# Wikipedia talk:WikiProject Mathematics/Archive 33

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## 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.]

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:

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
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 $\cos(c) = \cos(a) \cos(b) \,$" 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 $\scriptstyle\log^* n$ (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 $r\ne 0\,$.

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,
$e^{ix} = \cos(x) + i\sin(x) \!$

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 $e^{iz} = \cos(z) + i\sin(z) \!$ and follows with "In particular, taking z real .. we get Euler's relation. Sometimes $e^{iz} = \cos(z) + i\sin(z) \!$ 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 $\phi$ and $\theta$, others $\theta$ and $\phi$. 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 $r$ instead of $\rho$ prevents confusion with density. My assignment now is fluid mechanics, I need $\rho$ for this.
• Using $\theta$ for azimuth, because this way the definition is identical to what you see in cylindrical coordinates.
• Using $\phi$ for zenith, because that's what's left.
• Ordering them $r$, $\theta$, $\phi$, because again this follows cylindrical coordinates.

Main problem is confusing $\theta$ and $\phi$. Yesterday was the first time I worked in spherical coordinates. In cylindrical coordinates, $\theta$ 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 $\theta$ 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 $\sin(colatitude)$ 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 $(-1)^{1/2} = i = j$. -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
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

$\int f(x)\, dx$

or

$\int f(x)\cdot dx.$

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. $\int\frac{dx}{1+x^2}$. And I have seen at least one text consistently write $\int dx\,f(x)$. 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

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

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)

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)

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.

$\chi^2(\theta) = \sum_{i=1}^N \left(\frac{y_i - f(x_i;\theta)}{\sigma_i}\right)^2 = \sum_{i=1}^N w_i \left(y_i - f(x_i;\theta)\right)^2$
Les quantités $w_i$, inverses des variances des mesures sont appelés poids des mesures.

(Literal translation) The quantities $w_i$, 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) | id={{MathSciNet | id = 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
• 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)