Wikipedia talk:WikiProject Mathematics/Archive/2008/Mar

Help me not WP:BITE the newcomer

Katsushi (talk · contribs · logs) has made some less-than-useful changes to several articles. He removed a mention of Rosser's theorem [1] from Prime-counting function and deleted a reference to Dusart's prime number bounds [2] on Prime number theorem. He had earlier removed some results on Wieferich prime (since re-added), and his recent change there also seems not to benefit the article.[3]

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

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

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

That's WAREL, who else. I reverted the edits which have not been reverted before. Oleg Alexandrov (talk) 03:09, 2 March 2008 (UTC)

Ah, I guess that would explain it wouldn't it. Well, at least I assumed good faith properly... CRGreathouse (t | c) 05:28, 2 March 2008 (UTC)

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

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

Seems fairly uncontroversial to me. You might consider in addition putting a {{See also|List of mathematics articles}} at the top of the Lists of mathematics topics page. (Or, perhaps, an appropriate {{dab}} template. But that seems a bit pedantic.) Silly rabbit (talk) 16:58, 2 March 2008 (UTC)

I have redirected the page as proposed. Since the first paragraph of the article links prominently to List of mathematics articles, the proposed addition of a disambiguation notice as a hatnote seemed like overkill... --Orlady (talk) 19:03, 2 March 2008 (UTC)

I see about the hatnote. Quite right. Silly rabbit (talk) 23:06, 2 March 2008 (UTC)

Navigation versus browsing

At Wikipedia:Move navigational lists to portal namespace, it says:

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

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

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

Featured status

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

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

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

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

I have a hard enough time with featured articles, let alone featured lists. The page you mention (lists of mathematics topics) is quite nice. I like it; but I don't think I'll like it any more if it has a little star next to it. Why should we care if a list is featured or not? Is there any real benefit to be had? Before I spend time and energy arguing for featured status I want to know what there is to be gained. -- Fropuff (talk) 03:15, 4 March 2008 (UTC)

As I understand it, there's a question mark over whether this will even qualify for consideration for featured list status if it gets moved to Portal namespace (see previous section and Talk:Lists_of_mathematics_topics#Survey). Until that's resolved I don't see much point trying to get featured status back. (I'd agree that the main reason for its removal seems of questionable relavance for such a list.) By the way, I like this page but I wasn't even aware of its existence until yesterday; surely it should have a (fairly prominent) link from the Mathematics Portal? Qwfp (talk) 10:18, 4 March 2008 (UTC)

I do recognize some of the names, such as that of Michael Hardy :) and CBM, neither of which !voted Keep.  --Lambiam 12:00, 4 March 2008 (UTC)

To be fair, I didn't vote at all. I just pointed out the inanity of asking for references to verify that the topics in the list are actually related to mathematics. My personal opinion is that there isn't much benefit to adding them, so I don't mind that it's no longer a "featured list" if that is the concern. — Carl (CBM · talk) 22:32, 4 March 2008 (UTC)

Counting number

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

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

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

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

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

Good catch. But what a pain; there's no definitive answer and lots of potential for fruitless debate over trivia. Maybe we could redirect them both to natural number and then remove all discussion of "counting numbers", which after all is more an informal description for children than a precise technical term.

Reminds me of an exchange from The Restaurant at the End of the Universe, which from memory goes something like this:

"How many escape pods are there?" asked Ford.

"None", said Zaphod.

Ford goggled. "Did you count them?" he shrieked.

"Twice", said Zaphod.

--Trovatore (talk) 19:18, 4 March 2008 (UTC)

I've made less drastic changes. I've made counting number at Natural number share in the ambiguity of zero's membership, while at Cardinal number I've added the stipulation that 0 be included. Also the plural redirects now to Natural number.  --Lambiam 21:14, 4 March 2008 (UTC)

Tangent

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

Note also that Tangent function redirects to Trigonometric function. Not just a marriage of inconvenience, but also an apparent divorce. Silly rabbit (talk) 02:27, 22 February 2008 (UTC)

Yeah, I've noticed this a few times too. It needs fixing. What new article/linkage/redirection organisation are you proposing? Can we find a way to make incoming "Tangent" links go to some sort of disambiguation page where both meanings are listed (c.f. secant)? That way we'll be no worse off than at the moment (when users are thrown into the schizophrenic article), and we can pick away at disambiguating the links at our leisure. I notice there is already a Tangent (disambiguation) page though. Matt 12:03, 22 February 2008 (UTC). —Preceding unsigned comment added by 81.129.128.2 (talk)

I think the article should cover the geometric concept with a note at the beginning directing people interested in the trig function to the Trigonometric functions article. --agr (talk) 19:11, 22 February 2008 (UTC)

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

What precisely needs to be done? — Carl (CBM · talk) 14:26, 5 March 2008 (UTC)

Someone should go through the incoming links from articles seen in "what links here" and change all those links to "Tangent" that use the term in the sense of trigonometric functions to "Trigonometric functions" (or to the redirect "Tangent function", if that is preferable in any way). Arcfrk (talk) 20:46, 5 March 2008 (UTC)

I'll work on it. Most of the links that need to change should change to tangent (trigonometric function) in case that ever becomes an actual article. — Carl (CBM · talk) 14:58, 6 March 2008 (UTC)

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

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

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

Personally, I dislike having multiple articles, each consisting of nothing but a definition. I think the model of Eigenvalue, eigenvector, and eigenspace is far superior both from a professional and pedagogical viewpoint. So I think having all the trigonometric functions redirect to Trigonometric function is reasonable. — Carl (CBM · talk) 17:59, 6 March 2008 (UTC)

I advocate little disambiguation articles taking the opportunity to explain the ambiguity (which explanation might be buried deep in the main articles), as they sit at just the spots where readers are more likely to be confused; like street-signs at cross-roads. In particular in this case, it's not "nothing but a definition" as it explains the ambiguity (from the etymology of tangent)-- maybe not well. Pete St.John (talk) 18:33, 6 March 2008 (UTC)

Hoax?

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

Looks like a hoax to me: [4] [5] [6] [7] [8] [9] [10]. That and the language in the article is a bit.. overinflated. Reads alot like a hoax/fake bio. Troy Raeder appears to be a Notre Dame grad student in CS, and Danny Chen appears to be a young CS prof there (not the chair, certainly no chair named after him). --Cheeser1 (talk) 16:15, 5 March 2008 (UTC)

Danny Z. Chen is a prolific algorithms researcher at Notre Dame who likely warrants an article here, and it looks like there is some grain of truth to the page, under all the hoaxing. But I don't see the point in trying to tease it out from the article as written. —David Eppstein (talk) 16:26, 5 March 2008 (UTC)

Especially since it would need to be Danny Chen or Ziyi Chen or something - not Troy Raeder. I say speedy this thing, and if anyone wants to create Danny Chen they are welcome. --Cheeser1 (talk) 16:30, 5 March 2008 (UTC)

"Danny Z. Chen" is the form I've most commonly seen his name. I've added him to my list of missing computational geometry researchers, but there are several other names there that I would consider a higher priority. —David Eppstein (talk) 16:41, 5 March 2008 (UTC)

I tagged it with {{hoax}}. We typically don't speedy-delete hoaxes; at least, we should give it a couple days for the author to respond.

I agree Chen looks like a candidate for an article, although I am not yet sure that he meets any of the WP:PROF criteria. — Carl (CBM · talk) 16:39, 5 March 2008 (UTC)

We don't speedy hoaxes? Since when? WP:CSD#G3 seems to say we do. --Cheeser1 (talk) 16:48, 5 March 2008 (UTC)

I think that's for "obvious hoaxes" a la "Fred, the chicken from outer space". Nothing wrong with a {{prod}} here, IMO. Silly rabbit (talk) 16:57, 5 March 2008 (UTC)

It's pretty obvious to me. It doesn't say "patently stupid or nonsensical hoaxes," it just says "obvious." Regardless, I'm not objecting to the prod, I'm just voicing my opinion that CSD#G3 applies here. -- Cheeser1 (talk) 17:00, 5 March 2008 (UTC)

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

OR in calculations

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

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

Simple calculations are fine, provided that they are uncontentious and clear to anyone with a basic understanding of the area. The main OR concern is if the calculation is being used for a polemical purpose.

On the other hand, we probably shouldn't claim a published source is "wrong" based on our own calculations. If it is wrong, the right thing to do is usually just to ignore it and use other sources instead. If multiple published sources make the same "error", it may not be an error at all. — Carl (CBM · talk) 14:46, 6 March 2008 (UTC)

If it's a mistake in simple routine arithmetic of the kind referred to above, which anyone 7th-grader can check in a minute, I'd have no problem asserting in a Wikipedia article that it is an error. Michael Hardy (talk) 20:23, 6 March 2008 (UTC)

I wonder whether I crossed the line today in [11] where I corrected a 1000-digit prime in OEIS. It's easy to verify with bignum software, but is that acceptable? The only source I know with the right number is selfpublished by myself (Jens Kruse Andersen), so I didn't mention it: [12]. Maybe I could find another source somewhere but I have submitted the correct number to OEIS and will update the article when OEIS updates (which I assume they will). Getting a false online source to correct itself seems a good way to deal with the problem, but obviously impossible in many cases. PrimeHunter (talk) 23:50, 6 March 2008 (UTC)

All of a sudden your username makes sense. If we are quoting a source with a mistake, we use [sic] to indicate a problem. If we are simply saying "here is where the sequence is found on the OEIS" we can correct it, I believe, without remark - in this case especially, it was clearly a typo, and not a deliberate mistake or mistake worthy of any consideration (the fact that it's hard to find/fix notwithstanding). --Cheeser1 (talk) 01:02, 7 March 2008 (UTC)

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

Well it has happened where I have had a long fight with an admin who claimed that converting numbers like 312/783 into percentages is WP:OR. And now I am dealing with a slightly more complicated situation, but again being told that it is OR. And when I read math and physics pages, I see that people do all kinds of calculations and manipulations with seemingly no problem. Oh brother...--Filll (talk) 21:27, 6 March 2008 (UTC)

Who was that administrator? Michael Hardy (talk) 01:18, 7 March 2008 (UTC)

That was violet/riga.--Filll (talk) 01:40, 7 March 2008 (UTC)

I was in a situation once where some guy demanded a citation that 2 is the number that comes after 1. It was a strawman argument related to something else entirely, but the sheer misunderstanding of WP:V blew my socks off. One can verify in any text on, say, number theory that 2 is the successor of 1. It is verifiable. So too is the fact that 0.35 = 35%. WP:V demands that things be verifiable, not verified. WP:RS and WP:V don't demand sources of every sentence, and WP:OR only forbids things that are research and original conclusions. 0.35 = 35% is hardly original, research, or unverifiable. --Cheeser1 (talk) 21:30, 6 March 2008 (UTC)

Unfortunately Wikipedia is flooded by non-OR fundamentalists. Their fanatism is invariably caused by lack of underatanding. I have actually given up some battles in this area. JocK (talk) 21:52, 6 March 2008 (UTC)

Yes. Nice neologism, though. Pete St.John (talk) 22:16, 6 March 2008 (UTC)

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

Polynomial ring

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

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

with the formal series

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

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

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

I myself am arguing that the sums with limits appear first, to mimic what would be seen in an introductory college course. The limitless sums should appear in the formal definition section a little later, where polynomials are already quite formal. The sums for more general exponents appear even lower under generalizations, and look like:

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

where N is defined to be some monoid, and the inner sum of the cauchy product is explicitly mentioned to have i, j vary over all pairs in N×N summing to n.

Basically, Oleg feels the limitless notation requires complex ideas to explain the simple, and I say that we should include both points of view, but begin with the schoolbook (ok, English-centric schoolbook) version, and include the others after. JackSchmidt (talk) 16:22, 26 February 2008 (UTC)

I think that the infinitary expression requires more editing to make sense, as the sum of an infinite number of 0's is not necessarily 0. I've edited in what I consider necessary for it make sense without going to the formal power series domain. I'm willing to let other decide whether it's now more complicated than the correct finite formalism. — Arthur Rubin | (talk) 22:03, 26 February 2008 (UTC)

It is new to me that 'the sum of an infinite number of 0's is not necessarily 0'. What else can it be? x = Σ0 satisfies the equation 2·x = 2·(Σ0) = Σ(2·0) = Σ0 = x, implying x=0. Bo Jacoby (talk) 09:01, 27 February 2008 (UTC).

Bo, your argument assumes that the sum has one and only one value. It also assumes that the distributive law of multiplication over addition works for infinite sums. Both are questionable assumptions. JRSpriggs (talk) 09:54, 27 February 2008 (UTC)

Sure, if no assumptions are made then any definition can do. If an expression has more than one value then it is not well defined. If the distributive law does not apply then it is strange to call it a sum. Is there any sensible or standard mathematical theory where Σ0 ≠ 0 ? Bo Jacoby (talk) 10:02, 27 February 2008 (UTC).

Try formal power series or divergent series. To the real issue at hand: your notation is imprecise and nonstandard. The other two versions, both of which (I think) appear in the article are better and widely-used. Why are you (once again) trying to push nonstandard notation into articles? What's there is fine. There's no reason to change it, at least not to your notation. --Cheeser1 (talk) 19:22, 27 February 2008 (UTC)

Cheeser1, your two links show no examples of Σ0 ≠ 0 . What is the imprecision of the limitfree notation? The fourth sum in the multiplication formula is limitfree anyway, so why do you accept that? There exists no standard for mathematical notation, so stop talking about nonstandard notation. The formula with limits is not correct, as explained on the talk page. You are welcome to correct it if you don't want me to do it. I am pushing for simplicity and correctness here. So are you, I trust. Bo Jacoby (talk) 13:47, 29 February 2008 (UTC).

There exists no standard for mathematical notation, so stop talking about nonstandard notation. This comment reflects a gross misunderstanding of how mathematical notation works. Just because not all mathematicians use the exact same notation doesn't mean there are not standards and accepted notations. Notice above two versions of the same sum, and yet both are accepted. Your third version, however, is not a notation that is widely-used or commonly accepted. Every time you pull this nonsense, you make the same argument: "there's no such thing as standard notations, so you can't tell me not to fill the article with the notation I want to." Besides being based on shaky, if not patently false, presumptions about notation in mathematics, you have to realize that no one else uses this notation and no one else wants to change it: please follow consensus and stop wasting your time conjuring up new and interesting notation changes that are just going to cause conflict. --Cheeser1 (talk) 16:42, 29 February 2008 (UTC)

Cheeser1, I dont know what 'third version' you are talking about. The limitless notation $\sum _{k}a_{k}X^{k}\,$ is used in Polynomial_ring#Definition_of_a_polynomial, and another example, $\left(\sum _{i}a_{i}\right)\left(\sum _{j}b_{j}\right)=\sum _{i}\sum _{j}a_{i}b_{j}$, is found in summation. I did not put it there. So you are simply wrong in assuming that 'no one else uses this notation'. Actually it is commonly used and there is no reason for you to get upset. Bo Jacoby (talk) 00:37, 2 March 2008 (UTC).

Bo, a classic example is that clearly 0=+1-1, but the infinite series +1-1+1-1... does not sum to zero. There's even an entire WP article on this, I don't remember the name. I agree with Oleg, the concepts should be explained with the simplest possible terms. Infinity should be avoided: the more you get to know infinity, the more viciously complicated it turns out to be.linas (talk) 04:51, 29 February 2008 (UTC)

Linas, 1−1+1−1... ≠ (1−1)+(1−1)... because you are not allowed to insert an infinite number of parentheses in a series. The WP article you forgot may be this. I too agree that the concepts should be explained with the simplest possible terms. The explanation with the simplest possible terms is the one without limits. Unlimited notation does not imply an unlimited number of (nonzero) terms, and so infinity is avoided. Bo Jacoby (talk) 13:47, 29 February 2008 (UTC).

Linas' reference may have been Grandi's_series. Bo, I don't understand the rule "you are not allowed to insert an infinite number of parentheses in a series". Also, the notation "Summa (for a in A)" is unambiguous and defers to the cardinality of A; you might prefer that to "Summa (over a)" (and pardon my typography, I write in C not LaTex :-) Pete St.John (talk) 18:27, 29 February 2008 (UTC)

PeterStJohn, thank you for the link. Grandi's_series actually answers your question: to the extent that it is important to be able to bracket series at will, the series 1 − 1 + 1 − 1 + … has no sum, but if it is important to perform arithmetic its sum is 1⁄2. That means that if the series has a value, then you are not generally allowed to bracket series at will. Any geometric series, x = 1+a+a²+··· = 1+(a+a²+···) = 1+a(1+a+a²+···) = 1+ax , formally satisfies the equation x=1+ax. If a≠1 this equation has the unique solution x=(1−a)⁻¹. So

1 + 0 + 0 + 0 + ··· = (1−0)⁻¹ = 1,

1 + 1/10 + 1/100 + 1/1000 + ··· = (1−1/10)⁻¹ = 10/9,

1 + 1/2 + 1/4 + 1/8 + ··· = (1−1/2)⁻¹ = 2,

1 − 1 + 1 − 1 + ··· = (1−(−1))⁻¹ = 1/2,

1 + 2 + 4 + 8 + ··· = (1−2)⁻¹ = −1,

1 + 10 + 100 + 1000 + ··· = (1−10)⁻¹ = −1/9,

Not all rules for (finite) sums apply for infinite series: A (finite) sum of integers is an integer, and a (finite) sum of positive terms is positive, but here you see a series of positive integers having value which is neither positive nor integer. Many mathematicians find this counter-intuitive and prefer not to assign a value to a divergent series. This is legitimate. If you do not want to assign a value to some expression, nobody forces you. On the other hand, if you want to assign values to these expressions, there is no freedom as to which values the expressions should be given, assuming that you want the elementary arithmetic rules to apply. That the value of a series having only a finite number of nonzero terms is equal to the sum of the nonzero terms, is however uncontroversial. As to your suggestion, I do find it acceptable, but some other editors might not. Bo Jacoby (talk) 01:48, 1 March 2008 (UTC).

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

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

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

"Just because Bo said something, that doesn't make it untrue." But that is the way to bet. And, in this case, it really doesn't make sense without introducing either formal sums or the convention (or, perhaps, theorem, but it's more advanced mathematics than necessary for this article) that 0's can be removed from infinite sums without effecting the value. — Arthur Rubin | (talk) 18:17, 1 March 2008 (UTC)

Arthur Rubin, do you have an example of me saying something untrue? Bo Jacoby (talk) 00:37, 2 March 2008 (UTC).

That "you are not allowed to insert an infinite number of parentheses in a series." It's ANY infinite change in a non-absolutely convergent series.

That there may not be problems in summing an infinite number of zeros. $\int _{0}^{1}1\ dx$ looks like the sum of a continuum of terms, all equal to 0, in some formalisms.

However, it is true that any sum, in which only a finite number of terms are non-trivial, can be rearranged arbitrarily. If you rewrite the boundless sum to remove "trivial" terms, rather than terms whose value happens to be 0, it seems mathematically acceptable without being confusing.

— Arthur Rubin | (talk) 14:41, 2 March 2008 (UTC)

What is the difference between 'non-trivial' and 'non-zero'? Bo Jacoby (talk) 23:00, 2 March 2008 (UTC).

In most cases, there wouldn't be any. However, I'd like to emphasize that the terms that we are suppressing from the sums are structurally omitted, leaving all of the sums finite, rather than there being only a finite number of non-zero terms. As for omitting zeros in general, if you allow "1 - 1 + 1 - 1…" to have a meaningful value (1/2?) , you have to agree that it's different than "1 + 0 + 0 - 1 + 1 + 0 + 0 -1…" (3/4?), even though they differ only in the addition of 0's. — Arthur Rubin | (talk) 20:08, 3 March 2008 (UTC)

That Grandi's series is 1/2 is the result only of fixing the spectral asymmetry to a certain particular value. Choosing other asymmetries will give different answers. linas (talk) 17:54, 4 March 2008 (UTC)

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

Frequently viewed articles

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

I noticed a couple interesting things:

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

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

I did a similar thing a while back User:Salix alba/One day of mathematics page views and there was som discussion in the Jan archive.[13] --Salix alba (talk) 23:31, 8 March 2008 (UTC)

I think that's really informative, many thanks Carl. I found User:Salix alba's list interesting too but it's good to have results from a longer time window and to have it integrated with the other tables at Wikipedia:WikiProject_Mathematics/Wikipedia_1.0 and its subpages. Can I suggest moving the hitcount list to somewhere a bit more permanent than your sandbox, such as a subpage of Wikipedia:WikiProject_Mathematics/Wikipedia_1.0? Perhaps "frequentlyviewed=yes" could then give a link to there instead or as well as to http://stats.grok.se.

Just to be clear that I'm not suggesting hit counts are a substitute for human judgment of the "importance" rating, but they can help inform it. I'd argue that being frequently viewed is a sufficient but not a necessary condition for an article to be considered important (it seems unlikely people are looking at say "standard deviation" for entertainment or amusement, unlike say "Britney Spears"). Qwfp (talk) 11:04, 9 March 2008 (UTC)

Few people read Wikipedia math articles on Sundays

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

...maybe especially the frequently viewed statistics articles. Look at normal distribution. Every Sunday between 3000 and 4000 people view that article. On Mondays it's a bit higher; then on Tuesdays it jumps to almost 7000 and sometimes more than 8000. Similarly with Poisson distribution except that the numbers are somewhat lower. Michael Hardy (talk) 22:50, 9 March 2008 (UTC)

Perhaps many of the readers of statistics articles consult them in a professional capacity, while at work.  --Lambiam 23:00, 9 March 2008 (UTC)

Or school. --Cheeser1 (talk) 23:44, 9 March 2008 (UTC)

Maybe it's a time zone thing but I reckon it's Saturdays that have the lowest viewing figures for the statistics articles, closely followed by Sundays. I agree with Cheeser1 about the most likely explanation. Qwfp (talk) 10:32, 10 March 2008 (UTC)

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

Improvement drive

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

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

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

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

I would definitely like to see the CotM revitalized. I've worked on Group (mathematics) quite a bit, but it doesn't feel like a big concerted effort, and how could it be after six months! I admit I don't find anything on the list above too appealing, but perhaps a general statistics improvement drive? Median, Confidence interval, ANOVA, and Probability might be a decent collaboration, and might not die out so quickly if the CotM becomes the Cot6M? Also a wide variety of editors can assist: I think median and probability are covered in grade school these days, and a wide variety of college students have had some exposure to confidence intervals, and probably most social scientists have experience with ANOVA. JackSchmidt (talk) 23:24, 9 March 2008 (UTC)

I looked at the Analysis of variance article, and believe it is surprisingly well-done for a short article. It is not very beginner-friendly at present, and (like most math articles) it is not strong on the history. It should not be a ton of work to get it up to GA or FA, or whatever members of this project believe it is sensible to try for these days. I might be able to help on referencing and history. EdJohnston (talk) 19:45, 12 March 2008 (UTC)

Well, to my mind an article on ANOVA without a single ANOVA table is missing a vital element, as I said (less forcefully) a couple of months ago on the talk page. That's one reason I assessed it as "Start" class when I gave it its first {{maths rating}} a couple of days later, but feel free to revise it (preferably giving your reasons in the comments subpage. I've put some in most of the dozen or so articles I've assessed, but I didn't bother on that one as I'd already put something on the talk page). I think I've been put off contributing to it by the potential vastness of the topic and not knowing where to start, but that's no excuse really as I should just be bold and start anywhere. Qwfp (talk) 20:30, 12 March 2008 (UTC)

Another WikiProject

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

That's shockingly narrow. CRGreathouse (t | c) 19:27, 11 March 2008 (UTC)

Seems to be the invention of User:20-dude, who is also a major contributor to List of works designed with golden ratio. Gandalf61 (talk) 19:47, 11 March 2008 (UTC)

I put a note on the talk, what I like about the project (narrow in many ways, but oddly broad in lay-approachable examples and applications; the Fibonacci Quarterly ought to be too narrrow a topic, but it sorta isn't) and why I'm inclusionist (we will increasing able to filter and sort and so can define our own deletionist thresholds). Pete St.John (talk) 03:37, 12 March 2008 (UTC)

It's not in article space, so most of the usual inclusionist/deletionist arguments don't really apply. I just can't imagine that it's likely to have much activity. I expect it will be one of Wikipedia's ghost towns almost from day one. Which, I guess, is OK. --Trovatore (talk) 20:07, 12 March 2008 (UTC)

Game theory FAR

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

Is this a silly edit

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

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

I think it's a bit odd. WP:V does not demand that all explanatory material be supported by references. --Cheeser1 (talk) 18:53, 3 March 2008 (UTC)

There is a struggle (I think) between those of us concerned with content and pedagogy, first, vs editors concerned with policy in se. Cheeser's is a good distinction, that it's explanatory. Is there any policy reference that specifically permits explanation? What seems obvious, or even intrinsic, may be settled most conveniently with a policy ciation. Pete St.John (talk) 20:09, 3 March 2008 (UTC)

This doesn't address the larger issue, but I notice that this change was performed last October by a user who hasn't been back since, so there's not much chance of starting an edit war by reverting it, nor much point in responding with an airtight argument on the talk page. -- Dominus (talk) 20:16, 3 March 2008 (UTC)

But a couple of other people have deleted this same section over the past three years or so, each saying they found it somehow objectionable, but just what their objections were has never been clear to me. I think there may actually have been three others; I'm not sure. Is there some reason for objecting to it that can actually be explained by someone who knows what the reason is? Michael Hardy (talk) 21:11, 3 March 2008 (UTC)

I'm not one of the people deleting it, but to me the tone and approach is very colloquial, less formal than I expect the articles here to be. That may have something to do with it, I think. —David Eppstein (talk) 21:18, 3 March 2008 (UTC)

Problems with "tone" can be fixed by editing a few words, I would think. But I'm puzzled as to the specifics. Is it because the initial sentence is in the imperative mood that you find "tone" problems? As for "approach", is because it's essentially an intuitive argument rather than an attempt at mathematical rigor that you think the approach is too informal? The heading above the section tells the reader to expect something "intuitive". Can you be specific about your problems with the tone and approach? Michael Hardy (talk) 21:53, 3 March 2008 (UTC)

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

FWIW (I know, not much at all), I think the deleted explanation is quite awful, and the article is better without it. Surely there's a better way to intuitively explain the concept? Quale (talk) 04:01, 4 March 2008 (UTC)

I concur with the sentiment that the paragraph could either be rewritten to fit the article/encyclopedia better, and that it might not be as intuitive as whoever wrote it might think. But, like I said, "no references" is not reason to cut content like it was. I'd recommend explaining it more concisely, without so much "press this key, press that key" detail. --Cheeser1 (talk) —Preceding comment was added at 04:35, 4 March 2008 (UTC)

Any "justification", intuitive or not, should make it quite clear that the value of the empty product being equal to one is the result of a choice, the choice to define it thus, and that the rationale is one of expediency: because this is the more useful choice. Then only should we proceed to explain why and how this is more useful. A more appropriate title of the section might be "Rationale".

It might further help some of the mathematically untrained readers if we draw an analogy with the empty sum being 0, the neutral element of addition. For whatever reason, many people find the empty sum easier to grasp, and it is an obvious stepping stone to the empty product.

In terms of intuitive justifications, it is a fact that if you split a collection of numbers (a multiset, but for the purpose of exposition we might limit this to lists) into two parts, the product of the original collection is the same as the product of the products of the two parts. But what if one of the two parts is empty? Defining the empty product to be 1 allows means that in the statement of the fact no exception needs to be made for this case.

To top this off with an example that may appeal to people with some more mathematical background, consider the statement of the binomial theorem:

$(x+y)^{n}=\sum _{k=0}^{n}{n \choose k}x^{n-k}y^{k}\,.$

Without the empty-product convention (since raising to the power 0 is an instance of an empty product) we would be forced to write:

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "http://localhost:6011/wiki.riteme.site/v1/":): {\displaystyle (x+y)^n=x^n+\sum_{k=1}^{n-1}{n \choose k}x^{n-k}y^{k}+y^n\,.}

 --Lambiam 12:27, 4 March 2008 (UTC)

I prefer the standard this-is-like-a-sum explanation. The sum of no things is zero, because zero is the additive identity. The product of no things is 1, because 1 is the multiplicative identity. Extended examples that require too much thinking make my brain hurt. --Cheeser1 (talk) 15:09, 4 March 2008 (UTC)

It is a choice, but it is a good choice, particularly in light of the categorical result regarding empty products and coproducts (which yield terminal and initial objects, should they exist in the category, in a natural way via limits and colimits). That is, the underlying categorical structural view provides strong justification. I must admit, however, that the article section on empty categorical products is rather light, particularly when it ultimately provides the best justification for the choice that I know of. -- Leland McInnes (talk) 15:30, 4 March 2008 (UTC)

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

By fact, do you mean theorem? If so, what is the proof?  --Lambiam 20:47, 4 March 2008 (UTC)

Yes, of course I mean a theorem. If I write a proof on the fly, it will be needlessly long and complicated, but I will say this for now: I had occasion to mention this in a paper, which you can find here and was surprised by some reactions to it, so ultimately I wrote this footnote:

Perhaps as a result of studying set theory, I was surprised when I learned that some respectable combinatorialists consider such things as this to be mere convention. One of them even said a case could be made for setting the number of partitions to 0 when n = 0. By stark contrast, Gian-Carlo Rota wrote in \cite{Rota2}, p. 15, that "the kind of mathematical reasoning that physicists find unbearably pedantic" leads not only to the conclusion that the elementary symmetric function in no variables is 1, but straight from there to the theory of the Euler characteristic, so that "such reasoning does pay off." The only other really sexy example I know is from applied statistics: the non-central chi-square distribution with zero degrees of freedom, unlike its "central" counterpart, is non-trivial.

I was referring to the fact that the number of partitions of a set of size 0 is 1. The cited Rota paper was this:

\bibitem{Rota2} C-C.~Rota, Geometric Probability, {\em Mathematical Intelligencer}, {\bf 20 (4)}, 1998, pp.~11-16.

Michael Hardy (talk) 23:26, 5 March 2008 (UTC)

It is obvious from the definition of partition that ∅ is a partition, and in fact the only partition, of ∅. But how is that relevant to the meaning of the empty product? Is there a commonly accepted definition of product for which "empty product has value 1" is not part of the definition but instead a consequence?  --Lambiam 00:53, 6 March 2008 (UTC)

Categorical products (which specialize suitably to regular products of numbers when looked at the right way) are defined as limits of paritcular index categories. Taking the limit of the empty index category yields a terminal object (which gives 1 as a result under the aforementioned specialization), so that's a case of the result being a consequence of the definition. Of course whether you consider categorical definitions of products in terms of limits as "a commonly accepted definition of product" is another matter. -- Leland McInnes (talk) 19:21, 6 March 2008 (UTC)

I'd consider it a fact too (I can't imagine doing without "there is one way to choose zero things from a set of n things-- viz, the empty set") but I consider the Axiom of Infinity a fact, and the Axiom of Choice a choice (pun unfortunate), while others would disagree with me. I think for the purpose of most wiki articles we should present "the sum of zero things is zero" as mere fact, even if it doesn't hold in the Boolean Ring of Nonconscructible Categories :-) Pete St.John (talk) 19:32, 4 March 2008 (UTC)

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

I be not Quale. But I know this much: the explanation essentially says: "We multiply a by b, and then c, to get abc. Dividing abc by c, then b, then a, gives us 1. Hence, having reversed the operations to the point where no numbers have been multiplied, the empty product must be 1." Do you consider this a good explanation? --Sturm 21:13, 4 March 2008 (UTC)

I consider Sturm's explanation to be simple and to the point, in distinct contrast to the section in question. Problems with that section include: 1) it's too long, 2) introduces the extraneous "calculator", 3) appeal to intuition is difficult since the calculator doesn't resemble function of real world calculators very closely, 4) explanation of ENTER and CLEAR buttons are more extraneous details, 5) goes through a series of seemingly random steps ("CLEAR", 7 "ENTER", 3 "ENTER", 4 "ENTER") with randomly chosen small constants, piling on yet more extraneous details, 6) after all this the conclusion isn't obvious enough to be worth investing the time to figure it out. Sturm cuts the idea down to its essence, and this makes a world of difference. I don't think this is a question of a little wordsmithing. The original explanation was clunky and overly complex. Quale (talk) 00:11, 5 March 2008 (UTC)

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

Really. How should anyone instantly grasp a CLEAR button that doesn't set the value to 0 and an ENTER button that performs a multiplication? I haven't seen any calculator that behaves that way. I think the removed text was simply bad, and I may not have been the only one since it was removed several times by different people (none of them me). Quale (talk) 17:42, 5 March 2008 (UTC)

I don't love the wording in the example, however: I just brought up the MS calc in XP, which I'm sure we could call conventional and familiar. The display defaults at zero. I entered 2, multiply, 3, multiply, 5; and the display went up 2, 6, 30. Then I reversed: divide, 5, divide, 3, divide, 2; and was left with one in the display (instead of zero). After I have undone 3 multiplications with 3 divisions, I'm left with '1', related to saying that the product of zero multiplications is the multiplicative identity. I think this example has pedagogical use, but I agree it was not well worded originally. Pete St.John (talk) 19:22, 5 March 2008 (UTC)

OK, "pedagogical use", but really that's the problem here. WP is not supposed to be a textbook; it's a reference work. Anything "pedagogical" in tone is ipso facto jarring in a WP article. When you're teaching a subject you have a whole different set of goals and methodologies than when you're providing a resource for people to look things up (and, perhaps, teach it to themselves). --Trovatore (talk) 20:22, 5 March 2008 (UTC)

I've gotten that objection before ("not a textbook"); but if there were no pedagogy, the wiki would be a database, and not have prose. It's probably a matter of degree and I lean too far that way. Pete St.John (talk) 20:29, 5 March 2008 (UTC)

Well, certainly it's a matter of degree; I'm not proposing that there's a precise distinction to be had here. It's a "know it when I see it" type of thing. A rule of thumb: Would the proposed text seem too pedagogical if it were in Britannica? Then it's probably also too pedagogical here. And the text in question -- no offense meant to Michael -- is clearly on that side of the line. --Trovatore (talk) 20:54, 5 March 2008 (UTC)

Honestly, I think wikipedia should be more pedagogical. I'll take the hit here, sometimes I read these math sections can not make head or tails of them. I come to wikipedia to learn computer science, but when I have to use it for Math I often left confused. People should not have to already know the subject to understand the wiki for it. For example, the intermediate steps are weak. Not all the varibles are explained, or linked. I just spent almost an hour searching for what x meant in T(x,n). Some of you may know what that formula means, but if you do, you don't have to look it up in the first place. If you write for an audience of math teachers, your resource will never be as helpful as it could be. Math teachers probably have their own math books, already. The general tone is overly complicated. I think you should shoot for world book ease. Even if it requires a couple of extra sentences, it is worth it, if someone can undertsand a concept like O^0. —Preceding unsigned comment added by 71.175.58.64 (talk) 20:09, 13 March 2008 (UTC)

Cornu spiral images

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

I've removed the image. Although the term "clothoid" appears to be in use to describe some roller coaster loop profiles, the image was definitely not a Cornu spiral, and it's presence in the article was thoroughly misleading. I've also removed some other unsourced material. -- The Anome (talk) 11:05, 13 March 2008 (UTC)

I've now found a good cite for the use of the term "clothoid loop" in roller coaster design: the name comes from the incorporation of segments of the Cornu spiral in the loop, and the loop in its entirety is clearly not a clothoid. I've added cites to back this up, and created a redirect to clothoid loop that leads to a sourced explanation. The parametric image stays out of both articles; at the moment, it looks like a red herring. -- The Anome (talk) 11:39, 13 March 2008 (UTC)

Emmy Noether

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

I wish I paid more attention, I saw a great "life of Noether" lecture some months ago, but it's all fallen out of my head by now. Maybe I'll look up the presenter and ask for a few references and I could point you there. But don't hold your breath, I'm going to be mostly off-wiki for a while starting later today. I'll comment back here if I come up with anything. --16:02, 12 March 2008 (UTC)

Try to get Symmetry and the Beautiful Universe by Lederman and Hill. (Currently sold out at Amazon, I'm afraid.) JocK (talk) 17:42, 12 March 2008 (UTC)

Looks like I'll be able to get a copy at a nearby library. Thanks! – Scartol • Tok 19:05, 12 March 2008 (UTC)

• Unfortunately, given what she worked on, there is most unlikely to be. Noetherian rings, Noether's theorem, and the Isomorphism theorems are world-shaking, but you would have to know Lie algebra and group theory to understand even what they say. It would help if Hilbert's theorem 90 were taken down a notch, so the statement did not involve Class Field theory, but even a simplified version will still be several rungs above 3x = 15. Septentrionalis PMAnderson 19:16, 12 March 2008 (UTC)

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

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

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

I think those two are two of the ones referred to in the lecture I mentioned. Good finds. --Cheeser1 (talk) 19:29, 12 March 2008 (UTC)

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

Prisoner's dilemma

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

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

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

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

Logical connectives and hexadecimal numbers (Urgent)

Hi all, would someone please be so kind and a) check the contributions of User:Tilman Piesk regarding Logical connectives and hexadecimal numbers b) check uplodaded pictures by this user e.g. Image:Logictesseract.jpg, [14] and others. He just confirmed on de:WP that he actually invented these signs. I am not very familiar with the deletion policies within en:WP but I think this should be at least a massive breach of Wikipedia:No original research. Thanks and kind regards P.S: It might be worth for an sysop to check edits by this user on other wikipedia projects as well. --Meisterkoch (talk) 19:32, 13 March 2008 (UTC)

I've removed two images from Logical connective with "tesseract" Hasse diagrams, one with alchemy-like symbols and the other uninformative, and inserted in a bad spot. A cursory examination of Hexadecimal number shows an ill-explained but not terribly bad image with a bijection between the 16 "nibbles" and the 16 binary logical connectives. This user's edits may need some further investigation, but I don't see a great urgency.  --Lambiam 20:11, 13 March 2008 (UTC)

Great urgency is a little bit of an exageration ;-), but I was so surprised about the users boldness to spam this OR across different projects (not only in en:WP and de:WP, but also in es:WP and cs:WP. Thanks for the correction. KR --Meisterkoch (talk) 01:14, 14 March 2008 (UTC)

Mathematics Portals

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

I am not sure of the necessity of this category. Either way, it should be called Category:Mathematics portals rather than Category:Mathematical portal (so, plural and noun). Oleg Alexandrov (talk) 17:58, 8 March 2008 (UTC)

Whilst the mathematics portal get a good number of hits (4963/day [15]) as it linked from the main page, other portal do far worse, portal:Geometry only get about 44 hits/day[16]. --Salix alba (talk) 18:22, 8 March 2008 (UTC)

Based on that I tend to think that making more portals should be a fairly low priority. Who would maintain them? We haven't changed the Mathematics Collaboration of the Month for many months now and there quite a few mathematics pages that get over a thousand hits a day that are still (deservedly) rated Stub or Start class. I think these should be a higher priority. (But thanks for indirectly leading me to discover that there's a Category:Category-theoretic categories. ) Qwfp (talk) 18:55, 8 March 2008 (UTC)

I've renamed the category as suggested. Portal:mathematics is featured on the main page and portal:geometry is still in construction, the comparison is a bit rough. What about Portal:Somerset, [17] ? I think that all these subjects are vast enough, the usefulness of a portal as a navigational tool is clear here (the remark of Qwfp shows an example of that). Concerning the maintenance, I am ready to maintain portal:category theory, portal:set theory and portal:topology. I'll try to help portal:geometry too. I agree that it will take time and resources. I agree that it's a low priority but some wikipedians may be interested. Cenarium (talk) 19:14, 8 March 2008 (UTC)

I didn't mean a collaborative effort like a "collaboration of the month". Cenarium (talk) 19:20, 8 March 2008 (UTC)

That's fine, if you want to take it on I wish you good luck, just don't expect me to contribute. I recognise the content of Wikipedia is determined by enthusiasm rather than person-hours available or any particular notion of importance, whether based on page hits or otherwise. My particular enthusiasms are as quirky as anyone else's. Qwfp (talk) 19:38, 8 March 2008 (UTC)

Sadly, I'm not so knowledgeable in geometry. Maybe people interested in geometry could take a look at Portal:Geometry. Use of random portal components (see Wikipedia:Portal guidelines) makes it easier to maintain a portal, you don't have to change the selected article/image/etc regularly. Cenarium (talk) 21:59, 8 March 2008 (UTC)

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

We have already portal:Mathematics, but individual portals would be useful to navigate in a mathematical topics, for example Portal:Biology has a dozen of subportals. I wonder if anyone could find an icon for portal:category theory, like the logo of portal:mathematics. Thanks, Cenarium (talk) 22:31, 8 March 2008 (UTC)

Thanks, that clears it up - I'm not familiar with portals. --Cheeser1 (talk) 23:45, 9 March 2008 (UTC)

I also think that improving the articles is more important, many of the topics linked in the footer are B-class or even lower, for example applied mathematics. Jakob.scholbach (talk) 13:24, 10 March 2008 (UTC)

Personally, in the process of building portal:category theory, I edited some category theory articles and I think that it will be easier for me to improve them with this portal up. Cenarium (talk) 12:06, 14 March 2008 (UTC)

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

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

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

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

My proposal is to

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

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

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

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

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

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

This does seem to suggest that it may be easier to treat the topic in two separate articles. Say Gauss-Newton method (data-fitting) and Gauss-Newton method (optimization). --Salix alba (talk) 12:18, 13 March 2008 (UTC)

The algorithm is the same. It may converge a bit faster for data fitting as there it is used in a particular case. We don't fork an algorithm article just because it has more than one use. Oleg Alexandrov (talk) 15:48, 13 March 2008 (UTC)

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

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

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

• As for the history of the method (going back to Ceres, I presume?) that should really be another separate section, with its own sources; textbook accounts of the history of mathematics are notoriously unreliable. Septentrionalis PMAnderson 15:36, 13 March 2008 (UTC)

The sign convention is because Peter instead of using general functions $r_{i}(\beta )$ uses a particular case $r_{i}(\beta )=y_{i}-f(x_{i},\beta ),$ (where $f$ is the curve to fit) and then of course when you take the derivative in $\beta$ a minus pops up. This is all. Oleg Alexandrov (talk) 15:46, 13 March 2008 (UTC)

Quite so; but if that case were traditional in curve-fitting, we should explain that twist in the article, as part of the single explanation of the method. Septentrionalis PMAnderson 04:00, 14 March 2008 (UTC)

That assuming that one pauses to actually explain the method, instead of pushing the technical derivations before making clear the algorithm. Besides, the residues could as well be of the form, $r_{i}(\beta )=f(x_{i},\beta )-y_{i},$ as flipping the signs has no effect after squaring the thing. Then the sign problem goes away. Oleg Alexandrov (talk) 07:56, 14 March 2008 (UTC)

While they could be that way, that would be unconventional.  --Lambiam 08:09, 14 March 2008 (UTC)

That is probably correct. Back to the original point, data fitting is just one of the many applications of Gauss-Newton. Insisting too much on derivations for both data fitting and for a generic situation of a sum of squares, against first stating the algorithm, is, I think counter productive. See Talk:Gauss-Newton algorithm#Note for the most recent argument about this, you are welcome to weigh in. Oleg Alexandrov (talk) 13:00, 14 March 2008 (UTC)

Probability and Statistics sub-project?

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

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

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

Maybe just WikiProject Statistics. There actually is a reason why this is considered a separate subject. Michael Hardy (talk) 19:01, 12 March 2008 (UTC)

I've just written some thoughts relating to this in the comments section of the proposal. I suggest any further conversation continues there in order to keep it in one place. Qwfp (talk) 13:05, 13 March 2008 (UTC)

Or WikiProject Statistics?

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

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

Dense math pages

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

That is a rather general complaint and therefore hard to answer. Many advanced mathematical subjects require a considerable background in mathematics to even vaguely understand what it is about. An example is Étale cohomology. A crash course to bring someone with a fair knowledge of high-school maths as starting point up to speed, so that the article becomes accessible to them, would take many months. For more elementary topics, the fact is that among the people who understand these topics well, only a limited number is available as volunteers for working on these articles, and these volunteers have only a limited amount of time for that next, to their study or jobs. Finally, not everyone has equal prowess in writing clearly.

Wikipedia is not a textbook, and articles are not required to present proofs at all, or to present them in a didactic fashion. If a proof is given, however, a reader who understands the subject matter should be able to see that it is indeed a proof.  --Lambiam 08:06, 14 March 2008 (UTC)

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

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

WikiProject Statistics

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

Dunford-Pettis property

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

It certainly doesn't qualify for speedy deletion: there's enough context (if one knows to read it) that A1 doesn't apply, and it's about the wrong kind of thing for A7 to be relevant. But the many scholarly articles with that phrase in their titles convince me that it doesn't deserve deletion of any kind. Just a valid math stub, like many others. —David Eppstein (talk) 04:34, 19 March 2008 (UTC)

I have tried to bring the article more up to stub-standards. It is now wikified, categorized, has a few references, states the definition correctly (and gives more than one equivalent definition), and gives probably the most important property of these spaces (that they are "never" reflexive). silly rabbit (talk) 04:47, 19 March 2008 (UTC)

I've brought it up further. There is no doubt that this is an important, if fairly special, topic in functional analysis (as evidenced by the fact that at least two of the most influential persons in the linear functional analysis and two Fields medal winners have contributed to the theory). Arcfrk (talk) 06:24, 19 March 2008 (UTC)

Frobenius solution to the hypergeometric equation

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

I've de-TeXed (how often is that something we want?) the first section up to the beginning of the first subsection. This is very tedious, so if anyone else wants to submit to this treatment, it would be appreciated. I'm not even going to try to clean up the presentation until this is done. Ryan Reich (talk) 19:19, 20 March 2008 (UTC)

Wikipedia:Tools#Importing (converting) content from other formats to Wikipedia (MediaWiki) format has a link to User:Jmath666/latex2wiki. I haven't tried it and don't know anything about it. PrimeHunter (talk) 19:37, 20 March 2008 (UTC)

I think that converter expects ordinary latex like you would write for an article. This latex is different: all the text is inside \text{} blocks inside math mode. Hats off to Ryan for working on converting it. — Carl (CBM · talk) 20:16, 20 March 2008 (UTC)

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

Myrzakulov equations up for deletion

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

Link Starbureiy?

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

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

WP:OR discussion at Talk: Golden ratio

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

What exactly are you referring to? --Cheeser1 (talk) 07:25, 22 March 2008 (UTC)

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

Rationalisation (mathematics)

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

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

For some reason this is a big deal in the seconday-school curriculum of some spanish speaking countries (from experience) see for instance Baldor.--CSTAR (talk) 16:30, 22 March 2008 (UTC)

Now that I think of it this article [18] from the Spanish Wikipedia should also be in the English wikipedia. Baldor's algebra book, for better or worse, is probably the single most influential mathematics book in Spanish-speaking latin america. This article [19] also contains some useful information although a more reliable source would clearly be desirable. --CSTAR (talk) 16:47, 22 March 2008 (UTC)

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

Agreed. As someone who works with college students as they come in out of high school, many of them are very familiar with rationalization -- sometimes to the point where sin(π/4) = 1/√2 makes their heads explode. --Cheeser1 (talk) 17:11, 22 March 2008 (UTC)

Isn't the use of the term monomial strange? By the way, I think we should avoid making this essentially a how-to, which the Spanish version seems to be.  --Lambiam 22:48, 22 March 2008 (UTC)

Which makes me wonder if this isn't just a dictionary definition: rationalis(z)e - to make the denominator rational. --Cheeser1 (talk) 22:56, 22 March 2008 (UTC)

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

Move Proof that 22/7 exceeds π to Wikibooks?

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

I find it very annoying that the person proposing this ridiculous move has not even attempted to give any reasons for the proposal. It's hard to be patient with such things or treat them respectfully. If reasons were given one could decide whether one agrees with them and why. Michael Hardy (talk) 04:29, 17 March 2008 (UTC)

Clear consensus against the move has quickly developed. I've now closed the discussion. --Salix alba (talk) 08:27, 17 March 2008 (UTC)

Yeah, it is indeed very hard to be patient with such things, especially if an article in question is your baby, so to speak. It is nice to see that all parties did manage to keep patient and respectful, and that the issue was resolved. Oleg Alexandrov (talk) 16:36, 23 March 2008 (UTC)

Wiener sausage

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

---

Here are some things I've found on this:

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

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

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

Since you !voted, it's probably safest to wait for someone else to close it. It's not as if there's much danger of getting the wrong result. —David Eppstein (talk) 04:51, 23 March 2008 (UTC)

True, I'll hold off I suppose, but WP:SNOW (an extension of IAR) is intended to resolve bureaucratic processes like these, when they become meaningless or without merit, as soon as possible - I don't know that my !voting should matter (it is an extension of IAR, like I said). The point is to end a meaningless process as soon as possible. But I suppose caution couldn't hurt. --Cheeser1 (talk) 04:58, 23 March 2008 (UTC)

Now closed, WP:SNOW is becoming one of my favourite tools. In theory per WP:IAR a non-admin who has voted could close it as keep. The risk is that someone could contest your decision on procedural grounds leading to some further arguments. I've done a few which don't quite follow strict procedure and not had any comeback.

While the sources above are a good proof of its notability I'm not convinced they all need to be in the article, WP:NOT Google Scholar. --Salix alba (talk) 12:14, 23 March 2008 (UTC)

I was thinking the same thing about IAR, but I've been trying (quite unsuccessfully) to avoid problems on WP recently, and in anticipation of the worst, decided to leave it. And I agree - the references are great to demonstrate notability, but they aren't all necessary. Clearly, some were needed, and dropping them all in there seemed like a great way to throw the article a life preserver, but it's a bit overkill. --Cheeser1 (talk) 12:20, 23 March 2008 (UTC)

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

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

Also consider the following references:

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

but also:

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

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

Entropy (disambiguation)

I could use some more eyeballs on this page.

In my view, to help people get to the article they want most quickly, it is helpful to include structure in the page to group together meanings primarily related to Entropy in a thermodynamic sense, and those primarily related to Entropy in an Information Theory sense. However, because there is no provision for this is the WP:DAB guidelines, various editors specialising in disambiguation (who may know rather more about disambiguation than they do about entropy), would prefer to see all the links muddled together in a single (IMO much harder to navigate) long alphabetical list. Cf this diff: [20].

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

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

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

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

Update: as anticipated, logheads persisted, and the page is now protected, in their preferred, and factually wrong, version. None of them bothered to articulate his/her position at the talk page yet, although the latest edit summary referred to dab page "Zero" as a "swell example" to aspire to, and that page is very close in format to the Jheald's proposal. Arcfrk (talk) 04:01, 24 March 2008 (UTC)

The page is only protected for two days. I did get a response from two other editors on the talk page, where they explain what their concerns are. They have several concerns (well founded in my opinion) that are unrelated to the section headings. Let's continue this at Talk:Entropy (disambiguation). — Carl (CBM · talk) 12:22, 24 March 2008 (UTC)

Bibliographic references templates

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

On a similar note, last week I suddenly needed the mathematical citation finder at [21] and was dismayed when I couldn't find it on the project page. I had to grovel through the talk archives until I found it. I don't remember now who made this resource, but they put a lot of work into it, and it would be a shame if that work were wasted. -- Dominus (talk) 04:23, 24 March 2008 (UTC)

Wikipedia:WikiProject Mathematics/Reference resources has a list of different citation templates. I've also created Category:Mathematics referencing resources with all the mathematics citation templates that I know of. Hopefully this should make things easier to find. --Salix alba (talk) 09:11, 24 March 2008 (UTC)

Good work. I can never find these templates when I need them. Now they are all in one place. Gandalf61 (talk) 12:36, 24 March 2008 (UTC)

Fermat's Last Theorem in fiction on AfD

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

RfC at Talk:Connection (mathematics)

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

Locating engine

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

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

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

groups, group theory, and elementary group theory

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

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

The definition is presented twice in the group theory article, once in the poorly named "For non-mathematicians" section and again in the next section. I would move the {{main}} link up and remove the "definition" section. That would leave one definition in the group theory article, which I think is a good thing, but remove the second copy of it. — Carl (CBM · talk) 19:46, 23 March 2008 (UTC)

I think that it makes sense to have both "Group (mathematics)" and "Group theory", although, perhaps, the latter article should be rewritten from the "big picture" perspective and not repeat the basics. On the other hand, I am not entirely sure what the purpose of "Elementary group theory" might be. Looks like a good candidate for wikibooks. Does the term have a technical meaning in logic? There is a statement "Group theory" concerning undecidability that links to EGT, but it's not explained there. Arcfrk (talk) 22:09, 23 March 2008 (UTC)

It doesn't have any special meaning in logic. My impression is that it was being used to mean "group theory likely to be covered in an introductory course". — Carl (CBM · talk) 22:43, 23 March 2008 (UTC)

The article Group (mathematics) defines it thus: "Elementary group theory is concerned with basic facts that hold for all individual groups."  --Lambiam 00:50, 24 March 2008 (UTC)

I was asking about this statement, that links to EGT, but is not explained there. It seems to employ the term "Elementary group theory" in a different, precise and technical, sense. Arcfrk (talk) 05:01, 24 March 2008 (UTC)

From this review, it seems the elementary theory of groups is what I would call the first-order theory of groups. Algebraist 09:32, 24 March 2008 (UTC)

Given that groups are the central kind of structure considered in group theory, and that the definition is rather simple, it is appropriate that the Group theory article contain a definition of group. Compare Category (mathematics) and Category theory. I think the notion of group homomorphism might be treated more prominently in Group theory than it is now, even though that will increase the overlap with Category Group (mathematics). I don't see an encyclopedic need for articles in the style of Elementary group theory.  --Lambiam 00:17, 24 March 2008 (UTC)

I agree. Perhaps Elementary group theory can be merged into Group (mathematics), probably with no change to the latter article. --Hans Adler (talk) 14:33, 25 March 2008 (UTC)

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

EqWorld

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

FAR on Monty Hall problem

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

groups for good article?

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

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

Proofs in Wikipedia

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

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

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

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

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

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

Support move of project page to talk page, and developing a guideline. --Salix alba (talk) 18:00, 29 March 2008 (UTC)

Sounds like a great idea. I'm in favor. Feel free to sketch up some guidelines akin to what you've stated above. -- Fropuff (talk) 05:50, 30 March 2008 (UTC)

Page now moved to Wikipedia talk:WikiProject Mathematics/Proofs. --Salix alba (talk) 20:58, 30 March 2008 (UTC)

A task for LaTeXperts

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

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

Clearly it should say either

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

or

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

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

In my own work I prefer the first alternative - it flows better, even if the second one is formally correct. Try to read both aloud. Journal editors do not object. Jmath666 (talk) 20:06, 29 March 2008 (UTC)

I'd prefer the third, or the second except replace forall with a simlpe "for." Which to use would depend, I suppose, on how set-theoretic or formal the context is. --Cheeser1 (talk) 20:26, 29 March 2008 (UTC)

Done, with Scientific Word and my LaTeX to Wikicode translation tool this was easy. However the paper still requires some attention. Regarding style, true, it depends on the context. Too much formalism just gets in the way if the audience is not used to it. Jmath666 (talk)

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

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

Yes, I did that. And I used the style

$something=something,\quad i=1,\ldots ,N,$.

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

article needing attention

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

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

I see we already have Routh-Hurwitz stability criterion; if Derivation of the Routh array is meant to simply be a derivation "subpage" of that, I think moving it over to wikibooks might be in order. Do we have editors here who are also active on wikibooks, who can explain what the goals and standards are there? — Carl (CBM · talk) 15:35, 27 March 2008 (UTC)

It really seems like more of a small paper or something, it doesn't read like an article and I don't have confidence that it has the content to be an article. --Cheeser1 (talk) 15:37, 27 March 2008 (UTC)

The Routh-Hurwitz stability criterion is a fundamental theorem in control systems theory. While the very important result is posted in Routh-Hurwitz stability criterion article (and cited in dozens of other Wikipedia math articles), I sought not to burden the article detailing the result itself with the flow of its actual derivation. Being my first Wikipedia article, I apologize for my lack of familiarity with the various Wikipedia standards (although I'd hardly call it disregard). I'd never even used the Wikipedia TeX markup before writing it. Considering the importance of the theorem itself, and how the article breaks down very complicated and difficult to understand work done by various mathemiticians (and cites that work) into steps that your average math or engineering student could follow, I would hope that the article would stand on its merits. The amount of research in locating the original work, understanding it, and effort put into clearly expressing the steps of that work was hardly insignificant. The result it demonstrates is very significant, important and widely cited on Wikipedia. With respect to your statement regarding context, I could cite you many, many math articles on Wikipedia providing an equivalent lack of context in the article itself. Just look at any article found throught the Proofs page, like this.

--Zaxxonal (talk) 16:52, 27 March 2008 (UTC)

As a non-expert, I cannot assess whether the topic is significant enough to merit an article on Wikipedia. There is, as you point out, precedent for having articles with proofs in them, or as a subarticle. Perhaps we should explore the possibility of moving Derivation of the Routh array to a subarticle of Routh-Hurwitz stability criterion. silly rabbit (talk) 16:58, 27 March 2008 (UTC)

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

I feel rather strongly that proofs do belong in Wikipedia. The question to ask here is, does this proof deserve an article? In this case I'm not familiar with the area so I don't feel qualified to answer. CRGreathouse (t | c) 03:05, 28 March 2008 (UTC)

I respect Carl's position, but as he himself pointed out, there is no clear agreement on the matter. I personally see no harm in having proofs in Wikipedia. I have no opinion on whether they should be subpages or something else; I do agree they should not clutter up main articles. (I also express no opinion about this particular page since it is far from my specialty.) There is no reason why a proof is inherently unencyclopedic. Has this idea been revisited much lately? I know there have been some isolated discussions flaring up over the last few years, but maybe we need to work out a consensus once and for all about this proof business. Otherwise, we will see fragmented discussions just like this pop up every time someone challenges the existence of some proof page. VectorPosse (talk) 07:36, 28 March 2008 (UTC)

I am aware of the lack of agreement here, and was only offering a personal opinion. I have a lot of respect for the viewpoint that we should include a very complete collection of proofs, and I think it's mainly a question of project scope. I agree that some proofs belong in our articles, and I've put some in myself. I was trying to say above that lengthy derivations are what I'm not convinced about. In many cases I think it's better for us to discuss the ideas in the proof and the insights it provides. That sort of meta-analysis is what Wikipedia is good at. — Carl (CBM · talk) 12:56, 28 March 2008 (UTC)

I see now. The distinction between derivations and proofs is an important one and I would tend to agree with you on that count. VectorPosse (talk) 23:55, 28 March 2008 (UTC)

The issue here IMO is whether we're dumping this proof because people with experience in the subject don't think it's important, or because it's boring to that hypothetical bright 14-year-old that many people take to be the target audience around here. 24-hour news channels suck, in part, because they follow an iron rule that anything that isn't entertaining gets dumped instantly. Wikipedia does better, and must do better. It just seems inherently wrong to me to treat whether "boring" content stays as a fight, with winners and losers. Surely there's a way for everyone to win. What occurs to me, and I don't know if this has been tried, is to make more use of the the Wikibook icon, and it might say "Wikibooks has a proof of this at" with a link to the section giving the proof:

That is, if a proof is deemed too boring for Wikipedia, insert the wikibook link at a specific section in the Wikipedia text, and insert some kind of graphic in the Wikibooks text too with a link back to Wikipedia, so that people will know not to delete the text from Wikibooks without making a change back at Wikipedia. Is this a good idea? Is there something better? - Dan Dank55 (talk) 00:30, 29 March 2008 (UTC)

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

http://en.wikibooks.org/wiki/The_Book_of_Mathematical_Proofs is the link at Wikibooks for a module specifically intended to hold proofs of theorems stated outside of Wikibooks. Wikipedia is not a textbook, but Wikibooks is. I don't have an opinion on which proofs should be in Wikipedia, but for any algorithm or theorem in Wikipedia, is there any good reason to exclude a cited, important proof from Wikibooks, or not to have links going both ways, from the section with the theorem to the section on Wikibooks with the proof and vice versa? - Dan Dank55 (talk) 02:49, 29 March 2008 (UTC)

I can't see why we would avoid linking to wikibooks when the content there is relevant. It's a Wikimedia Foundation project, after all. — Carl (CBM · talk) 21:23, 29 March 2008 (UTC)

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

But, with the exception of the first paragraph, it still fails "Wikipedia is not a textbook". Arcfrk (talk) 04:32, 31 March 2008 (UTC)

Last 4 comments copied to, and conversation continued at, WT:WikiProject Mathematics/Proofs, per discussion below. - Dan Dank55 (talk) 14:58, 31 March 2008 (UTC)

Function (mathematics)

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

Excessive wikilinking?

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

I think that editor wants to make sure we know who Isaac Newton is.--CSTAR (talk)

Wikipedia:Manual of Style (links) is the relevant guideline. Yes overlinking of the same term is not good form, but the guide line does not prohibit the same term being linked to twice.

However, note that duplicating an important link distant from a previous occurrence in an article may well be appropriate (but see the exception about dates, below). Good places for link duplication are often the first time the term occurs in each article subsection. Thus, if an important technical term appears many times in a long article, but is only linked once at the very beginning of the article, it may actually be underlinked. Indeed, readers who jump directly to a subsection of interest must still be able to find a link. But take care in fixing such problems. If an editor finds themselves "reflexively" linking a term without having a good look around the entire article, it is often time to stop and reconsider.

In this case it might be appropriate to link to Newton at the start of the Newton section. In the current revision [22] it is actually quite hard to find where the link to newton is. --Salix alba (talk) 09:05, 31 March 2008 (UTC)