarithm article has at the very top two shots of pages with alternative definitions for the log. The question is, do they belong there, and are they more important than the log graph picture? Is that useful or pretty? Comments welcome at Talk:Logarithm#New old definition images. Oleg Alexandrov (talk) 03:30, 14 February 2008 (UTC)

# Feb 2008

## Calyx

The recently created stub, Calyx (mathematics), has been nominated for deletion. Is this surface notable? AfD discussion linked above. Geometry guy 19:02, 14 February 2008 (UTC)

Of the two sources, this one is a list of random shapes (some of which are inaccurate - see it's "cube"), but this one seems to mention it in a somewhat relevant mathematical context. However, I'm not sure if this is any sort of standard name, or if this surface has any meaningful notability beyond this single use. Note that the image in this PDF seems to be the same one as from the first source (not sure why/how that occurred or if it tells us anything). --Cheeser1 (talk) 19:37, 14 February 2008 (UTC)

## Gauss-Markov-Aitken theorem?

Aitken's generalization of the Gauss-Markov theorem does not appear to get the recognition it deserves. Would it be in order to call the general theorem Gauss-Markov-Aitken? It it called this in any text book? Petergans (talk) 15:10, 15 February 2008 (UTC)

It is for instance here.  --Lambiam 19:29, 15 February 2008 (UTC)

## Coordinated math vandalism

I noticed some rather disturbing vandalism over at Runge-Kutta methods. Apparently this is part of a wider coordinated effort to vandalize the math articles. See [19]. A bit of Googling shows that there are indeed attempts to organize an attack from outside Wikipedia. I don't know for how long this has been going on, although it seems relatively recent. So be on the lookout for dubious edits from anon IPs. Silly rabbit (talk) 21:58, 16 February 2008 (UTC)

It seems to stem from Encyclopedia_Dramatica:Today's_featured_article/February_16,_2008. Their todays featured article is on vandalising the Runge-Kutta article. Hence the damage is likely to go down tomorrow but it may get low level vandalism after that. --Salix alba (talk) 00:51, 17 February 2008 (UTC)
When people are doing the final cleanup, someone should check if this anon edit with no edit summary from 2008-01-21 is valid: 4101 -> 4104. I figure there is no point right now. JackSchmidt (talk) 18:03, 17 February 2008 (UTC)
I noticed some subtle vandalism too recently in ODE articles [20] [21] [22]. It would be a big problem if it were part from a trend. Such things are missed by people reverting vandalism and would be hard to catch later. Oleg Alexandrov (talk) 21:08, 17 February 2008 (UTC)

## Invalid proofs

I think that here it is not clear why substitution is an invalid operation.--Pokipsy76 (talk) 20:53, 18 February 2008 (UTC)

The argument is correct. I will try to add a comment. Loisel (talk) 21:36, 18 February 2008 (UTC)
Substituting is correct, but taking the principle cube root is not. CRGreathouse (t | c) 21:37, 18 February 2008 (UTC)
Well, whatever. Substituting does add a root which is not part of the original system. Think of it this way. Let f(x,y)=x^2+y+1 and g(x)=-1-1/x. The first equation says that f(x,x)=0, its solutions are ${\displaystyle exp(\pm 2\pi i/3)}$. The third equation says that, for such an x, we have g(x)=x. However, this relation is not verified for all x. The substitution is f(x,g(x))=0. This new equation is solved whenever g(x)=y and f(x,y)=0. Apart from the solutions of the first equation, observe that also g(1)=-2 and f(1,-2)=0. Hence, substitution does introduce new solutions, and that is because x=g(x) is not verified for all x, but rather only for the solutions of f(x,x)=0. Loisel (talk) 21:41, 18 February 2008 (UTC)

Please. Write ${\displaystyle \exp(\pm 2\pi i/3)\,}$, not ${\displaystyle exp(\pm 2\pi i/3)\,}$. Michael Hardy (talk) 22:10, 18 February 2008 (UTC)

Oh bite me, on the talk page! Loisel (talk) 00:27, 19 February 2008 (UTC)

This has come up before, and I'd like to direct people's attention to this article's talk page. This article is seriously unencyclopedic, and it would require either alotof work, or deletion. I feel like maybe some opinions are needed there to hash out whether the article is worth fixing (instead of deleting the article after wasting time improving it). --Cheeser1 (talk) 22:15, 18 February 2008 (UTC)

Why this proof have ben removed? I found it interesting...--Pokipsy76 (talk) 08:12, 19 February 2008 (UTC)

## Radius of curvature

I'm think that someone who understands this stuff should take a look at Radius of curvature. It starts with a strange and confusing definition, and it never really becomes clear what the article is supposed to be about. As far as I know, the "radius of curvature" (of a plane curve) is simply the reciprocal of the curvature, so there's no need to explain both things separately in separate articles. On the other hand, the Radius of curvature article seems to be preoccupied with the radii of curvature of ellipsoidal surfaces and suchlike. Is that a different meaning of the term, or is it just a specific application of the usual definition? I wonder if all the information about the generic meaning should be merged into the one article: curvature, and a separate article created to deal solely with the specifics of ellipsoids. Matt 19:46, 20 February 2008 (UTC).

Thanks for the note. I've converted that page into a disambiguation page, fixed the links to the best of my abilities, and moved the text to Radius of curvature (applications) (where it is crying for attention from someone understanding what all these incoming links want it to be). Arcfrk (talk) 00:09, 22 February 2008 (UTC)
Some of the link changes associated with that move and the new dab page are incorrect. Radius of curvature (optics), for example, is particular to the curvature of optical surfaces as used in optical design. You have changed "radius of curvature" in many optics articles to link there, when it should link to the standard definition of r.o.c. instead. In addition, this page move should have been discussed first. I have proposed reversing it at Talk:Radius of curvature (applications).--Srleffler (talk) 14:33, 22 February 2008 (UTC)
Well, they are optics articles, aren't they? Then it would stand to reason to discuss all possible uses of radius of curvature in optics in the article "Radius of curvature (optics)". Certainly, from the point of view of maintenance this would be preferable (why should anyone be left guessing that a use in optics is not the use in optics?). In the short run, feel free to change them to correct links — radius of curvature is presently explained best in the article "Curvature". Arcfrk (talk) 22:20, 22 February 2008 (UTC)
I think there are several definitions of "radius of curvature" in use. Since the concepts are similar/related, it makes sense to have one article that deals with all of them, explains them clearly, and explains the differences between them.--Srleffler (talk) 14:33, 22 February 2008 (UTC)
The disambiguation page seems more prudent. Arcfrk (talk) 22:20, 22 February 2008 (UTC)
But are they really different definitions, or is there really only one underlying mathematical definition which crops up in a number of different situations? Whatever the answer, I think that the old Radius of curvature article is/was a mess, so I don't think we should just put things back to how they were and leave it at that. Unless I am totally wrong, "Radius of curvature" (unqualified) needs to kick off with the standard, general mathematical meaning (i.e. the reciprocal of curvature). Then details of the applications (such as to lenses, to ellipsoids, or whatever) can follow, or links to separate articles where there is enough application-specific detail to warrant it. If there are any fundamentally different definitions of RoC then that needs to be made clear. Matt 18:51, 22 February 2008 (UTC).

## Insulting mathematicians?

The new article Proof by intimidation appears to be an attempt to insult mathematicians. Instead of talking in a general way about the logical fallacy of that name, it ascribes it especially to lectures in mathematics. JRSpriggs (talk) 06:45, 22 February 2008 (UTC)

I don't think the article is meant to be insulting. It definitely needs some cleanup. One of the lecturers accused of proof by intimidation is the physicist Richard Feynman, so I don't think the focus is entirely on mathematicians. It is a little unclear to me how much humor should be in the article itself (the article is categorized as humor, joke, etc.). I think it is intending to be funny by citing a source that is clearly not reliable, but it is unclear to me if that is a good idea. I stopped cleaning it up because the use of English was strange, and I was not positive if it was a dialect problem. There were several near-homophones (I'm sure there is a word for that), being used instead of the "correct" word, but it happened too many times for me to be sure. At any rate, the article definitely needs work, and probably needs several editors editing it to make sure the article itself does not become an In-joke. JackSchmidt (talk) 07:19, 22 February 2008 (UTC)
I like the article as it stands (currently), if the citation of Rota is accurate. I once spent an hour in Lazebnik's office arguing about whether something was obvious. Sometimes even math is funny in both senses of the term ("haha" and "peculiar"). Pete St.John (talk) 20:15, 22 February 2008 (UTC)

## Probability semi-protected until 1 March

Thanks to Jmlk17, "probability" is semi-protected for one week to prevent vandalism by unregistered and newly registered users. I requested this as I was getting fed up with the level of vandalism and disruptive edits. As I said in my request,

This is a vital article rated by WikiProject Maths as Top priority but only Start-class quality and the relatively small number of editors with the necessary expertise to improve it are likely either to be distracted or put off entirely by the level of vandalism.

So come on all you probabalists out there, you've now got a week free of distracting vandalism to improve the flagship article for your subject! (Nothing like a tight deadline to help concentrate the mind...) --Qwfp (talk) 12:29, 23 February 2008 (UTC)

## Solution description of Monty Hall problem

Can some of you folks comment at Talk:Monty Hall problem#RfC: Consensus for rephrased solution? Thanks. -- Rick Block (talk) 16:40, 23 February 2008 (UTC)

## The numbers template

{{numbers}} has again popped up over coutnless math articles, right on top, above any pictures, and rather wide. I suggested that we remove it. Should we perhaps even nominate it for deletion? Oleg Alexandrov (talk) 16:54, 23 February 2008 (UTC)

The reason I included it on the pages for basic number sets is because I couldn't get to any of the other sets from a given set's page. As I forgot the name for the set Z ("Integers"), it wasn't under "Z", and I couldn't navigate to it by looking up similar pages like "natural number" or "complex number". Since N, Z, Q, R, C etcetera are related, I think there should be a menu that connects them. Perhaps a smaller one than what we see now, but it's greatly appreciated if the pages are more linked. It now appears that these sets don't have any connection. A footer menu could also be helpful. SuperMidget (talk) 17:38, 23 February 2008 (UTC)
It might be better rewritten as a {{navbox}} and moved to the bottom of these articles , if [itex] mark-up will work within a navbox. Maybe you'd like to have a look at that SuperMidget? (in your userspace to start with i'd suggest) --Qwfp (talk) 17:50, 23 February 2008 (UTC)
I like the template, but maybe a navbox would be better. CRGreathouse (t | c) 18:34, 23 February 2008 (UTC)
What do you think of SuperMidget/navboxNumbers? It's quite difficult to make it look nice, since not all sets have symbols, and it seems impossible to use wikitables inside the navbox. Please don't edit it directly on my userpage, but copy it first. SuperMidget (talk) 18:57, 23 February 2008 (UTC)
Blimey, that was quick! Nice work. I think it's already a big improvement on {{numbers}}. Oleg? --Qwfp (talk) 19:42, 23 February 2008 (UTC)
Looks good. I think we should overwrite {{numbers}} with any of these (which are by the way horisontal, not vertical), and move them to the bottom of articles. We should not leave {{numbers}} the way it is since at some point it will again pop up tall and wide on top of all number articles. Oleg Alexandrov (talk) 22:13, 23 February 2008 (UTC)
The navboxes themselves are oriented horizontally, but the lists in them are either horizontal or vertical. If we would replace the {{Numbers}} by any of the navboxes, I think a lot of pages in the Maths portal will get distorted. The original template might be of use there. Probably if we replace the whole thing, it will be reverted instantly. It may be better to create a new template {{NumberSystems}}. This name would also be better so that it won't be used on every page about a number in general. SuperMidget (talk) 10:35, 24 February 2008 (UTC)
Looks better. The last section could be in three columns, too. If one of the items in the 2nd section could be suppressed, it would look even more smooth. Another suggestion is to make the subsections hideable. Jakob.scholbach (talk) 20:09, 23 February 2008 (UTC)
Another point is to decide which items should actually be included. I have personally never met Tessarines, which doesn't say anything about their notability, but as a general idea I'd suggest to include in the template only topics which have a non-stub-coverage in the corresponding article. One link I do miss in the template right now would be p-adic numbers. Jakob.scholbach (talk) 20:16, 23 February 2008 (UTC)
The template has the p-adics uner other. Personally, I find that having terms I don't know (likewise, tessarines for me) if the best part of such templates. CRGreathouse (t | c) 13:33, 24 February 2008 (UTC)
I don't think this is large enough to benefit from hideable subsections (unlike, say, {{ProbDistributions}} which certainly would). To make it a bit smaller, might I suggest suppressing the word "numbers" from the entries where it occurs in the same way that {{ProbDistributions}} suppresses "distribution" ? --Qwfp (talk) 20:33, 23 February 2008 (UTC)
I tried out some ideas, see SuperMidget/navboxNumbers. Personally I prefer the compact vertical table layout (first one). The vertical lists may be unconventional for a navbox, but it's much more readable than the horizontal navbox (see for yourself). I will not bother with questions of what should be in the box and what not.. I just want to put something on the pages for easy navigation. SuperMidget (talk) 21:41, 23 February 2008 (UTC)
I also like the compact vertical table. CRGreathouse (t | c) 21:44, 23 February 2008 (UTC)
Wouldn't Number systems be a better heading than Numbers?  --Lambiam 22:57, 23 February 2008 (UTC)

I removed the template from the articles for now. I see there is good progress here towards an alternative version of this template to go to the bottom of articles. On top it was really staying in the way of the very nice illustrations many of the number articles have. 01:55, 24 February 2008 (UTC) —Preceding unsigned comment added by Oleg Alexandrov (talkcontribs)

Since there's no more response to this discussion, I created a new template {{Number Systems}} that can be used at the bottom of the relevant pages. Please continue any discussions about the template there. I put it on Natural number for a start, but I leave the rest up to you. SuperMidget (talk) 19:47, 26 February 2008 (UTC)

## Mortgage-related entries

FYI: Entries related to mortgages, such as Mortgage Calculator, Mortgage, and Mortgage loan could use some attention from WikiProject Mathematics. --Pleasantville (talk) 23:24, 25 February 2008 (UTC)

## Vector formatting

I don't want to cause more of a fuss than I have already, but I am concerned about some formatting changes to vector-related articles (so far only cross product and vector (spatial).) The question is whether a vector, when written inline in the text, should be typeset at ${\displaystyle \langle a,b,c\rangle }$ or as (a,b,c). I favor the latter since it doesn't force inline PNG rendering (which takes time, may cause the text to format badly, etc.) Furthermore the ${\displaystyle \langle \cdot ,\cdot \rangle }$ is the preferred notation of most physicists and differential geometers for an inner product, such as a metric. Silly rabbit (talk) 21:52, 26 February 2008 (UTC)

Concur. — Arthur Rubin | (talk) 22:00, 26 February 2008 (UTC)
I also concur. To be thorough, one might check if physicists would write |1,2,3> for a vector, but I would stick with (1,2,3), or [1,2,3] if one is not worried about the wiki-parser and wants the vector to be a "row vector". If someone knows of a plain text alternative for \langle and \rangle, I would love to fix lots of other articles. In most fonts, ⟨ and ⟩ are not much different than < and >. JackSchmidt (talk) 23:08, 26 February 2008 (UTC)
Concur. In physics, |•> is Dirac's bra-ket notation for a quantum state. Although a quantum state can be represented as a vector in Hilbert space, it's not used as general notation for a vector in simpler contexts (see that article for full story). (I've seen <•> sometimes used to denote a mean in physics books, rather confusingly, and i'm sure but i've seen it somewhere on WP but I think WP is best avoiding that particular notation.) Qwfp (talk) 11:20, 27 February 2008 (UTC)
I don't recall seeing the notation ${\displaystyle \langle a,b,c\rangle }$ for a vector in any mathematics, physics, or engineering text. -- Fropuff (talk) 00:16, 27 February 2008 (UTC)
Yep, (1,2,3) is the standard notation. There may be a little of confusion with the notation for points, but after all, a point can be thought of as a vector starting at the origin. Oleg Alexandrov (talk) 04:43, 27 February 2008 (UTC)
I've seen those in texts or maybe at least in classes (they're "chevrons" as I recall), but parentheses are just as good. Parens are easier, although other html alternatives are available; these are the two that come to mind:
 less thans < x , y > < x , y > chevrons ‹ x , y › ‹ x , y ›
I assume these are helpful (?) --Cheeser1 (talk) 05:16, 27 February 2008 (UTC)
There has been quite a debate on Talk:Bracket about the proper symbols used to represent angle brackets.
Description Characters
Standard keyboard symbols ("less than" & "greater than") < >
Unicode characters (left-pointing angle bracket) U+2329 (〈) and U+232A (〉)
more Unicode characters (left angle bracket) U+3008 (〈) and U+3009 (〉)
mathematical left angle bracket U+27E8 (⟨) and U+27E9 (⟩)
single-left angle quotation U+2039 (‹) and U+203A; (›)

Some are vigorously against less than or greater than as semantically incorrect, however the strange unicode characters don't display unless people have fancy fonts installed, so other prefer to keep things simple. --Salix alba (talk) 07:50, 27 February 2008 (UTC)

I don't have fancy fonts (I don't think) and I see "single-left angle quotation" (which is what I called "chevrons" above). I don't see the others. --Cheeser1 (talk) 08:12, 27 February 2008 (UTC)
While I can see there's an argument that an article on Brackets should distinguish these and make clear the limitations of most current computer set-ups (including mine), I'd take the pragmatic line that other articles are ok using <> for angle brackets until such time as most computer set-ups can display the proper left angle bracket or mathematical left angle bracket or both. (single-left angle quotation should be used only for what its name suggests, i.e. languages such as French that often use this instead of quote marks. It's too small for an angle-bracket) Qwfp (talk) 11:35, 27 February 2008 (UTC)
I would like to "vote" on using the Standard keyboard symbols ("less than" & "greater than") (< >), since it seems like using the [itex] option is frowned upon.
The book that I have been using shows vectors as < a, b, c >, (as it uses ( x, y, z ) for points.) I also would like to argue that unless given a starting point, all vectors (technically) begin at the origin.
Ajl772 (talk) 21:06, 27 February 2008 (UTC)

## Revision of navigational template for probability distributions

After some discussion at Template talk:ProbDistributions#Too large I've drafted a revised navigational template to replace {{ProbDistributions}}, which has grown too large. (This is the template at the bottom of some but not all of the probability distribution articles, not the infobox on the right.) For the moment the draft version is at User:Qwfp/tempprobdist. To keep all the conversation in one place, please post comments at Template talk:ProbDistributions not here. If I don't hear any views to the contrary, I'll go ahead and replace {{ProbDistributions}} at the weekend. Thanks, Qwfp (talk) 18:53, 27 February 2008 (UTC)

## award-winner categories

Working with awards and award-winners and CFDs -- and now TFDs! -- all this time it occurred to me that perhaps the best solution is a single compressed template. So, I drafted Template:Awardwinners; other editors' thoughts would be appreciated. Maybe it'll work, maybe not, but I thought I'd at least ping some other folks involved in award-winner discussions for their opinions and thoughts. The math folks were particularly enamored of the math awards, so those of you with thoughts -- pro or con -- about award-winner categories being applied to articles, please stop by the template page and give your thoughts and reactions. --Lquilter (talk) 19:23, 27 February 2008 (UTC)

## Trolling at Vector (spatial)

Any chance someone else is willing to handle the issue over at Talk:Vector (spatial)? I'm a bit stressed, and I don't feel like putting up with this trolling user. Silly rabbit (talk) 21:58, 21 February 2008 (UTC)

I spend all my time at the WQA, I might as well step in on this one. I've removed the entire new thread the user started to launch personal attacks at you. Hopefully that's a start. --Cheeser1 (talk) 22:13, 21 February 2008 (UTC)
I believe I'm the one labelled a trolling user. I would beg to differ. I believe I have some significant contributions to make to Talk:Vector (spatial), given a fair opportunity. --Firefly322 (talk) 03:41, 25 February 2008 (UTC)
One's editing experience is generally more pleasant if one manages to refrain from personal attacks, insulting qualifications, and snide remarks. Labelling editors you disagree with "Intellectually Unqualified" or their edits "Irrational Behavior" is not in accordance with proper Wikiquette, and may evoke a suspicion of trolling. Also, while the use of talk pages is generally recommended and commendable, flooding a talk page is not productive.  --Lambiam 14:01, 25 February 2008 (UTC)
I took a look there, and thought that some of the difficulty was from defining vectors as "quantities". So as to distinguish vectors from scalars clearly, I said that (paraphrasing myself), "vectors are quantitative but not quantities. The are objects composed from numbers (e.g. ordered lists of numbers), but not numbers themselves". Imagine my surprise when they found numerous physisics textbooks referring to vectors as quanitities :-) I'd forgotten that nomenclature. They point out that quaternions are numbers, and quaternions are vectors, therefore vectors are numbers :-) Pete St.John (talk) 19:24, 25 February 2008 (UTC)
Physicists say "dimensioned quantity" when they mean a number with some unit of measurement attached, such as 1.8755459 × 10 −18 C. Perhaps by "vector quantity" they similarly mean something like an "oriented quantity", a number with a direction attached. Something like this: "In some contexts, e.g. in the formula for kinetic energy, velocity can be handled as a scalar quantity, but in the law of conservation of linear momentum it is a vector quantity."  --Lambiam 22:51, 25 February 2008 (UTC)
I think that's about right, except to get even more pedantic, i think velocity is always a vector; speed is the corresponding scalar... Qwfp (talk) 23:46, 25 February 2008 (UTC)
That's why I wrote "can be handled as" and not "is". In any case, dictionaries typically make no such distinction, and plenty of professional articles written by physicists (including Michelson) freely use "velocity of light" where clearly the scalar quantity is meant.  --Lambiam 10:13, 26 February 2008 (UTC)
My apologies Lambiam, I regret writing that now. I clicked "edit" meaning to say i agree ((as does Google)) that "vector quantity" and "scalar quantity" are commonly used in physics. I see little wrong with these phrases myself. I'm sorry I went off into needless and distracting late-night pedantry instead. Qwfp (talk) 13:55, 26 February 2008 (UTC)

Can we have an extra pair of eyes at Vector? I fear that the quality of the article is rapidly deteriorating thanks largely to the efforts of one persistent new editor qwho behaves like a troll. In particular, I've rewritten the lead to take care of the basics of vectors (and remove the cruft) which quickly got reverted with no reason. Sockpuppetry is also a concern, since he alternately uses an anon account and a registered account. Arcfrk (talk) 02:09, 26 February 2008 (UTC)

Mr. Silly Rabbit and I have already apologized to each other for what happened a few days ago. Since then, the discussion seemed to be moving rapidly towards consensus. I believe Mr. Arcfrk's comments here and in the other discussion are rash and have slowed progress towards mutual agreement as to the type of vector described in vector (spatial). In my mind, Mr. Arcfrk really seems out of touch with Mr. Johnson's and my consensus on some points. And how critical such a consensus is and how it has not happened before now. --Firefly322 (talk) 03:39, 28 February 2008 (UTC)
I haven't figured out the (three?) senses of vector in discussion, yet, but I think patience will pay off. I suspect we would be better off with "Vector (abstract)" vs "Vector (introduction)" but we don't organize articles the way I would myself. The "spatial" vs "physical" distinction still confuses me. Pete St.John (talk) 20:15, 28 February 2008 (UTC)

There's now also a related deletion discussion: Wikipedia:Articles for deletion/Vector (physical). —David Eppstein (talk) 22:02, 28 February 2008 (UTC)

## Respect external references or internal consistency?

At Gauss-Newton algorithm, Petergans would like the step be given by

${\displaystyle (\mathbf {J} ^{T}\mathbf {J} )\delta {\boldsymbol {\beta }}^{k}=\mathbf {J} ^{T}\mathbf {r} ,}$

to be consistent with what is used at non-linear least squares, which he wrote.

I prefer the formula

${\displaystyle (\mathbf {J} ^{T}\mathbf {J} )\delta {\boldsymbol {\beta }}^{k}=-\mathbf {J} ^{T}\mathbf {r} ,}$

(note the minus), because that's all the references I've seen use. The discrepancy with the sign is because Petergans uses residuals of a special form, while the formula with the minus works for general residues.

So, what would readers prefer, to be consistent with other books and websites, or with another Wikipedia article (written by the same editor who wants the change at Gauss-Newton). We've been going back and forth for a few days on this, with no agreement. More comments are welcome at Talk:Gauss-Newton algorithm#Latest changes. Oleg Alexandrov (talk) 06:00, 27 February 2008 (UTC)

In general, I would prefer that articles be consistent, provided that someone uses the notation. Certainly, if two related Wikipedia articles use different notation, that should be noted.
See, for example, matrix calculus, where our references use different notations.
I haven't checked this particular article set, though. — Arthur Rubin | (talk) 13:09, 27 February 2008 (UTC)
Two suggestions: 1) rewrite the other article to use "general residues" instead of the special form, or 2) Add some variant of the following sentence to the article: Many textbooks place a minus sign in the above formula; this is correct when general residues are used, but not the special residues used in this and other articles. linas (talk) 04:58, 29 February 2008 (UTC)

## Super-recursive algorithm

A new editor has started working to improve this article, but as a new editor is unfamiliar with NPOV and NOR. It would be helpful to have a few other experienced editors look through the article to smooth out any biased claims, while still trying to keep the changes that improve the article or add detail in a neutral way. — Carl (CBM · talk) 23:25, 28 February 2008 (UTC)

# Mar 2008

## Help me not WP:BITE the newcomer

Katsushi (talk · contribs · logs) has made some less-than-useful changes to several articles. He removed a mention of Rosser's theorem [23] from Prime-counting function and deleted a reference to Dusart's prime number bounds [24] on Prime number theorem. He had earlier removed some results on Wieferich prime (since re-added), and his recent change there also seems not to benefit the article.[25]

But I don't think these were done in bad faith, though his small number of edits made me wonder. I mainly think that we need to (1) show him how to discuss changes before removing material, and (2) keep an eye out on his changes in the meantime.

I also bring this up as a sanity check: if someone thinks I'm wrong to revert these changes, please say so!

CRGreathouse (t | c) 00:26, 2 March 2008 (UTC)

That's WAREL, who else. I reverted the edits which have not been reverted before. Oleg Alexandrov (talk) 03:09, 2 March 2008 (UTC)
Ah, I guess that would explain it wouldn't it. Well, at least I assumed good faith properly... CRGreathouse (t | c) 05:28, 2 March 2008 (UTC)

## Proposal: Redirect List of mathematics topics to Lists of mathematics topics

I can't see the point of retaining List of mathematics topics as a disambiguation page, but I may be overlooking something... Please comment on my redirect proposal at Talk:List of mathematics topics. --Orlady (talk) 16:35, 2 March 2008 (UTC)

Seems fairly uncontroversial to me. You might consider in addition putting a {{See also|List of mathematics articles}} at the top of the Lists of mathematics topics page. (Or, perhaps, an appropriate {{dab}} template. But that seems a bit pedantic.) Silly rabbit (talk) 16:58, 2 March 2008 (UTC)
I have redirected the page as proposed. Since the first paragraph of the article links prominently to List of mathematics articles, the proposed addition of a disambiguation notice as a hatnote seemed like overkill... --Orlady (talk) 19:03, 2 March 2008 (UTC)
I see about the hatnote. Quite right. Silly rabbit (talk) 23:06, 2 March 2008 (UTC)

## Navigation versus browsing

Currently, there are several lists in the mainspace that solely exist for purposes of navigation, cluttering up the mainspace needlessly.

Then it mentions lists of mathematics topics among the examples. I have added language to the effect that that is NOT a page that exists solely for the purpose of navigation. At Wikipedia talk:Move navigational lists to portal namespace it is also mentioned, and I've added some lengthier comments there. I understand "navigation" to mean finding your way to something when you already know what you're trying to get to. I don't think that's the main purpose of the page, let alone the only purpose.

Could others add their opinions to those discussions? Michael Hardy (talk) 22:52, 3 March 2008 (UTC)

## Featured status

At the end of December, lists of mathematics topics ceased to be a featured list after this discussion. I don't recognize any of the names of the discussants. The MANY people who voted for featured list status did not participate. None of the participants gives any evidence of genuine understanding of the list.

This featured status was lost only because we who actually know something neglected to rescue it. I think we should try to get the featured status back.

Note the objection: lack of references. For some of the topics, references could come from the AMS subject categorization. For things like list of factorial and binomial topics or list of exponential topics, I think the references in the listed article suffice. It is unreasonable to ask for a reference for that particular name for a collection of articles on related topics.

So maybe we should add references when they exist and for those that don't, add some explanation to the article and mention the references in the articles linked to. Michael Hardy (talk) 23:40, 3 March 2008 (UTC)

I have a hard enough time with featured articles, let alone featured lists. The page you mention (lists of mathematics topics) is quite nice. I like it; but I don't think I'll like it any more if it has a little star next to it. Why should we care if a list is featured or not? Is there any real benefit to be had? Before I spend time and energy arguing for featured status I want to know what there is to be gained. -- Fropuff (talk) 03:15, 4 March 2008 (UTC)
As I understand it, there's a question mark over whether this will even qualify for consideration for featured list status if it gets moved to Portal namespace (see previous section and Talk:Lists_of_mathematics_topics#Survey). Until that's resolved I don't see much point trying to get featured status back. (I'd agree that the main reason for its removal seems of questionable relavance for such a list.) By the way, I like this page but I wasn't even aware of its existence until yesterday; surely it should have a (fairly prominent) link from the Mathematics Portal? Qwfp (talk) 10:18, 4 March 2008 (UTC)
I do recognize some of the names, such as that of Michael Hardy :) and CBM, neither of which !voted Keep.  --Lambiam 12:00, 4 March 2008 (UTC)
To be fair, I didn't vote at all. I just pointed out the inanity of asking for references to verify that the topics in the list are actually related to mathematics. My personal opinion is that there isn't much benefit to adding them, so I don't mind that it's no longer a "featured list" if that is the concern. — Carl (CBM · talk) 22:32, 4 March 2008 (UTC)

## Counting number

Is there a definitive definite definition of the notion of counting number? According to the article Cardinal number, to which Counting numbers redirects,

In informal use, a cardinal number is what is normally referred to as a counting number. They may be identified with the natural numbers beginning with 0 (i.e. 0, 1, 2, ...). The counting numbers are exactly what can be defined formally as the finite cardinal numbers.

However, according to the our article Natural number, to which Counting number redirects,

In mathematics, a natural number can mean either an element of the set {1, 2, 3, ...} (the positive integers or the counting numbers) or an element of the set {0, 1, 2, 3, ...} (the non-negative integers).

According to the first article, 0 is definitely a counting number; according to the second article, it definitely is not. BTW, I think that Counting numbers and Counting number should redirect to the same article.  --Lambiam 18:51, 4 March 2008 (UTC)

Good catch. But what a pain; there's no definitive answer and lots of potential for fruitless debate over trivia. Maybe we could redirect them both to natural number and then remove all discussion of "counting numbers", which after all is more an informal description for children than a precise technical term.
Reminds me of an exchange from The Restaurant at the End of the Universe, which from memory goes something like this:
"How many escape pods are there?" asked Ford.
"None", said Zaphod.
Ford goggled. "Did you count them?" he shrieked.
"Twice", said Zaphod.
--Trovatore (talk) 19:18, 4 March 2008 (UTC)
I've made less drastic changes. I've made counting number at Natural number share in the ambiguity of zero's membership, while at Cardinal number I've added the stipulation that 0 be included. Also the plural redirects now to Natural number.  --Lambiam 21:14, 4 March 2008 (UTC)

## Tangent

In this article we have a marriage of inconvenience: Tangent lines and Tangent function coexisting in the same article, but not speaking to each other. Moreover, the geometric part, at least, is severely deficient (it's covered up by the overall length of the article). In particular, it doesn't even begin to address tangent lines to space curves and tangent planes to surfaces. Here is the problem: there are hundreds of incoming links, each of which will have to be fixed when the article is split. Can someone with a bit of time and AWB or similar experience commit to fixing these links? Then I'll go ahead and carry out the split. Arcfrk (talk) 02:07, 22 February 2008 (UTC)

Note also that Tangent function redirects to Trigonometric function. Not just a marriage of inconvenience, but also an apparent divorce. Silly rabbit (talk) 02:27, 22 February 2008 (UTC)
Yeah, I've noticed this a few times too. It needs fixing. What new article/linkage/redirection organisation are you proposing? Can we find a way to make incoming "Tangent" links go to some sort of disambiguation page where both meanings are listed (c.f. secant)? That way we'll be no worse off than at the moment (when users are thrown into the schizophrenic article), and we can pick away at disambiguating the links at our leisure. I notice there is already a Tangent (disambiguation) page though. Matt 12:03, 22 February 2008 (UTC). —Preceding unsigned comment added by 81.129.128.2 (talk)
I think the article should cover the geometric concept with a note at the beginning directing people interested in the trig function to the Trigonometric functions article. --agr (talk) 19:11, 22 February 2008 (UTC)

I've removed the obsolete section on the trigonometric function "tangent" and would like to reiterate a request to volunteers with automated editing experience to fix the incoming links. Arcfrk (talk) 05:54, 1 March 2008 (UTC)

What precisely needs to be done? — Carl (CBM · talk) 14:26, 5 March 2008 (UTC)
Someone should go through the incoming links from articles seen in "what links here" and change all those links to "Tangent" that use the term in the sense of trigonometric functions to "Trigonometric functions" (or to the redirect "Tangent function", if that is preferable in any way). Arcfrk (talk) 20:46, 5 March 2008 (UTC)
I'll work on it. Most of the links that need to change should change to tangent (trigonometric function) in case that ever becomes an actual article. — Carl (CBM · talk) 14:58, 6 March 2008 (UTC)

Perhaps we should have an article "Tangent (trigonometric function)" besides the redirect. Just informally, I'd say something like:

The tangent function is one of the three basic trigonometric functions: sine or SIN, cosine or COS, and tangent or TAN. Tangent is not to be confused with tangent vector or tangency; however, they are closely related. The TAN of an angle is equivalent to the slope of a line; in calculus, the derivative of a function is the slope of the tangent vector, that is, the slope of a line which has (local) tangency to the graph of the function.

So I'd suggest a paragraph along those lines (no pun) explaining the differences and relationships, with links to everything for precise definitions and limitless elaborations. Pete St.John (talk) 17:47, 6 March 2008 (UTC)

Personally, I dislike having multiple articles, each consisting of nothing but a definition. I think the model of Eigenvalue, eigenvector, and eigenspace is far superior both from a professional and pedagogical viewpoint. So I think having all the trigonometric functions redirect to Trigonometric function is reasonable. — Carl (CBM · talk) 17:59, 6 March 2008 (UTC)
I advocate little disambiguation articles taking the opportunity to explain the ambiguity (which explanation might be buried deep in the main articles), as they sit at just the spots where readers are more likely to be confused; like street-signs at cross-roads. In particular in this case, it's not "nothing but a definition" as it explains the ambiguity (from the etymology of tangent)-- maybe not well. Pete St.John (talk) 18:33, 6 March 2008 (UTC)

## Hoax?

Does anyone know anything about Troy Raeder? It has been suggested that the article is a hoax. Is it? Michael Hardy (talk) 16:02, 5 March 2008 (UTC)

Looks like a hoax to me: [26] [27] [28] [29] [30] [31] [32]. That and the language in the article is a bit.. overinflated. Reads alot like a hoax/fake bio. Troy Raeder appears to be a Notre Dame grad student in CS, and Danny Chen appears to be a young CS prof there (not the chair, certainly no chair named after him). --Cheeser1 (talk) 16:15, 5 March 2008 (UTC)
Danny Z. Chen is a prolific algorithms researcher at Notre Dame who likely warrants an article here, and it looks like there is some grain of truth to the page, under all the hoaxing. But I don't see the point in trying to tease it out from the article as written. —David Eppstein (talk) 16:26, 5 March 2008 (UTC)
Especially since it would need to be Danny Chen or Ziyi Chen or something - not Troy Raeder. I say speedy this thing, and if anyone wants to create Danny Chen they are welcome. --Cheeser1 (talk) 16:30, 5 March 2008 (UTC)
"Danny Z. Chen" is the form I've most commonly seen his name. I've added him to my list of missing computational geometry researchers, but there are several other names there that I would consider a higher priority. —David Eppstein (talk) 16:41, 5 March 2008 (UTC)
I tagged it with {{hoax}}. We typically don't speedy-delete hoaxes; at least, we should give it a couple days for the author to respond.
I agree Chen looks like a candidate for an article, although I am not yet sure that he meets any of the WP:PROF criteria. — Carl (CBM · talk) 16:39, 5 March 2008 (UTC)
We don't speedy hoaxes? Since when? WP:CSD#G3 seems to say we do. --Cheeser1 (talk) 16:48, 5 March 2008 (UTC)
I think that's for "obvious hoaxes" a la "Fred, the chicken from outer space". Nothing wrong with a {{prod}} here, IMO. Silly rabbit (talk) 16:57, 5 March 2008 (UTC)
It's pretty obvious to me. It doesn't say "patently stupid or nonsensical hoaxes," it just says "obvious." Regardless, I'm not objecting to the prod, I'm just voicing my opinion that CSD#G3 applies here. -- Cheeser1 (talk) 17:00, 5 March 2008 (UTC)

Note that this page has been deleted. --Cheeser1 (talk) 21:23, 6 March 2008 (UTC)

## OR in calculations

A couple of times on Wikipedia, I have run into problems with simple calculations being branded as WP:SYN, WP:OR, and so on. When I say simple, I mean really simple. For example, if I have 3 surveys that give results as percentages, and one survey that gives its results as a ratio, I have been told that converting the 4th survey result into a percentage to compare with the other 3 constitutes OR (which I strongly disagree with). Recently I am dealing with a very simple probability and chemical concentration problem where the literature as far as I can tell has the calculation slightly incorrect (or does not include the correct caveats etc). I am told that correcting this oversight or error is possibly WP:SYN.

However, when I look at articles in physics or mathematics, I see all kinds of simple manipulations and calculations that are not repeated verbatim from some reference, but are simple restatements of the information with minor manipulations for the purposes of presentation. Where exactly is the line for OR in these situations?--Filll (talk) 14:04, 6 March 2008 (UTC)

Simple calculations are fine, provided that they are uncontentious and clear to anyone with a basic understanding of the area. The main OR concern is if the calculation is being used for a polemical purpose.
On the other hand, we probably shouldn't claim a published source is "wrong" based on our own calculations. If it is wrong, the right thing to do is usually just to ignore it and use other sources instead. If multiple published sources make the same "error", it may not be an error at all. — Carl (CBM · talk) 14:46, 6 March 2008 (UTC)
If it's a mistake in simple routine arithmetic of the kind referred to above, which anyone 7th-grader can check in a minute, I'd have no problem asserting in a Wikipedia article that it is an error. Michael Hardy (talk) 20:23, 6 March 2008 (UTC)
I wonder whether I crossed the line today in [33] where I corrected a 1000-digit prime in OEIS. It's easy to verify with bignum software, but is that acceptable? The only source I know with the right number is selfpublished by myself (Jens Kruse Andersen), so I didn't mention it: [34]. Maybe I could find another source somewhere but I have submitted the correct number to OEIS and will update the article when OEIS updates (which I assume they will). Getting a false online source to correct itself seems a good way to deal with the problem, but obviously impossible in many cases. PrimeHunter (talk) 23:50, 6 March 2008 (UTC)
All of a sudden your username makes sense. If we are quoting a source with a mistake, we use [sic] to indicate a problem. If we are simply saying "here is where the sequence is found on the OEIS" we can correct it, I believe, without remark - in this case especially, it was clearly a typo, and not a deliberate mistake or mistake worthy of any consideration (the fact that it's hard to find/fix notwithstanding). --Cheeser1 (talk) 01:02, 7 March 2008 (UTC)

If anyone ever tells me that converting 0.35 to 35% is "original research", I will respond that he should be ashamed of himself. Reading, writing, and 'rithmetic are taught in elementary school. What you were taught in elementary school is not your "original research". Michael Hardy (talk) 20:17, 6 March 2008 (UTC)

Well it has happened where I have had a long fight with an admin who claimed that converting numbers like 312/783 into percentages is WP:OR. And now I am dealing with a slightly more complicated situation, but again being told that it is OR. And when I read math and physics pages, I see that people do all kinds of calculations and manipulations with seemingly no problem. Oh brother...--Filll (talk) 21:27, 6 March 2008 (UTC)
Who was that administrator? Michael Hardy (talk) 01:18, 7 March 2008 (UTC)
That was violet/riga.--Filll (talk) 01:40, 7 March 2008 (UTC)
I was in a situation once where some guy demanded a citation that 2 is the number that comes after 1. It was a strawman argument related to something else entirely, but the sheer misunderstanding of WP:V blew my socks off. One can verify in any text on, say, number theory that 2 is the successor of 1. It is verifiable. So too is the fact that 0.35 = 35%. WP:V demands that things be verifiable, not verified. WP:RS and WP:V don't demand sources of every sentence, and WP:OR only forbids things that are research and original conclusions. 0.35 = 35% is hardly original, research, or unverifiable. --Cheeser1 (talk) 21:30, 6 March 2008 (UTC)
Unfortunately Wikipedia is flooded by non-OR fundamentalists. Their fanatism is invariably caused by lack of underatanding. I have actually given up some battles in this area. JocK (talk) 21:52, 6 March 2008 (UTC)
Yes. Nice neologism, though. Pete St.John (talk) 22:16, 6 March 2008 (UTC)

A useful reference to use as ammunition in these arguments: Wikipedia:Scientific citation guidelines#Examples, derivations and restatements. —David Eppstein (talk) 02:20, 7 March 2008 (UTC)

## Polynomial ring

Here we go, Bo Jacoby again. He has replaced the formula for polynomial multiplication

${\displaystyle \left(\sum _{i=0}^{n}a_{i}X^{i}\right)\cdot \left(\sum _{j=0}^{m}b_{j}X^{j}\right)=\sum _{k=0}^{m+n}\left(\sum _{i+j=k}a_{i}b_{j}\right)X^{k}.}$

with the formal series

${\displaystyle \left(\sum _{n}a_{n}X^{n}\right)\cdot \left(\sum _{n}b_{n}X^{n}\right)=\sum _{n}\left(\sum _{i+j=n}a_{i}b_{j}\right)X^{n}}$

(he states below that only a finite number of terms is non-zero).

Other two of us are arguing on the talk page against it, that you should not invoke something as complex as formal power series to explain something as simple as polynomials. So far, we have no success. Any additional comments at Talk:Polynomial ring would be welcome. Oleg Alexandrov (talk) 15:55, 26 February 2008 (UTC)

I myself am arguing that the sums with limits appear first, to mimic what would be seen in an introductory college course. The limitless sums should appear in the formal definition section a little later, where polynomials are already quite formal. The sums for more general exponents appear even lower under generalizations, and look like:
${\displaystyle \left(\sum _{n\in N}a_{n}X^{n}\right)\cdot \left(\sum _{n\in N}b_{n}X^{n}\right)=\sum _{n\in N}\left(\sum _{i+j=n}a_{i}b_{j}\right)X^{n}}$
where N is defined to be some monoid, and the inner sum of the cauchy product is explicitly mentioned to have i, j vary over all pairs in N×N summing to n.
Basically, Oleg feels the limitless notation requires complex ideas to explain the simple, and I say that we should include both points of view, but begin with the schoolbook (ok, English-centric schoolbook) version, and include the others after. JackSchmidt (talk) 16:22, 26 February 2008 (UTC)
I think that the infinitary expression requires more editing to make sense, as the sum of an infinite number of 0's is not necessarily 0. I've edited in what I consider necessary for it make sense without going to the formal power series domain. I'm willing to let other decide whether it's now more complicated than the correct finite formalism. — Arthur Rubin | (talk) 22:03, 26 February 2008 (UTC)
It is new to me that 'the sum of an infinite number of 0's is not necessarily 0'. What else can it be? x = Σ0 satisfies the equation 2·x = 2·(Σ0) = Σ(2·0) = Σ0 = x, implying x=0. Bo Jacoby (talk) 09:01, 27 February 2008 (UTC).
Bo, your argument assumes that the sum has one and only one value. It also assumes that the distributive law of multiplication over addition works for infinite sums. Both are questionable assumptions. JRSpriggs (talk) 09:54, 27 February 2008 (UTC)
Sure, if no assumptions are made then any definition can do. If an expression has more than one value then it is not well defined. If the distributive law does not apply then it is strange to call it a sum. Is there any sensible or standard mathematical theory where Σ0 ≠ 0 ? Bo Jacoby (talk) 10:02, 27 February 2008 (UTC).
Try formal power series or divergent series. To the real issue at hand: your notation is imprecise and nonstandard. The other two versions, both of which (I think) appear in the article are better and widely-used. Why are you (once again) trying to push nonstandard notation into articles? What's there is fine. There's no reason to change it, at least not to your notation. --Cheeser1 (talk) 19:22, 27 February 2008 (UTC)
Cheeser1, your two links show no examples of Σ0 ≠ 0 . What is the imprecision of the limitfree notation? The fourth sum in the multiplication formula is limitfree anyway, so why do you accept that? There exists no standard for mathematical notation, so stop talking about nonstandard notation. The formula with limits is not correct, as explained on the talk page. You are welcome to correct it if you don't want me to do it. I am pushing for simplicity and correctness here. So are you, I trust. Bo Jacoby (talk) 13:47, 29 February 2008 (UTC).
There exists no standard for mathematical notation, so stop talking about nonstandard notation. This comment reflects a gross misunderstanding of how mathematical notation works. Just because not all mathematicians use the exact same notation doesn't mean there are not standards and accepted notations. Notice above two versions of the same sum, and yet both are accepted. Your third version, however, is not a notation that is widely-used or commonly accepted. Every time you pull this nonsense, you make the same argument: "there's no such thing as standard notations, so you can't tell me not to fill the article with the notation I want to." Besides being based on shaky, if not patently false, presumptions about notation in mathematics, you have to realize that no one else uses this notation and no one else wants to change it: please follow consensus and stop wasting your time conjuring up new and interesting notation changes that are just going to cause conflict. --Cheeser1 (talk) 16:42, 29 February 2008 (UTC)
Cheeser1, I dont know what 'third version' you are talking about. The limitless notation ${\displaystyle \sum _{k}a_{k}X^{k}\,}$ is used in Polynomial_ring#Definition_of_a_polynomial, and another example, ${\displaystyle \left(\sum _{i}a_{i}\right)\left(\sum _{j}b_{j}\right)=\sum _{i}\sum _{j}a_{i}b_{j}}$, is found in summation. I did not put it there. So you are simply wrong in assuming that 'no one else uses this notation'. Actually it is commonly used and there is no reason for you to get upset. Bo Jacoby (talk) 00:37, 2 March 2008 (UTC).
Bo, a classic example is that clearly 0=+1-1, but the infinite series +1-1+1-1... does not sum to zero. There's even an entire WP article on this, I don't remember the name. I agree with Oleg, the concepts should be explained with the simplest possible terms. Infinity should be avoided: the more you get to know infinity, the more viciously complicated it turns out to be.linas (talk) 04:51, 29 February 2008 (UTC)
Linas, 1−1+1−1... ≠ (1−1)+(1−1)... because you are not allowed to insert an infinite number of parentheses in a series. The WP article you forgot may be this. I too agree that the concepts should be explained with the simplest possible terms. The explanation with the simplest possible terms is the one without limits. Unlimited notation does not imply an unlimited number of (nonzero) terms, and so infinity is avoided. Bo Jacoby (talk) 13:47, 29 February 2008 (UTC).
Linas' reference may have been Grandi's_series. Bo, I don't understand the rule "you are not allowed to insert an infinite number of parentheses in a series". Also, the notation "Summa (for a in A)" is unambiguous and defers to the cardinality of A; you might prefer that to "Summa (over a)" (and pardon my typography, I write in C not LaTex :-) Pete St.John (talk) 18:27, 29 February 2008 (UTC)
PeterStJohn, thank you for the link. Grandi's_series actually answers your question: to the extent that it is important to be able to bracket series at will, the series 1 − 1 + 1 − 1 + … has no sum, but if it is important to perform arithmetic its sum is 1⁄2. That means that if the series has a value, then you are not generally allowed to bracket series at will. Any geometric series, x = 1+a+a2+··· = 1+(a+a2+···) = 1+a(1+a+a2+···) = 1+ax , formally satisfies the equation x=1+ax. If a≠1 this equation has the unique solution x=(1−a)−1. So
1 + 0 + 0 + 0 + ··· = (1−0)−1 = 1,
1 + 1/10 + 1/100 + 1/1000 + ··· = (1−1/10)−1 = 10/9,
1 + 1/2 + 1/4 + 1/8 + ··· = (1−1/2)−1 = 2,
1 − 1 + 1 − 1 + ··· = (1−(−1))−1 = 1/2,
1 + 2 + 4 + 8 + ··· = (1−2)−1 = −1,
1 + 10 + 100 + 1000 + ··· = (1−10)−1 = −1/9,
Not all rules for (finite) sums apply for infinite series: A (finite) sum of integers is an integer, and a (finite) sum of positive terms is positive, but here you see a series of positive integers having value which is neither positive nor integer. Many mathematicians find this counter-intuitive and prefer not to assign a value to a divergent series. This is legitimate. If you do not want to assign a value to some expression, nobody forces you. On the other hand, if you want to assign values to these expressions, there is no freedom as to which values the expressions should be given, assuming that you want the elementary arithmetic rules to apply. That the value of a series having only a finite number of nonzero terms is equal to the sum of the nonzero terms, is however uncontroversial. As to your suggestion, I do find it acceptable, but some other editors might not. Bo Jacoby (talk) 01:48, 1 March 2008 (UTC).

If I might offer a suggestion, having dealt with Mr. Jacoby before: It is pointless to let him draw you into endless discussions. No matter how logical or correct you are, he will always find some argument to keep the discussion going. I recommend that we drop the discussion here before we fill up this talk page with irrelevant arguments. Use consensus to overrule him at Polynomial ring and be done with it. He seems to thrive on baiting unsuspecting editors. VectorPosse (talk) 01:15, 1 March 2008 (UTC)

No sir, I don't argue against what is logical and correct, nor do I argue ad hominem. Bo Jacoby (talk) 01:55, 1 March 2008 (UTC).

As Silly Rabbit pointed out in the article's talk page, using "limitless" sums (with only finitely many nonzero terms) is quite standard, and, indeed, in many ways preferable. Moreover, I am stunned that mathematically educated people can argue that the sum 0 + 0 + 0 + … (or even ∑ 0 over any indexing set) can be anything but 0. Huh? Just because Bo said something, that doesn't make it untrue. However, all this tilting at windmills misses the point: that article doesn't have much content beyond defining the operations in a ring of polynomials in one variable, mumbling something about generalizations (including several variables), and giving a tangle of links. Our time would be spend much more productively if we concentrate on good quality exposition, rather than on the minor issues of the notation. I invite everyone to take a look and contribute to improving the article. Arcfrk (talk) 04:27, 1 March 2008 (UTC)

"Just because Bo said something, that doesn't make it untrue." But that is the way to bet. And, in this case, it really doesn't make sense without introducing either formal sums or the convention (or, perhaps, theorem, but it's more advanced mathematics than necessary for this article) that 0's can be removed from infinite sums without effecting the value. — Arthur Rubin | (talk) 18:17, 1 March 2008 (UTC)
Arthur Rubin, do you have an example of me saying something untrue? Bo Jacoby (talk) 00:37, 2 March 2008 (UTC).
That "you are not allowed to insert an infinite number of parentheses in a series." It's ANY infinite change in a non-absolutely convergent series.
That there may not be problems in summing an infinite number of zeros. ${\displaystyle \int _{0}^{1}1\ dx}$ looks like the sum of a continuum of terms, all equal to 0, in some formalisms.
However, it is true that any sum, in which only a finite number of terms are non-trivial, can be rearranged arbitrarily. If you rewrite the boundless sum to remove "trivial" terms, rather than terms whose value happens to be 0, it seems mathematically acceptable without being confusing.
Arthur Rubin | (talk) 14:41, 2 March 2008 (UTC)
What is the difference between 'non-trivial' and 'non-zero'? Bo Jacoby (talk) 23:00, 2 March 2008 (UTC).
In most cases, there wouldn't be any. However, I'd like to emphasize that the terms that we are suppressing from the sums are structurally omitted, leaving all of the sums finite, rather than there being only a finite number of non-zero terms. As for omitting zeros in general, if you allow "1 - 1 + 1 - 1…" to have a meaningful value (1/2?) , you have to agree that it's different than "1 + 0 + 0 - 1 + 1 + 0 + 0 -1…" (3/4?), even though they differ only in the addition of 0's. — Arthur Rubin | (talk) 20:08, 3 March 2008 (UTC)
That Grandi's series is 1/2 is the result only of fixing the spectral asymmetry to a certain particular value. Choosing other asymmetries will give different answers. linas (talk) 17:54, 4 March 2008 (UTC)

Ladies and gentlemen, I think all this talk about infinite sums is entirely beside the point (and probably due to the fact that our education exposes us to the difficult subject of convergent sums before the simpler matter of formal sums is well understood). In the polynomial setting there is (or should be) no topoplogy but the discrete one, and talking of convergence in any other sense is out of place. Using the limitless sums is not using formal power series expressions to define polynomial operations (which would be like using real arithmetic to define rational number arithmetic). Rather it is a simple question about linear combinations of infinite families. In linear algebra a linear combination cannot have infinitely many nonzero terms, that is simply not defined. However this does not exclude making linear combinations of infinite families of elements, or describing those combinations by the coefficients of each member; one just has to refrain from doing so with infinitely many nonzero coefficients. This is true in finite dimensional vector spaces like in infinite dimensional ones, but in the latter the discussion cannot be avoided if one wants to give any meaning to the notion of a basis (of which every vector should be a linear combination). And like it or not, a polynomial ring (over a field) is an infinite dimensional vector space, with a basis formed by the monomials. It is therefore quite natural to describe polynomials as limitless sums of distinct monomials each with a coefficient, as long as it can be checked that only finitely many coefficients (not terms!) are nonzero. This has nothing to do with convergence (but if you really want, you can observe that in a vector space that is given the discrete topology, the convergent sums are precisely those for which only finitely many terms are nonzero). Marc van Leeuwen (talk) 07:19, 7 March 2008 (UTC)

## Frequently viewed articles

I was inspired by Qwfp's comment above to look at the ratings of our most frequently viewed articles. I tagged the top 500 articles by hitcount, and now VeblenBot will generate ratings data that you can view at Wikipedia:WikiProject_Mathematics/Wikipedia_1.0/Frequently_viewed. Each of these articles received at least 18000 hits between Feb. 1 and Feb. 23, based on data I was given by User:Henrik from his site http://stats.grok.se; I made a list of the articles by hitcount here.

I noticed a couple interesting things:

• Statistics articles are particularly popular.
• We have only 17 stubs among these 500, but a lot of start-class articles.

— Carl (CBM · talk) 23:10, 8 March 2008 (UTC)

I did a similar thing a while back User:Salix alba/One day of mathematics page views and there was som discussion in the Jan archive.[35] --Salix alba (talk) 23:31, 8 March 2008 (UTC)
I think that's really informative, many thanks Carl. I found User:Salix alba's list interesting too but it's good to have results from a longer time window and to have it integrated with the other tables at Wikipedia:WikiProject_Mathematics/Wikipedia_1.0 and its subpages. Can I suggest moving the hitcount list to somewhere a bit more permanent than your sandbox, such as a subpage of Wikipedia:WikiProject_Mathematics/Wikipedia_1.0? Perhaps "frequentlyviewed=yes" could then give a link to there instead or as well as to http://stats.grok.se.
Just to be clear that I'm not suggesting hit counts are a substitute for human judgment of the "importance" rating, but they can help inform it. I'd argue that being frequently viewed is a sufficient but not a necessary condition for an article to be considered important (it seems unlikely people are looking at say "standard deviation" for entertainment or amusement, unlike say "Britney Spears"). Qwfp (talk) 11:04, 9 March 2008 (UTC)

### Few people read Wikipedia math articles on Sundays

One thing that's really conspicuous in the graphs given by this site is that fewer people view Wikipedia math articles on Sundays than on other days of the week. Michael Hardy (talk) 22:39, 9 March 2008 (UTC)

...maybe especially the frequently viewed statistics articles. Look at normal distribution. Every Sunday between 3000 and 4000 people view that article. On Mondays it's a bit higher; then on Tuesdays it jumps to almost 7000 and sometimes more than 8000. Similarly with Poisson distribution except that the numbers are somewhat lower. Michael Hardy (talk) 22:50, 9 March 2008 (UTC)
Perhaps many of the readers of statistics articles consult them in a professional capacity, while at work.  --Lambiam 23:00, 9 March 2008 (UTC)
Or school. --Cheeser1 (talk) 23:44, 9 March 2008 (UTC)
Maybe it's a time zone thing but I reckon it's Saturdays that have the lowest viewing figures for the statistics articles, closely followed by Sundays. I agree with Cheeser1 about the most likely explanation. Qwfp (talk) 10:32, 10 March 2008 (UTC)

It's not ONLY statistics; I've seen it in some geometry articles too. Michael Hardy (talk) 13:52, 10 March 2008 (UTC)

## Improvement drive

Can we use the page Wikipedia:WikiProject Mathematics/Wikipedia 1.0/Frequently viewed as a source of inspiration for reviving or revitalizing the Wikipedia:Mathematics Collaboration of the Month? The urgency of improvement corresponds to some formula like F/Q, where F = frequency of viewing and Q = current quality, both on a scale from 0 to infinity.

The following all have viewing rank < 100 and quality assessment Start or Stub:

rank frequency quality article
15 225847 Start Definition
21 208253 Start Newton's laws of motion
34 162784 Stub Dependent and independent variables
46 133395 Start Median
54 124845 Start Confidence interval
55 124585 Start Area
57 119522 Start Volume
60 117634 Start Butterfly effect
65 109750 Start Analysis of variance
68 107413 Start Hexagon
76 100266 Start Probability

Definition looks like a good place to start. The current article contains almost nothing about definitions in mathematics. It is actually a bit embarrassing hodgepodge, and we might be better off with an article Definition (mathematics) with a summary in the other article.  --Lambiam 23:04, 9 March 2008 (UTC)

I would definitely like to see the CotM revitalized. I've worked on Group (mathematics) quite a bit, but it doesn't feel like a big concerted effort, and how could it be after six months! I admit I don't find anything on the list above too appealing, but perhaps a general statistics improvement drive? Median, Confidence interval, ANOVA, and Probability might be a decent collaboration, and might not die out so quickly if the CotM becomes the Cot6M? Also a wide variety of editors can assist: I think median and probability are covered in grade school these days, and a wide variety of college students have had some exposure to confidence intervals, and probably most social scientists have experience with ANOVA. JackSchmidt (talk) 23:24, 9 March 2008 (UTC)
I looked at the Analysis of variance article, and believe it is surprisingly well-done for a short article. It is not very beginner-friendly at present, and (like most math articles) it is not strong on the history. It should not be a ton of work to get it up to GA or FA, or whatever members of this project believe it is sensible to try for these days. I might be able to help on referencing and history. EdJohnston (talk) 19:45, 12 March 2008 (UTC)
Well, to my mind an article on ANOVA without a single ANOVA table is missing a vital element, as I said (less forcefully) a couple of months ago on the talk page. That's one reason I assessed it as "Start" class when I gave it its first {{maths rating}} a couple of days later, but feel free to revise it (preferably giving your reasons in the comments subpage. I've put some in most of the dozen or so articles I've assessed, but I didn't bother on that one as I'd already put something on the talk page). I think I've been put off contributing to it by the potential vastness of the topic and not knowing where to start, but that's no excuse really as I should just be bold and start anywhere. Qwfp (talk) 20:30, 12 March 2008 (UTC)

## Another WikiProject

Someone has created this page: Wikipedia:WikiProject Golden ratio. Michael Hardy (talk) 16:17, 11 March 2008 (UTC)

That's shockingly narrow. CRGreathouse (t | c) 19:27, 11 March 2008 (UTC)
Seems to be the invention of User:20-dude, who is also a major contributor to List of works designed with golden ratio. Gandalf61 (talk) 19:47, 11 March 2008 (UTC)
I put a note on the talk, what I like about the project (narrow in many ways, but oddly broad in lay-approachable examples and applications; the Fibonacci Quarterly ought to be too narrrow a topic, but it sorta isn't) and why I'm inclusionist (we will increasing able to filter and sort and so can define our own deletionist thresholds). Pete St.John (talk) 03:37, 12 March 2008 (UTC)
It's not in article space, so most of the usual inclusionist/deletionist arguments don't really apply. I just can't imagine that it's likely to have much activity. I expect it will be one of Wikipedia's ghost towns almost from day one. Which, I guess, is OK. --Trovatore (talk) 20:07, 12 March 2008 (UTC)

## Game theory FAR

Game theory has been nominated for a featured article review. Articles are typically reviewed for two weeks. Please leave your comments and help us to return the article to featured quality. If concerns are not addressed during the review period, articles are moved onto the Featured Article Removal Candidates list for a further period, where editors may declare "Keep" or "Remove" the article from featured status. The instructions for the review process are here. Reviewers' concerns are here. — Preceding unsigned comment added by Peter Andersen (talkcontribs)

## Is this a silly edit

In this edit, someone deleted some material from an article, complaining of a lack of any reference. It seems to me that any mathematics article that contains elementary material includes derivations that are justified by the fact that the reader sees the steps in the argument, not by references. This section is easy to understand.

Are there other opinions about this here? Michael Hardy (talk) 18:49, 3 March 2008 (UTC)

I think it's a bit odd. WP:V does not demand that all explanatory material be supported by references. --Cheeser1 (talk) 18:53, 3 March 2008 (UTC)
There is a struggle (I think) between those of us concerned with content and pedagogy, first, vs editors concerned with policy in se. Cheeser's is a good distinction, that it's explanatory. Is there any policy reference that specifically permits explanation? What seems obvious, or even intrinsic, may be settled most conveniently with a policy ciation. Pete St.John (talk) 20:09, 3 March 2008 (UTC)
This doesn't address the larger issue, but I notice that this change was performed last October by a user who hasn't been back since, so there's not much chance of starting an edit war by reverting it, nor much point in responding with an airtight argument on the talk page. -- Dominus (talk) 20:16, 3 March 2008 (UTC)
But a couple of other people have deleted this same section over the past three years or so, each saying they found it somehow objectionable, but just what their objections were has never been clear to me. I think there may actually have been three others; I'm not sure. Is there some reason for objecting to it that can actually be explained by someone who knows what the reason is? Michael Hardy (talk) 21:11, 3 March 2008 (UTC)
I'm not one of the people deleting it, but to me the tone and approach is very colloquial, less formal than I expect the articles here to be. That may have something to do with it, I think. —David Eppstein (talk) 21:18, 3 March 2008 (UTC)
Problems with "tone" can be fixed by editing a few words, I would think. But I'm puzzled as to the specifics. Is it because the initial sentence is in the imperative mood that you find "tone" problems? As for "approach", is because it's essentially an intuitive argument rather than an attempt at mathematical rigor that you think the approach is too informal? The heading above the section tells the reader to expect something "intuitive". Can you be specific about your problems with the tone and approach? Michael Hardy (talk) 21:53, 3 March 2008 (UTC)

I personally don't like the deleted passage, but that has nothing to do with lack of references. I think the explanation kinda sucks, apologies to the author of that passage. I can just imagine some student sitting there staring at it and wondering "what does enter' and clear' have to do with anything?" It's like a joke with a twenty minute setup. Loisel (talk) 03:56, 4 March 2008 (UTC)

FWIW (I know, not much at all), I think the deleted explanation is quite awful, and the article is better without it. Surely there's a better way to intuitively explain the concept? Quale (talk) 04:01, 4 March 2008 (UTC)
I concur with the sentiment that the paragraph could either be rewritten to fit the article/encyclopedia better, and that it might not be as intuitive as whoever wrote it might think. But, like I said, "no references" is not reason to cut content like it was. I'd recommend explaining it more concisely, without so much "press this key, press that key" detail. --Cheeser1 (talk) —Preceding comment was added at 04:35, 4 March 2008 (UTC)
Any "justification", intuitive or not, should make it quite clear that the value of the empty product being equal to one is the result of a choice, the choice to define it thus, and that the rationale is one of expediency: because this is the more useful choice. Then only should we proceed to explain why and how this is more useful. A more appropriate title of the section might be "Rationale".
It might further help some of the mathematically untrained readers if we draw an analogy with the empty sum being 0, the neutral element of addition. For whatever reason, many people find the empty sum easier to grasp, and it is an obvious stepping stone to the empty product.
In terms of intuitive justifications, it is a fact that if you split a collection of numbers (a multiset, but for the purpose of exposition we might limit this to lists) into two parts, the product of the original collection is the same as the product of the products of the two parts. But what if one of the two parts is empty? Defining the empty product to be 1 allows means that in the statement of the fact no exception needs to be made for this case.
To top this off with an example that may appeal to people with some more mathematical background, consider the statement of the binomial theorem:
${\displaystyle (x+y)^{n}=\sum _{k=0}^{n}{n \choose k}x^{n-k}y^{k}\,.}$
Without the empty-product convention (since raising to the power 0 is an instance of an empty product) we would be forced to write:
${\displaystyle (x+y)^{n}=x^{n}+\sum _{k=1}^{n-1}{n \choose k}x^{n-k}y^{k}+y^{n}\,.}$
--Lambiam 12:27, 4 March 2008 (UTC)
I prefer the standard this-is-like-a-sum explanation. The sum of no things is zero, because zero is the additive identity. The product of no things is 1, because 1 is the multiplicative identity. Extended examples that require too much thinking make my brain hurt. --Cheeser1 (talk) 15:09, 4 March 2008 (UTC)
It is a choice, but it is a good choice, particularly in light of the categorical result regarding empty products and coproducts (which yield terminal and initial objects, should they exist in the category, in a natural way via limits and colimits). That is, the underlying categorical structural view provides strong justification. I must admit, however, that the article section on empty categorical products is rather light, particularly when it ultimately provides the best justification for the choice that I know of. -- Leland McInnes (talk) 15:30, 4 March 2008 (UTC)

I will dispute the assertion that it's a matter of choice or expediency or convention. It is not a convention; it is a fact. Michael Hardy (talk) 19:14, 4 March 2008 (UTC)

By fact, do you mean theorem? If so, what is the proof?  --Lambiam 20:47, 4 March 2008 (UTC)
Yes, of course I mean a theorem. If I write a proof on the fly, it will be needlessly long and complicated, but I will say this for now: I had occasion to mention this in a paper, which you can find here and was surprised by some reactions to it, so ultimately I wrote this footnote:
Perhaps as a result of studying set theory, I was surprised when I learned that some respectable combinatorialists consider such things as this to be mere convention. One of them even said a case could be made for setting the number of partitions to 0 when n = 0. By stark contrast, Gian-Carlo Rota wrote in \cite{Rota2}, p. 15, that "the kind of mathematical reasoning that physicists find unbearably pedantic" leads not only to the conclusion that the elementary symmetric function in no variables is 1, but straight from there to the theory of the Euler characteristic, so that "such reasoning does pay off." The only other really sexy example I know is from applied statistics: the non-central chi-square distribution with zero degrees of freedom, unlike its "central" counterpart, is non-trivial.
I was referring to the fact that the number of partitions of a set of size 0 is 1. The cited Rota paper was this:
\bibitem{Rota2} C-C.~Rota, Geometric Probability, {\em Mathematical Intelligencer}, {\bf 20 (4)}, 1998, pp.~11-16.
Michael Hardy (talk) 23:26, 5 March 2008 (UTC)
It is obvious from the definition of partition that ∅ is a partition, and in fact the only partition, of ∅. But how is that relevant to the meaning of the empty product? Is there a commonly accepted definition of product for which "empty product has value 1" is not part of the definition but instead a consequence?  --Lambiam 00:53, 6 March 2008 (UTC)
Categorical products (which specialize suitably to regular products of numbers when looked at the right way) are defined as limits of paritcular index categories. Taking the limit of the empty index category yields a terminal object (which gives 1 as a result under the aforementioned specialization), so that's a case of the result being a consequence of the definition. Of course whether you consider categorical definitions of products in terms of limits as "a commonly accepted definition of product" is another matter. -- Leland McInnes (talk) 19:21, 6 March 2008 (UTC)
I'd consider it a fact too (I can't imagine doing without "there is one way to choose zero things from a set of n things-- viz, the empty set") but I consider the Axiom of Infinity a fact, and the Axiom of Choice a choice (pun unfortunate), while others would disagree with me. I think for the purpose of most wiki articles we should present "the sum of zero things is zero" as mere fact, even if it doesn't hold in the Boolean Ring of Nonconscructible Categories :-) Pete St.John (talk) 19:32, 4 March 2008 (UTC)

I'm really puzzled as to why a 20-minute set-up would be needed rather than a 30-second set-up. I can't imagine a simpler intuitive explanation; this seems like a model of simplicity. No complications at all. So "Quale", can you explain your objections instead of merely telling us your bottom-line conclusion? Michael Hardy (talk) 19:19, 4 March 2008 (UTC)

I be not Quale. But I know this much: the explanation essentially says: "We multiply a by b, and then c, to get abc. Dividing abc by c, then b, then a, gives us 1. Hence, having reversed the operations to the point where no numbers have been multiplied, the empty product must be 1." Do you consider this a good explanation? --Sturm 21:13, 4 March 2008 (UTC)
I consider Sturm's explanation to be simple and to the point, in distinct contrast to the section in question. Problems with that section include: 1) it's too long, 2) introduces the extraneous "calculator", 3) appeal to intuition is difficult since the calculator doesn't resemble function of real world calculators very closely, 4) explanation of ENTER and CLEAR buttons are more extraneous details, 5) goes through a series of seemingly random steps ("CLEAR", 7 "ENTER", 3 "ENTER", 4 "ENTER") with randomly chosen small constants, piling on yet more extraneous details, 6) after all this the conclusion isn't obvious enough to be worth investing the time to figure it out. Sturm cuts the idea down to its essence, and this makes a world of difference. I don't think this is a question of a little wordsmithing. The original explanation was clunky and overly complex. Quale (talk) 00:11, 5 March 2008 (UTC)

Certainly the "CLEAR" button is found on all calculators. The "ENTER" button is found on many. These seem like easy points that anyone would grasp instantly. Michael Hardy (talk) 16:01, 5 March 2008 (UTC)

Really. How should anyone instantly grasp a CLEAR button that doesn't set the value to 0 and an ENTER button that performs a multiplication? I haven't seen any calculator that behaves that way. I think the removed text was simply bad, and I may not have been the only one since it was removed several times by different people (none of them me). Quale (talk) 17:42, 5 March 2008 (UTC)
I don't love the wording in the example, however: I just brought up the MS calc in XP, which I'm sure we could call conventional and familiar. The display defaults at zero. I entered 2, multiply, 3, multiply, 5; and the display went up 2, 6, 30. Then I reversed: divide, 5, divide, 3, divide, 2; and was left with one in the display (instead of zero). After I have undone 3 multiplications with 3 divisions, I'm left with '1', related to saying that the product of zero multiplications is the multiplicative identity. I think this example has pedagogical use, but I agree it was not well worded originally. Pete St.John (talk) 19:22, 5 March 2008 (UTC)
OK, "pedagogical use", but really that's the problem here. WP is not supposed to be a textbook; it's a reference work. Anything "pedagogical" in tone is ipso facto jarring in a WP article. When you're teaching a subject you have a whole different set of goals and methodologies than when you're providing a resource for people to look things up (and, perhaps, teach it to themselves). --Trovatore (talk) 20:22, 5 March 2008 (UTC)
I've gotten that objection before ("not a textbook"); but if there were no pedagogy, the wiki would be a database, and not have prose. It's probably a matter of degree and I lean too far that way. Pete St.John (talk) 20:29, 5 March 2008 (UTC)
Well, certainly it's a matter of degree; I'm not proposing that there's a precise distinction to be had here. It's a "know it when I see it" type of thing. A rule of thumb: Would the proposed text seem too pedagogical if it were in Britannica? Then it's probably also too pedagogical here. And the text in question -- no offense meant to Michael -- is clearly on that side of the line. --Trovatore (talk) 20:54, 5 March 2008 (UTC)
Honestly, I think wikipedia should be more pedagogical. I'll take the hit here, sometimes I read these math sections can not make head or tails of them. I come to wikipedia to learn computer science, but when I have to use it for Math I often left confused. People should not have to already know the subject to understand the wiki for it. For example, the intermediate steps are weak. Not all the varibles are explained, or linked. I just spent almost an hour searching for what x meant in T(x,n). Some of you may know what that formula means, but if you do, you don't have to look it up in the first place. If you write for an audience of math teachers, your resource will never be as helpful as it could be. Math teachers probably have their own math books, already. The general tone is overly complicated. I think you should shoot for world book ease. Even if it requires a couple of extra sentences, it is worth it, if someone can undertsand a concept like O^0. —Preceding unsigned comment added by 71.175.58.64 (talk) 20:09, 13 March 2008 (UTC)

## Cornu spiral images

Please can someone have a look at my comment on Talk:Fresnel integral#Cornu spiral images. Articles like this will slowly decay if they are not watched by people with mathematical knowledge. JonH (talk) 12:58, 10 March 2008 (UTC)

I've removed the image. Although the term "clothoid" appears to be in use to describe some roller coaster loop profiles, the image was definitely not a Cornu spiral, and it's presence in the article was thoroughly misleading. I've also removed some other unsourced material. -- The Anome (talk) 11:05, 13 March 2008 (UTC)
I've now found a good cite for the use of the term "clothoid loop" in roller coaster design: the name comes from the incorporation of segments of the Cornu spiral in the loop, and the loop in its entirety is clearly not a clothoid. I've added cites to back this up, and created a redirect to clothoid loop that leads to a sourced explanation. The parametric image stays out of both articles; at the moment, it looks like a red herring. -- The Anome (talk) 11:39, 13 March 2008 (UTC)

## Emmy Noether

I'm beginning an expansion/reconstruction of the Emmy Noether article, with a goal of making it an FA. Alas, I know next to nothing about math (beyond how to solve 2x+10=5). Once I'm done with the biographical data, I'll be enlisting some folks to help explain her theories – but in the meantime, I wonder if there is a book or two which might help me (a numerically illiterate English teacher) understand what she worked on. =) Thanks in advance. – Scartol • Tok 15:43, 12 March 2008 (UTC)

I wish I paid more attention, I saw a great "life of Noether" lecture some months ago, but it's all fallen out of my head by now. Maybe I'll look up the presenter and ask for a few references and I could point you there. But don't hold your breath, I'm going to be mostly off-wiki for a while starting later today. I'll comment back here if I come up with anything. --16:02, 12 March 2008 (UTC)
Try to get Symmetry and the Beautiful Universe by Lederman and Hill. (Currently sold out at Amazon, I'm afraid.) JocK (talk) 17:42, 12 March 2008 (UTC)
Looks like I'll be able to get a copy at a nearby library. Thanks! – Scartol • Tok 19:05, 12 March 2008 (UTC)

I've found two volumes dedicated to Noether that discuss both her biography and her scientific contributions:

• Emmy Noether. A tribute to her life and work. Edited by James W. Brewer and Martha K. Smith. Monographs and Textbooks in Pure and Applied Mathematics, 69. Marcel Dekker, Inc., New York, 1981. x+180 pp. ISBN 0-8247-1550-0
• Dick, Auguste, Emmy Noether, 1882–1935. Translated from the German by Heidi I. Blocher. With contributions by B. L. van der Waerden, Hermann Weyl and P. S. Alexandrov [P. S. Aleksandrov]. Birkhäuser, Boston, Mass., 1981. xiv+193 pp. ISBN 3-7643-3019-8

They also contain personal recollections of Noether by her colleagues and students and the famous obituary of Noether by van der Waerden. Arcfrk (talk) 19:20, 12 March 2008 (UTC)

I think those two are two of the ones referred to in the lecture I mentioned. Good finds. --Cheeser1 (talk) 19:29, 12 March 2008 (UTC)
Okay, I've got all of the books mentioned here. I'll return to this page once I've got something ready for all the math folks to look at and fix all the horrible problems with. =) Thanks, everyone! (The Symmetry book is nicely layperson-oriented. Cheers, J.) – Scartol • Tok 12:50, 13 March 2008 (UTC)

## Prisoner's dilemma

Is a featured article review, please comment and help bring up to current featured article standards! Judgesurreal777 (talk) 01:52, 13 March 2008 (UTC)

Direct link: Wikipedia:Featured article review/Prisoner's dilemma. Algebraist 14:53, 13 March 2008 (UTC)

## Wikipedia:Articles for deletion/Megalithic geometry (2nd nomination)

A deletion discussion of a (fringe) mathematical article. I put it in a category that I'm not sure mathbot will pick up on for its current activity lists, but project participants might find the discussion of interest. Wikipedia:Articles for deletion/Megalithic geometry (2nd nomination). —David Eppstein (talk) 18:02, 13 March 2008 (UTC)

## Logical connectives and hexadecimal numbers (Urgent)

Hi all, would someone please be so kind and a) check the contributions of User:Tilman Piesk regarding Logical connectives and hexadecimal numbers b) check uplodaded pictures by this user e.g. Image:Logictesseract.jpg, [36] and others. He just confirmed on de:WP that he actually invented these signs. I am not very familiar with the deletion policies within en:WP but I think this should be at least a massive breach of Wikipedia:No original research. Thanks and kind regards P.S: It might be worth for an sysop to check edits by this user on other wikipedia projects as well. --Meisterkoch (talk) 19:32, 13 March 2008 (UTC)

I've removed two images from Logical connective with "tesseract" Hasse diagrams, one with alchemy-like symbols and the other uninformative, and inserted in a bad spot. A cursory examination of Hexadecimal number shows an ill-explained but not terribly bad image with a bijection between the 16 "nibbles" and the 16 binary logical connectives. This user's edits may need some further investigation, but I don't see a great urgency.  --Lambiam 20:11, 13 March 2008 (UTC)
Great urgency is a little bit of an exageration ;-), but I was so surprised about the users boldness to spam this OR across different projects (not only in en:WP and de:WP, but also in es:WP and cs:WP. Thanks for the correction. KR --Meisterkoch (talk) 01:14, 14 March 2008 (UTC)

## Mathematics Portals

I think that it would be positive to have more portals related to mathematics, we have enough good content for that. In fine, one for each topic from Template:Mathematics-footer (just one for algebra). We have already portal:logic, portal:category theory and portal:geometry. I would like to launch a collaborative effort for that. Cenarium (talk) 17:42, 8 March 2008 (UTC)

I am not sure of the necessity of this category. Either way, it should be called Category:Mathematics portals rather than Category:Mathematical portal (so, plural and noun). Oleg Alexandrov (talk) 17:58, 8 March 2008 (UTC)
Whilst the mathematics portal get a good number of hits (4963/day [37]) as it linked from the main page, other portal do far worse, portal:Geometry only get about 44 hits/day[38]. --Salix alba (talk) 18:22, 8 March 2008 (UTC)
Based on that I tend to think that making more portals should be a fairly low priority. Who would maintain them? We haven't changed the Mathematics Collaboration of the Month for many months now and there quite a few mathematics pages that get over a thousand hits a day that are still (deservedly) rated Stub or Start class. I think these should be a higher priority. (But thanks for indirectly leading me to discover that there's a Category:Category-theoretic categories. ) Qwfp (talk) 18:55, 8 March 2008 (UTC)
I've renamed the category as suggested. Portal:mathematics is featured on the main page and portal:geometry is still in construction, the comparison is a bit rough. What about Portal:Somerset, [39] ? I think that all these subjects are vast enough, the usefulness of a portal as a navigational tool is clear here (the remark of Qwfp shows an example of that). Concerning the maintenance, I am ready to maintain portal:category theory, portal:set theory and portal:topology. I'll try to help portal:geometry too. I agree that it will take time and resources. I agree that it's a low priority but some wikipedians may be interested. Cenarium (talk) 19:14, 8 March 2008 (UTC)
I didn't mean a collaborative effort like a "collaboration of the month". Cenarium (talk) 19:20, 8 March 2008 (UTC)
That's fine, if you want to take it on I wish you good luck, just don't expect me to contribute. I recognise the content of Wikipedia is determined by enthusiasm rather than person-hours available or any particular notion of importance, whether based on page hits or otherwise. My particular enthusiasms are as quirky as anyone else's. Qwfp (talk) 19:38, 8 March 2008 (UTC)
Sadly, I'm not so knowledgeable in geometry. Maybe people interested in geometry could take a look at Portal:Geometry. Use of random portal components (see Wikipedia:Portal guidelines) makes it easier to maintain a portal, you don't have to change the selected article/image/etc regularly. Cenarium (talk) 21:59, 8 March 2008 (UTC)

I'm just curious, would a centralized portal be better than several branches? I don't know if we're making it harder by dividing up things so finely. --Cheeser1 (talk) 22:10, 8 March 2008 (UTC)

We have already portal:Mathematics, but individual portals would be useful to navigate in a mathematical topics, for example Portal:Biology has a dozen of subportals. I wonder if anyone could find an icon for portal:category theory, like the logo of portal:mathematics. Thanks, Cenarium (talk) 22:31, 8 March 2008 (UTC)
Thanks, that clears it up - I'm not familiar with portals. --Cheeser1 (talk) 23:45, 9 March 2008 (UTC)
I also think that improving the articles is more important, many of the topics linked in the footer are B-class or even lower, for example applied mathematics. Jakob.scholbach (talk) 13:24, 10 March 2008 (UTC)
Personally, in the process of building portal:category theory, I edited some category theory articles and I think that it will be easier for me to improve them with this portal up. Cenarium (talk) 12:06, 14 March 2008 (UTC)

## Request for outside editorial review on the Gauss-Newton algorithm article

I and another editor have been involved in an editing dispute at Gauss-Newton algorithm for around a month now, with no solution in sight. I would really appreciate it to get other editors opinion about how it is best to present the material.

As it currently stands, the article does not present the algorithm in one piece. Instead, parts of it are mixed together within a derivation of the algorithm for data fitting theory, even if

• Data fitting theory is not necessary to understand the algorithm, and is a rather specialized topic
• The derivation of the algorithm is not necessary to state the algorithm

My proposal is to

• First state the algorithm, as it can be used for any application, not just for data fitting
• Afterward, state its derivation, and its applications

Some more background can also be found at Talk:Gauss-Newton algorithm, although I would appreciate a discussion here, where more people could get involved. Thanks. Oleg Alexandrov (talk) 02:48, 13 March 2008 (UTC)

I think that data fitting is very important, but that its derivation is too specialized to include. I would remove it, or perhaps move it to a quasi-subpage Gauss-Newton algorithm/Proofs. CRGreathouse (t | c) 03:44, 13 March 2008 (UTC)

The nub of this problem is that there are two quite different areas of application of the Gauss-Newton method (GN).

1. Traditionally, that is, from about 1800 onward, it has been used extensively in science for data fitting. Most scientists would expect to see data fitting in an article on on GN. Also, there are links from, amongst others, Linear regression, Least squares, Linear least squares, Regression analysis, Levenberg-Marquardt algorithm, Total least squares and Nonlinear regression, which all deal with data fitting. That is why the data fitting part belongs in the article. For historical reasons least squares and regression analysis are presented in WP in separate articles, though they cover much the same ground. It makes sense that both strands should link to the same article on GN, where additional detail may be found.
2. With the advent of electronic computers it became possible to use GN for optimization problems. The derivation of the algorithm is different in the two applications and, in consequence, the properties are different. The only relevant links that I could find are Backpropagation and BHHH algorithm.

In the final revision of the article I present both areas of application with roughly equal importance, pointing out both the similarities and the differences between them. This compromise was an attempt to satisfy User: Oleg Alexandrov in the light of the extensive discussion on Talk:Gauss-Newton algorithm. However, Oleg is not satisfied and wants the article to treat GN as a single algorithm. I believe that this is wrong because, although the defining equations are the same, they are obtained by making different assumptions and for that reason the implementations of the algorithm are different. After repeated attempts had been made to revise the article in terms of a single algorithm, it finally became clear to me that it was an impossible task; the two applications have to be treated separately in spite of their similarities. Petergans (talk) 09:08, 13 March 2008 (UTC)

This does seem to suggest that it may be easier to treat the topic in two separate articles. Say Gauss-Newton method (data-fitting) and Gauss-Newton method (optimization). --Salix alba (talk) 12:18, 13 March 2008 (UTC)
The algorithm is the same. It may converge a bit faster for data fitting as there it is used in a particular case. We don't fork an algorithm article just because it has more than one use. Oleg Alexandrov (talk) 15:48, 13 March 2008 (UTC)

The differences between the two fields do not appear to be great.

• The present version asserts a difference in sign convention. I suspect that this is in fact a difference within both fields of application, even if there is a tendency to use one sign in one field and the other in the other.
• Curve fitting guarantees the method will converge, because the curves chosen to model with will have derivatives that don't explode. (This is likely to be optimism; surely someone has attempted to fit nasty curves?) Optimization doesn't give any such guarantee.

The first should really be dealt with by giving the method, with a note that the sign convention varies' the second can be combined into a single section on Convergence. Neither justifies a double presentation.

• As for the history of the method (going back to Ceres, I presume?) that should really be another separate section, with its own sources; textbook accounts of the history of mathematics are notoriously unreliable. Septentrionalis PMAnderson 15:36, 13 March 2008 (UTC)
The sign convention is because Peter instead of using general functions ${\displaystyle r_{i}(\beta )}$ uses a particular case ${\displaystyle r_{i}(\beta )=y_{i}-f(x_{i},\beta ),}$ (where ${\displaystyle f}$ is the curve to fit) and then of course when you take the derivative in ${\displaystyle \beta }$ a minus pops up. This is all. Oleg Alexandrov (talk) 15:46, 13 March 2008 (UTC)
Quite so; but if that case were traditional in curve-fitting, we should explain that twist in the article, as part of the single explanation of the method. Septentrionalis PMAnderson 04:00, 14 March 2008 (UTC)
That assuming that one pauses to actually explain the method, instead of pushing the technical derivations before making clear the algorithm. Besides, the residues could as well be of the form, ${\displaystyle r_{i}(\beta )=f(x_{i},\beta )-y_{i},}$ as flipping the signs has no effect after squaring the thing. Then the sign problem goes away. Oleg Alexandrov (talk) 07:56, 14 March 2008 (UTC)
While they could be that way, that would be unconventional.  --Lambiam 08:09, 14 March 2008 (UTC)
That is probably correct. Back to the original point, data fitting is just one of the many applications of Gauss-Newton. Insisting too much on derivations for both data fitting and for a generic situation of a sum of squares, against first stating the algorithm, is, I think counter productive. See Talk:Gauss-Newton algorithm#Note for the most recent argument about this, you are welcome to weigh in. Oleg Alexandrov (talk) 13:00, 14 March 2008 (UTC)

## Probability and Statistics sub-project?

Inspired (provoked?) by the above, as well as mention in recent discussions that statistics articles are frequently viewed but need improvement, I wonder if there would be an interest in creating a "probability and statistics" sub-project of Wikiproject Mathematics? There's a first draft of a subproject page in my sandbox. If interested, please add your name and any comments at WP:WikiProject Council/Proposals#Probability and statistics.

A sub-project (aka task force or work group) seems more suitable than a separate Wikiproject for the reasons discussed at WP:task force, not least that WikiProject Mathematics has already has good procedural and technical infrastructure including an excellent assessment procedure.

I know there's already a WikiProject Probability but that's been virtually inactive for the last 18 months. I guess I am suggesting that it should be "frozen" and interest redirected to this sub-project. Regards, Qwfp (talk) 10:57, 12 March 2008 (UTC).

Maybe just WikiProject Statistics. There actually is a reason why this is considered a separate subject. Michael Hardy (talk) 19:01, 12 March 2008 (UTC)
I've just written some thoughts relating to this in the comments section of the proposal. I suggest any further conversation continues there in order to keep it in one place. Qwfp (talk) 13:05, 13 March 2008 (UTC)

### Or WikiProject Statistics?

After sleeping on Michael's and others' comments and starting to see their point, I'd like to invite further discussion on whether statistics / probability and statistics should be a sub-project/task force/work group of WP:WPM or whether it would be better to set up a separate (but related) full WikiProject. Again please comment over at WP:WikiProject Council/Proposals#Probability and statistics rather than here so the conversation is in one place. I just thought I'd notify you of its expanded scope. I seem to be largely debating with myself over there just at present and I'd appreciate some informed opinion. I'll post again here when we close the debate to let you know the outcome and to close this thread. Qwfp (talk) 09:16, 14 March 2008 (UTC)

The consensus of the discussion (archived here) clearly favoured creation of WikiProject Statistics, which has now taken place. Further discussion is very welcome on the WikiProject Statistics talk page and new members are of course also very welcome (most of whom I imagine will wish to also remain members of WikiProject Mathematics). I expect WikiProject Statistics will coordinate with WikiProject Mathematics on many articles and activities of mutual interest. Qwfp (talk) 22:30, 16 March 2008 (UTC)

## Dense math pages

Why are so many math pages so dense? They often show mathematical proofs with the sparsest of explanation. Seems contradictory to the spirit of wikipedia... Alex Andrei —Preceding unsigned comment added by 68.118.181.220 (talk) 01:36, 14 March 2008 (UTC)

That is a rather general complaint and therefore hard to answer. Many advanced mathematical subjects require a considerable background in mathematics to even vaguely understand what it is about. An example is Étale cohomology. A crash course to bring someone with a fair knowledge of high-school maths as starting point up to speed, so that the article becomes accessible to them, would take many months. For more elementary topics, the fact is that among the people who understand these topics well, only a limited number is available as volunteers for working on these articles, and these volunteers have only a limited amount of time for that next, to their study or jobs. Finally, not everyone has equal prowess in writing clearly.
Wikipedia is not a textbook, and articles are not required to present proofs at all, or to present them in a didactic fashion. If a proof is given, however, a reader who understands the subject matter should be able to see that it is indeed a proof.  --Lambiam 08:06, 14 March 2008 (UTC)

Still, Alex does have a point -- there are plenty of math pages that are not easily accessible even by those who have the background to understand the material, because the articles are just poorly written and/or omit needed context. Such articles are still usually (though not always) better than nothing -- they'll be useful to some people, and those people can then go clean them up. That strikes me as very much in the Wiki spirit. --Trovatore (talk) 08:32, 14 March 2008 (UTC)

That is what I meant, but perhaps expressed too euphemistically, by "not everyone has equal prowess in writing clearly".  --Lambiam 02:25, 17 March 2008 (UTC)

## WikiProject Statistics

Wikipedia:WikiProject Statistics now exists. On that page you can add your name to a list of participants. Michael Hardy (talk) 17:06, 18 March 2008 (UTC)

## Dunford-Pettis property

I've just declined this for speedy deletion after a quick Google check. I'd appreciate help on fixing this article up, since my math is rudimentary. If it does deserve to be deleted, please let me know. Thanks, bibliomaniac15 Midway upon life's journey... 04:14, 19 March 2008 (UTC)

It certainly doesn't qualify for speedy deletion: there's enough context (if one knows to read it) that A1 doesn't apply, and it's about the wrong kind of thing for A7 to be relevant. But the many scholarly articles with that phrase in their titles convince me that it doesn't deserve deletion of any kind. Just a valid math stub, like many others. —David Eppstein (talk) 04:34, 19 March 2008 (UTC)
I have tried to bring the article more up to stub-standards. It is now wikified, categorized, has a few references, states the definition correctly (and gives more than one equivalent definition), and gives probably the most important property of these spaces (that they are "never" reflexive). silly rabbit (talk) 04:47, 19 March 2008 (UTC)
I've brought it up further. There is no doubt that this is an important, if fairly special, topic in functional analysis (as evidenced by the fact that at least two of the most influential persons in the linear functional analysis and two Fields medal winners have contributed to the theory). Arcfrk (talk) 06:24, 19 March 2008 (UTC)

## Frobenius solution to the hypergeometric equation

I've marked Frobenius solution to the hypergeometric equation for cleanup. Please help. Michael Hardy (talk) 17:04, 20 March 2008 (UTC)

I've de-TeXed (how often is that something we want?) the first section up to the beginning of the first subsection. This is very tedious, so if anyone else wants to submit to this treatment, it would be appreciated. I'm not even going to try to clean up the presentation until this is done. Ryan Reich (talk) 19:19, 20 March 2008 (UTC)
Wikipedia:Tools#Importing (converting) content from other formats to Wikipedia (MediaWiki) format has a link to User:Jmath666/latex2wiki. I haven't tried it and don't know anything about it. PrimeHunter (talk) 19:37, 20 March 2008 (UTC)
I think that converter expects ordinary latex like you would write for an article. This latex is different: all the text is inside \text{} blocks inside math mode. Hats off to Ryan for working on converting it. — Carl (CBM · talk) 20:16, 20 March 2008 (UTC)

I'm no expert in differential equations - does this warrant its own article, rather than just a note in the article on hypergeometric equation? It appears to be a somewhat lengthy textbook derivation. — Carl (CBM · talk) 20:56, 20 March 2008 (UTC)

## Myrzakulov equations up for deletion

FYI, Myrzakulov equations (2nd nomination) to delete this article. Benjiboi 22:19, 20 March 2008 (UTC)

Does anyone know who Link Starbureiy is? An article about him was created and deleted with no "prod" template and no AfD discussion. What's the story? Michael Hardy (talk) 22:59, 20 March 2008 (UTC)

Some of the deleted content looks false. For example, the link to the math genealogy project isn't for him, and he isn't in the genealogy DB. Also, it claims he has Erdos number 2, but I don't find him in mathscinet or the list of people with Erdos number 2. On the other hand, he does get google hits. — Carl (CBM · talk) 23:28, 20 March 2008 (UTC)

## WP:OR discussion at Talk: Golden ratio

Y'all talk amongst yourselves ;-) Ling.Nut (talk) 02:50, 21 March 2008 (UTC)

What exactly are you referring to? --Cheeser1 (talk) 07:25, 22 March 2008 (UTC)
I think this is referring to the discussion at Talk:Golden_ratio#Suggested_Addition_to_Mathematics about whether the sources for this proposed addition are sufficient. Gandalf61 (talk) 09:59, 22 March 2008 (UTC)

## Rationalisation (mathematics)

Rationalisation (mathematics) appears to have originated just yesterday as a translation of an article on Spanish Wikipedia. I did a bit of cleanup on it, then I thought it should probably get merged into an existing article. But I'm not sure such an article exists.

Whatever is done, the article in its present form clearly needs more work. Michael Hardy (talk) 15:38, 22 March 2008 (UTC)

For some reason this is a big deal in the seconday-school curriculum of some spanish speaking countries (from experience) see for instance Baldor.--CSTAR (talk) 16:30, 22 March 2008 (UTC)
Now that I think of it this article [40] from the Spanish Wikipedia should also be in the English wikipedia. Baldor's algebra book, for better or worse, is probably the single most influential mathematics book in Spanish-speaking latin america. This article [41] also contains some useful information although a more reliable source would clearly be desirable. --CSTAR (talk) 16:47, 22 March 2008 (UTC)

Well, it seems to be a moderately big deal in secondary-school mathematics in the USA too. But I don't see that we have any article about it except this one, and I find that a bit surprising. Michael Hardy (talk) 16:59, 22 March 2008 (UTC)

Agreed. As someone who works with college students as they come in out of high school, many of them are very familiar with rationalization -- sometimes to the point where sin(π/4) = 1/√2 makes their heads explode. --Cheeser1 (talk) 17:11, 22 March 2008 (UTC)
Isn't the use of the term monomial strange? By the way, I think we should avoid making this essentially a how-to, which the Spanish version seems to be.  --Lambiam 22:48, 22 March 2008 (UTC)
Which makes me wonder if this isn't just a dictionary definition: rationalis(z)e - to make the denominator rational. --Cheeser1 (talk) 22:56, 22 March 2008 (UTC)

Definitely we need an article on rationalizing denominators and rationalizing numerators, and it won't be just a dictionary defintion. Michael Hardy (talk) 23:28, 22 March 2008 (UTC)

## Move Proof that 22/7 exceeds π to Wikibooks?

It has been proposed to move Proof that 22/7 exceeds π to Wikibooks. Discuss at Talk:Proof that 22/7 exceeds π#Move/Copy to Wikibooks.  --Lambiam 02:22, 17 March 2008 (UTC)

I find it very annoying that the person proposing this ridiculous move has not even attempted to give any reasons for the proposal. It's hard to be patient with such things or treat them respectfully. If reasons were given one could decide whether one agrees with them and why. Michael Hardy (talk) 04:29, 17 March 2008 (UTC)
Clear consensus against the move has quickly developed. I've now closed the discussion. --Salix alba (talk) 08:27, 17 March 2008 (UTC)
Yeah, it is indeed very hard to be patient with such things, especially if an article in question is your baby, so to speak. It is nice to see that all parties did manage to keep patient and respectful, and that the issue was resolved. Oleg Alexandrov (talk) 16:36, 23 March 2008 (UTC)

## Wiener sausage

A heads up that the article Wiener sausage has been put up for AfD. Regards. --Malcolmxl5 (talk) 00:02, 23 March 2008 (UTC)

Here are some things I've found on this:

• Jean-François Le Gall, "Fluctuation Results for the Wiener Sausage", Annals of Probability, 1988, volume 16, number 3, pages 991–1018
• M. van den Berg, E. Bolthausen, F. den Hollander, "Moderate deviations for the volume of the Wiener sausage", Annals of Mathematics, 2001, volume 153, pages 355–406
• E. Bolthausen, "On the Volume of the Wiener Sausage", Annals of Probability, 1990, volume 18, number 4, pages 1576–1582
• Uwe Schmock , "Convergence of the normalized one-dimensional wiener sausage path measures to a mixture of brownian taboo processes", Stochastics An International Journal of Probability and Stochastic Processes, Volume 29, Issue 2 February 1990 , pages 171–183
• T. Eisele and R. Lang, "Asymptotics for the wiener sausage with drift", Probability Theory and Related Fields, Volume 74, Number 1 / March, 1987, pages 125–140
• Yuji Hamana, Harry Kesten, " A large-deviation result for the range of random walk and for the Wiener sausage", Probability Theory and Related Fields, Volume 120, Number 2 / June, 2001, Pages 183–208
• A. S. Sznitman, "Some bounds and limiting results for the measure of Wiener sausage of small radius associated with elliptic diffusions", Stochastic processes and their applications, 1987, volume 25, number 1, pages 1–25
• Isaac Chavel, Edgar A. Feldman, "The Lenz shift and wiener sausage in riemannian manifolds", Compositio Mathematica, volume 60, number 1, (1986), pages 65–84
• M. D. Donsker and S. R. S. Varadhan, "Asymptotics for the Wiener sausage", Communications in Pure and Applied Mathematics, volume 28 (1975), pages 525–565

...and a large number of others found by Google Scholar. Michael Hardy (talk) 01:44, 23 March 2008 (UTC)

I'm thinking that at this point a close per WP:SNOW might be in order - does anyone think I should go ahead and do it as a nonadmin? (I know, generally if one !votes, one does not close, but in this case it seems irrelevant, no?) --Cheeser1 (talk) 04:12, 23 March 2008 (UTC)

Since you !voted, it's probably safest to wait for someone else to close it. It's not as if there's much danger of getting the wrong result. —David Eppstein (talk) 04:51, 23 March 2008 (UTC)
True, I'll hold off I suppose, but WP:SNOW (an extension of IAR) is intended to resolve bureaucratic processes like these, when they become meaningless or without merit, as soon as possible - I don't know that my !voting should matter (it is an extension of IAR, like I said). The point is to end a meaningless process as soon as possible. But I suppose caution couldn't hurt. --Cheeser1 (talk) 04:58, 23 March 2008 (UTC)
Now closed, WP:SNOW is becoming one of my favourite tools. In theory per WP:IAR a non-admin who has voted could close it as keep. The risk is that someone could contest your decision on procedural grounds leading to some further arguments. I've done a few which don't quite follow strict procedure and not had any comeback.
While the sources above are a good proof of its notability I'm not convinced they all need to be in the article, WP:NOT Google Scholar. --Salix alba (talk) 12:14, 23 March 2008 (UTC)
I was thinking the same thing about IAR, but I've been trying (quite unsuccessfully) to avoid problems on WP recently, and in anticipation of the worst, decided to leave it. And I agree - the references are great to demonstrate notability, but they aren't all necessary. Clearly, some were needed, and dropping them all in there seemed like a great way to throw the article a life preserver, but it's a bit overkill. --Cheeser1 (talk) 12:20, 23 March 2008 (UTC)

This list of references was chosen specifically for use in the AfD discussion. From Google Scholar I picked out cases with the term "Wiener sausage" in the title. How best to pick references to put in the article may be a different sort of question. Michael Hardy (talk) 13:19, 23 March 2008 (UTC)

Thanks to R.e.b. for fixing it up, including replacing the references with a more useful set. —David Eppstein (talk) 15:57, 23 March 2008 (UTC)

Also consider the following references:

• M. van den Berg, "On the expected volume of intersection of independent Wiener sausages and the asymptotic behaviour of some related integrals", Journal of Functional Analysis, Volume 222, Issue 1, 1 May 2005, Pages 114-128
• I. McGillivray, "Large Time Volume of the Pinned Wiener Sausage", Journal of Functional Analysis, Volume 170, Issue 1, 10 January 2000, Pages 107-140
• Alain-Sol Sznitman, "Lifschitz tail and Wiener sausage, I" Journal of Functional Analysis, Volume 94, Issue 2, December 1990, Pages 223-246
• Alain-Sol Sznitman, "Lifschitz tail and Wiener sausage, II" Journal of Functional Analysis, Volume 94, Issue 2, December 1990, Pages 247-272
• Jean-François Le Gall, "Wiener sausage and self-intersection local times", Journal of Functional Analysis, Volume 88, Issue 2, February 1990, Pages 299-341

but also:

• Günter Last, "On mean curvature functions of Brownian paths", Stochastic Processes and their Applications, Volume 116, Issue 12, December 2006, Pages 1876-1891
• Robin Pemantle, "The probability that Brownian motion almost contains a line", Annales de l'Institut Henri Poincare (B) Probability and Statistics, Volume 33, Issue 2, 1997, Pages 147-165
• Yu. A. Makhnovskii, M. E. Maslova and A. M. Berezhkovskii, "On the span of Brownian motion in a field in one dimension", Physica A: Statistical and Theoretical Physics, Volume 225, Issue 2, 15 March 1996, Pages 221-234
• A. M. Berezhkovskii and George H. Weiss, "Some generalizations of the trapping problem", Physica A: Statistical and Theoretical Physics, Volume 215, Issues 1-2, 15 April 1995, Pages 40-50
• Kalvis M. Jansons and Christopher G. Phillips, "On the application of geometric probability theory to polymer networks and suspensions, I", Journal of Colloid and Interface Science, Volume 137, Issue 1, June 1990, Pages 75-91

83.112.141.114 (talk) 16:54, 23 March 2008 (UTC)

## Entropy (disambiguation)

I could use some more eyeballs on this page.

In my view, to help people get to the article they want most quickly, it is helpful to include structure in the page to group together meanings primarily related to Entropy in a thermodynamic sense, and those primarily related to Entropy in an Information Theory sense. However, because there is no provision for this is the WP:DAB guidelines, various editors specialising in disambiguation (who may know rather more about disambiguation than they do about entropy), would prefer to see all the links muddled together in a single (IMO much harder to navigate) long alphabetical list. Cf this diff: [42].

Since dab pages are supposed to help readers who do know something about the subject find the article they want, I'd greatly appreciate if members of this project could look at the two versions above, and then leave their thoughts on the talk page.

Thanks, Jheald (talk) 23:23, 23 March 2008 (UTC)

I noticed that the edit mentioned above also substituted a totally different characterization of Topological entropy, one that seems completely off the mark.  --Lambiam 00:57, 24 March 2008 (UTC)

There is certainly a problem with having an article "Entropy" that develops the notion of thermodynamical entropy without giving even a hint of important alternative uses (there is a half-hearted attempt to mention them in the last third of the text, which is too late for all practical purposes and just turns the article into a sort of a bloated disambiguation page). Specifically concerning the revert war going on: whatever the rules say, it's unacceptable to substitute wrong definitions for the correct ones. There are quite a few disambiguation pages with the meanings structured according to the disciplines that they belong to. I also see nothing at the dab manual of style preventing this format, which is obviously superior to alphabetical lists where, for example, anasthesiological entropy comes ahead of the primary uses in information theory and ergodic theory. I have made my attempt at clearing the mess, but don't hold your breath. Arcfrk (talk) 03:00, 24 March 2008 (UTC)

Update: as anticipated, logheads persisted, and the page is now protected, in their preferred, and factually wrong, version. None of them bothered to articulate his/her position at the talk page yet, although the latest edit summary referred to dab page "Zero" as a "swell example" to aspire to, and that page is very close in format to the Jheald's proposal. Arcfrk (talk) 04:01, 24 March 2008 (UTC)
The page is only protected for two days. I did get a response from two other editors on the talk page, where they explain what their concerns are. They have several concerns (well founded in my opinion) that are unrelated to the section headings. Let's continue this at Talk:Entropy (disambiguation). — Carl (CBM · talk) 12:22, 24 March 2008 (UTC)

## Bibliographic references templates

I have accidentally discovered the templates {{Zbl}} and {{JFM} , which automatically link to Zentralblatt and JFM databases much in the same way as {{MathSciNet}} links to MathSciNet (Math Reviews online) and {{Springer}} links to the Springer EOM. These templates make entering bibliographical links a lot easier and should be better known. Shouldn't they be described at the Math Editor's resources page? There is apparently also a template {{Scholarpedia}}, but it is presently very basic, without a field for the full bibliographical record or even the author's (as opposed to curator's) name. Arcfrk (talk) 03:25, 24 March 2008 (UTC)

On a similar note, last week I suddenly needed the mathematical citation finder at [43] and was dismayed when I couldn't find it on the project page. I had to grovel through the talk archives until I found it. I don't remember now who made this resource, but they put a lot of work into it, and it would be a shame if that work were wasted. -- Dominus (talk) 04:23, 24 March 2008 (UTC)
Wikipedia:WikiProject Mathematics/Reference resources has a list of different citation templates. I've also created Category:Mathematics referencing resources with all the mathematics citation templates that I know of. Hopefully this should make things easier to find. --Salix alba (talk) 09:11, 24 March 2008 (UTC)
Good work. I can never find these templates when I need them. Now they are all in one place. Gandalf61 (talk) 12:36, 24 March 2008 (UTC)

## Fermat's Last Theorem in fiction on AfD

Fermat's Last Theorem in fiction has been nominated for deletion: Wikipedia:Articles for deletion/Fermat's Last Theorem in fiction.  --Lambiam 00:27, 25 March 2008 (UTC)

## RfC at Talk:Connection (mathematics)

I am currently engaging in a debate with a User:RQG who seems to feel that the lead paragraph of Talk:Connection (mathematics) should be rewritten to include references to Teleparallelism. He has started an RfC on it, but so far the wider community has not yet gotten involved. It is becoming quite tiresome. silly rabbit (talk) 22:17, 25 March 2008 (UTC)

## Locating engine

User:Niemeyerstein en is working on a new article called Locating engine. He's a relatively new editor, and the technical applications are relatively new, but this article is mainly on the math and statistics involved, which is not new. If anyone here is interested in contributing or helping locate sources, that would be great. The technology involves, quoting:

• Measurement computation to cope with the stochastic errors of metered distance values, thus reducing noise.
• Modeling the mesh of nodes and distances as a stable network of controlled topology and as a virtual surface.
• Conformal modeling matching the real operational surfaces, to serve location data for physically purposeful positions e.g. outside obstacles and driving or settled on a plane.
• Providing stable tracks according to inherited motion capabilities, i.e. not jumping aside nor forth and aback and keeping steady speed and acceleration.

- Dan Dank55 (talk) 03:56, 26 March 2008 (UTC)

## groups, group theory, and elementary group theory

These three articles have a considerable overlap. Is there any general consensus about what should be included in the articles?

For example, is it OK to trim the definition section and any other content of group theory which is already present in the group article? Jakob.scholbach (talk) 19:30, 23 March 2008 (UTC)

The definition is presented twice in the group theory article, once in the poorly named "For non-mathematicians" section and again in the next section. I would move the {{main}} link up and remove the "definition" section. That would leave one definition in the group theory article, which I think is a good thing, but remove the second copy of it. — Carl (CBM · talk) 19:46, 23 March 2008 (UTC)
I think that it makes sense to have both "Group (mathematics)" and "Group theory", although, perhaps, the latter article should be rewritten from the "big picture" perspective and not repeat the basics. On the other hand, I am not entirely sure what the purpose of "Elementary group theory" might be. Looks like a good candidate for wikibooks. Does the term have a technical meaning in logic? There is a statement "Group theory" concerning undecidability that links to EGT, but it's not explained there. Arcfrk (talk) 22:09, 23 March 2008 (UTC)
It doesn't have any special meaning in logic. My impression is that it was being used to mean "group theory likely to be covered in an introductory course". — Carl (CBM · talk) 22:43, 23 March 2008 (UTC)
The article Group (mathematics) defines it thus: "Elementary group theory is concerned with basic facts that hold for all individual groups."  --Lambiam 00:50, 24 March 2008 (UTC)
I was asking about this statement, that links to EGT, but is not explained there. It seems to employ the term "Elementary group theory" in a different, precise and technical, sense. Arcfrk (talk) 05:01, 24 March 2008 (UTC)
From this review, it seems the elementary theory of groups is what I would call the first-order theory of groups. Algebraist 09:32, 24 March 2008 (UTC)
Given that groups are the central kind of structure considered in group theory, and that the definition is rather simple, it is appropriate that the Group theory article contain a definition of group. Compare Category (mathematics) and Category theory. I think the notion of group homomorphism might be treated more prominently in Group theory than it is now, even though that will increase the overlap with Category Group (mathematics). I don't see an encyclopedic need for articles in the style of Elementary group theory.  --Lambiam 00:17, 24 March 2008 (UTC)
I agree. Perhaps Elementary group theory can be merged into Group (mathematics), probably with no change to the latter article. --Hans Adler (talk) 14:33, 25 March 2008 (UTC)

The wikipedia convention has been that articles with the word "elementary" in the title are directed at secondary-school or high-school readers. Unfortunately, this does not describe the elementary group theory article. If/when a merge is performed, I would really really like to call on someone to present groups at the secondary/high-school level, at least abelian groups if nothing else. Heck, you could teach abelian groups of order 3,4,5 in primary school, and I view it as a major loss that this is not done so. It would be a natural fit during discussions of fractions and prime numbers. linas (talk) 03:00, 27 March 2008 (UTC)

## EqWorld

I just started a stub on this mathematical equation site, and someone added a speedy deleteion tag to it. Comments to its talk page. R.e.b. (talk) 01:29, 28 March 2008 (UTC)

## FAR on Monty Hall problem

Monty Hall problem has been nominated for a featured article review. Articles are typically reviewed for two weeks. Please leave your comments and help us to return the article to featured quality. If concerns are not addressed during the review period, articles are moved onto the Featured Article Removal Candidates list for a further period, where editors may declare "Keep" or "Remove" the article from featured status. The instructions for the review process are here. Reviewers' concerns are here. - Chardish (talk) 06:13, 28 March 2008 (UTC)

## groups for good article?

I'd like to propose this article as a good article. Before formally doing so, I would like to ask for some help concerning grammar and prose etc. (I'm not a native speaker, so my linguistic abilities are modest). Obviously, any other improvements are also welcome. (This article is the current collaboration of the month, but the collaboration currently involves only two editors - somehow this collaboration needs a renaissance). Thank you, Jakob.scholbach (talk) 22:25, 24 March 2008 (UTC)

I have done the nomination of groups for a good article. Jakob.scholbach (talk) 11:14, 28 March 2008 (UTC)

## Proofs in Wikipedia

We have a page Wikipedia:WikiProject Mathematics/Proofs, which states:

In the course of several years valuable ideas and insights have been presented there, but no conclusions have been extracted from the discussions. I suggest that we use that page to try to work on some tentative guidelines concerning:

• when to include proofs in (or as) Wikipedia articles, and when not;
• how to present such proofs as are included;
• verifiability criteria for proofs.

It should be clear that it is undesirable to include proofs for every single mathematical proposition stated in some article. In general there should be something special about it, such as that the proof itself (rather than just the theorem) is notable (as for the proof by infinite descent that the square root of 2 is irrational), or gives additional value that is not evident from the bare statement of the theorem (as may be the case for constructive proofs). In some cases (0.999... = 1, Monty Hall) the argument for giving proofs may be that many people find the well-known result hard to believe. Particular elegance may also be a factor, as for the proof that 22/7 exceeds π.

If a proof is given, it should either be included in a section of the article that discusses the theorem being proved, or get an article of its own, with a title like "Proof of the abc conjecture", or "Proof that γ is irrational". There are no subpages in article space: "7 exceeds π" is not a subpage of "Proof that 22".

There is no talk page Wikipedia talk:WikiProject Mathematics/Proofs. What we could do is move Wikipedia:WikiProject Mathematics/Proofs to its own talk page, and use the then free main page for working on a text giving guidance on when and how to include proofs. Does this idea appeal to a sufficient number of people that we may hope to actually get somewhere?  --Lambiam 16:37, 29 March 2008 (UTC)

Support move of project page to talk page, and developing a guideline. --Salix alba (talk) 18:00, 29 March 2008 (UTC)
Sounds like a great idea. I'm in favor. Feel free to sketch up some guidelines akin to what you've stated above. -- Fropuff (talk) 05:50, 30 March 2008 (UTC)
Page now moved to Wikipedia talk:WikiProject Mathematics/Proofs. --Salix alba (talk) 20:58, 30 March 2008 (UTC)

## A task for LaTeXperts

Energy minimization is a new article in which the "displayed" math does not conform to Wikipedia conventions in some respects. But it's all non-editable images. We can't have that; we need to change to TeX. One thing I'd change is where it says

${\displaystyle {\text{something}}={\text{something}}\quad \forall \,i=1,\dots ,N.\,}$

Clearly it should say either

${\displaystyle {\text{something}}={\text{something}}\quad \forall \,i\in \{1,\dots ,N\}.\,}$

or

${\displaystyle {\text{something}}={\text{something}}\quad {\text{for }}i=1,\dots ,N.\,}$

Michael Hardy (talk) 18:49, 29 March 2008 (UTC)

In my own work I prefer the first alternative - it flows better, even if the second one is formally correct. Try to read both aloud. Journal editors do not object. Jmath666 (talk) 20:06, 29 March 2008 (UTC)
I'd prefer the third, or the second except replace forall with a simlpe "for." Which to use would depend, I suppose, on how set-theoretic or formal the context is. --Cheeser1 (talk) 20:26, 29 March 2008 (UTC)
Done, with Scientific Word and my LaTeX to Wikicode translation tool this was easy. However the paper still requires some attention. Regarding style, true, it depends on the context. Too much formalism just gets in the way if the audience is not used to it. Jmath666 (talk)

BACK TO THE MAIN POINT: It's all non-editable images. It needs to get replaced. (I did replace ONE of them.) Michael Hardy (talk) 05:10, 30 March 2008 (UTC)

It appears they've all been replaced, unless I'm mistaken. --Cheeser1 (talk) 06:52, 30 March 2008 (UTC)

Yes, I did that. And I used the style
${\displaystyle something=something,\quad i=1,\ldots ,N,}$.

(I realize some may not like the implied "for all".) Jmath666 (talk) 03:51, 31 March 2008 (UTC)

## article needing attention

Derivation of the Routh array disregards most standard Wikipedia conventions and lacks any initial context-setting. It seems as if whoever wrote it expected it to be seen ONLY by those who follow links from one or more other articles that set the context.

It could use some attention. Michael Hardy (talk) 15:26, 27 March 2008 (UTC)

I see we already have Routh-Hurwitz stability criterion; if Derivation of the Routh array is meant to simply be a derivation "subpage" of that, I think moving it over to wikibooks might be in order. Do we have editors here who are also active on wikibooks, who can explain what the goals and standards are there? — Carl (CBM · talk) 15:35, 27 March 2008 (UTC)
It really seems like more of a small paper or something, it doesn't read like an article and I don't have confidence that it has the content to be an article. --Cheeser1 (talk) 15:37, 27 March 2008 (UTC)
The Routh-Hurwitz stability criterion is a fundamental theorem in control systems theory. While the very important result is posted in Routh-Hurwitz stability criterion article (and cited in dozens of other Wikipedia math articles), I sought not to burden the article detailing the result itself with the flow of its actual derivation. Being my first Wikipedia article, I apologize for my lack of familiarity with the various Wikipedia standards (although I'd hardly call it disregard). I'd never even used the Wikipedia TeX markup before writing it. Considering the importance of the theorem itself, and how the article breaks down very complicated and difficult to understand work done by various mathemiticians (and cites that work) into steps that your average math or engineering student could follow, I would hope that the article would stand on its merits. The amount of research in locating the original work, understanding it, and effort put into clearly expressing the steps of that work was hardly insignificant. The result it demonstrates is very significant, important and widely cited on Wikipedia. With respect to your statement regarding context, I could cite you many, many math articles on Wikipedia providing an equivalent lack of context in the article itself. Just look at any article found throught the Proofs page, like this.
--Zaxxonal (talk) 16:52, 27 March 2008 (UTC)
As a non-expert, I cannot assess whether the topic is significant enough to merit an article on Wikipedia. There is, as you point out, precedent for having articles with proofs in them, or as a subarticle. Perhaps we should explore the possibility of moving Derivation of the Routh array to a subarticle of Routh-Hurwitz stability criterion. silly rabbit (talk) 16:58, 27 March 2008 (UTC)

Zaxxonal and silly rabbit: It isn't a question of whether the topic is notable enough - we already have an article on the topic. The question is whether including this derivation runs afoul of our mission of being an encyclopedia rather than a textbook. There is no clear agreement at the moment about "proof subpages" or "derivation subpages"; in any case, the existence of some such subpages can't be used as an argument for including more of them. My personal opinion is that lengthy derivations are not in line with our mission, but may be in line with the mission of our sister project Wikibooks. — Carl (CBM · talk) 19:12, 27 March 2008 (UTC)

I feel rather strongly that proofs do belong in Wikipedia. The question to ask here is, does this proof deserve an article? In this case I'm not familiar with the area so I don't feel qualified to answer. CRGreathouse (t | c) 03:05, 28 March 2008 (UTC)
I respect Carl's position, but as he himself pointed out, there is no clear agreement on the matter. I personally see no harm in having proofs in Wikipedia. I have no opinion on whether they should be subpages or something else; I do agree they should not clutter up main articles. (I also express no opinion about this particular page since it is far from my specialty.) There is no reason why a proof is inherently unencyclopedic. Has this idea been revisited much lately? I know there have been some isolated discussions flaring up over the last few years, but maybe we need to work out a consensus once and for all about this proof business. Otherwise, we will see fragmented discussions just like this pop up every time someone challenges the existence of some proof page. VectorPosse (talk) 07:36, 28 March 2008 (UTC)
I am aware of the lack of agreement here, and was only offering a personal opinion. I have a lot of respect for the viewpoint that we should include a very complete collection of proofs, and I think it's mainly a question of project scope. I agree that some proofs belong in our articles, and I've put some in myself. I was trying to say above that lengthy derivations are what I'm not convinced about. In many cases I think it's better for us to discuss the ideas in the proof and the insights it provides. That sort of meta-analysis is what Wikipedia is good at. — Carl (CBM · talk) 12:56, 28 March 2008 (UTC)
I see now. The distinction between derivations and proofs is an important one and I would tend to agree with you on that count. VectorPosse (talk) 23:55, 28 March 2008 (UTC)
The issue here IMO is whether we're dumping this proof because people with experience in the subject don't think it's important, or because it's boring to that hypothetical bright 14-year-old that many people take to be the target audience around here. 24-hour news channels suck, in part, because they follow an iron rule that anything that isn't entertaining gets dumped instantly. Wikipedia does better, and must do better. It just seems inherently wrong to me to treat whether "boring" content stays as a fight, with winners and losers. Surely there's a way for everyone to win. What occurs to me, and I don't know if this has been tried, is to make more use of the the Wikibook icon, and it might say "Wikibooks has a proof of this at" with a link to the section giving the proof:
That is, if a proof is deemed too boring for Wikipedia, insert the wikibook link at a specific section in the Wikipedia text, and insert some kind of graphic in the Wikibooks text too with a link back to Wikipedia, so that people will know not to delete the text from Wikibooks without making a change back at Wikipedia. Is this a good idea? Is there something better? - Dan Dank55 (talk) 00:30, 29 March 2008 (UTC)

I concur with Carl. As the author has admitted, this is his first piece of writing on wikipedia. I feel that we should provide some guidance to him about what wikipedia is and what it is not. It may be tempting to view wikipedia as a universal depository of all knowledge, whether it be done for altruistic or selfish reasons, but there are inherent dangers in such inclusiveness. Hence, we have policies such as "Wikipedia is not a textbook" which restrict the scope of the project. The piece under discussion (I will not go so far as to call it an article) is a textbook case of violating this policy. There are many wikis out there that collect technical information of various sorts, which usually have a narrow topical focus and may aim at supplanting or even replacing the monographs on their subject, e.g. Dispersive PDE wiki. But wikipedia's primary aim is to be an encyclopaedia. In this sense, I think that distiction between derivations and proofs is an important one, and we should be careful not to open the floodgates to all sorts of technical writing and data storage (the criterion here is not whether it is boring, but whether it is encyclopaedic). Arcfrk (talk) 02:17, 29 March 2008 (UTC)

http://en.wikibooks.org/wiki/The_Book_of_Mathematical_Proofs is the link at Wikibooks for a module specifically intended to hold proofs of theorems stated outside of Wikibooks. Wikipedia is not a textbook, but Wikibooks is. I don't have an opinion on which proofs should be in Wikipedia, but for any algorithm or theorem in Wikipedia, is there any good reason to exclude a cited, important proof from Wikibooks, or not to have links going both ways, from the section with the theorem to the section on Wikibooks with the proof and vice versa? - Dan Dank55 (talk) 02:49, 29 March 2008 (UTC)
I can't see why we would avoid linking to wikibooks when the content there is relevant. It's a Wikimedia Foundation project, after all. — Carl (CBM · talk) 21:23, 29 March 2008 (UTC)

Michael - The changes your have indicated as needed have been made. Your feedback has been constructive and exceptional. Thank you. --Zaxxonal (talk) 16:28, 30 March 2008 (UTC)

But, with the exception of the first paragraph, it still fails "Wikipedia is not a textbook". Arcfrk (talk) 04:32, 31 March 2008 (UTC)
Last 4 comments copied to, and conversation continued at, WT:WikiProject Mathematics/Proofs, per discussion below. - Dan Dank55 (talk) 14:58, 31 March 2008 (UTC)

## Function (mathematics)

The discussion is essentially a debate on the content of this article, so it has been moved to talk:function (mathematics)#Definitions. CenariumTalk 17:55, 31 March 2008 (UTC)

Can someone with good knowledge of formatting conventions take a look at "History of Calculus"? A certain editor went through it recently linking every instance of Newton's and Leibniz's name being mentioned. What are the rules here? Arcfrk (talk) 04:27, 31 March 2008 (UTC)

I think that editor wants to make sure we know who Isaac Newton is.--CSTAR (talk)
Wikipedia:Manual of Style (links) is the relevant guideline. Yes overlinking of the same term is not good form, but the guide line does not prohibit the same term being linked to twice.
However, note that duplicating an important link distant from a previous occurrence in an article may well be appropriate (but see the exception about dates, below). Good places for link duplication are often the first time the term occurs in each article subsection. Thus, if an important technical term appears many times in a long article, but is only linked once at the very beginning of the article, it may actually be underlinked. Indeed, readers who jump directly to a subsection of interest must still be able to find a link. But take care in fixing such problems. If an editor finds themselves "reflexively" linking a term without having a good look around the entire article, it is often time to stop and reconsider.
In this case it might be appropriate to link to Newton at the start of the Newton section. In the current revision [44] it is actually quite hard to find where the link to newton is. --Salix alba (talk) 09:05, 31 March 2008 (UTC)

# Apr 2008

## Wiener sausage

has been linked from the main page. Unfortunately this means it is picking up some juvenile vandalism, and could do with watching. R.e.b. (talk) 16:10, 1 April 2008 (UTC)

## Werdnabot is back

FYI, according to Wikipedia:Wikipedia_Signpost/2008-03-31/Features_and_admins, Werdna (talk · contribs) and his Werdnabot (talk · contribs) have returned. Werdnabot appears to be archiving again. JRSpriggs (talk) 12:19, 2 April 2008 (UTC)

## Combinatorial number theory

I just noticed that we have no article titled combinatorial number theory. Should I be surprised? Michael Hardy (talk) 02:48, 2 April 2008 (UTC)

Not while we have (as far as I can see) no article which even mentions compactness arguments in combinatorics. Algebraist 13:10, 2 April 2008 (UTC)
I'd like to see that article, but I'm not up to the task of writing it. CRGreathouse (t | c) 14:30, 2 April 2008 (UTC)
I second those sentiments. --Cheeser1 (talk) 15:34, 2 April 2008 (UTC)

In the article space, exactly five articles link to combinatorial number theory, and two of those are lists. Michael Hardy (talk) 13:17, 3 April 2008 (UTC)

## Area theorem

Right now, area theorem redirects to black hole thermodynamics. But there's an important theorem about conformal mappings called the area theorem. I checked, and there's nothing that links to area theorem. I'm planning on writing an area theorem article. What should I do, just erase the redirect? (I'm a wiki-newbie.) Oded (talk) 05:07, 4 April 2008 (UTC)

If you are sure that the article does not already exist under another name, then change the redirect into a disambiguation page (see Wikipedia:Disambiguation). That page should have links to: your new article (perhaps called area theorem (conformal mapping)), the article on black hole thermodynamics, and any other articles which talk about "area theorems" (such as Heron's formula for the area of a triangle). JRSpriggs (talk) 05:38, 4 April 2008 (UTC)

I've made it into a disambiguation page. Maybe that could use a bit more polishing. Michael Hardy (talk) 19:50, 4 April 2008 (UTC)

## Maths Short Cuts

Maths Short Cuts is as clumsily written an article as you'll ever see. Delete? Michael Hardy (talk) 13:15, 3 April 2008 (UTC)

Delete. silly rabbit (talk) 13:18, 3 April 2008 (UTC)
The first revision of the article contained a {{db-nocontext}}, so this is probably a recreation of some sort. I don't think the clumsy style itself should be a concern for deletion (but if the article does stick around, it needs to be moved to appropriate capitalization, it needs a grammatical rewrite, and it needs re-wikification). It is not too hard to imagine a well written article on the topic: there are a reasonable number of articles in math(s) ed. about shortcuts, and process versus understanding, so one could have a nice section surveying the ed. literature, using one of Polya's books perhaps as a guide. Similarly, there is a huge business worldwide in "cram schools", "crib sheets", etc. and one could have a section surveying the business aspects, perhaps including links to series such as Schaum's outlines, or Kaplan's preparation things.
None of this precludes deleting the current article, which is unsourced (and nearly blank after removing unsourceable material and WP:NOT#Textbook problems). The current editor is probably not signing in, but still working from changing IPs in the 59.* range. JackSchmidt (talk) 13:33, 3 April 2008 (UTC)
The page was created before, by the same author, with the same content, and deleted once. My personal opinion is that we want to avoid making a "list of ways to guess the answer to a math problem." Unless someone has an idea of what an encyclopedia article on this topic could contain, I also would agree with deletion. But we should contact the author as well to explain this. Also, remember that issues with English presentation can be easily fixed later, so it's really only issues of content that should be relevant to deletion. — Carl (CBM · talk) 13:43, 3 April 2008 (UTC)
Generally I would agree that poor Englsh can be fixed in an otherwise useful article. But the problems with this article run much deeper than grammar and spelling. How do you even begin to make sense of a sentence such as "To know the nature of a triangle,just assume the angles keeping in the mind that the sum is 3600". This particular article is such an incoherent jumble that it is unfixable. Anyway, I had already attached a prod tag before I saw this discussion. But if it is a recreation of a previously deleted article, that is sufficient grounds for speedy deletion isn't it ? Gandalf61 (talk) 21:25, 4 April 2008 (UTC)
No, {{db-g4}} requires that the article was deleted after an afd process. Since it was a speedy deletion, it doesn't apply. CenariumTalk 16:33, 6 April 2008 (UTC)

Delete + salt = 3600n+1. --Cheeser1 (talk) 21:58, 4 April 2008 (UTC)

Contested prod, nominated for deletion, see Wikipedia:Articles for deletion/Maths Short Cuts. If you think that you can make a decent encyclopedic article on the subject, you have 5 days. However, it will certainly still fails WP:NOT#MANUAL and WP:N, so it will be deleted anyway. CenariumTalk 15:40, 6 April 2008 (UTC)

I agree with all of you.Thanks a lot for your response.But my purpose of starting this article is to help EAMCET aspirants in wikipedian way.As wikipedia users increasing in India are incresing,shortly it will be found to be a very useful page.Undoubtly, talented lecturers will contribute to this page,IF IT IS NOT DELETED.Many students in India are craving for Maths Short Cuts as succeeding in the test is a do or die problem for them.If you encourage this article,including my self and many others will start to make this a very useful page.Feel free to delete if still it is felt useless.Thank you--Chintapalli David Raju (talk) 16:36, 6 April 2008 (UTC)

The problem is that Wikipedia is an encyclopedia, and the primary purpose of a page is not to be useful for some people, but to be an encyclopedia article. Internet is vast and diversified, I'm sure that EAMCET aspirants can find specific help on other sites. CenariumTalk 16:49, 6 April 2008 (UTC)

## Hadamard finite part integral

The new article titled Hadamard finite part integral uses the word "hypersingularities". I don't know what those are, so I searched for hypersingularity and hypersingularities and found nothing. Should we edit this to say [[hypersingularity|hypersingularities]]? Michael Hardy (talk) 19:45, 4 April 2008 (UTC)

Hypersingular integral equations are integral equations whose kernel has a singularity of an order greater than one. They arise in the study of spatial problems in air and fluid dynamics, elasticity, the theory of diffraction of electromagnetic and acoustic waves, ecology, etc. Usually, hypersingular integral equations are obtained as a result of reducing Neumann boundary value problems for the Laplace or Helmholtz equation to integral equations by means of the double-layer potential. 81.249.161.2 (talk) 08:47, 6 April 2008 (UTC)

Well, I see that we had no page titled singular integral equation, so I created it as a redirect to integral equation. Now a question is whether to do the same with hypersingularity? Or can that term also be used elsewhere than in integral equations? Michael Hardy (talk) 14:54, 6 April 2008 (UTC)

If the page for the technical term frobnitz redirects to Frotzian, then I think the term frobnitz should be introduced somewhere on the target page.  --Lambiam 16:52, 6 April 2008 (UTC)

If so, that's not a reason not to introduce the redirect BEFORE the mention of frobnitz is on the target page. Instead it's a reason to add some mention of frobnitz to the target page. And if the added material is extensive enough, in some cases the mention should be a link to the redirect page which should then get converted into an article. Michael Hardy (talk) 16:55, 6 April 2008 (UTC)

Only if frobnitz will get mentioned in a reasonable amount of time after the redirect is created. The page Frobnitz has been a redirect page since 11:04, April 24, 2006, but the term is not mentioned on the target page (although in this case actually because someone deleted an existing mention).  --Lambiam 20:52, 6 April 2008 (UTC)

Shall I propose Hypersingular Integral Equations and Their Applications by I.K. Lifanov, G. Vainikko, L. N. Poltavskii, MG.M. Vainikko (Taylor & Francis, Inc. publisher) 2003 - ISBN-13: 9780415309981 and Hypersingular Integrals and Their Applications by Stefan G. Samko, Samko Samko (CRC Press) 2001 - ISBN-13: 9780415272681 as possible references to hypersingular integral equations? 81.249.161.2 (talk) 21:57, 6 April 2008 (UTC)

## Axiom schema of replacement

The article on the Axiom schema of replacement is so poorly written that I cannot bear to even look at it. Too many versions are discussed and the formulas and explanation are all awful. JRSpriggs (talk) 14:06, 30 March 2008 (UTC)

What do you think of this formula (from Axiom of infinity):
${\displaystyle \exists \mathbf {N} \forall n(n\in \mathbf {N} \iff ([\forall k\in n(\bot )\lor \exists k\in n(\forall j\in k(j\in n)\land \forall j\in n(j=k\lor j\in k))]\land }$
${\displaystyle \forall m\in n[\forall k\in m(\bot )\lor \exists k\in n(k\in m\land \forall j\in k(j\in m)\land \forall j\in m(j=k\lor j\in k))]))\,?}$
--Lambiam 20:53, 30 March 2008 (UTC)
Perhaps JRSpriggs is referring to the fact that both formulae in the 'variants' section are incorrect? Algebraist 21:11, 30 March 2008 (UTC)
That was a temporary error as I was editing the page to try to help JRSpriggs edit it again. I copied and pasted some improved LaTeX code but didn't remember to fix it before I hit save. Things are better now, in every sense. — Carl (CBM · talk) 21:12, 30 March 2008 (UTC)
Sorry, I missed that. That is an improvement. Algebraist 21:14, 30 March 2008 (UTC)
To CBM: Thank you for your edits. The article is much better now. JRSpriggs (talk) 10:44, 31 March 2008 (UTC)
I've had the same experience before - I open a page, look at it, and can't bear to look at it any more. I've been through that process with Propositional logic more than once. — Carl (CBM · talk) 18:26, 31 March 2008 (UTC)
Open the page, make one very small change, then don't come back to it for a month. Repeat for the next five years, or until satisfied. linas (talk) 02:29, 8 April 2008 (UTC)

To Lambiam: As you know, I wrote that formula in the axiom of infinity. Obviously, it is correct and written in the best style of formal language. However, it is difficult to understand because it is entirely formal using the element relation and equality rather than derivative concepts. There also was an English rendering which is much clearer. To help you and others, I just added another rendering of intermediate formality. JRSpriggs (talk) 11:01, 31 March 2008 (UTC)

I did some more work on the axiom of infinity. I hope you like it better now. JRSpriggs (talk) 06:08, 1 April 2008 (UTC)
We have no notational convention for quantifications, and indeed the notations are all over the place in different articles. Personally I find
${\displaystyle \exists \,\mathbf {I} :\emptyset \in \mathbf {I} \,\land \,(\forall x\in \mathbf {I} :x\,{\cup }\,\{x\}\in \mathbf {I} )}$
easier to read than
${\displaystyle \exists \mathbf {I} \,(\emptyset \in \mathbf {I} \,\land \,\forall x\in \mathbf {I} \,(\,(x\cup \{x\})\in \mathbf {I} )).}$
Since the formal language of ZFC has not been presented, it is not obviously meaningful to state that one formal formula is more formal than another formal formula, and presenting the allegedly more formal version to the reader serves no clear purpose.  --Lambiam 09:03, 1 April 2008 (UTC)
Do you know where the colon notation comes from? I see it in a few place on WP. There is a well established standard in contemporary mathematical logic, and I think it's reasonable for us to use that standard here. The convention is that in general we quantify θ like so: ${\displaystyle \forall x(\theta )}$ or ${\displaystyle \forall x\theta }$, depending on whether the scope of the quantifier is clear. I don't think I've ever seen a contemporary mathematical logic text that uses commas, periods, or colons to delimit formulas. Of course this isn't an issue of being "more formal", it's just a convention for syntax of first-order formulas. — Carl (CBM · talk) 12:17, 1 April 2008 (UTC)
I see the style with the colon often, but perhaps not in logic textbooks as such. I'll check Enderton when I get home. CRGreathouse (t | c) 13:43, 1 April 2008 (UTC)
I have Enderton's book here, and he doesn't use colons. Neither do Mendelson's or Kleene's undergraduate texts (Mendelson does use the older (x)(Ey) notation). I also looked at a few set theory books: none of Jech, Kanamori, Kunen, or Levy use colons, periods, or commas.
It must be that someone uses colons; maybe it's common in some other field? — Carl (CBM · talk) 13:53, 1 April 2008 (UTC)

To Linas: The changes (by CBM and myself) to both axiom schema of replacement and axiom of infinity as a result of this discussion were substantial, not minor. JRSpriggs (talk) 07:54, 8 April 2008 (UTC)

## Knaster–Tarski theorem vs Kleene fixpoint theorem

The second page has no reference at all and the result is a direct consequence of the first one. The two pages should probably, at least, be merged. 81.249.161.2 (talk) —Preceding comment was added at 07:51, 7 April 2008 (UTC)

## Bieberbach conjecture

Copied from User talk:Oleg Alexandrov

Requested move: De Branges' theorem --> Bieberbach conjecture

I left a comment on the talk page a couple years ago:

So the article says it was formerly called the Bieberbach conjecture. I found that odd as I've always thought of it as Bieberbach conjecture, and heard it often referred that way. Do specialists really call it de Branges' theorem? A preliminary look through MathSciNet, seems to indicate that "the de Branges theorem" actually refers to a more general theorem that implies (among other important stuff) the Bieberbach conjecture. --C S (Talk) 07:36, 15 April 2006 (UTC)

I looked through search results on Google Scholar, and I don't find any reference to De Branges' theorem other than those refer to either other or more general results. It appears the name is still "Bieberbach conjecture".

--C S (talk) 18:48, 7 April 2008 (UTC)

Any comments on this? I can easily do the move on the technical grounds using the admin buttons but perhaps people familiar with the topic in question can comment on this first. Thanks. Oleg Alexandrov (talk) 05:51, 8 April 2008 (UTC)
I am somewhat familiar with the topic albeit as an observer. My impression is that the term "Bieberbach conjecture" is still widely used, and the people working in the field have not switched to "de Branges' theorem". The wiki entry should certainly be entitled "Bieberbach conjecture", his distasteful sympathies for nazism notwithstanding. Katzmik (talk) 10:53, 8 April 2008 (UTC)
I agree that it is still mostly reffered to as the Bieberbach conjecture. However, both names are legitimate. It is somewhat of an editorial choice at this point. If we think that it should be called de Brange's theorem, then that's what we should call it. Oded (talk) 15:00, 8 April 2008 (UTC)
According to the naming conventions we should use what is the most common name, and not what we think it ought to be.  --Lambiam 20:18, 8 April 2008 (UTC)
Bieberbach conjecture is definitely the common name. Both names were mentioned in the complex analysis courses I took, and the preferred name was always B.c. Neither of the men involved have bland histories, so trying to chose a name that gives the most "dignity" is not likely to succeed for this article. JackSchmidt (talk) 20:28, 8 April 2008 (UTC)
If that's the common name, then it should be moved back. Whether it should be called "de Branges' theorem" is completely irrelevant; we are not in the business of language reform. When and if that becomes the accepted name, it can always be moved again. --Trovatore (talk) 20:58, 8 April 2008 (UTC)

One could make the point that the situation in mathematics is different and that the discussion in naming conventions does not apply. The issue here is not like the distinction between using the common dog rather than the scholarly Canis lupus familiaris. In mathematics, naming a result is also a way of attributing (and often mis-attributing) credit. The discussion in naming conventions does recognize that exceptions are sometimes beneficial. Oded (talk) 21:00, 8 April 2008 (UTC)
It is not our job to correct historical injustices. We reflect the common usage in the field. This is by no means a unique situation -- for example Zorn's lemma was not, or at least not essentially, original to Zorn (and he never claimed it was). --Trovatore (talk) 21:02, 8 April 2008 (UTC)
Agreed. L'Hôpital's rule being another classic example. --Cheeser1 (talk) 21:17, 8 April 2008 (UTC)
Incidentally, do we have an article listing such cases (misattributed names in math)? I imagine it would be rather large, but interesting to peruse. Hamming number might be another example of this. CRGreathouse (t | c) 03:51, 9 April 2008 (UTC)
I seem to recall that maybe there is such a list. In my opinion, though, there should not be. It's too subjective. --Trovatore (talk) 03:55, 9 April 2008 (UTC)
Sounds like one of many places to edit war about who stole calculus from whom. Not to make any WP:BEANy suggestions. --Cheeser1 (talk) 04:44, 9 April 2008 (UTC)
List of misnamed theorems. —David Eppstein (talk) 04:45, 9 April 2008 (UTC)

OK, I performed the move. The move can be of course undone should in the future be agreement about it. Oleg Alexandrov (talk) 02:46, 9 April 2008 (UTC)

## Dubious math

Don't know if this is the best way of handling this, but on Random article patrol I came across Straferunning, about a technique in video-gaming. My math is a bit rusty, but I've a feeling that the "Mathematical proof" in this article is a hoax...input appreciated... Camillus (talk) 00:07, 9 April 2008 (UTC)

Although I go by a preliminary, brief glance here, I concur: this seems to be a collection of mathematical phrases such as "tangent", thrown together with some nice formatting. Particularly, "df = tan (ψ) / cos (ψ), when df = 0 then ψ = 0." seems completely irrelevant with regards to video-gaming. I have wiped the dubious material. Anthøny 00:27, 9 April 2008 (UTC)
I don't claim the proof is not a hoax or a joke, but it is more or less correct. It appears to be appealing to calculus to prove an elementary statement about real numbers or even more intuitive statement about right triangles: the hypotenuse of a right triangle is longer than either its adjacent or opposite side. The calculus is standard, if f(0) >= 0 and f'(x) >= 0 for 0 < x < 1, then f(x) >= 0 for 0 < x < 1. The proof apparently iterates this method to avoid doing any analysis on trig functions. In my opinion the proof given in the lead is just fine, or if one wanted to be formal, quote the pythagorean theorem. JackSchmidt (talk) 00:41, 9 April 2008 (UTC)
I have heard of this issue elsewhere. In some games that limit speed independently for forward and sideways movement, you can get a higher maximum speed by running both forward and sideways at the same time. This is a simple consequence of vector addition (or, as JackSchmidt says, the Pythagorean theorem). — Carl (CBM · talk) 17:49, 9 April 2008 (UTC)
If you can also move diagonally, it just means the game has the Chebyshev distance as its metric, so then that is "normal" in the game's virtual world. If you use a screen on which the pixels are 2mm by 2mm instead of 0.2mm by 0.2mm, do you go ten times faster than normal?  --Lambiam 18:18, 9 April 2008 (UTC)
This is off-topic, but: games like this keep track of each player's position using some internal coordinates, not based on pixels. Distance between players is measured in the ordinary Euclidean metric for purposes like telling how long it takes for a projectile from one player to reach the other player. So outrunning other opponents is important, which is why people learn to do things like run diagonally in order to get a competitive edge. The archetypal technique of this sort is probably circle strafing. — Carl (CBM · talk) 18:31, 9 April 2008 (UTC)

## New template for talk pages, expecially the larger ones

{{Unanswered}} Some pages, such as this one have lots of post, and it requires some work to see what has been answered or acknowledged. therefore I have helped make the {{Unanswered}} template that can be put above a section allowing one to quickly glimpse what has been answered. If you were waiting for an answer but never got one as the post in somewhere in the middle tag it! please voice any queries or comments in the talk page ofTemplate:Unanswered (links, talk) and not here. Cheers --Squidonius (talk) 15:12, 13 April 2008 (UTC)

## Wanted: Ring theorists and abstract algebraists

Hello math people. I have been working to reconstruct the article about Emmy Noether on my drawing board. I have completed her biography and have now come to the part where I must explain (briefly, but in some detail) her contributions to mathematics and theoretical physics.

However, I – as an English teacher who dropped out of pre-calculus in high school – can't understand a single word of the math involved. I'm hoping one of you is willing (or can recommend someone) to help me write these final sections about Ms. Noether's work in the fields of ring theory, abstract algebra, Galois theory, and algebraic geometry. If so, please leave a note here (I'll watch the page) or – preferably – on my talk page. I thank you in advance and will now recede to my lair of Balzac and Achebe. – Scartol • Tok 00:18, 14 April 2008 (UTC)

The drawing board has now been shipped out to the main article. Scartol has done a great job and has asked me (among others) to help with the math. Although I can probably wax lyrical about Noether's theorem and Noetherian rings, I'm not a physicist or an algebraist, so I would encourage anyone here, especially those who have expertise in these areas, to dive in! Geometry guy 21:02, 15 April 2008 (UTC)

## WP:Featured article candidates/Emery Molyneux

There's an FAC here with math related content (Emery Molyneux) which needs content-expert input. Can editors here provide some? Thanks, Geometry guy 00:28, 16 April 2008 (UTC)

## Introduction to M-theory

An AfD debate: Wikipedia:Articles for deletion/Introduction to M-theory.

I would really, really like to have WP policy changed so that AfD debates could take place under the guidance of specific wikiprojects, rather than be open to general debate. This latest AfD is not unlike previous drive-by deletes, where those voting for deletion are non-mathematicians who have no clue or interest in the topic, and those voting to keep are the usual crowd you'd see here.

I think this wikiproject is entirely capable of self-policing, and of deleting bad articles. At the same time, we mostly don't run around trying to delete articles on pokemon or high-schools. Thus, I'd really like to see a policy where non-wikiproject editors would be discouraged from "meddling" in wikiproject affairs, including the deletion of good/bad articles. linas (talk) 03:15, 16 April 2008 (UTC)

Reposting from WP:Physics:

Introduction to M-theory was completely rewritten in 2004 by an editor who included large swaths of text copied verbatim from the book Turn of the Century. The article was brought up for concerns about no references being cited in such a large article and the general format of 'introduction to...' articles when the copying was noticed (see Wikipedia:Administrators' noticeboard/Incidents#X for Dummies fork). Due to the volume of the material copied, and subsequent wording changes being derivatives of the copyrighted text, all revisions of the article since January 2004 were deleted. Since this was a lengthy article, I would appreciate it if members of this wikiproject could get it back up to speed. Four years is a long time to miss things in most theoretical science fields :) -Mask? 09:00, 14 April 2008 (UTC)

There is Wikipedia:WikiProject Deletion sorting. I notice that this project has yet to include any science categories. I don't know if there are other Wikipedia initiatives to categorize deletion discussions. It seems like a good idea. Better, at least, than having someone post here every time there is a deletion discussion within the scope of the project. silly rabbit (talk) 14:03, 16 April 2008 (UTC)

## "Formal Laurent series" redirect to .... ?

Formal Laurent series now redirects to formal power series. I can imagine it redirecting to Laurent series. I can also imagine it being a page with links to both of those and little else until someone decides to make an article of it, but then someone might be tempted to call it a "disambiguation page" and of course that's not what it would be. What is the best thing to do with that page? Michael Hardy (talk) 03:03, 17 April 2008 (UTC)

It could redirect to the section Formal power series#Formal Laurent series. PrimeHunter (talk) 03:13, 17 April 2008 (UTC)

## Problem editor

I am sick and tired of User:Mathsci making snide, disparaging, factually inaccurate, and incivil comments in the edit summaries (as well as on talk pages) any time I happen to be editing an article that he considers his own. He apparently believes that no sentence he has ever breathed upon can be changed without his sanction. I have ceased working on several articles because I do not appreciate being personally attacked in return for my efforts to improve Mathematics coverage at Wikipedia, which includes correcting errors made by people who don't believe that they could make an error and rearranging material to be helpful to the reader, not the author. If anyone else here thinks that his attitude runs contrary to the spirit of Wikipedia (or even violates some policies that we have here), will that person or persons be so kind as to let it known to him? In the meantime, I'm withdrawing from Wikipedia. All the best, Arcfrk (talk) 23:04, 6 April 2008 (UTC)

It's hard to tell exactly which edits or articles you're looking at. A quick scan turned up this edit, but there must be more than that to be this distressing. These things are often better handled by discussion talk pages, rather than edit summaries, even though it seems like the least efficient way at times. — Carl (CBM · talk) 23:29, 6 April 2008 (UTC)
This has been reported before: at the ANI. But I don't have the time now to read through it at all. --Cheeser1 (talk) 23:37, 6 April 2008 (UTC)
Such editors are not that uncommon indeed. Arcfrk, I'd suggest you don't give up on editing, and please notify us on this page if in the future you need extra opinions on how something should be written (from my experience just going back and forth with the same editor and no outside input is not always a productive way of doing things). Oleg Alexandrov (talk) 01:15, 7 April 2008 (UTC)
The only recent edit summary I can find that Arcfk might be referring to is [45], but that's over 2 months ago. Both of you appear to have made valuable contributions to Wikipedia. There are bound to be some personal(ity) clashes in any community but it's a shame if they cause valued people to leave. YoMaybe a short wikibreak would be enough? Qwfp (talk) 05:25, 7 April 2008 (UTC)
A fellow mathematician just told me that this was going on. I am unaware of any serious content dispute that User:Arcfrk has had with me in mathematics. He did propose splitting up the Orbifold article, but with little or no attempt to discuss or justify the matter on talk pages. Is it possible that I might have blinded him with science? (BTW, Cheeser, we are not discussing my edits to Marseille and Aix-en-Provence here, where I am still apparently being wikistalked by the Australian User:Michellecrisp.) For those that are interested, I have had a wikibreak while giving a graduate course in the UK, but will now probably be preparing articles on Weyl-Kodaira theory and spherical functions for SL(2,R) and SL(2,C), with applications to the Selberg trace formula. With no history of prolonged edit conflicts or revert wars in mathematics articles (or elsewhere), I have no idea why User:Arcfrk has brought his complaints here. No diffs were provided from mathematics articles and there's probably quite a simple explanation for that :) Differences are usually easily resolved in advanced mathematics articles (for example the slight clarification to the lead in Kazhdan's property (T) following CBM's intervention). Mathsci (talk) 20:33, 9 April 2008 (UTC)
For the record, the name just rang a bell, I have no familiarity with or opinion on this issue - old or new. Just providing a link to anyone who cares to click it, in the interests of transparency. --Cheeser1 (talk) 22:29, 9 April 2008 (UTC)
Transparency? I have no idea what you could mean by that; nor can I pretend to compete with you for visibility on WP:AN/I. Mathsci (talk) 20:12, 11 April 2008 (UTC)
I'm afraid I can't help you learn common definitions of English words, although you might try the OED entry for transparent, meaning 2a. As to whether or not you and I are more "visible" on the ANI, that is I'm afraid, not an appropriate nor relevant point of discussion. Excuse me if I have somehow struck a raw nerve by providing a helpful and at least somewhat, if not completely, relevant link. --Cheeser1 (talk) 23:35, 11 April 2008 (UTC)

I think this is a problem in communication, arising partially from anonymity. Some people aren't as careful with their words as they may be in real life. There is, in fact, a way to tell someone they're wrong nicely. Some people find the lack of authority in anonymity troubling. Additionally, consistently hinting of one's real life authority will usually only serve to annoy others (especially in contexts to bolster one's arguments). There are lessons for all involved parties here. But there is no "problem editor" here, I think. Thank goodness. A candidate for "problem editor" is more likely to be found at Talk: complex number, although s/he doesn't really compare to the last time I recall a section called "problem editor" here. --C S (talk) 02:15, 10 April 2008 (UTC)ic

Even on that page, I think that everyone involved has the interests of the article in mind. The pages on elementary topics such as number systems, functions, etc. have a well deserved reputation for being more difficult to work on, but I think it is more due to the bike shed effect than to bad intentions. I try to limit my own participation on those articles to balance stress against benefit. — Carl (CBM · talk) 02:28, 10 April 2008 (UTC)
In fact, in the article on the Surfaces, there was no account at all of Gauss' contributions (differential geometry), even though most of this is often regarded as undergraduate material (if, following Gauss, connections are not used). I added the standard classic material and did not object when User:Arcfrk split off the material. However, he failed to provide a short summary of the material removed from Surfaces, which therefore has not improved the article. (I pointed this out on the talk page of the article, but there was no response.) Moreover the lead he wrote for the newly-formed Differential geometry of surfaces was a short essay in WP:OR which bore no relation at all to the actual considerable content and was unsourced: it did not even mention the name of Gauss. I therefore altered the lead to reflect what was actually covered by the article, which at that stage was all my own work. I have no idea why he decided to add unsourced personal material in the lead, but that is possibly a problem with his editing. In Boundedly generated groups he seemed not to want the the now classic 2 page "automaton" counterexample of Grigorchuk to be cited. He also does not seem to allow sufficient time to discuss these splits before making them. Instead of moaning here, why doesn't User:Arcfrk write a mainspace article on the Gromov boundary? Mathsci (talk) 07:10, 10 April 2008 (UTC)
Aha, caught in the act: [46]! But seriously, regardless of what you may think of Arcfrk's style, I think Wikipedia is much better off with his/her contributions than without them. My suggestion is that the two of you should make amends. You are both valuable to the project. It's unfortunate that this thread is a referendum on you personally, and it is understandable that you would become defensive. But I myself see no evidence that you are, or have ever been, a problem editor. Same with Arcfrk. silly rabbit (talk) 22:09, 11 April 2008 (UTC)
If you examine the edit history, prior to Arcfrk deciding on the move, you will see that I wrote all of the lengthy main text. Arcfrk's lead did not reflect the content of the article, was unsourced and possibly WP:OR. He should get out of the habit of chopping up articles so hastily. As you will see on the talk page of Surfaces, I was not against the move. However, as I've said above he did not even bother to summarise the material excised from Surfaces. I don't think that is very helpful for Wikiproject Mathematics. Mathsci (talk) 08:09, 17 April 2008 (UTC)
We seem to be singing from the same hymsheet, silly rabbit (even citing the same edit). Glad to see you're still around too! (Red sig is a cute trick..)Qwfp (talk) 23:11, 11 April 2008 (UTC)

The only things that MathSci has blinded me with are his bad manners, amount of bile he spits into the edit summaries and comments on the talk pages, and his unjustified cockishness. Ah, sorry, forgot the scale of his hypocrisy. I first encountered him when he was engaged in an ugly dispute with another editor concerning the spelling of von Neumann's name, making his trademark insinuations about the level of intelligence and/or professional knowledge and ordering another editor not to touch his article. One of the things he said then was

But I am a little upset that you choose to be rude to mathematicians. They are only the people who could have created this article.

— obviously, not the principle he would follow himself. He complained ad nauseam about the widely supported split of the "Differential geometry of surfaces" that I had performed, opting for attacking my rather extensive edit for the epsilon that it was lacking, instead of "graciously accept"ing (another of his free advices to others that he doesn't like to follow himself) the consensus to fork, and helping to smoothen it (incidentally, "Differential geometry of surfaces" is one of the articles that badly need improvement but which I wouldn't touch given the inevitable attacks on anyone who dares to emend MathSci's "all my own work").

Those interested can look over his talk page archives to test the validity of his statement about "no history of prolonged edit conflicts or revert wars in mathematics articles (or elsewhere)", as well as the talk page of "Orbifold", where his non sequitur response to my forking off proposal included an attack on my mathematical competence. Although to this day he did not condescend to write a substantive reply, he (hypocritically) accused me of "little or no attempt to discuss or justify the matter on talk pages" in this very thread! I am far from surprised, though, given the belligerent spiel that he posted on my talk page after my earnest attempt to clean up "Boundedly generated group". And so on, and so forth. Instead of calling my well-founded concerns "moaning", why doesn't he look in the mirror, and apply the same standards to himself as he does to the others?

Sorry for the long ramble, and I do wish that we were spending the time more productively, by adding new content and improving the quality of existing articles through editing and reasoned discussion that does not involve personalities of the editors. I reckon I was dreaming. Arcfrk (talk) 07:34, 13 April 2008 (UTC)

Arcfrk seems to be attempting to prolong a non-existent drama. Meanwhile, off-wiki the Weyl-Kodaira article is coming along apace :) Mathsci (talk) 08:09, 17 April 2008 (UTC)

Arcfrk, I agree with many of your sentiments, seems like Mathsci enjoys disparagaing behind my back here on the maths page. Look at this talk page (some of it has been archived), quite a few editors have complained to him about his behaviour especially when he doesn't get his way, he accuses legitimate editors of vandalism or trolling. Look at my contributions, I am neither a troll nor a vandal, and contribute to a wide range of location articles all around the world. Mathsci tried to strongly discourage me from contributing to any French place articles in a display of WP:OWN. Michellecrisp (talk) 13:13, 17 April 2008 (UTC)

Mathsci's accusation of wikistalking is absolute WP:KETTLE when he himself has engaged in it against me. He has only ever edited one Australian article (while I have edited many French and European locations)...Mount Isa straight after I edited it, he did this nonsensical edit [47] which another editor clearly saw as deliberately disruptive [48]. Classic wikistalking if I ever saw it. Michellecrisp (talk) 15:54, 17 April 2008 (UTC)
What are you doing here on this mathematics wikiproject page, unless you are wikistalking me? As far as I am aware, you have little or no familiarity with higher mathematics. Stop trying to create wikidrama. You tried completely unsuccessfully to complain about me on WP:AN/I with no result whatsoever. (Apart from you and me, there was only one brief comment by another editor on that thread, which you needlessly prolonged.) What on earth are you doing here, apart from yet again trying to disrupt WP? Mathsci (talk) 18:59, 17 April 2008 (UTC)
But since you are here, let me point out a consistent failure in your use of logic. In mathematics it is usually not possible to prove things by producing one example. Similarly on the WP, we have a three revert rule. As far as I am aware I reverted something you wrote once in my wikipast. On dear. You claimed that I WP:OWN French place articles: however, again this was something you were unable to support by a reasonable number of diffs. Since I also occasionally help in stopping misguided edits to Prime number, perhaps you consider I also own that page too. I would be interested to hear your thoughts on vandalism to Prime numbers, since you have strayed to this page. (How did you find this page, unless you looked at my list of contributions?) Mathsci (talk) 19:09, 17 April 2008 (UTC)
User_talk:Michellecrisp#Random_comment.2Fquestion Djk3 (talk) 19:35, 17 April 2008 (UTC)
Thank you. The community at work as usual :) Mathsci (talk) 19:43, 17 April 2008 (UTC)
Some irony perhaps (failure in the use of logic)... ;] Tparameter (talk) 12:03, 18 April 2008 (UTC)
Since this is really a page for discussing math, I have to point out that the statement, "in mathematics it is usually not possible to prove things by producing one example", is false. In fact, there are as many proofs by counter example (one example) as there are real numbers. There are as many proofs using 'one example' as there are any other thing you can imagine. Tparameter (talk) 07:49, 19 April 2008 (UTC)

OK I'll come clean. It's all my fault. --CSTAR (talk) 16:49, 17 April 2008 (UTC)

Or von Neumann's :) Mathsci (talk) 18:59, 17 April 2008 (UTC)
As I member of the community I am always glad to help. Since effort had been made to mention Michellecrisp's name in a discussion she was not a part of, I thought it only fitting to invite her to the conversation. While I wouldn't call you a problem editor, you do seem to go "straight for the jugular" when it comes to mathematical prowess. When you use phrases like "you are simply completely out of your depth" you shouldn't be surprised people get insulted. Thenub314 (talk) 00:49, 18 April 2008 (UTC)
Isn't this just WP:SPADE? Why waste time trying to analyse other editors' personalities? That is not what WP is about. Isn't it enough that experts are willing to spend time adding useful mathematical content to the WP project? Mathsci (talk) 10:51, 18 April 2008 (UTC)
No, it's not enough. Not when an expert may chase away other experts with a confrontational attitude. It's not just Arcfrk; I just realized a day ago when editing free group that you had a hand in encouraging Jim Belk to not contribute as much as he would have. The talk page discussion seems to me to be a good example of why people may find you difficult. Just like any other open source project, sometimes it is more beneficial in the long run to turn away some experts who cannot learn to work with others. It has happened more than a few times before on math Wikipedia, and I'm sure it'll happen again. I don't think you deserve all or even many of the harsh remarks that have come your way, but I think you ought to realize there's a reason you've aroused such anger in your fairly limited time and interaction on Wikipedia. --C S (talk) 12:29, 18 April 2008 (UTC)
I was not analyzing your personality. I was not trying to offend you. I was just pointing out one reason why I think you tend to make people angry. I think C S remarks are well put. And I agree the answer to your question is clearly no. Thenub314 (talk) 21:27, 18 April 2008 (UTC)

I agree with thenub314, they indeed informed me as the subject of discussion here. I am here to defend myself and accusations on my character on Wikipedia. If this is a violation of Wikipedia policy then report me. I am concerned over Mathsci's behaviour on Wikipedia and it seems that I'm not the only one. Threats like this [49] don't help either. Especially as the Mount Isa example above demonstrates stalking behaviour that he so detests. I have also been contacted by another editor on another topic area concerning Mathsci's behaviour. Certainly, if we can all stick to the assumption of good faith this would be a better place. Michellecrisp (talk) 02:59, 18 April 2008 (UTC)

Meanwhile I have now started the task of writing Spectral theory of ordinary differential equations. If Michellecrisp wants to help write the section on Inverse Scattering Theory (Gelfand-Levitan) at some later stage she is free to pitch in. Otherwise I suggest she discuss my single edit to Mount Isa somewhere else where it might possibly have some relevance. Mathsci (talk) 10:47, 18 April 2008 (UTC)
Such a patronising comment (am I surprised?). I have as much interest in maths articles on Wikipedia as you have in Mount Isa. Michellecrisp (talk) 11:15, 18 April 2008 (UTC)
Under a thread about your snide remarks - a thread where you implicitly invited Michellecrisp to participate (by making an accusation of stalking) - I'm not sure if a random challenge to an intellectual bench-press contest on some specialized topic in math goes to support your side very well. Tparameter (talk) 12:12, 18 April 2008 (UTC)
Tparameter, I think now-vanished user User:Cheeser1, who recently disgraced himself on WP:AN/I, brought up Michellecrisp. Please could you use this page for making comments on mathematical edits: this is not WP:AN/I, no matter how much you might want it to be. BTW, on a different note, it was a great pleasure to encounter User:OdedSchramm helping with the lede to Differential geometry of surfaces. Sigh. Anyway back to Titchmarsh, Kodaira and good old Hermann Weyl. Are people on this page interested in writing mathematics articles or just in scoring points? Mathsci (talk) 20:02, 18 April 2008 (UTC)
For the record, I have never commented in, participated in, or paid any attention whatsoever to any WP:AN/I activity of any kind, so let's not let conspiracy theory get the better of us. Anyway, back on topic - all I'm saying is that if you accuse a user of some random infraction (for example, the aforementioned Michellecrisp stalking accusation that you made), then expect them to reply directly. Tparameter (talk) 00:23, 19 April 2008 (UTC)

I agree with Tparameter, Mathsci, you referred to off topic claim of wikistalking by me, first and here on this page and now say it should be restricted to maths only discussion. True, WP:KETTLE if I ever saw it. Then you tell me not to discuss it on your talk page [50] If someone is accused of violation of Wikipedia policy it should be discussed before further action is taken. Seems like Mathsci thinks he is always right on everything and no correspondence shall be entered into. Michellecrisp (talk) 04:15, 19 April 2008 (UTC)

Let's end this discussion now. I think there is wide concensus that (a) Mathsci is doing good editing work, (b) he/she tends to offend people and (c) we all ask him/her to be more considerate in the future. Let's try to put this behind us. Oded (talk) 17:36, 19 April 2008 (UTC)

Seems he hasn't learned to be considerate after Oded's message here, besides still complaining about me [[51], Mathsci accuses me of vandalism today [52] for this good faith edit [53]. Michellecrisp (talk) 08:00, 21 April 2008 (UTC)

Michellecrisp - you are being disruptive. You regrouped the Municipal library and the Friche visual arts centre under a section that you headed "Opera and Theatre" in Marseille. That was a capricious edit. An unjustified and unhelpful edit like that gives the impression of someone idly trying to make a suoerficial content-free change to the page, possibly to be provocative. And for Aix-en-Provence you included a reference to a claimed "cultural centre", citing a one sheet tourist guide as your only reference. This guide has no mention of a cultural centre, either in the french and english versions (usually available as rubbish on the streets of Aix). However, as I know, because I have attended performances at both places, there is a new "Grand Theatre de Provence" (already mentioned in the article) and a new "Pavillion Noir" for dance (this has been added to the article with a link to its website). Michellecrisp, you are vandalising articles, trolling, forum shopping, following me around (to other editors' talk pages) and disrupting the WP project. In future avoid capricious edits and find references that amount to more than a one-sheet fold out guide. Do you really have nothing better to do with your time? I will be forced to report you on WP:AN/I if you continue following me around. As I have said your persistent attempts to generate incidents artificially (eg as you have just done) does not place you in a very good light. Please stop making WP:TROLLish WP:POINTy edits to articles to provoke other editors. It gives the appearance of a scheming busybody.
Please also stay off this Wikiproject Mathematics page, unless you have comments to make on mathematics. I am still eager to here any of your thoughts on Fredholm determinants or Spectral theory of ordinary differential equations (which I fear, even unfinished, is too long, but that is partly because the articles on bounded variation and spectral theory are not quite up to par). Perhaps you think you can besmirch my mathematical reputation by heckling from the gallery, who knows. Mathsci (talk) 11:09, 24 April 2008 (UTC)
(ec) Here is the diff [54] that Michellecrisp was referring to. She is misrepresenting the edit summary which I include in full here.

rv capricious edit - restore previous form - Municipal library and the Friche Arts Centre have nothing to do with either theatre or opera

Nothing about vandalism. I also left a message on her talk page, not here, but she didn't see fit to mention that. In Michellecrisp's case it is very hard to assume good faith any more. As an act of kindness, mathematical editor User:R.e.b. tried to remove one of her provocative edits from my talk page (where she had left a comment about something that was none of her business). She rudely reverted it. [55] How can one assume good faith in such circumstances? Mathsci (talk) 11:38, 24 April 2008 (UTC)
Nothing about vandalism? you use that exact word here [56] Michellecrisp (talk) 11:44, 24 April 2008 (UTC)
I said "effectively vandalism" on your talk page, because you had effectively vandalised the article by making a foolish edit. I will try to get a mathematics adminstrator to archive this discussion to stop your trolling. The Municipal library is not a theatre, Michellecrisp. A visual arts centre is not a theatre or an opera house, Michellecrisp. Yet that is what your edits implied. You now come her complaining that somebody reverted these edits as "capricious". Kindly stop trolling and gaming the system. Resume your mainspace editing and stop wasting other people's time. Mathsci (talk) 12:01, 24 April 2008 (UTC)
Report me if you think I have violated Wikipedia policy because you keep wanting to, not sure why you haven't already, that's unless you're gaming. Others (not just me) above have commented on your lack of consideration and civility. I have not engaged invandalism or trolling, check the article in question or edits of any article that I've edited. the Aix reference seemed to be an official tourist guide not some "rubbish" this is where you really display lack of good faith and display WP:OWN by saying I've been there, therefore I am better. If it is an unsatisfactory reference then edit it out and let it be, not persist with this personal vendetta. your statement regarding "unless you have comments to make on mathematics" is another classical piece of WP:KETTLE, because you've spent the previous paragraph discussing your French article edits. I have made some contribution in terms of references to both the Aix en Provence and Marseille articles such as this [57] that have not been removed. Anyone else see the aggression and personal attacks in Mathsci comments? And let's not forgot his wikistalking on the [58] Mount Isa article. Michellecrisp (talk) 11:24, 24 April 2008 (UTC)
What is it that you don't understand that you don't understand about, Please stop following me around? Leaving gratuitous "busybody" messages here and on my talk page seems like provocative disuption. Please stop this, no matter how much pleasure it may give you. I'm still extremely busy editing mathematics articles. Get on with your own mainspace editing instead of making a nuisance of yourself here. Mathsci (talk) 11:44, 24 April 2008 (UTC)

You basically character assassinate me above accusing me of trolling and vandalism yet not reporting me, and I see fit to defend myself with evidence, that is permitted. Perhaps if you never even wrote about this today (seems you had the time to write a few paragraphs), I wouldn't have responded. simple. Michellecrisp (talk) 11:49, 24 April 2008 (UTC)

The diffs I provide above, with explanations, tell WP editors all they need to know about your currently not-quite-rational and seemingly emotional behaviour. I also would ask you please to leave this page if you only want to discuss edits to Aix-en-Provence and Marseille. You are deliberately trying to prolong a discussion ended by Oded Schramm. BTW I have never made any attempt to analyse your character, only your edits. Mathsci (talk) 12:13, 24 April 2008 (UTC)
P.S. It was you who posted after Schramm's winding up. What you wrote was nonsense, Now please just go away. I am currently preparing the section on hypergeometric functions from the original article in German. Your trolling here is a completely unwanted and irritating distraction. Mathsci (talk) 12:17, 24 April 2008 (UTC)

## "Formally defined"

Many maths articles contain a phrase like "X is formally defined as Y". Does this have a different meaning than just "X is defined as Y", or is the word "formally" noise? Its use here does not correspond to any of the meanings listed under Formal#Mathematics.  --Lambiam 20:55, 8 April 2008 (UTC)

Can you give a few examples? I can imagine that in some situations one would say "X means this and that, but is formally defined as Y", because the first definition, while not entirely precise, might be helpful in conveying some intuition better than "Y". Oded (talk) 21:09, 8 April 2008 (UTC)

I think "formally defined as" is shorthand for "if you're looking for a high-level explanation, go ahead and skip this part". --Trovatore (talk) 21:10, 8 April 2008 (UTC)

I tend to agree it's often just noise, and in those cases I remove it as part of copyediting. For example,
A function is injective if distinct inputs are always mapped to distinct outputs. Formally, this means that if f(a) = f(b) then a = b.
Here the "formal" definition is no more or less formal than the other definition, it is just written using symbolic notation. I think it's a misperception among some writers that mathematics can't be rigorous or formal without using a lot of complicated symbols.
On the other hand, sometimes an article will have a nice intuitive explanation in the lede, and a more technical definition lower down. In that situation, it makes sense to indicate that the first "definition" is only intended to be approximately correct, and that the other one is the "formal definition". Combinatorial species and Universal property are examples of this type of article. — Carl (CBM · talk) 22:06, 8 April 2008 (UTC)

I can point to Matrix (mathematics)#Matrices without entries (which I contributed) where it says that "matrices should formally be defined, [...] as quadruples (A, r, c, M), where A is the set in which the entries live, r and c are the (natural) numbers of rows and columns, and M is [...] the matrix in the usual sense". A clear case where the formal definition is meant to coexist with, and differ from, the usual definition Marc van Leeuwen (talk) 07:16, 9 April 2008 (UTC)

An example is the first sentence of Complex number: "In mathematics, a complex number is a number which can be formally defined as an ordered pair of real numbers ...". This cannot be a case of a more precise definition after an intuitive one. (Personally I also think this is a bad way of introducing the concept; I once wrote a beautiful lede, but unfortunately other editors were not capable of recognizing its beauty.)  --Lambiam 17:26, 9 April 2008 (UTC)
That's a good example of a bad use of "formally defined". Although complex numbers can be represented as pairs of reals, there are other ways of defining the complex numbers (some are discussed lower in the complex numbers article) that don't require first defining real numbers. So to say they "are defined" that way is misleading. — Carl (CBM · talk) 17:45, 9 April 2008 (UTC)
To say that something "is defined" in a certain way never means that that's the only way to do it. And complex numbers do very frequently get defined in that way. Michael Hardy (talk) 17:47, 9 April 2008 (UTC)
It's a matter of context. If I say that a group "is defined" to be a set with an associative binary operation with identity and inverses, what I am trying to convey is that, for all practical purposes, this is the only definition of a group that one is likely to encounter. (Of course there are other definitions, such as a category with one object and every morphism invertible, but they are much less common). But that isn't true for the complex numbers; the representation as pairs of real numbers is akin to taking coordinates, but a coordinate-free viewpoint is equally important. Anyway, in that article, it is easy to rephrase the lede in a way that I think everyone can agree with. — Carl (CBM · talk) 18:20, 9 April 2008 (UTC)

To me it seems like a typical case of a precise definition that might follow a more intuitive one (but what precedes it in this case, I don't know; I haven't looked yet). Michael Hardy (talk) 17:46, 9 April 2008 (UTC)

I'm surprised by Carl's observation that complex numbers can be defined without first defining real numbers (although if one really wants to it is not hard, for instance as a topological closure of the "Gaussian rationals", but I cannot see any reason why one should do so). Note that Complex number#Characterization as a topological field is about characterising complex numbers, not about defining them, and nothing else I saw inthe article tries to forget about real numbers first. But this is probably beside the point of the current discussion. Probably you just meant to say complex numbers can be defined in other ways than by defining arithmetic operations on R2, which of couse is quite true. Marc van Leeuwen (talk) 12:07, 11 April 2008 (UTC)
Every definition is, ultimately, no more than a characterization that fixes the definiend up to isomorphism.  --Lambiam 00:09, 12 April 2008 (UTC)
Is that definiendum or definiens? JRSpriggs (talk) 06:40, 12 April 2008 (UTC)
Definiend is an English form for Latin definiendum, like operand for operandum, solvend for solvendum, and so on.  --Lambiam 19:58, 12 April 2008 (UTC)

Hi, I am new to this section, having only very recently started to venture beyond spelling/grammar copyedits into deeper problems such as where rigour might rigourously require a 'form' (representation) that might not be strictly correct English grammar/spelling.

Right here right now what draws me into this piece of the page is wondering whether formal refers to form as in such things as G. Spencer Brown's "Laws of Form", or in such ideas as tokens, symbols, and representations?

Because, if it does, then the English gloss which is followed by the use of the term 'formally' and a representation in a 'form' (maybe even a 'formal system' in a Godelian sense???) makes sense to me, as it seems potentially to be saying that the English representation is not, or might not, be as 'formal' (in a Godelian sense even, maybe? Executable? Machine-readable? Machine-executable?) as the (possibly rigourous???) representation by means of a 'form' involving symbols rather than words.

Mind you, this ambiguity or potential ambiguity might be addressable by means of writing 'represented in [label of formal system aka 'form in the G. Spencer Brown sense'] as' instead of using the token or word 'formally'.

That is, maybe a distinction could be useful between 'formally' and 'in a form' (aka in a specific 'form', such as algebraic form or LISP form or FORTRAN form or C++ form or oilpainting form or whatever form one is about to use...)

Knotwork (talk) 10:59, 18 April 2008 (UTC)

## Definitions in mathematics

Although this is a reply to a remark above I prefer to start a new section, as I am drifting away from the original discussion. I quote the remark:

Every definition is, ultimately, no more than a characterization that fixes the definiendum up to isomorphism.  --Lambiam 00:09, 12 April 2008 (UTC)

I disagree here, whether really every definition is meant, or just those of the complex numbers. For one, this gives too much importance to category theory, as if it were that one cannot define something before one has introduced a category first in which it is to live (so that "up to isomorphism" makes sense). As for the complex numbers, I'm not sure what that category should be; topological field seems to capture most uses of complex numbers, but I would hesitate to claim it allows expressing all important aspects of complex numbers. Second, there is a difference between on one had definitions of the complex numbers like R2 equipped with a ring structure, or as R[X]/(X2+1), or as a subring of the real 2×2 matrices, and on the other hand characterisations like being the algebraic closure of the real numbers, or a particluar kind of topological field. The former are three really different definitions, even though one could do with any one of them because correspondences between the representations are easily established. The latter are two different characterizations of the complex numbers as an object in two different categories, and each determines the complex numbers only up to isomorphism in that category (and not even up to canonical isomorphism, because neither caracterization distinguishes complex conjugates). A characterization does not necessarily prove that anything exists that meets its requirements (even if often, as in case of algebraic closures, one knows this to be true). One of the points of category theory is that in many cases one does not have to, or want to, worry about which precise definition is used, since many questions only require knowing the object up to isomorphism; this is why one often characterizes structures as universal objects. But not everything in mathematics takes place within category theory, and in certain cases there is a choice between constructions that does not appear to related to isomorphisms in any particular category (think of constructions of the natural numbers or the real numbers).

There is an important lesson to learn here for wikipedia. Whether for reasons of category thoery or other reasons, one is in mathematics often less interested in what things are than how they behave (or are related), so several viewpoints about the former question can peacefully coexist (one one may even hold that it is immaterial what something is). However a wikipedia article, and particularly its lede, normally focusses on its subject itself, rather than on the context in which it appears, which gives a conflict with what one would like to do mathematically. I've seen long discussions along these lines in Talk:Polynomial and Talk:Complex number and they probably exist for other articles as well. However, I don't see any easy solutions; if one wants to cater for a broad and not necessarily knowledgeable public, one cannot just begin with saying that the structure is really all that matters: I'm sure that starting "A polynomial is an element of a polynomial ring" would put a lot of people off. (In the case of polynomials there is a separate article on polynomial rings, but there seems no point in having a separate article on the field of complex numbers.) It would maybe be interesting to have a discussion about guidelines how to handle this kind of question in general. Marc van Leeuwen (talk) 12:30, 12 April 2008 (UTC)

One issue I find interesting is that for certain objects, such as natural numbers, we begin with a naive understanding, and formal definitions are only valid to the extent that they accurately represent the naive version. This is particularly blatant for topics like 1 (number). It would be absurd to start that article with the sentence:
In mathematics, 1 is the set ${\displaystyle \{\varnothing \}}$.
even though that is an extremely common and important formal definition of the number 1. At a certain level of sophistication, which I don't think it precisely defined, we no longer have naive understandings of things, and so the definition and the object itself become identified. Banach algebra is at this level of sophistication.
The first sentence from Natural number makes me smile:
In mathematics, a natural number (also called counting number) can mean either an element of the set {1, 2, 3, ...} (the positive integers) or an element of the set {0, 1, 2, 3, ...} (the non-negative integers).
Despite being circular from a technical point of view, I think this sentence is able to convey the naive understanding of natural number to almost every reader. — Carl (CBM · talk) 17:58, 12 April 2008 (UTC)
Category theory offers a way of formalizing many situations, but certain observations about mathematical constructs that can be conveniently expressed in the language of category theory do not depend on category theory for their validity. Whatever the "behaviour" of complex numbers, the blue complex numbers are not behaviourally distinguishable from the red complex numbers, and in he ordered-pair representation we can have (a,b) in one representation for (b,a) in another – and isn't (a,b) actually {{a},{a,b}}, or is it {{0,a},{1,b}}?
Although articles usually start with a definition of the subject, it is usually not a definition in the mathematical sense. Rather than following some format mechanically, I'm all in favour of the presentation that best brings the essence across. If that requires a variation on the "X is Y" format, let's be flexible about it.  --Lambiam 20:42, 12 April 2008 (UTC)

Part of what brought me to this project is that the structure of the math pages I wandered into from the quantum mechanics pages has so far subjectively seemed to require maybe too many pages open in my browser at a time due to so darn many terms I need to grasp to get anywhere in all this sea of knowledge. It has started to seem to me that it would help if there were a more blatantly obvious way to get enough overview into me faster. I seem to vaguely recall way back when, once upon a time, somehow Wikipedia had managed to reasonably succinctly get across to me some kind of general idea of the shape of the dependency tree of the math terms such that I was reading about rings and ring theory and entanglement and so on nice and easy. Now I have over thirty pages open digging deeper and deeper looking to grasp this stuff and still have not come across anywhere where it maps out for me some kind of an 'up to' sequence that would allow me to navigate it all better. It seems to me this is part and parcel of the general problem of mathematicians assuming too much background on the part of the reader instead of developing concise succinct background-providing preambles that will bring the reader up to speed as efficiently as possible.

It occured to me that I might be a good example of a kind of person the pages should be accessible to, yet for some reason this year I am finding them less accessible than they were a year or few ago.

Maybe motivation is part of it. When I click to a page I am motivated by the page I am actually trying to read, whereas the page I have clicked through to might have such a totally different motivation that it maybe doesn't nicely address the reader who was sent from where I was sent from. I am not ready to go so far as to suggest that it would help to have dynamic pages that re-arrange themselves based on the referring URL so as to be maximally useful to someone who has just come from that specific referring URL, but by mentioning this hypothetical prescription I might get across a sense of part of the problem I am having. I am pretty sure by now, having already closed many more pages than I still have open, that this process of clicking a hypothetically explanatory link is looking like a non-converging algorithm: it does not seem to be leading me toward an understanding of what motivated my click, instead it seems to be exploding out farther and farther from relevance to where I started.

Part of that will be me having a hyperactive reticular activating system or some such: my own reaching too far into irrelevance. But gosh darn it isn't there at least some kind of heirarchy or collection of different proposed heirarchies for what is really needed to understand which parts of what? I wonder if the 'up to' idea, or something like it, might help sequence the portions of maths pages, so that (for a hand-waving not necessarily good example) as you read down the page you don't reach "up to isomorphism" until you read far enough down the page ('down to isomorphism'? ;)). Heck, no use I have yet seen of the phrase "up to isomorphism" has even taken the trouble to inform me as to whether that is farther up than "up to simple arithmetic", "up to computability", "up to long division", "up to multiplication", "up to the discovery of calculus" ("by Issac Newton in such and such a century"? ;))", and so on. Like, how far up is isomorphism? What is next up from it, what is one down from it, what is left of it or beside it etc etc etc? (Which direction is up?!?!?! Is there a sequence, order, heirarchy, or graph indicating what is upward, downward, whateverward of what?)

Maybe the pages should go like "up to primary school, blah blah blah; up to high school etc etc etc; up to 1984 (Bell et al) etc etc etc; whereas if allowed down to Godel then of course (complete? formal? etc)" and so on (up to the bleeding edge... ;))

Knotwork (talk) 11:47, 18 April 2008 (UTC)

## No abbreviations! (?)

At Wikipedia talk:Citing sources, under the heading "We shouldn't abbreviate journal names", I posted this:

We often read that something was published in J. Am. Phys. Soc. or something like that. That's standard in scholarly journals. I'd prefer to have a policy against such abbreviations, in favor of writing Journal of the American Physical Society instead. Wikipedia does not have the limitations of print journals, and hence doesn't have the need for such abbreviations, and often there can be uncertainty about the name of the journal, especially when it's not in one's own field. If such a policy were established,[...]

A somewhat long discussion has gotten underway there. Perhaps some who take part in this WikiProject can contribute their wisdom. Michael Hardy (talk) 20:35, 15 April 2008 (UTC)

Embarassing question: Is there some kind of central online repository of mathematics journal abbreviations? I mean, most of them are obvious. But some of them, particularly the non-English ones, really give me a hard time. silly rabbit (talk) 21:10, 15 April 2008 (UTC)
MathSciNet has such a facility, if you can access it. Ryan Reich (talk) 21:18, 15 April 2008 (UTC)
I think the list is actually publicly released, on this page. — Carl (CBM · talk) 21:23, 15 April 2008 (UTC)
Embarassing question No. 2: Is there some standard for journal abbreviations in science, not just math? Thanks. Jmath666 (talk) 04:10, 16 April 2008 (UTC)
Well, there's the Web of Science list of journal title abbreviations. Not sure if all can access it or only subscribers. Qwfp (talk) 05:39, 16 April 2008 (UTC)
There is no standard. MathSciNet abbreviates "Proceedings of the American Mathematical Society" as "Proc. Amer. Math. Soc.", Zentrallblatt MATH uses "Proc. Am. Math. Soc." and Web of Science uses "P AM MATH SOC". -- Jitse Niesen (talk) 10:36, 16 April 2008 (UTC)
I've seen other lists of abbreviations, as well. I strongly suggest avoiding abbreviations: I've had trouble tracking down citations for just this reason several times, and I don't think I'm unusual in that respect. We can afford the space. CRGreathouse (t | c) 13:54, 16 April 2008 (UTC)
The AMS maintains a list of abbreviations at [59]. 83.112.134.6 (talk) 21:36, 16 April 2008 (UTC)

...and the fact that it is the AMS, a specialized organization, rather than something like the Library of Congress, seems to suggest there is no standard that applies simultaneously to mathematics, geography, theology, sociology, etc., so they're best avoided. Michael Hardy (talk) 00:02, 17 April 2008 (UTC)

Two comments: (1) Acronyms must be expanded on first use; shouldn't abbreviations, too? (2) If they were made into links to each journal's own encyclopaedia-entry page, they could be clicked on to find out not only the full name but maybe even where to find them, how authoritative they are regarded (if not enough to warrant a page of their own why mention them at all?)

Knotwork (talk) 14:37, 18 April 2008 (UTC)

## Synergetics coordinates

Synergetics coordinates. Merge into barycentric coordinates? Michael Hardy (talk) 03:26, 17 April 2008 (UTC)

No, correct it instead. From a quick look at

, this seems to be a different thing though somewhat related. Jmath666 (talk) 04:37, 17 April 2008 (UTC)

I've redirected it. Maybe the target page ought to get moved to synergetics coordinates? Michael Hardy (talk) 05:02, 17 April 2008 (UTC)

Does the Bary in Barycentric coordinates have any relation at all to the Bary in Baryon (physics)??? Knotwork (talk) 12:09, 18 April 2008 (UTC)

Seems likely. If we believe Wiktionary, the etymology of baryon is from Greek βαρύς "heavy" and the etymology of barycentre/barycentric is from from Greek βάρος "weight". So the first is a "heavy one" and the second is a "centre of heaviness". Gandalf61 (talk)

## Linkifying (e.g. as in s/Consistent/Consistent/)

Recently User:Gregbard apparently decided that it would be a good idea to link every occurrence of the word consistent on Wikipedia to the mathematical logic article Consistent. The user has stopped, but since he was using AWB, there are about 100 edits to revert in my estimation. Anyone want to help out? silly rabbit (talk) 12:04, 18 April 2008 (UTC)

Hmm this sounds like skirting the edge of an idealised need for all words to in principle be clickable (tho not necessarily visually-cued as being so) for details as to which of the definitions in which dictionary the author actually intend{s|ed} by that specific use of that token. If there is any chance that the token/word wasn't meant in the mathematical-logic sense, which sense was it intended in? Is a disambiguation page called for?
Similar to my mention earlier of pages varying based on referring URL, maybe ideally it'd be nice if mathematicians viewing pages that don't mean mathematical-logic consistency when they use that token would automagickally link to whichever other possible interpretation of that token seems most likely to be the default interpretation in general usage within whatever field the article is purported to belong? (Is 'Consistent (International Law)' identical to 'Consistent (Pre-1776 Confederate Law)', 'Consistent (Godel)', 'Consistent (Colloquial English(U.S.A.))', 'Consistent (Colloquial English (Ireland))' etc etc etc?)
Knotwork (talk) 12:19, 18 April 2008 (UTC)
Indeed, in nearly all of the edits, the word was not meant in the mathematical-logic sense. The basic threshhold in the Manual of style (links) is that a link should be relevant to the context. Thus, although consistency in the legal sense may (to a logician) be the same thing as consistency in the sense of mathematical logic, a legal article should not have a wikilink from the term to a logic article. In fact, even in some mathematics articles, the term is used in a completely different sense than the logical one, and this creates a real danger of confusion if the word is linked to another (different) definition. silly rabbit (talk) 12:36, 18 April 2008 (UTC)

response copied from my talk page

[...] I am working through a rather large list at a steady clip. I am not wiki-linking every one. There are some that refer to consistency as texture, consistency in databases, consistent performance at a task, etc. I am avoiding those. Feel free to revert any you think are gratuitous --HOWEVER... I do not agree with a very strict interpretation that only the technical sense is worthy. I would like for people who use logical terminology in common discourse to become more aware of it, and use it correctly. Wiki-linking these common English usages will help bring logical concepts closer to the average person's understanding. Be well, Pontiff Greg Bard (talk) 12:27, 18 April 2008 (UTC)

end of paste

Actually, I am gradually going through the most important terms (Using Template:logic as a rough guide), and making sure that they are wiki-linked as appropriate, as I have done in the past. As usual, my view is not as narrow as some others. Consistency is not exclusively the domain of math (and yes I mean that "consistency"). Be well, Pontiff Greg Bard (talk) 12:46, 18 April 2008 (UTC)
Large-scale edits AWB campaigns like this should, in my opinion, be done with community sanction. Also, please read WP:MOSLINKS for general guidelines on when to make wikilinks, and also see WP:MOSQUOTE (please don't add wikilinks into direct quotes). silly rabbit (talk) 12:59, 18 April 2008 (UTC)
To respond to the other part of your post, although it is true that "consistency" is not exclusively the domain of math, the article consistency is a mathematics and logic article. Links to this article should only be made when the context indicates that the author's intention was for the term to be used in this rigorous sense. silly rabbit (talk) 13:14, 18 April 2008 (UTC)
Neither WP:MOSLINKS, nor WP:CONTEXT has any guideline as narrow as the one you have enunciated. This is not a math encyclopedia, it a general audience reference. It seems to me that an author should mean what he writes. I don't disagree with some of your reverts, but certainly not over 100. That's a narrow view, and I think we are better served by a broader view. Be well, Pontiff Greg Bard (talk) 13:29, 18 April 2008 (UTC)
Gregbard frequently goes through to add links to math articles, and generally the links he adds are just fine. In this case, there were a few articles he linked that I would disagree with (Australia-United States Free Trade Agreement) but most of the links are fine technically. If anyone disagrees with a particular edit they can of course undo it; I think Silly rabbit has undone several.
I agree with Silly rabbit that the math article should only be linked if that is the sense intended - in particular, only if there is a formal system at hand. — Carl (CBM · talk) 13:22, 18 April 2008 (UTC)
this was accidentally deleted, so I restored it at the end.— Carl (CBM · talk) 13:48, 18 April 2008 (UTC)

I like Gregbard's idea that encouraging awareness of the potential for rigour is a nice idea, that is part of why I mentioned the idea of a disambiguation page. That way instead of always reverting links that are not intended to mean mathematical consistency one can turn them into hints that the word is possibly too ambiguous. This need not be a blanket thing for all usages of the token but could be used in regions where a reader might reasonably wonder just how rigourous or colloquial or texture or industriousness -related the term is intended to be or to be taken to be. Basically if someone took the trouble to try to make the token into a link maybe it'd be better to [put in the additional work of making the link be the correct link] than to [revert to no link]. (I hope that is legible. ;)) Knotwork (talk) 16:09, 18 April 2008 (UTC)

I have twice now encountered terms I wanted to know the meaning of, found that the token matched a Wikipedia page if turned into a wikilink, but lacked the formal rigourous content knowledge to know whether maybe the author might even have deliberately not made it a link due to actually not intending the token to be interpreted by means of the article found at that link. For example, look at section 7 of Universal algebra, it uses the term 'free algebra' but does it actually mean free algebra or is it trying to use that token to denote some other notion? In the other instance I went and ranted/rambled/whatever on the talk page of the offending page, and even plugged in that nice new talk-page macro to try to bring it to your attention. But I was not (likely still am not) sure whether its best to mention it here so project people will know, or mention it on the offending page's talk page where anyone and/or their pet might stumble upon it. It even occurs to me the answer might differ depending on whether the offending page has the adopted-by-this-project logo/infobox on it... Knotwork (talk) 16:35, 18 April 2008 (UTC)

I reverted one in the title of a physics paper that seemed completely irrelevant. If the rest are as bad, he should be told to stop. —David Eppstein (talk) 17:07, 18 April 2008 (UTC)
To answer a specific comment unrelated to the section heading: The usage of "free algebra" in the article on universal algebra is much more general than the usage on the free algebra page. Linking from universal algebra to free algebra would likely be more confusing than useful (roughly equivalent to linking to the article on 65535 (number) instead of the article on number; it is accidental that the most common usage of "free algebra" is more or less a random type of "free algebra" in the universal algebra sense). However, the lead of the free algebra article indicated its usage was all throughout abstract algebra, which should probably have been taken to include universal algebra. I specified the context a bit more narrowly ("ring theory") but left open the idea that it is used more broadly in mathematics (it is, but to refer to the ring theory concept, algebra (ring theory)). JackSchmidt (talk) 17:12, 18 April 2008 (UTC)
Luckily someone had already given a very stub class article on free algebras in universal algebra. I wikified it a little, and put something new in the lead. I'm not sure now if you want to link or not. Right now the article is just an unsourced definition (that I have not checked for accuracy). However, at least now if someone searches for "Free algebra" to see what it means, they will be advised of the two similar usages, and hopefully will manage to click on the right set of wiki links (the ring theory set, or the universal algebra set). JackSchmidt (talk) 17:22, 18 April 2008 (UTC)

Thanks! (unrelated? oops... better now? ;)) :twisted: Knotwork (talk) 17:24, 18 April 2008 (UTC)

Another issue with automatic links is that they can miss context. For example, one link that was added to "relative consistency" should really be to "relative consistency". So the manual approval part of AWB does need to be done right. But in general I have found Gregbard's links are generally fine. They show up on my watchlist from time to time. I think these are an exception to previous edits rather than the normal situation. — Carl (CBM · talk) 17:27, 18 April 2008 (UTC)

Still trying to get an overview of relations/dependencies between terms, I found List_of_first_order_theories and found similar 'should these be links?' issues in the section on second order theories, the tokens involved being 'Robinson arithmetic', 'induction' and 'comprehension'; and ranted/rambled about it at Talk:List_of_first-order_theories Knotwork (talk) 17:57, 18 April 2008 (UTC)

## Dwyer function ?

The function D(x,y) has been studied by several university project students in Combinatorics & Graph Theory in the context of Euler Circuits and rapidly-increasing functions. They have sought to create and edit pages related to it and the idea use of using the name "Dwyer" was theirs and not mine. For my part (Dwyer) I have read around various mathematical functions pages, including wiki, hoping to suggest any inaccuracies and to make cross references where appropriate, an activity which I would not consider self promoting. [User:Dwyerj]

Fairly new editor User:Dwyerj created a new article called Dwyer Function. The obvious issues with title capitalisation and formatting could be fixed, but my main concern is that article does not cite a reference to show that this function is known by this name. A quick Google search turned up nothing relevant. I put a note on the editor's talk page to suggest that they provide references if they have them. In the meantime, has anyone else heard of this function under this name ? Gandalf61 (talk) 08:24, 18 April 2008 (UTC)

Dwyerj (talk · contribs) appears to be mainly concerned (so far) with writing his own autobiography, John Dwyer (Professor), which might be considered to be a conflict of interest (in addition to his original research on various articles). JRSpriggs (talk) 08:43, 18 April 2008 (UTC)

The algana link duplicate has been notified and should be fixed soon.[User:Dwyerj]

I haven't turned up anything, but the link provided by Dwyer is to papers from March and April 2008. They are apparently self-published or at the least, not reviewed. The first states that it is introducing a new function D(x,y). So apparently this is new. The second introduces the term "Dwyer's function" in the abstract (although the link to the pdf is to a duplicate of the first article). Two possibilities: 1) Dwyer has, in rapid fashion, simply named the function after himself. 2) Dwyer has delayed writing about this function and in the meanwhile some people call it the Dwyer function; however, no mention of "Dwyer function" or "Dwyer's function" (in this sense) appears in the literature because either it or its name is not notable. --C S (talk) 18:05, 19 April 2008 (UTC)

## Singular Integral

Singular Integral redirects to singular measure, this seems a little off to me. The phrase "Singular Integrals" usually refers to a subject in its own right. For example, the classic reference is "Singular Integrals and Differentiability Properties of Functions. (PMS-30) by Elias M. Stein (Hardcover - Feb 1, 1971)". Does anyone object to deleting this redirect? —Preceding unsigned comment added by Thenub314 (talkcontribs) 14:31, 18 April 2008 (UTC)

Not at all. Please start this important article, if you feel up to it. The redirect is offbase. silly rabbit (talk) 14:40, 18 April 2008 (UTC)
I spoke too soon. There already is an article singular integral, which is on the subject in question. I have adjusted the redirect. silly rabbit (talk) 14:44, 18 April 2008 (UTC)
Excellent. The authors did good work it is a nice beginning. Perhaps we should set up a redirect from Singular Integral Operator to this page. Some pages seem to have a reference to this not existent page. Well, at least one page did, and I fixed it today. But other pages might, and it sounds like a good idea to me.Thenub314 (talk) 18:53, 20 April 2008 (UTC)
Just a note: article names are case-sensitive (except for the first letter). For instance Differential Operator is a redlink, but Differential operator is an article. Of course, neither Singular Integral Operator nor Singular integral operator is linked (as of this writing). silly rabbit (talk) 18:57, 20 April 2008 (UTC)

I've just created Differential Operator, with a capital "O", as a redirect page. I'd do the same for Singular Integral Operator if there were not an obnoxious policy of considering redirects created before their target pages to be "broken". (The manner in which that policy got established was dishonest, and those who cheated won in this case.) Michael Hardy (talk) 19:06, 20 April 2008 (UTC)

OK, now I've created the latter redirect page. Let's see how long it lasts. Michael Hardy (talk) 19:08, 20 April 2008 (UTC)

## Relating important tokens

I seem relatively frequently to have observed recurring tokens, such as class, group, sheaf, function, set, topos, and various others.

Some tokens seemed to, or were even explicitly stated or defined to, provide or implement the relating of tokens or to be useful for relating tokens.

For example at Inventio#Topoi I found 'In classical rhetoric, arguments are obtained from various sources of information, or topoi (from the Greek for "places"; i.e. "places to find something"). Topoi are categories that help delineate the relationships among ideas; Aristotle divided these into "common" and "special" groups.'

Another example: at Literary_topos I found "Ernst Robert Curtius expanded this concept in studying topoi as commonplaces: reworkings of traditional material, particularly the descriptions of standardised settings, but extended to almost any literary meme. Critics have traced the use and re-use of such topoi from the literature of classical antiquity to the 18th century and beyond into postmodern literature", which seems (prima facie?) potentially somewhere in or near the-or-a neighborhood of some kind of WP:V guideline or policy or at least a possible leaning in some such direction. (Hmm, seeds that eventually grew, in one of more of our pastward-lightcones, into such constructs, objects, observables (or some such notion?) as WP:V ???)

At Dispositio I found "The first part of any rhetorical exercise was to discover the proper arguments to use, which was done under the formalized methods of inventio. The next problem facing the orator or writer was to select various arguments and organize them into an effective discourse." and "Finally, dispositio was also seen as an iterative process, particularly in conjunction with inventio. The very process of organizing arguments might lead to the need to discover and research new ones. An orator would refine his arguments and their organization until they were properly arranged."

Might some kind of tables be useful to persons attempting such tasks as discovering the proper tokens (or maybe even arguments) to use? For example at Scheme (mathematics) I found "a scheme is an important concept connecting the fields of algebraic geometry, commutative algebra and number theory", at Inventio I found

Aristotle, in his works on rhetoric, answered Plato's charges by arguing that reason and rhetoric are intertwined ("Rhetoric is the counterpart of Dialectic" is the first sentence of his Rhetoric). In Aristotle's view, dialectic reasoning is the mechanism for discovering universal truths; rhetoric is the method for clarifying and communicating these principles to others. And in order to communicate effectively, an orator must be able to assemble proper arguments that support his thesis. Inventio, therefore, is the systematic discovery of arguments. Aristotle, as well as later writers on rhetoric, such as Cicero and Quintilian, devoted considerable attention to developing and formalizing the discipline of rhetorical invention. Two important concepts within invention were topoi and stasis.

At Inventio#Stasis I found "The procedure known as stasis was another important part of the invention process. This involved the practice of posing and exploring questions relevant to clarifying the main issues in the debate. There were four types of stasis: definitional, conjectural, translative, and qualitative", in which (to my mind 'unfortunately' but what do I know?) the four tokens 'definitional', 'conjectural', 'translative', and 'qualitative' all lacked clickability (aka were not wikilinks/wikilinked), leaving me to wonder what kind of translations, between what categories, groups, sheafs, arithmoquines, or whatevers the token 'translative' might (or might not) denote or refer to translations (or some such notion?) between (aka relations between?)

Imagine a two-dimensional table (e.g. in the HTML sense) such that its rows and columns are labelled using 'offending or potentially offending tokens' and whose cells contain symbols indicating properties of the intersection of their column with their row and/or their row with their column, such that, for example, the labels might include 'common ideas', 'special ideas', 'categories', 'classes', 'sets', 'arithmoquines', etc etc etc, including in particular the four tokens 'scheme', 'algebraic geometry', 'commutative algebra', and 'number theory'. Might the previously-quoted text from Scheme (mathematics) hint that the cells at the intersections of the columns and rows labeled by these four labels might reasonably be expected to be potentially usefully populable with data derived from some such construct as the page located at Scheme (mathematics) ??? The naive intuition here is that if there is, as that page seems to imply, some useful relation or relating possible between those four terms then there might well, in principle, be potential utility in assigning symbols or tokens to relations, types of relations, families, species, geni, groups, categories, or some such notion(s), with which to populate some such table, whereby to construct a reference table succinctly and/or concisely indicating which tokens usefully or potentially-usefully relate to which tokens by what manner (or category, or class, or family, or species, or genus, etc etc etc) of relation.

Knotwork (talk) 04:10, 19 April 2008 (UTC)

Similarly/relatedly, imagine a function, maybe even representable in C or C++ or some such language/representation/form with the ... final argument indicating it could accept more arguments, into which one inputs the tokens one is interested in relating, and that returns as result a (maybe even 'the' in some sense or context or some such notion) token which refers to the art and/or science of relating precisely the tokens that were provided as input... Knotwork (talk) 04:30, 19 April 2008 (UTC)

Now: given such a function, maybe the token 'original research' as used at fictonics can be worked-around by means of plugging the token fictonics or the token ficton ("or some such token"? ;)) into some such function, possibly accompanied by one or more other tokens that might occur to one or more occurrers or occurences or implementations or results ("or some such notion? ;)) of [something?] ??? Knotwork (talk) 04:39, 19 April 2008 (UTC)

KW, not to be too rude, but is there in fact some coherent idea that you think is conveyed by the above mass of text? Or are you just putting us all on, Social Text style? --Trovatore (talk) 04:44, 19 April 2008 (UTC)

Probably more than one, if any. Some candidates might include "research is historically citably purported to be expected in the creation of a text" and "if that research is not original then what is? (are there possible answers other than 'a random agglomeration of tokens' and 'a non-original agglomeration of tokens aka mere quotation and/or plagiarism'?) I gotta go look up Social Text... Knotwork (talk) 05:00, 19 April 2008 (UTC)

Does this have something to do with building an encyclopedia describing standard known mathematical material? If it does, I can't discern what it is. We're not here for philosophical maunderings. —David Eppstein (talk) 15:16, 20 April 2008 (UTC)
I agree. Knotwork, you are welcome to use Wikipedia as a source for learning about mathematics. You are also welcome to learn it from books and then to contribute constructively to Wikipedia articles about things that you have (at least approximately) understood. But I am afraid that's not what you are doing [60]. Now a lot of experts will have to go over your past contributions and remove all your misunderstandings that you have introduced into articles. --Hans Adler (talk) 15:39, 20 April 2008 (UTC) OK, it's not as bad as I thought. I reverted you edits to abstract nonsense, but it seems you have done no damage to other mathematics pages, only grammar corrections. --Hans Adler (talk) 15:49, 20 April 2008 (UTC)

Re "Knotwork, you are welcome to use Wikipedia as a source for learning about mathematics. You are also welcome to learn it from books and then to contribute constructively to Wikipedia articles about things that you have (at least approximately) understood.": My feeling or belief seems to be that I would prefer to learn it from Wikipedia and then to contribute, in which construction adjectives applicable by append not necessarily by prepend to the term 'contribute' might include such adjectives as 'clarity', 'rigour', 'utility', 'computability', 'executability', 'efficaciously' (etc etc etc) Knotwork (talk) 17:49, 20 April 2008 (UTC)

Al? Is that you? silly rabbit (talk) 17:53, 20 April 2008 (UTC)
Taking the last paragraph of the above
Imagine a two-dimensional table (e.g. in the HTML sense) such that its rows and columns are labelled using 'offending or potentially offending tokens' and whose cells contain symbols indicating properties of the intersection of their column with their row and/or their row with their column, such that, for example, the labels might include 'common ideas', 'special ideas', 'categories', 'classes', 'sets', 'arithmoquines', etc etc etc, including in particular the four tokens 'scheme', 'algebraic geometry', 'commutative algebra', and 'number theory'. Might the previously-quoted text from Scheme (mathematics) hint that the cells at the intersections of the columns and rows labeled by these four labels might reasonably be expected to be potentially usefully populable with data derived from some such construct as the page located at Scheme (mathematics) ??? The naive intuition here is that if there is, as that page seems to imply, some useful relation or relating possible between those four terms then there might well, in principle, be potential utility in assigning symbols or tokens to relations, types of relations, families, species, geni, groups, categories, or some such notion(s), with which to populate some such table, whereby to construct a reference table succinctly and/or concisely indicating which tokens usefully or potentially-usefully relate to which tokens by what manner (or category, or class, or family, or species, or genus, etc etc etc) of relation.
If I understand correctly you would like to develop some sort of taxononomy of mathematical content. While this is a laudable aim, it is a giant undertaking and beset by problems. Indeed I would say that neither the universe of mathematics nor the world at large fits neatly into such a scheme. You might like to have a look at Ontology (information science) and related articles. Perhaphs Category theory may be to your liking. There is some attempt at structuring data in wikipedia but it is limited, possibly Lists of mathematics topics may be the most structured thing we have.
Should we include such a taxomony in wikipedia, in general I would say not. Wikipedia's primary representation method is links, which provide a graph structure, and the category system, which form a directed graph. This less formal systems is one of the strengths of wikipedia and considerably more flexible. Then we have the issue of original research if such a systems were developed it would amount to original research, unless it was a well established system used by wider mathematical world.
So if you wish to work withi the wikipedia system, by all means add links, articles, lists and work on improving our category system. Beyond that it is probably better developed off wiki. --Salix alba (talk) 18:26, 20 April 2008 (UTC)

## Managing prerequisites?

Hello everyone. I have a suggestion that might take a lot of work to implement, but I think it would be a tremendous improvement if implemented. Basically, it would be really nice if there was someway to manage the prerequisites needed to read a particular article. Basically, to read a lot of math articles on Wikipedia often require you to understand a number of concepts, abbreviations, even symbolic conventions in order for you to understand the article. Now, I'm fine with clicking on links in order to find the information, but in many cases this spirals out of control. For example, to understand article M, I need to read article N; to understand article N, I need to read article P; to understand article P, I need to read article Q, and so on. And, in even worst cases, this becomes circular: M requires N, N requires P, and P requires M.

What I have in mind is if you divide up all the math articles into a set of subjects: for example, elementary algebra, arithmetic, calculus, linear algebra, and so on. Then, within each of the subjects, you have a set of *base articles* which are then assumed to be understood as a prerequisite for all the other articles within that subject. Any concepts or conventions that haven't been introduced in any of the base articles would then need to be explained within any article that wants to use them. This can even be hierarchically arranged, so that calculus might depend on the base articles under algebra.

I think the arrangement of articles should be pedagogically based rather than mathematically based. That is, for the fourth-grader looking for help factoring a number into primes, he doesn't need to read what, for him, are confusing terms about matrices and polynomials.

Anyway, just a suggestion. — Preceding unsigned comment added by Parody of Language (talkcontribs)

"And, in even worst cases, this becomes circular: M requires N, N requires P, and P requires M": Just as in the real life. This is one the reasons why learning at school proceeds in a spiral fashion and it takes quite a few trips around to get to complicated concepts. WP:NOT. Same frustration here when I am trying to look up something I am not ready for. Still Wikipedia does a quick introduction into almost anything better than anything else I know.
Lead paragraphs should play the role of introducing the subject, at the level accessible to a fourth-grader, if possible. Or a section like Elementary description for this purpose.
Jmath666 (talk) 01:54, 21 April 2008 (UTC)

## Induced homomorphism

Induced homomorphism (meaning the homomorphism of fundamental groups induced by a continuous function of topological spaces) has been nominated for deletion. As it is now, it's just a dictionary-definition stub; it was even worse before I cleaned it up. If anyone thinks it's worth keeping as a separate article, I think adding some actual content beyond the definition (and references supporting that content) would be the way to go; right now, the same material is covered better in Fundamental group#Functoriality. —David Eppstein (talk) 18:38, 20 April 2008 (UTC)

I think this one should go. Induced homomorphism could mean so many different things in different contexts. For example, a proper coloring of a graph by k colors induces a graph homomorphism into the complete graph on k vertices. However, there is a more general issue (which I'm pretty sure must have been discussed): it is often the case that while writing an article you need to refer to some notion which does not warrant an article but does require a definition, and the insertion of the definition in the present article would not work well. The obvious solutions, such as having an article containing only a definition or having the definition as a subpage run contrary to WP style conventions, if I understand them correctly. Is there an established recommended solution to this issue? Oded (talk) 18:53, 20 April 2008 (UTC)
Actually, I would like to see an article on this. Admittedly, that's not necessarily an argument against deletion -- maybe there should be an article, but a clean start would be better. CRGreathouse (t | c) 20:33, 21 April 2008 (UTC)

## Substitution principle/substitution rule

Can someone (with a background in math) write a rigorous proof of the "substitution rule" or "substitution principle"?

As far as I know this principle applies everywhere... except for special cases in integration. I vaguely remember that one needs to use trigonometric identities to properly integrate certain trigonometric functions. Is there another case where it doesn't apply?

Thanks, Nephron  T|C 19:26, 20 April 2008 (UTC)

I have a background in math, but it is not clear what you want this article to be. Every thing I checked (approx 1/4 of the articles) that liked to this article really should have been linking to integration by substitution. I am guessing all should. Correct me if this is wrong. Your article seems trying to make the point that in algebra we may give names to quantities and operates with names as we would with the quantities. I was not aware this had a formal name.
Thenub314 (talk) 20:52, 20 April 2008 (UTC)
I agree. I have reverted Nephron's change to the redirect at substitution rule. Gandalf61 (talk) 12:05, 21 April 2008 (UTC)

## References for "Shallow water equations"

Shallow water equations includes a striking picture that has "featured" status, but the article has a "no references" tag. Does someone know what the most suitable references are? Michael Hardy (talk) 16:51, 21 April 2008 (UTC)

I can't answer your question, but I noticed the picture before and that there is no information at all about how it is produced. I really should go after it and either get somebody to fill some more details or get the featured status removed. -- Jitse Niesen (talk) 20:10, 21 April 2008 (UTC)

## Substitution principle (mathematics)

Sigh..................... Please look at Substitution principle (mathematics) and improve it if it's worth improving. Michael Hardy (talk) 05:24, 21 April 2008 (UTC)

I am strongly in favor of deleting the article. Thenub314 (talk) 11:44, 21 April 2008 (UTC)
It has been {{prod}}-ed. silly rabbit (talk) 11:52, 21 April 2008 (UTC)
Yes, I prod-ed it. I think it is a neologism - I have never heard this operation in elementary algebra called the "substitution principle", and a quick Google search showed up no relevant hits. Happy to be proved wrong if anyone can add a reference to the article !
User:Nephron created the article when they renamed the previous "substitution principle" article to substitution principle (sustainability). They also changed the redirect at substitution rule to point to substitution principle (mathematics), which was completely wrong, as "substitution rule" is used as a synonym for integration by substitution - as pointed out by Thenub314 above. So I fixed that redirect too. Gandalf61 (talk) 12:02, 21 April 2008 (UTC)
Perhaps it is a confused and poorly done attempt to make an article on the substitution property of equality or the instantiation of universals? JRSpriggs (talk) 06:40, 22 April 2008 (UTC)
I doubt this would satisfy the author of that article. I think the article is not really about mathematics, but rather about the kind of operations that one can perform while doing mathematical calculations without messing them up. In some sense, mathematical logic does that too, but the logic treatment of the subject would not be comprehensible to the target readership. Oded (talk) 14:21, 22 April 2008 (UTC)

## Another "wave"-topic featured image question

Frequency dispersion in bichromatic groups of gravity waves on the surface of deep water. The red dot moves with the phase velocity, and the green dots propagate with the group velocity. In this deep-water case, the phase velocity is twice the group velocity. The red dot overtakes two green dots, when moving from the left to the right of the figure.
New waves seem to emerge at the back of a wave group, grow in amplitude until they are at the center of the group, and vanish at the wave group front.
For gravity surface-waves, the water particle velocities are much smaller than the phase velocity, in most cases.

Here's an image found in group velocity. It's not visually stunning like some "Featured" images, but its purpose is to make a concept clear rather than to hit you between the eyes before you've read anything. This seems like a perfect example of a well-explained picture being worth a very large number of words. Should this one have "Featured" status? Michael Hardy (talk) 20:47, 21 April 2008 (UTC)

I say yes. This is a very nice and illuminating animation. –Henning Makholm 20:37, 22 April 2008 (UTC)
As much as animation does add to articles, I find it can also be quite distracting. Does it seem like a good idea to suggest in the manual of style that a potentially distracting image should be placed into a show/hide box (defaulted to [show])? Once upon a time there was Template:Linkimage, which served roughly this purpose, but defaulted to [hide]. (It was deleted because of censorship concerns, which quite frankly I find a bit unconvincing.) silly rabbit (talk) 20:48, 22 April 2008 (UTC)
I doubt that a collapsible box would significantly enhance the usability of the encyclopedia (in proportion to the visual clutter and monitor real estate taken up by the box itself) unless it defaults to "collapsed". However, isn't that a quite orthogonal discussion? The fact that the image may, in the context of a specific article, be presented in a collapsible box, does not prevent the image itself from being featured, does it? –Henning Makholm 21:38, 22 April 2008 (UTC)
Is there a way to have a show/hide box around the image in just one chosen article without constraining the use of the image in other articles? JRSpriggs (talk) 01:47, 23 April 2008 (UTC)
Oh yes, the collapsible box is markup of its own that must be inserted in the page that includes the image. See examples in Fictitious force -- one of the collapsed animations is used without a enclosing box at Talk:Centrifugal force. –Henning Makholm 01:59, 23 April 2008 (UTC)
The problems with the show/hide box are: (1) the image repeatedly freezes for a moment and then starts moving again, and (2) the image now covers part of the text, which can now be seen only when the box gets collapsed. Michael Hardy (talk) 03:11, 23 April 2008 (UTC)
Oh. The comment above was intended to apply to the picture in shallow water equations. Someone's put that one into a collapsible box. I notice that it's now been further edited so that it doesn't cover up the text. But it still seems to move more slowly than it did before. Michael Hardy (talk) 13:50, 23 April 2008 (UTC)

## Huge set of pictures of mathematicians available

Good news for authors of biographies of mathematicians. The Mathematisches_Forschungsinstitut_Oberwolfach features a huge photo collection of mathematicians (roughly 10,000) and has recently allowed the use of the majority of them in wikipedia. A large set of pictures has already been uploaded to wiki commons and is available at commons:Category:Pictures from Oberwolfach Photo Collection.--Kmhkmh (talk) 11:04, 24 April 2008 (UTC)

See #Photographs from the Oberwolfach photograph collection for the caveats. --Hans Adler (talk) 12:00, 24 April 2008 (UTC)
Thanks I completely overlooked that a note regarding this was already posted.--Kmhkmh (talk) 13:58, 24 April 2008 (UTC)

## Taxicab geometry and more

This is list of mathematical and chess topics you may want to consider within the scope of WikiProject Mathematics.

SunCreator (talk) 14:47, 24 April 2008 (UTC)
Thanks for the note. I think you will find most or all of those articles are already listed on the List of mathematics articles. If you would like to add a mathematics project template to the talk pages, please feel free; remember to fill in the quality, importance, and field parameters, using the instructions at Template:maths rating. But the talk page template is not necessary for making the list of mathematics articles. — Carl (CBM · talk) 15:19, 24 April 2008 (UTC)
Okay, glad they are already listed. SunCreator (talk) 20:15, 24 April 2008 (UTC)

# May 2008

## Émile Lemoine

This recently got promoted to FA. I was late on the scene and was about to raise some serious objections, but the article got promoted before I provided my review. I don't think this would currently pass a mathematics A-Class review (is A-Class review still active?). I've left some comments on the talk page. Have I missed the mark, or do others agree that this article needs some work? Even better, is anyone willing to fix it? Geometry guy 23:52, 24 April 2008 (UTC)

As the main contributor to the article, I've responded on the talk page. I'm very willing to address the concerns, and I believe there are fairly simple solutions to about half of them at first glance. Nousernamesleftcopper, not wood 00:13, 26 April 2008 (UTC)

## Marden's theorem, Steiner inellipse, Complex variables

Concerning links to Marden's theorem, Steiner inellipse: Other things are demanding my attention today; could others help me decide which articles ought to link to these new articles (I just created them) and put the links there? Concerning links to complex variables: it now redirects to several complex variables. But many people use the term to mean complex analysis. Should we make it a disambiguation page? Michael Hardy (talk) 22:54, 29 April 2008 (UTC)

I two way linked Steiner inellipse and inscribed circle. I didn't see the circular version of Marden's theorem so haven't touched it. I think the dab page is a good idea, though I think "complex variables" is short for "one or several complex variables", a book title that almost always says virtually nothing about several complex variables, but has a complete introduction to complex analysis of a single variable. JackSchmidt (talk) 00:03, 30 April 2008 (UTC)

## Photographs from the Oberwolfach photograph collection

Mathematisches Forschungsinstitut Oberwolfach has released a large collection of photographs under a free license (CC-BY-SA) at http://owpdb.mfo.de/ . We can use these without restriction to illustrate articles as appropriate. The photos should be uploaded to commons, not here; I am working out the details of how to track which ones are already uploaded. — Carl (CBM · talk) 13:00, 18 April 2008 (UTC)

That's very good news, but the discussion at de:Portal Diskussion:Mathematik#Mathematisches Forschungsinstitut Oberwolfach stellt seine Bilder unter freie Lizenz contains an important warning: While most photos in the database are available under this licence, it's not true for all of them. All photos marked "Copyright: MFO", like this one have been released. But the MFO cannot release photos for which it doesn't have the copyright, like this one. --Hans Adler (talk) 13:46, 18 April 2008 (UTC)
Thanks for pointing that out. Do you know if there is a category on commons for these images yet? — Carl (CBM · talk) 13:51, 18 April 2008 (UTC)
Apparently not. I suppose it would make sense to create commons:Category:Mathematisches Forschungsinstitut Oberwolfach as a subcategory of commons:Category:Image sources, or something like this. Some German editors talked about uploading to Commons, but it seems they haven't started yet. I didn't see anything in commons:Category:Mathematicians that looks as if it comes from the site. --Hans Adler (talk) 14:40, 18 April 2008 (UTC)
The category commons:Category:Pictures from Oberwolfach Photo Collection has been created. --Mathemaduenn (talk) 18:08, 19 April 2008 (UTC)
I obtained permission from George Mark Bergman to use the 1888 photographs from OPC on which he holds the copyrights. Where should I record this permission so that we don't bother him repeatedly, or so that we don't sigh and regretfully eschew use of his pictures? -- Dominus (talk) 18:38, 24 April 2008 (UTC)
"Permission" meaning he's releasing them for anyone anywhere to use under an open source or public domain license, or permission meaning he doesn't mind that we use them only within Wikipedia? If the latter, they would fall under our fair use provisions (meaning, it has to be a photo for which no free equivalent can be found, of a dead person, etc). —David Eppstein (talk) 19:57, 24 April 2008 (UTC)
Permission for Wikipedia to use them under the terms of the GFDL, which is what the boilerplate letter I copied from WP:ERP said to ask for. -- Dominus (talk) 20:06, 24 April 2008 (UTC)
Excellent! I've been adding photos from this collection to the various biographical articles I can find that they match up to, and had several times found good Bergman photos I couldn't use. Now we can. I think where you put the permission statement, on the commons category page, is the right place. —David Eppstein (talk) 06:12, 25 April 2008 (UTC)

So if we find a photo that might be useful in one of the articles, and it's listed as copyright MFO, we're free to upload it to commons ourselves? Where should we link to for a statement of the permissions? E.g., I've found this photo and want to link it to Gyula O. H. Katona (it only says "Katona" but it's obviously not the other Katona, from the date): what do I need to do to accomplish this? —David Eppstein (talk) 19:33, 19 April 2008 (UTC)

Yes, you can upload it to commons yourself (you'll have to make a account there if you don't already have one). You should be safe if you just copy the formatting from one of the other MFO images, such as commons:Image:Helmut_Hasse.jpg. — Carl (CBM · talk) 19:40, 19 April 2008 (UTC)

### Bergman photographs will eventually be in color

Also relevant: Dr. Bergman (see above) informs me that most of his pictures are actually color photographs, although the scans online at present are grayscale scans. He says that OPC is currently in the process of rescanning these in color, so that OPC will eventually have the color versions online in place of the grayscale ones.

I am going to create a new category, commons:Category:Pictures from Oberwolfach Photo Collection (Bergman), and put the Bergman pictures into it, in the hope that when the color scans become available, someone will remember to replace the grayscale images with the color images.

If anyone reading this has uploaded any Bergman images to commons:Category:Pictures from Oberwolfach Photo Collection, please go to the image page on commons and add the category commons:Category:Pictures from Oberwolfach Photo Collection (Bergman). Thanks, -- Dominus (talk) 18:37, 30 April 2008 (UTC)

## Persistent vandal

The IP user 167.206.204.68 has vandalized Joe Harris (mathematician) three times in about a day and a half and been reverted three times by three different editors. Perhaps he should be blocked? Ryan Reich (talk) 18:02, 28 April 2008 (UTC)

The talk page says it's a school IP. The edits look like garden-variety vandalism; who knows why he chose Joe Harris. I'll keep an eye out for a day or two, but I agree the IP is working towards a block. — Carl (CBM · talk) 18:42, 28 April 2008 (UTC)
See Wikipedia:Administrator intervention against vandalism. JRSpriggs (talk) 15:01, 29 April 2008 (UTC)
The IP was blocked by Edgar181 for 48 hours starting this morning. --Pleasantville (talk) 15:20, 30 April 2008 (UTC)

## Implicit function

Some folks are making noises over at Talk:Implicit function about possibly renaming the article. Their objection is essentially that the term "implicit function" may refer to one of two things: an "implicitly defined function" or an "implicit relation". The article, they feel, fails to distinguish adequately between these two uses, and so deserves a major overhaul and/or possible move to implicitly defined function (or other unspecified location). I for one think that this is an awful idea. The term "implicit function" is indeed used to refer to a function, given implicitly, or to a single branch of a possibly multiply defined implicit function. The two editors advocating a change seem to feel the lack of rigor or clarity to be a major problem in the article. I'd appreciate another opinion on the matter. Thanks, silly rabbit (talk) 23:05, 30 April 2008 (UTC)

## David M. Young, Jr.

A stub on the inventor of SSOR (which is in every numerical analysis textbook, and was the king of iterative methods in its time) was deleted. Can somebody restore it please? Obviously, "known for SSOR" or something like that which was there was not good enough for that particular admin. Thanks. Jmath666 (talk) 03:55, 1 May 2008 (UTC)

Done. I agree that it did not warrant A7 deletion. Will add some more to protect it from future attempts. —David Eppstein (talk) 04:31, 1 May 2008 (UTC)

## Proposal - List of mathematics disambiguation pages

Although Category:Disambig-Class mathematics pages has not been created, Category:Mathematical disambiguation has. Over three hundred WikiProjects use the disambiguation talk page to categorize their disambiguation pages. See Category:Disambig-Class articles. Category:Mathematical disambiguation takes the unusual step of using the disambiguation page itself to categorize. There seems to be no reason that Math disambig pages should be an exception by using the disambiguation page to categorize. As indicated in List of mathematics topics, WikiProject Mathematics uses the meta list List of mathematics categories as a way of keeping track of mathematics category pages. To be consistent, the information in Category:Mathematical disambiguation should be placed in Wikipedia:WikiProject Mathematics/List of mathematics disambiguation pages to keep track of mathematics disambiguation pages and the disambiguous pages tagged with {{mathdab}} instead only should be tagged with {{disambig}}. If you agree, please implement this. Thanks. GregManninLB (talk) 14:28, 2 May 2008 (UTC)

Somehow that seems like a lot of work for a system that is slightly worse (as it would be more fragile). Why would you recommend this, other than for conformity with other projects? CRGreathouse (t | c) 14:42, 2 May 2008 (UTC)
I think the main argument in favor of the present way of doing things is the stability. Anytime an appropriate category is added to a page, the page is added to the List of mathematics articles. Anytime Template:mathdab is added to a page, it is recognized as a disambiguation mathematics page. It would be more fragile to require a second template to be added to the talk page to do this, and would also be redundant to the pre-existing article categories. — Carl (CBM · talk) 15:01, 2 May 2008 (UTC)
If a disambiguation page has some links to mathematical articles and some links to non-mathematical articles, then do we use the "mathdab" template or not? JRSpriggs (talk) 16:34, 2 May 2008 (UTC)
I think we should reserve mathdab for pages that are (almost) entirely about mathematical topics, like Whole number. Pages that are more mixed should just get the regular disambig tag. This is similar to this issue with disambiguation pages for school names.
As a proof of concept, I made a list at User:CBM/Sandbox5 of all disambig pages that link to a mathematics article - this can be done without any special tagging of disambig or talk pages, using the list of mathematics articles, and I think it is much more likely to be reliable than manual talk page tagging. So I think the only benefit of mathdab (if there is one) is to mark disambig pages that are particularly mathematical. — Carl (CBM · talk) 17:48, 2 May 2008 (UTC)
That came up recently at Quadratic. I wasn't sure what to do. -- Dominus (talk) 18:36, 2 May 2008 (UTC)
I made an error in my earlier query. The list is actually much longer, and is now divided over User:CBM/Sandbox6 and User:CBM/Sandbox7. The point remains that the list can be generated without the necessity of tagging any pages beyond what is already done. — Carl (CBM · talk) 02:34, 3 May 2008 (UTC)

Here's another related question (but probably not a very important one). Why are just a few of the pages at Category:Mathematical disambiguation called "Foo (disambiguation)"? VectorPosse (talk) 18:27, 2 May 2008 (UTC)

Well, in general you're supposed to use foo (disambiguation) when there's one overwhelmingly primary encyclopedic meaning of foo, that should get the undisambiguated title. On the other hand foo itself should be a disambiguation page if there are two or more meanings that are reasonably competitive with one another. I haven't tried to evaluate how well the math dab pages conform to that principle. --Trovatore (talk) 18:34, 2 May 2008 (UTC)

## Template:CSB/Math

Now what should we think of {{CSB/Math}} and Category:Mathematics-centric? WP:POINT? This is getting out of hand.  --Lambiam 22:59, 2 May 2008 (UTC)

## Interpretation (logic)

There is a mathematician who believes that an interpretation in logic does not have to assign unique names to each object in the domain of discourse, also believes that it is objects that we assign, not truth values. Third party requested. Pontiff Greg Bard (talk) 17:10, 30 April 2008 (UTC)

This is a somewhat interesting dispute. Cokaban writes (in response, essentially, to the above): "It is the other way around: unique object for every name." and "How can you name all real number, for example, using only words in English alphabet (words of finite length)?".
I don't follow the discussion on objects vs. truth values, though.
CRGreathouse (t | c) 17:21, 30 April 2008 (UTC)
I found it interesting too (for only a short while however). So everyone knows that you can't put the reals into one to one correspondence with the naturals. So with a finite alphabet, a formal language has that type of limitation. I don't think logicians who use this type of interpretation have a problem with that. I am pretty sure about the definition that I have promulgated on this Wikipedia. Pontiff Greg Bard (talk) 17:30, 30 April 2008 (UTC)

This is an amusing discussion. Most discussions are difficult to judge, because both parties make sensible statements, in spite of their dispute. This one is different however:

• Cokaban is entirely right;
• Pontiff Greg Bard is entirely wrong, or more precisely most things said do not make much sense at all;
• the current article is a complete mess, in spite of the fact that the MathWorld article to which it refers to (twice) is fairly clear;
• most other participants in the discussion disagree with Pontiff, as long as they manage to not get tangled up in their own phrases

I think the last point should be enough reason for Pontiff Greg Bard to no longer edit the page in question, and leave it to other editors to clean up the page by concensus.

I am a mathematician not specialised in logic, but I know that a first order formal language is something like the language of elementary group theory: there are names for constants (the neutral element) and functions (the inverse (unary) and the product (binary)), predicates ("=") and variables; terms can be formed by applying functions to the required number of arguments (constants, variables or the result of other function applications), and these can be combined by predicates, logical connectives and quantification to sentences like ∀x∀y: x*y=y*x; some sentences are given as axioms. Now giving an interpretation of the first order language of group theory means just giving a group: specifying the domain of discourse means giving the undelying set of the group; to each name one should assign an element of that domain (in the case of constants, so one should specify which element is to be called the neutral element) or a function of one or more values in the domain to the domain (so the symbol for inverse should correspond to a function from the underlying set to itself, and the product symbol should correspond to function mapping a pair of elements to another element), and every predicate should similarly correspond to a relation on the domain (for "=" the equality relation). Thus each sentence will get a truth value, determined by the meaning of logical operations; and it is required that the given axioms get the value "true". Other sentences could have any truth value, for instance the mentioned sentence ∀x∀y: x*y=y*x will be true if the group happens to be commutative, and false otherwise. Note that

• An interpretation does not change the language (the language of group theory is independent of any particular group), in particular it does not add any names
• There is no need for all elements of the domain to correspond to some name; indeed most theories have very few explicit names (which does not prevent variables from ranging over anonymous elements)
• There is no need for different names to refer to different elements: for instance in the elementary language of rings the names "0" and "1" could refer to the same element (in the interpretation given by the zero ring)
• Names for functions correspond to actual functions with arguments and results in the domain (not truth values)
• Names for predicates corresposond to relations: functions with arguments in the domain and as result a truth value
• Only (closed) sentences correspond directly to truth values

Marc van Leeuwen (talk) 12:02, 1 May 2008 (UTC)

That's pretty harsh there Marc. Listen, I didn't pull this stuff out of my a**. There are several sources that I provided, and I learned this stuff formally in a class, not independently. It seem that there is different terminology out there, and as usual that's fine with me to include all of it, but it's not okay by you guys. If there is different terminology, then it should be accounted for, not omitted. If you notice I got at least one show of support in the discussion. It says something about possibly you guys have missed the point entirely. Be well, Pontiff Greg Bard (talk) 21:49, 1 May 2008 (UTC)
The diff you provide supports unique objects for every name, not unique names for every object. I thought Cokaban suggested the former and you the latter...?
Unique objects for every name would mean that j mean Joe and not Jim, but that Person("Joe Smith") could also refer to Joe. Unique names for every object would mean that if j meant Joe than Person("Joe Smith") would have to be someone else, but j could refer to Jim as well.
CRGreathouse (t | c) 22:37, 1 May 2008 (UTC)
If you look at the whole discussion, he was intending to say that its obvious that we need unique names for each object because that's the whole point of putting it into a formal language. He clarified that here. Pontiff Greg Bard (talk) 22:59, 1 May 2008 (UTC)
I don't think that's what he was saying at all -- though he does concede that "when starting from scratch" synonyms "fall to the wayside". I'm slightly confused by your position, though, Greg. I mean, what would ontology be without multiple names of uncertain providence? I would think that a philosopher would be most interested in the case of multiple names (though perhaps that is just my own metaphysics bent). CRGreathouse (t | c) 02:17, 2 May 2008 (UTC)
I think we covered this on its talk page. The whole point of putting this concept of an interpretation into a formal language, is that we can deal with the issue rigorously. (He agreed on this point). It would make no sense to set out creating an interpretation with two different names for one object. However it is logically possible that there happen to be to objects which we discover are identical to each other, and therefore we find that really there are two names for one object. This would be an interesting discovery after the fact, but no one sets forth an interpretation intending for two names to designate one object. That is what this article is supposed to be talking about designating the various aspects of the interpretation. There is a big difference between what we designate, and what we discover happens to be identical.Pontiff Greg Bard (talk) 02:31, 2 May 2008 (UTC)
As someone else pointed out above, there is an interpretation of the language of rings in which both the constant symbol 0 and the constant symbol 1 are assigned to the same object. There is no other way to make a ring with only one object, when there are two constant symbols in the language. Here I am using interpretation in the sense of structure (mathematical logic). It is possible that some other meaning of interpretation is being confused with this meaning. — Carl (CBM · talk) 02:44, 2 May 2008 (UTC)

Cokaban has added a reference from Benson Mates that supports my formulation (although it does not specify unique names), and Cokaban who was entirely right while I was either entirely wrong or didn't make sense has accepted that formulation as have I. So I would appreciate at least some concilliation from all the harsh criticism of myself here. If I had listened to Marc there would have been NO progress at all. Stay cool. Pontiff Greg Bard (talk) 19:55, 2 May 2008 (UTC)

I agree I was harsh, and I'm happy to provide some concilliation. In fact I just wanted to be clear, and did not intend personal critcism, although I was not so naive to ignore that I could hurt your feelings. In any case I did not make any judgement of your intentions, I just said that in this particular discussion you were (in my opinion) wrong. And in saying you did not make any sense at all was certainly sloppy, I just meant that the arguments you supplied did not seem to support the point you were defending; therefore saying you were wrong was somewhat missing the point. In my opinion the main issue of the discussion was whether an interpretation maps names (in the language) to objects (in the domain of discourse) or objects to names, and you seemed to defend the latter point of view, but I could not see many arguments or sources that supported this. To me it would seem that in a natural interpretation of a language that formalises a sentence like "if all humans are mortal and Socrates is a human then Socarates is mortal" the domain of discourse could well be the set of all creatures, without any need for the language to have names for each and every one of them (in fact the language only needs the name "Socrates" to formulate the sentence; being human or and being mortal are predicates). That's all. By the way the reference from Benson Mates seems to be added by Djk3, not Cokaban, see this diff. I see Interpretation (logic) is improved since I posted my remarks above (even though some of it resembles a talk page); I'll leave it in the middle whether this was thanks to or in spite of the fact that anybody did or did not listen to what I said. Marc van Leeuwen (talk) 11:03, 3 May 2008 (UTC)
The rephrased writing has removed the comments about names, which were the part that was most problematic. On the one hand, I think Hans's question whether the names were meant to be formulas, objects in the domain, or something else, was never answered. On the other hand, Marc pointed out above that if names are part of the language, the original phrasing in the article was wrong, and I discussed on the article talk page how the text in the article had accidentally reversed the meaning of reference that it was drawing from. — Carl (CBM · talk) 11:40, 3 May 2008 (UTC)

## Mathematics bias

Please have a look at Wikipedia:WikiProject Countering systemic bias/Mathematics. Is this an apt analysis of a justified complaint?  --Lambiam 12:38, 1 May 2008 (UTC)

Looks like a one-man movement, by the history. This WikiProject should probably be deleted, as it's clearly an attempt by one person to create an issue out of nothing. As far as I know, logicians between philosophy and math get along just fine - well, except for maybe this guy. Tparameter (talk) 12:54, 1 May 2008 (UTC)
Isn't it a bit late for April Fools pranks? --C S (talk) 13:38, 1 May 2008 (UTC)
Unfortunately I am sure that Gregbard is serious about this. But I think the worst thing we can do is to be confrontational about it. I suppose the systemic bias people will deal with this.
Actually I am not sure if the problem exists. Some philosophical sources on logic contain passages that look like they are intended to be mathematical definitions, but these sources rarely if ever use these definitions in any significant way. I don't know what that means. It could be anything from "I will show my students the mathematical definition to scare them" via some kind of metaphorical use to serious transgression of boundaries. If it is the former, it should be covered only by mathematics articles, because everything else would be a POV fork. If it is the latter, then Wikipedia shouldn't cover the philosophical part per WP:FRINGE.
If it's something solidly between these two extremes, then it may well be worth covering from a philosophical angle. The problem in this case would be that we don't seem to have anybody with the necessary qualification and interest to write such articles. That would in fact be a mild case of systemic bias. --Hans Adler (talk) 14:34, 1 May 2008 (UTC)
PS: Gregbard is doing some very dedicated work on logic articles; if anybody has an overview of that part of Wikipedia then it's him. Much of what he does is actually quite beneficial. --Hans Adler (talk) 14:43, 1 May 2008 (UTC)
I've noticed a systemic bias against gemology articles. Did you realize that the WP:PHILO talk page has ten times as many page views as the WP:GEM talk page? Something should be done about this. CRGreathouse (t | c) 17:37, 1 May 2008 (UTC)
Thank you Hans, that was very kind and open minded of you to say. This effort certainly isn't personal. I think you guys (is it almost all guys btw?) here are sincere, of course. Nobody questions that. There is an interesting theorem that is described at doxastic logic, the one about the "inconsistency conceited reasoners" (not a slight). It says basically that 'If you live in a bubble, you can never really know that you live in a bubble.' I don't expect anyone in the Math department to either admit, recognize, or otherwise acknowledge the issue that I am trying to address. My effort is a sincere one, and yes so far it's just me. This seems to be the "work within the system" thing to do for me. I don't want to be a jerk about things anymore than you guys do when there's a flurry of edits dealing with some of my edits made to to a supposedly 'mathematical' article. I think this is a way to bring wider attention to the issue. I think WP:MATH will most likely benefit from the attention as well. In any case, I do not see that there is any threat of harm in it. It could turn out to be a big nothing, or a flash in the pan, or it may evolve into a project dealing with general anti-philosophical bias from whatever source, etc. You guys are certainly welcome to laugh about it if you like. Ha ha ha, Greathouse, an inductive argument doesn't get by on one claim you know. I will try to avoid anything too personal under the supporting evidence section, which I admit could use more specifics. Although the proposal to delete within 12 hours could qualify. Be well, Pontiff Greg Bard (talk) 19:05, 1 May 2008 (UTC)
May I ask what, specifically, is different between logic in philosophy and logic in mathematics? I've taken the logic course offered by the math department at my college as well as the one offered by the philosophy department. The focus was different, but the logic was the same. In the math course, we primarily covered meta-theorems and talked about model theory. In the philosophy course, we mostly did derivations. The philosophy course was less rigorous, but the logic was not different. I understand that there are systems of logic that are studied by philosophers that are not generally studied by mathematicians (modal, relevant, paraconsistent, etc.), but in terms of classical logic, what constitutes the bias? I'm sorry, but I don't even really understand how there can be a bias. Please explain. Djk3 (talk) 19:32, 1 May 2008 (UTC)
This is certainly a fair question. After all its MATH, what could be more unambiguous, objective, and rigorous? And this WikiProject...it's full of geniuses --no shortage at all. They aren't going to let anything inaccurate through. All of this is the truth --no sarcasm.
In the history of philosophy we have seen an evolution. Back in the day there were NO scientists, they were called "natural philosophers." As the knowledge they accumulated became greater, and more understood, specialized fields developed, and the idea that it was "philosophy" went by the wayside. These days science and philosophy only intersect (in an academically recognized way) where there is a frontier: theoretical physics, artificial intelligence, etc.
Well guess what? Math used to only be done by philosophers too. However, math is a little different from other "natural sciences." It deals with abstraction, and there is no limit to the frontier of abstraction. So math is still philosophy in certain areas especially in logic. Some here at WP:MATH will probably vehemently disagree with that statement. I have seen on a talk page more than once about "mathematical logic isn't logic," or "these are two different concepts we are talking about," or "the logicist project was a failure," or how about "I don't know much about philosophy, but I know x is not philosophy," etc. These sentiments, all of which have been seen here in some formulation, are more about personal identity with an academic group, than it is about the actual nature of the concepts being considered.
We have a very large group of mathematicians, some are introverted, some are very critical because of their appreciation of rigor, some are attracted to the idea of certainty, some are just left brained, etc. There are all kinds of generalizations that could be made, however in the aggregate we get a self selecting group of whatever stripe. Certain patterns have developed some of which I have noted under "supporting evidence" at this CSB/Math project.
For certain articles the issue is obvious: Consistency. There is almost no philosophical treatment even though it is obviously a very important concept for philosophy. This kind of issue is widespread, and it is basically the philosophy department's fault because we are so small, and not nearly as active as the math people. However, when efforts are made to provide the philosophical aspect, there is an intellectually hostile tendency due to this environment to either delete it as irrelevant, or unimportant (even if sourced as we are seeing at interpretation (logic)), or there is a proposal to disintegrate the article covering what really is one concept into two (see Theory and theory (mathematical logic), for instance). These are a few small examples, however the tendency behind them is solidly in place in this culture. Over time we get what we expect: a math department with very mathematically complete, rigorous articles, with almost no connection to any other areas. So is it really true that there are no connections or is it just the case that you aren't in a position to see all the connections? The tendency is a self-segregation into math and everybody else. That just doesn't make quality for a general use encyclopedia. Intelligence involves being able to make connections between ideas. If WP is to promote intelligence, we need to endeavor to make those connections.
So the way it manifests itself isn't necessarily in any particular statements in any particular article: they are all accurate just fine. The issue is about the organization of articles among each other, and the organization of the outline within some others, for some it is hostility to alternate terminology, for many others it's the omission of important aspects that mathematicians would never themselves see as important. The issue is real, the question is what do we do about it? Pontiff Greg Bard (talk) 21:00, 1 May 2008 (UTC)
So what exactly, then, is the difference between logic in philosophy and logic in mathematics? Djk3 (talk) 22:57, 1 May 2008 (UTC)
Greg, frankly, most of the time when you complain about an "anti-philosophy bias", my observation is that you really mean things that don't agree with your philosophy. Not all of us mathematicians are clueless about philosophy -- some of us know at least a little about it. Your views, at least if I've understood them correctly, are sharply at variance with most of the prevailing currents in philosophy of math. That doesn't mean they're wrong, of course, but casting the disputes as tensions between a "mathematical" and "philosophical" worldview is inaccurate. --Trovatore (talk) 19:56, 1 May 2008 (UTC)
I think that's a little 'very' unfair. I may be the only person really bringing up the issue, but that doesn't mean its all about me. You are trying portray me as some kind of radical or fringe, and that is very unfair. At some point I thought it was important that the article on set include the fact that a set is an abstract object. It was you guys who really are on the fringe making a big discussion of it and trying to say that this isn't actually quite important. FOR INSTANCE. My views and more importantly, my edits, are well within the academic mainstream. As usual I give examples, but when I am accused it's just rhetoric. Don't get me wrong Trov. I appreciate you quite a bit, but you are being unfair in that last paragraph.Pontiff Greg Bard (talk) 21:00, 1 May 2008 (UTC)
Naturally, you'd feel this way, being susceptible to the "living in a bubble" theorem that Greg Bard described above. Your photo on your user page even seems to show this bubble, although I wonder how you managed to get a realistic nature backdrop in there. --C S (talk) 20:10, 1 May 2008 (UTC)
Yes the theorem applies to me too. Feel free to jab at it so as to make it pop, please. That would be doing me a favor. But I don't have any image on my user page?? To what are you referring? Pontiff Greg Bard (talk) 21:00, 1 May 2008 (UTC)
The comment was to Trovatore, as the indenting indicates. --C S (talk) 21:17, 1 May 2008 (UTC)
It all makes sense. Pontiff Greg Bard (talk) 21:35, 1 May 2008 (UTC)

Could this be part of the larger phenomenon: Wikipedia has covered the topic of mathematics more succesfully than it has philosophy? Michael Hardy (talk) 22:07, 1 May 2008 (UTC)

If you mean to say that there really isn't a bias issue, but rather the math articles are just more complete because of the sheer numbers, and the philosophy articles just need to catch up but are slow to do so because of the numbers, that's just not the whole story. For certain articles that really that need attention from both, there is intellectual hostility, and segregation. I am constantly watching things being deleted from articles: for example. Also, I pretty much go through hell just to add any logical or philosophical foundations/connections in these articles. For example the idea that a set is a abstract object. Where does the idea come from to fight about these things? Then there is the tendency to split an article into (math) and (everyone else). These are tendencies that hold back progress toward any eventual GA. So there is more to this issue than completeness or numbers. Be well, Pontiff Greg Bard (talk) 19:41, 2 May 2008 (UTC)
When I see a statement in an article that is incorrect, I tend to correct it. In mathematics, there is no such thing as "the notion of completeness". There are various uses of the term "complete", which are only marginally related, and are not instances of an embracing notion of "completeness". Therefore, a sentence making a claim about "the notion of completeness" in mathematics is in error and should be corrected. It is obvious that the notion of completeness in mathematical logic is a precisely defined version of that notion as used by logicians who are not mathematicians; I did not think that needed to be pointed out. For the rest: is the set of members of WikiProject Philosophy an abstract object?  --Lambiam 21:39, 2 May 2008 (UTC)
You are really proving my point here Lambiam. Everything has to be within mathematics or it doesn't seem to exist under that view. It's a common view. However it is missing an opportunity to improve a great many of these articles to a much higher level. Yes, a set is an abstract object, so therefore the set of members of WP:PHILO is itself an abstract object, and yes the empty set is too. Pontiff Greg Bard (talk) 22:50, 2 May 2008 (UTC)
From personal experience - the mathematicians I know are very precise with their language and definitions. This makes it difficult for someone with a little training in logic to contribute substantive logical content on wikipedia without running into true logicians, who are very precise, and who tend to read every word in this manner. I suspect this is the nature of the aforementioned so-called "bias". Instead of a interpreting this as a problem, I would suggest that those of us lower on the totem pole should be humble and learn from the PhDs. (Not directed at Lambiam, obviously) Tparameter (talk) 22:10, 2 May 2008 (UTC)
I have no problem deferring to any PhD's. The problem is for the precious tiny little logic I do know about, which is being deleted or omitted as irrelevant or unimportant, that's not a rigor issue. That's pov. The links to meaning, name, and reference were all taken out of this article on interpretation. I'm pretty sure there are plenty of PhDs who understand that there are relevant connections to these concepts in an article on interpretation. Be well, Pontiff Greg Bard (talk) 22:50, 2 May 2008 (UTC)
Are you aware of WP:OVERLINK? In articles that use plenty of technical terms that people may not know the definition of, you have an inclination to make wiki links for words that are used in their natural language sense. These wiki links go to articles that sometimes give the correct definition for the context, sometimes a wrong and utterly misleading one (as in the case when you linked to consistency from a natural language use of "consistent" in a legal text). In both cases they are only helpful for people who don't want to understand the article and prefer surfing away on a random link. --Hans Adler (talk) 23:06, 2 May 2008 (UTC)
You guys all have a knack for exaggeration. I did not indiscriminately added a wikilink to consistency in all wikipedia articles containing the word "consistent." I had a list of a few hundred, I looked at each one to exclude things like consistency like oatmeal, consistency in performance, etc. I took a look at the article on precision and recall, and I found it interesting, so thank you for that. However, the key disagreement between us is the idea about how relevant these links are.
As far as completeness, I didn't push anything to the front as you describe... it was there by some mathematician's hand believe it or not, originally. It was removed by one too and has remained out. So stop with the exaggerating and all that "pushing" baloney. I'm just bringing the issue up, and if you view that as pushy, well then that also supports my thesis about the math-centric view: Just bringing up the logical and philosophical aspects of these things alone is viewed as pushy. You should see this as an opportunity to improve a lot of articles in a way that isn't being covered. It seems to me that that should be a wonderful thing for WP:MATH. The fact that it isn't seen that way is why there is the whole CSB/Math thing. Be well, Pontiff Greg Bard (talk) 23:32, 2 May 2008 (UTC)
When there is something like "syntax (structure)" and "semantics (meaning)" in an article, then it seems bleedingly obvious that "syntax" and "semantics" must be linked at the first occurrence because they are technical words that many people don't understand, and that even those who do might want to look up in connection with the article where they occur, and "structure" and "meaning" must not be linked because they are just vague natural language explanations of the technical terms. I really don't understand what's the problem with that. And it's exactly the same for mathematical technical terms.
The problem with your overlinking is that people no longer know which are the technical terms they need to look up to understand the article. That was the problem with the abstract object link in set, for example. It's hard enough to learn what sets are about if you are explained the basics, and only the basics, in a systematic fashion. But when your teacher starts with digressions about abstract objects, formal languages, meaning, and giraffes, without making it clear that these are digressions rather than essential for the subject, then you will be so confused that you never learn it. I am talking about teaching mathematics. Teaching philosophy is probably the other side of the coin. The point is that they need to be taught separately, because it's almost impossible to learn both aspects at the same time. --Hans Adler (talk) 00:06, 3 May 2008 (UTC)

GregBard, I wanted to address your complaint about the segregation of mathematics and non-mathematics content. I sympathize with your point of view that there are advantages to a broader perspective. However, there are very good reasons to insist on a clear separation between math and non math in WP. There are plenty of people who are often confused by mathematics (in fact, perhaps that’s true of every person exposed to mathematics, including mathematicians). If you mix mathematics and non-mathematics in a way which is not clear, that is likely to add to the confusion. A very important aspect of mathematical education is in the learning of what constitutes a mathematical argument, a mathematical statement and a mathematical definition. Exposure to mixed content is likely to result in some unlearning. This is less of a problem for fluent mathematicians, and much more of a problem for the lay person. For this reason, we are very reluctant to mix in some philosophy within a mathematics article. Oded (talk) 06:54, 3 May 2008 (UTC) P.S. I now notice that essentially the same point was raised earlier by Hans Adler above. Sorry about the repeat. Oded (talk) 18:05, 3 May 2008 (UTC)

To be fair, most of the articles that Gregbard is referring to are the mathematical logic articles. I don't think anyone is proposing that we should add philosophical stuff to articles like fibre bundle or even group (mathematics).
The articles where this issue arises tend to be those where a single word has several meanings. For example, there is a concept of atomic sentence in predicate logic, and another concept of atomic sentence in natural-language philosophy. These are (distantly) related, and my initial guess is that the terminology in predicate logic was chosen exactly because of the similarity between the them. My impression of Gregbard's argument is that he would like to see articles that cover both aspects of the terminology, and I agree with that. But I view the two terms as substantially different, although similar, rather than the same. Another example is theory: I don't view theories in mathematical logic (which are sets of formal expressions) as identical to scientific theories (which are natural language things, typically not formalized).
Unfortunately, a few editors who are interested in these philosophical aspects have not added the philosophical stuff to the articles, they have instead been duplicating the mathematical material that appears in other articles. One example of this is atomic sentence, which in predicate logic is a trivial intersection of two definitions and not interesting enough for more than a couple sentences. Its real interest is in the context of philosophy. — Carl (CBM · talk) 11:36, 3 May 2008 (UTC)

## "List of mathematics articles (A)" is badly misalphabetized

List of mathematics articles (A) is not in alphabetical order. I've done enough nitpicking for today; can someone help. Michael Hardy (talk) 18:25, 2 May 2008 (UTC)

Mostly it looks fine? It is sorted in the "C" locale way, with upper case letters coming before lower case letters. I think the list is mostly machine made, so this makes some sense. Probably the machine could be asked to sort case insensitively, and just fix the list on the next update. Are there (m)any that are not explained by the case sensitive issue? JackSchmidt (talk) 18:46, 2 May 2008 (UTC)
If that's true, then it should say "ANO" where it says "Ano". It is absurd to put "Ano" before "Abh". Michael Hardy (talk) 21:27, 2 May 2008 (UTC)
When Mathbot generates the heading, it replaces an all-caps title by one in which only the first letter is capitalized. The same happened for RTC. It's smarter than it looks, perhaps being too smart here; perhaps its trainer can dumb it down a bit.  --Lambiam 22:38, 2 May 2008 (UTC)
Good points. I made sorting case-insensitive. Oleg Alexandrov (talk) 20:07, 3 May 2008 (UTC)

## Exterior algebra for peer review

I've nominated Exterior algebra for peer review. Perhaps this article can be brought up to GA status [61]. silly rabbit (talk) 20:58, 3 May 2008 (UTC)

## 10-millionth Bernoulli number computed

Someone's just added to the Bernoulli number article an external link to an article on Wolfram's web site reporting that a new algorithm as made it possible to compute the first 10,000,000 Bernoulli numbers (the denominator in the last one is 9601480183016524970884020224910 and the numerator has a very large number of digits). Michael Hardy (talk) 22:24, 1 May 2008 (UTC)

The algorithm is not new, just running it for longer than anyone has attempted before. Still, it's a nice achievement. Fredrik Johansson 18:23, 2 May 2008 (UTC)
It's the 10,000,000th Bernouilli number only. The algorithm in principle goes back to Euler; its advantage is that it's not recursive. Septentrionalis PMAnderson 23:40, 6 May 2008 (UTC)

## template:logic

Someone is requesting comment on the philosophy of logic section of the logic template. Pontiff Greg Bard (talk) 23:16, 6 May 2008 (UTC)

## Problem of Apollonius

The problem of Apollonius is gradually oozing towards its Featured Article candidacy. If any of you wanted to contribute or offer suggestions on how to improve it, I'd be most grateful! :) Willow (talk) 00:09, 7 May 2008 (UTC)

## Compact Spaces *

What shall we do with the new article titled Compact Spaces *? Does its creator know that Wikipedia article titles are not usually supposed to be plural or that the capitalization of the initial s is against Wikipedia conventions? What's the asterisk for? And then there's the question of the article's content. Take a look. Michael Hardy (talk) 13:17, 30 April 2008 (UTC)

It is User:Topology Expert (of Induced homomorphism fame). Nearly every one of this editor's edits has been problematic, but I'm not sure what to do about it. Invariably I would inadvertently bite the newbie. I do feel that some kind of intervention is needed. silly rabbit (talk) 13:21, 30 April 2008 (UTC)
Induced homomorphism though revised, is still of questionable accuracy. Though the case discussed there (fundamental group) currently is an example of an induced homomorphism it's far too restrictive. For example given an invertible linear map S on a vector space V
${\displaystyle T\mapsto STS^{-1}}$
is an induced homomorphism on algebra of linear operators.--CSTAR (talk) 13:30, 30 April 2008 (UTC)
I revised it this morning to take a more general point of view. Please take a look at it again. —David Eppstein (talk) 19:54, 30 April 2008 (UTC)
Back to the original question, I suggestion undoing the recent move: i.e., moving the article back to supercompact space. Though I see you have already done that. silly rabbit (talk) 14:21, 30 April 2008 (UTC)

Can someone please check out some of these other edits. To my mind, almost all of them degrade the articles.
JackSchmidt (talk) 21:03, 30 April 2008 (UTC)
I agree with your assessment. If these are all the same person (is WP:RFCU called for?), then someone clearly needs to have a heart-to-heart with User:Topology Expert. silly rabbit (talk) 21:17, 30 April 2008 (UTC)
someone might wanna check out those links again. Mct mht (talk) 13:24, 4 May 2008 (UTC)
Call me an optimist, but I think that this editor will be fine after some guidance. Silly rabbit, please do not let WP:BITE stop you from talking to Topology Expert. People won't learn unless their mistakes are pointed out to them. -- Jitse Niesen (talk) 14:17, 4 May 2008 (UTC)
You optimist! But seriously, although I have no doubt that User:Topology Expert will eventually be able to contribute constructively to the encyclopedia, the problems continue. Now he or she keeps adding (inexplicably) the {{db-repost}} template to the Supercompact space article. I explained that the correct procedure is {{AfD}}, as have other editors, but this doesn't seem to have made an impression. silly rabbit (talk) 14:30, 7 May 2008 (UTC)

## Moving the math section from WP:Words to avoid to WP:Manual of Style (mathematics)

WP:Words to avoid#Special considerations for naturally talks about different meanings in mathematics for the word "natural". Does anyone here know a reason why this shouldn't this be in WP:Manual of Style (mathematics)? WP:WORDS is one of just 6 pages in the "Wikipedia style guidelines" category that's a requirement at Good article nominations, so this guideline should be just as short and non-subject-specific as possible. Why should we make people learn about mathematical terms as preparation for writing any Good Article? Full disclosure: my degree is in math, and if I have a bias, it's pro math/sci/tech. - Dan Dank55 (talk)(mistakes) 15:55, 7 May 2008 (UTC)

That section would serve no function in WP:Manual of Style (mathematics). Mathematicians already know that it is not evil to claim that some numbers are more natural than others. They do not need to be lectured that the words "natural" or "naturally" may have precise technical meanings.
However f that section is removed, then, when a maths article is up for Good Article review, the reviewers will naturally balk at occurrences of the words "natural" and "naturally".  --Lambiam 21:44, 7 May 2008 (UTC)
Exactly. The whole point of that section is to inform those who don't already know, not those who do. Michael Hardy (talk) 02:32, 8 May 2008 (UTC)
If a reviewer says "I can't pass this article, you're using the wrong word", which is extremely unlikely anyway, then you could just point them to this section in WP:Manual of Style (mathematics). Why is it that everyone on Wikipedia who wants to learn about Good Article criteria needs to read about mathematical definitions? Would you want to have to study terms from medieval art or biophysics as part of your WP:GAN process? - Dan Dank55 (talk)(mistakes) 03:41, 8 May 2008 (UTC)
Why the repeated emphasis on GA? This has nothing directly to do with GA; it is a Wikipedia style guide that applies to all articles. Using your argument, does it make sense to have every Wikipedian read this style guideline before editing articles? I think not. In fact, I think this page's purpose is to be a reference to point people towards, rather than something one is supposed to read before editing Wikipedia articles. Many dedicated, thoughtful Wikipedians don't need most of the advice in the guideline. But some need to be gently guided to a relevant passage should something arise. So your questions presuppose an argument that nobody is advocating. The passage could be improved to be a more general statement about technical writing, if that would make you happier. That is really the content there; it is not aimed at only mathematics. --C S (talk) 04:41, 8 May 2008 (UTC)

## List of scientific publications of Albert Einstein

Hi all,

I'm about to nominate List of scientific publications of Albert Einstein as a Featured List candidate, but if any of you had any suggestions, I'd be happy to incorporate them. I know this falls somewhat outside the scope of the Math WikiProject, but many of you might be interested, so I thought it couldn't hurt to mention it here. :) Willow (talk) 19:50, 6 May 2008 (UTC)

I've now nominated it as a Featured List. Your input there would be welcome; follow the link! :) Willow (talk) 20:23, 8 May 2008 (UTC)

## No new math articles for several days

If we can believe Wikipedia:WikiProject Mathematics/Current activity, then no new math article have been created for several days. Is this just a case of someone who takes care of that page being on vacation? Michael Hardy (talk) 02:31, 8 May 2008 (UTC)

User:Oleg Alexandrov's bot maintains the lists of mathematical articles, and has not made any recent changes to the mathlists. JackSchmidt (talk) 02:52, 8 May 2008 (UTC)
Oleg says it is fixed now and will work as normal tomorrow. JackSchmidt (talk) 04:16, 8 May 2008 (UTC)
Sorry, the computer on which the bot ran had issues. Working now. Oleg Alexandrov (talk) 15:13, 8 May 2008 (UTC)

## Request for comment on Linear least squares

I am having a big disagreement at the linear least squares article with another editor. I believe it is very important to state early on in the article that a linear least squares problem amounts to solving an overdetermined linear system of equations. The other editor disagrees, claiming that the article in question is not about mathematics, that its primary readership is people in experimental data fitting, and that matrix notation is an advanced topic. Other editors views on this are very welcome, at Talk:Linear least squares#Overdetermined systems. Thanks. Oleg Alexandrov (talk) 15:13, 8 May 2008 (UTC)

## Disambiguation help at Quasilinear?

Hello wonderful Math-smart editors!

I'm trying to clean up the disambiguation page Quasilinear, and in that, the best thing that I could figure to do would find the most relevent article for each fo the three terms there, in order to clean up the page. For the middle item, it seems like Big_O_notation#Orders_of_common_functions could provide the necessary information, but I've become lost trying to find related articles for the other two entries. I was hoping there might be some good ideas here, at least for the first one (I know the third is economics related). On a similar note, are all of these topics close enough to make this not a disambiguation page, but actually an article? If only I understood the concepts enough to know... but since I do not, I defer to you all. Many thanks, -- Natalya 20:35, 9 May 2008 (UTC)

Wow, that dab page does need clean up! I think the meanings are very close, but perhaps not close enough for a single article. Basically "quasilinear" means "linear is easy, here is something that superficially resembles linear and still happens to be somewhat easy". However, the definition of "linear" is different in each of three cases, and the way it resembles it differs as well, making a single article very hard to write.
For the first meaning, differential equations#Types of differential equations might be the best link. I don't know if you want to make quasilinear differential equations a section redirect (until someone can write an article on it, it is the name of a chapter in my intro pde book, so probably easily its own article).
For the second, I think you are good, and I've no idea on the third. Thanks for taking on such a difficult dab, and asking here rather than just deleting it. JackSchmidt (talk) 21:34, 9 May 2008 (UTC)
Thanks for the help! That first link seems like it will be good for the first entry - thank you! Two down, one to go.  :) I'll see if I can get any ideas out of some economics folks. Thanks again, -- Natalya 12:11, 10 May 2008 (UTC)

## New number articles

What do people think about these number articles?

— Carl (CBM · talk) 02:30, 10 May 2008 (UTC)

314 and 3141 are obvious deletion candidates per Wikipedia:Notability (numbers), particularly given Wikipedia:Articles for deletion/3.14. I would just prod these and cite the precedents. Best play it safe and AfD the other two. My own vote is delete both as non-notable. silly rabbit (talk) 02:46, 10 May 2008 (UTC)
I don't think they need to be deleted; we can always redirect them to the nearest round integer instead. But I'm not well-versed in esoteric number properties the way some people are. — Carl (CBM · talk) 02:56, 10 May 2008 (UTC)
Well, 1033 (number) contains only one section 1033 in computing, and apparently it refers to the numerical encoding of a certain locale on some operating systems. This is really rather a silly thing to have an encyclopedia article on. It would be better to have one like Numerical encodings of locales on Windows XP, and I'm not even sure that deserves an article (per WP:INDISCRIMINATE). As for 12765 (number), this may be more significant: it is (apparently) an internet meme in Finland. But the article does a rather poor job of establishing notability. Of all four, this is the one I could be most persuaded to keep. As for 314 and 3141, the only notable feature the articles establish is that they are a power of 10 multiplied by π with the trailing decimal then truncated. Plenty of articles involving digits of π have already been deleted. I see no particular reason these should be kept. silly rabbit (talk) 13:43, 10 May 2008 (UTC)

## Notations for Cartesian products

This appears in copula (statistics):

${\displaystyle B=\times _{i=1}^{n}[x_{i},y_{i}]\subseteq [0,1]^{n};}$

I'm wondering if there are particular views on advantages and disadvantages of this particular notation for Cartesian products, as contrasted with this:

${\displaystyle B=\prod _{i=1}^{n}[x_{i},y_{i}]\subseteq [0,1]^{n};}$

Michael Hardy (talk) 18:17, 9 May 2008 (UTC)

I use capital Pi myself; but this may well be one of those things on which we can afford to differ. We will never have a Bourbakian uniformity of notation; the only functional difference is that one may be more familiar than the other. Septentrionalis PMAnderson 19:16, 9 May 2008 (UTC)
A slightly more important question, though, is if the former notation is used at all. (I have not seen it myself, which is not to say that there isn't some reference out there for it.) It isn't Bourbakian to choose standard notation over nonstandard notation. But like I said, it's entirely possible that the first notation is commonly used. VectorPosse (talk) 05:54, 10 May 2008 (UTC)
I have seen ${\displaystyle \times _{i=1}^{n}}$ a few times, but in my experience it is not nearly as common as ${\displaystyle \prod _{i=1}^{n}}$. Oded (talk) 05:57, 10 May 2008 (UTC)
I've seen it in collections of algebraic topology papers; my memory suggests it was one of the large Springer paperbacks, but I have no idea which. Bringing it up on the article talk page, and seeing if anybody minds switching, may be best. Septentrionalis PMAnderson 16:42, 10 May 2008 (UTC)
For cartesian products, I would have thought that
${\displaystyle B=\otimes _{i=1}^{n}[x_{i},y_{i}]\subseteq [0,1]^{n};}$
was most common.
I would think use of capital pi (Π) should be kept to just the case of arithmetical products. Jheald (talk) 19:43, 11 May 2008 (UTC)
One should not use ${\displaystyle \otimes }$ for Cartesian product because, in my experience at least, it is always used for the tensor product which is quite a different thing. Personally, I prefer to use ${\displaystyle \Pi }$ or ${\displaystyle \prod }$ when taking the Cartesian product of a sequence of spaces, but an infixed ${\displaystyle \times }$ for the Cartesian product of just two spaces. JRSpriggs (talk) 20:16, 11 May 2008 (UTC)
I whole heartedly agree (don't use ⊗), but my experience has been a bit more disturbing. I have seen ⊗ used for the direct product of abelian groups (I think Fulton, I'll have to check at the office), and × used for the tensor products of algebras (A.A. Albert). At any rate, the world is crazy, we do not need to fix it, but I think we should stick to whatever notation is common in the community. Has someone considered simply:
B = [x1,y1] × ⋯ × [xn,yn] ⊆ [0,1]n
which might be easier on everyone. JackSchmidt (talk) 22:52, 11 May 2008 (UTC)

Just to add to the notational confusion, Cartesian product of graphs uses a box symbol, while in graph theory the × symbol instead refers to the tensor product of graphs. The symbols have some visual resemblance to the graph products they create. —David Eppstein (talk) 22:59, 11 May 2008 (UTC)

## Linear algebra for algebraists

I was trying to help cleanup symplectic group, but I noticed I would need to counter a very real systematic bias in our linear algebra articles. That is, most articles assume the field is the real numbers, but a few particularly enlightened articles also allow the complex numbers. Some claim to allow any field, but actually mean any field of characteristic 0.

What is the right way to handle this?

1. Should I go around breaking all sort of physicists articles so that they apply to all fields (in the sense of algebra), but maybe not fields with a riemannian metric on them?
2. Should I create parallel articles that handle the algebraist's idea of linear algebra?
3. Should I create "Over arbitrary fields" sections of every article?

I don't personally have the expertise to simultaneously address the analytical / physicist audience and the algebraist audience. In fact, I don't even have the number theory or topology expertise to handle linear algebra over complete DVRs. My main references are Kaplansky's textbook for a Second Course in Linear Algebra, and Grove's textbook on Classical Groups. I don't think I can give a complete, broad perspective, just a different perspective, and I am not sure how to use that to help out. JackSchmidt (talk) 16:40, 10 May 2008 (UTC)

In your situation, I would go through the articles, remove all spurious mention of the field, and put a note at the top of the articles that the field can be arbitrary. Then, if something isn't true over an arbitrary field, you can go and put back in R, C, or "characteristic zero" wherever necessary. Sometimes, of course, an "in arbitrary fields" section is necessary, especially to balance a discussion of a theorem which requires special fields but has a limited generalization to others (for example, the Jordan canonical form). If it's an interdisciplinary article (i.e., a "physicists' article"), you can instead put at the top of the article "these results are true for any field; for illustration, this article will use R as an example", thus satisfying everyone. You could save yourself work and do that even for the pure math articles, if you wanted to sacrifice absolute correctness (but also avoid a lot of arguments). Ryan Reich (talk) 16:35, 11 May 2008 (UTC)
We don't get much feedback from people actually trying to learn from our articles, but what there is suggests that we do best beginning from a well-known, comprehensible, case, and increasing in generality as we go down the article. This would mean beginning over R or C (which is usually what the physicists will be using and linking to), and expanding first to characteristic zero and then to arbitrary fields. Septentrionalis PMAnderson 18:09, 11 May 2008 (UTC)
This approach is very reasonable in many circumstances. However, I think that WP will be increasingly useful for mathematicians to look up a concept that is outside their experties and to refresh their memory with regards to a definition, find a reference, etc. Depending on the subject of the article, we can try to make an educated guess who the likely readers would be and write accordingly. Oded (talk) 18:51, 11 May 2008 (UTC)
If I'm looking for a particular fact about symplectic groups, the arrangement doesn't really hurt me; I'll search down until I find what I;m looking for. (And unless it's the dimension, or the homology group, I won't find it.) So we should accommodate the students for whom it does matter. Septentrionalis PMAnderson 19:44, 11 May 2008 (UTC)

Ok, to make sure Im summing this up right: we prefer keeping R, C, char 0, and all fields together in one article, but with a section nearer the bottom describing the general field case, while the top of the article pretends we are working in the one (or two) true field(s), R (or C). For the most part this bottom section will be "the previous holds with obvious modifications over all fields of characteristic not 2, and for char 2, we do the following non-obvious modification. We also have the following algebra-y facts that don't matter much over R or C, but that are important over more or less every other field." We will ignore linear algebra over non-fields for now, and assume it will mostly get put into articles about the functors measuring how weird that stuff is.

Assuming so, I'll go add *references*, transvections, perfection, centers, and orders to symplectic group, and have a go at adding the general field / char 2 stuff to all of the various symplectic/alternate articles. JackSchmidt (talk) 22:37, 11 May 2008 (UTC)

## "Theorem"?

The initial sentence of the article titled theorem offended me and accordingly I did this edit. Opinions? Michael Hardy (talk) 20:21, 11 May 2008 (UTC)

has been proved, surely? Septentrionalis PMAnderson 20:22, 11 May 2008 (UTC)
The article originally mentioned the mathematical use of the word, until it was changed by (guess who): [62]. silly rabbit (talk) 20:27, 11 May 2008 (UTC)
.....sigh........ That whole culture needs to get some sense talked into them, not just that one Wikipedian. Michael Hardy (talk) 20:31, 11 May 2008 (UTC)

Not "surely" at all. Mathematical logicians speak of whether or not there is an algorithm that decides of statements in a formal language, whether of not they are theorems. In that context, "has been proved" is wrong. And the article seems biased toward that particular context, although I hope my recent edits have left it less so. Michael Hardy (talk) 20:30, 11 May 2008 (UTC)

This led me to notice Formula (mathematical logic), which is currently in extreme need of improvement (permanent link). I'm going to work on that, if someone else can work on the theorem article. — Carl (CBM · talk) 20:49, 11 May 2008 (UTC) h

I have no objection to your clarification at all, M Hardy. The distinction you make is correct. I don't understand the offense, however. Be well. Pontiff Greg Bard (talk) 20:55, 11 May 2008 (UTC)
The offense lies in replacing an understandable lede describing a concept used widely in both mathematics and mathematical logic, and turning them into unintelligible technicality focusing only on the usage in logic, as you did in these edits. Or, in other words, consider the audience: how many people reading the theorem article will find it helpful to have the second and third links of the article be to abstract object and type-token distinction? If they follow those links, will it help them to learn about what a theorem is? —David Eppstein (talk) 21:27, 11 May 2008 (UTC)

Both these articles will benefit from having a few more people participating on them, so that the editing pool has more breadth. — Carl (CBM · talk) 21:05, 11 May 2008 (UTC)

To Gregbard: You should not be defining words like "theorem" and "formula" in terms of "token" which, as far as I am concerned, is a meaningless noise. "Abstract object" is also nonsense. JRSpriggs (talk) 23:37, 11 May 2008 (UTC)
To be fair, they aren't really nonsense. It's more a question of weight, and presenting things in a way that conveys the correct sense of the field to others. Given that essentially no mathematical logic text will define a first-order formula as a token, I don't think the first sentence of our article should dwell on it. But it may be relevant to include lower down. — Carl (CBM · talk) 23:42, 11 May 2008 (UTC)
Basically, you guys place little to no priority on explicating the foundations of things. In my eye, that view is as inexplicable as how irrelevant you my edits appear to you. Here I am trying to tell what the thing is in some fundamental way. That clarifies it, and clarification is the main project of analytic philosophers. The audience to which I write is a reasoner in the spirit of the doxastic logic article. That means everybody: the average person, the logician, the mathematician (in so far as they follow reason). I take my cues from what an analytic philosopher would say x is for any article within the purview of logic. That is the perspective that should be in the first paragraph of all of the most important logic articles: template:logic. I am not worried about confusing your mathematical brethren. If that is a priority, then further clarifying language will be the way to handle it, rather than deleting, marginalizing, etc. Hopefully this type of knowledge will bridge the gap in the future. Be well, Pontiff Greg Bard (talk) 02:25, 12 May 2008 (UTC)
No, Greg, you take positions as to what the foundations of things are and present them as non-controversial, when they are anything but. Your insistence on conflating "theorem" with "formal theorem" cannot be left unchallenged. If they were the same thing, then no one would have proved any theorems before, maybe, Frege. --Trovatore (talk) 02:35, 12 May 2008 (UTC)
Could you provide any mathematics or mathematical logic text that defines a theorem as a token? It seems to me (and I am probably among the more accommodating people) that at best the articles abstract object and type-token distinction are tangential to the article on theorems. Everyone has things that they wish were done differently in the literature, but we generally try to avoid reconstructing foundations, and stick to the way that things are presented in mainstream textbooks. — Carl (CBM · talk) 02:31, 12 May 2008 (UTC)
I changed the wording from "can be proved" to "proven". If I say "the Riemann hypothesis is a theorem", it means I think someone has proved it, not that I simply accept the conjecture. CRGreathouse (t | c) 15:49, 12 May 2008 (UTC)
Well, a quibble: I think the conjecture is not really that RH can be proved in any particular fixed theory, but simply that it's true. So the example is not exactly on point the way you've worded it.
That said--you've given a pretty good example of the theorem-v-formal-theorem distinction. The collection of formal theorems of, say, ZFC, is a mathematical object that we can study in its own right (noting, say, that it's computably enumerable but not computable). If we code RH into a formal string in the language of set theory, then whether that string is an element of the collection of formal theorems of ZFC, is not a time-dependent question -- if it is, then it always has been and always will be, independently of whether some human mathematician has proved it. But whether it's a theorem in the more usual sense used in everyday mathematical discourse is a time-dependent question. Thus "theorem" and "formal theorem" are not the same thing. --Trovatore (talk) 21:09, 12 May 2008 (UTC)

Concerning the "offense". I am beginning to suspect that some people take this to mean that the person who wrote the words has sinned somehow, and that's why it alarms them to read that someone was offended. That, however, is not what I intended.

Mathematical logicians sometimes distinguish between "theorems" and "meta-theorems". But the things they call "meta-theorems" are really theorems, and the things they call "theorems" are really mathematical models of theorems in the same way that one might use a mathematical model of a bridge over a river, and the model isn't really a bridge. Michael Hardy (talk) 00:21, 13 May 2008 (UTC)

## discourse, interpretation, model

I'm afraid a lot of articles are in a shambles right now. I am not a professional mathematician - though, I have a hard-earned degree, and am working toward another. I believe that these terms describe different things, though lately there has been a ton of work done to blur, if not eliminate, this distinction. Here is what I believe is the difference, simplified, between these terms:

The discourse contains primitive terms, like elements, relations, operations, and so forth. It also contains a set of unproved statements about the primitives, which we can call 'axioms' or 'postulates'. All other definitions and statements in the discourse come from the primitives and axioms. 'Theorems' are logically deduced from previous statements.

If for the primitives we substitute definite terms that convert all of the postulates into true statements, then this set of substituted terms are called an interpretation of this particular discourse. If all deductions are correct, then the theorems are now true statements as well. The result of such an interpretation is called a model of this particular discourse.

There.

Now, can some experts please, please, please clarify the above for any non-experts who are drastically modifying (if not vandalizing) these articles so that we can start to repair the related articles? Tparameter (talk) 14:13, 12 May 2008 (UTC)

In contemporary math logic, the terms are used somewhat differently than that. The term discourse isn't used at all. An interpretation gives semantic meaning to the symbols of a language; in first-order logic an interpretation is also called a structure. So for example, if the language has a single binary function symbol, +, an interpretation is a set together with a concrete function that interprets the + symbol. A model of a set of axioms is an interpretation that also makes the axioms true. So for example, the interpretation above might be a model of the group axioms, or it might not. — Carl (CBM · talk) 14:19, 12 May 2008 (UTC)
Look at interpretation (logic) and Formal interpretation, and see how these various terms are at times combined and confused. Search each for "discourse", "interpretation", and "model", and you'll see that they are at times used as synonyms. In fact, various model articles and interpretation articles have recently experienced various degrees of combining/inter-meshing.
I was taught the type of meaning I noted above, though I'm not sure that I've summarized it well enough - but, I'll defer to PhDs, and hope for the best. Tparameter (talk) 14:30, 12 May 2008 (UTC)
Yes, there is a lot of confusion about interpretation (logic) and formal interpretation. I was hoping you would be able to shed some light on the philosophical use of the terminology. — Carl (CBM · talk) 14:32, 12 May 2008 (UTC)
First, let me clarify that your definition of model is consistent with what I believe to be true, which distinguishes it from the definition of interpretation. In fact, I'm not sure how what you said really differs from what I said, other that being more specific to logic.
I took a formal course in math logic (taught in the Philosophy department) not that long ago, so I'll dig the Boolos text out and refer to it specifically - but, I'm not a logician. I'm sure several logicians here could attack this with much more accuracy than me. I really just wanted to bring attention to the ambiguity that has recently arisen. Tparameter (talk) 14:36, 12 May 2008 (UTC)

## Is ugly duckling hocus pocus?

The article Ugly duckling theorem which is in Category:Set theory seems to me to be a bogus article. What do you think? JRSpriggs (talk) 18:58, 3 May 2008 (UTC)

On first sight, I would say the "theorem" is probably a meme rather than a theorem, and it seems to have been around for some time. [63] Google Books confirms that the PDF file linked from the article is not a hoax either. [64] I would say the real question is whether it's notable, but that's probably not a mathematical question. --Hans Adler (talk) 19:18, 3 May 2008 (UTC)
(e/c) It appears legitimate to me (see Scholar). The article is poorly expressed, and poorly categorized as well (Category:Set theory is pretty obviously inappropriate). This may be an actual theorem, although a proper statement and reference would obviously be need to establish this. silly rabbit (talk) 19:24, 3 May 2008 (UTC)
I have run into this article before. My impression is that this is an interesting issue for artificial intelligence; the argument given in the article is enough to imply that artificial intelligence software may need to be programmed to value some relationships more than others if it is going to simulate human judgment. But the topic is unrelated to set theory. I changed the categories some. — Carl (CBM · talk) 20:00, 3 May 2008 (UTC)
Update: Arthur Rubin (talk · contribs) has PRODed this article. JRSpriggs (talk) 12:17, 4 May 2008 (UTC)
I have de-PRODed it, and provided an additional reference. There are about 60 links to this theorem on Google Scholar, so Arthur's PROD reason doesn't hold up. More references are available, but I don't have time to sort through all of them to find those which will enhance a reader's understanding of the article: many of them are technical reports and papers, which only mention the theorem in passing. At any rate, the theorem is notable, and more references establishing notability can be given if needed. I think this article should be kept (but cleaned up significantly). silly rabbit (talk) 12:55, 4 May 2008 (UTC)
I think if we frame it right that is the important part. I knocked it down a bit, myself. Pontiff Greg Bard (talk) 23:16, 6 May 2008 (UTC)
What a profound theorem. If we discard all information about objects, we cannot systematically classify them. Has this ever surprised anyone, expect perhaps by its hocus-pocus (pseudo)mathematical explanation? CRGreathouse (t | c) 16:09, 13 May 2008 (UTC)

## mathscinet bibliography format

Hello,

I noticed that bibliographical references in math articles tend to follow the format usually used for physics papers. This is a bit odd. I suggest the mathscinet format. I have used it in all the articles I have written. There are a number of differences. For example, the year, instead of appearing in parentheses at the beginning of the entry, appears toward the end (before page numbers). Katzmik (talk) 14:25, 7 May 2008 (UTC)

I think you mean the format that Mathscinet uses for search results, e.g.:
Wiles, Andrew Modular elliptic curves and Fermat's last theorem. Ann. of Math. (2) 141 (1995), no. 3, 443--551.
I prefer the year near the beginning when I use author-date referencing such as (Wiles 1995), since the year is needed to look up the reference. This is the format produced by Template:citation as well:
Wiles, Andrew (1995), "Modular elliptic curves and Fermat's last theorem", Annals of Mathematics. Second Series, 141 (3): 443–551, ISSN 0003-486X, MR 1333035