Wikipedia talk:WikiProject Mathematics

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ambiguity of "any"

Another reminder of the hazards of the word "any". This is from a new article titled Tsen rank:

We say that F is a T_i-field if any such system, of degrees d₁, ..., d_m has a common non-zero solution whenever[...etc...]

Does this mean "[...]if there is any system of degrees that has a common non-zero solution whenever[...etc...]", or does it mean "[...]if it is the case that _any_ such system, no matter which one, has a common non-zero solution whenever[...etc...]"? A reasonable person might read it either way. In the first case, changing "any" to "some" would resolve the ambiguity; in the second case, changing "any" to "every" would do it. "Any" is sometimes a hazardous word. I've changed it to "every" in the article. Michael Hardy (talk) 20:23, 15 July 2012 (UTC)

This seems to me to be a grammatical parsing ambiguity rather than any ambiguity of the word. Not being familiar with the context, I can't judge this instance, but my suggestion would be to try to solve this type of problem by using grammatically unambiguous sentence structures. Simply replacing the word does not technically resolve the grammatical ambiguity. — Quondum^☏ 05:09, 16 July 2012 (UTC)

I disagree. In mathematical usage, "... any X has property P" can mean either "for all X, P is true" or "there exists an X such that P is true". Changing "any" to "every" removes the ambiguity: the first meaning is indicated. For the case under discussion, this seems to be the only interpretation that makes sense. (I'm not a specialist in this area, but it seems clear that if the other interpretation is followed then every field would have Tsen rank zero.) Jowa fan (talk) 05:33, 16 July 2012 (UTC)

Nicely explained. I stand corrected. — Quondum^☏ 06:35, 16 July 2012 (UTC)

If the whole sentence just says "Any A is B", I would take it to mean "every". But if it says "If any A is B, then...", then it could reasonably be construed as meaning "If there is any A that is B, then...", which would be the same as "If there is some A that is B". So in that case it's ambiguous. Michael Hardy (talk) 23:05, 16 July 2012 (UTC)

Free logic

The quantifier "any" lacks existence claims.

("Any" is often used where free-logic pussyfooting is not intended, and where "every" or "some" should have been specified. Thus Halmos thinks that "any" should be avoided by mathematicians writing it gooder.)

Jaakko Hintikka has a nice article on "any" and ordinary English.

I forget whether Charles Sanders Peirce and his students considered free logical quantification. I think Mitchell has a paper on quantification in the 1878 Johns Hopkins Studies. Kiefer.Wolfowitz 17:13, 24 July 2012 (UTC)

Another drive-by deletion

Help! We're getting another drive-by deletion being pushed bynon-physicists of a physics topic. Wikipedia:Categories for discussion/Log/2012 July 13#Category:Introductory physics. To express my frustration: the drive-by deletion process brings out the very worst in wikipedia behavior, and creates a huge amount of damage (remember the deletion of Category:Proof, carefully nurtured for years, here, and shot dead with only three votes?) Please help get these hooligans under control. linas (talk) 01:35, 21 July 2012 (UTC)

At least some ongoing/old CfDs are listed at Wikipedia:WikiProject Mathematics/Current activity. But it is not clear how any given category is counted as part of the project. There may be several layers of bots involved, which I can't follow. Melcombe (talk) 07:38, 25 July 2012 (UTC)

Nomination for deletion of Template:Ring structures

Template:Ring structures has been nominated for deletion. You are invited to comment on the discussion at the template's entry on the Templates for discussion page. DH85868993 (talk) 11:07, 21 July 2012 (UTC)

Mizar system external links discussion

Members of the Mathematics WikiProject are cordially invited to chime-in in the on-going discussion of the pro and con of placing Mizar system external deep links on mathematical articles. Yaniv256 (talk) 16:19, 24 July 2012 (UTC)

Andreas Griewank

Professor Griewank is one of the principal architects of automatic differentiation, a co-founder of the theory of partially separable functions (the usage of which is an important part of the success of AMPL's modeling language and the large-scale optimization packages Lancelot and Galahad), an initiate of the mysteries of semi-analytic geometry, and an amateur guitarist:

• Griewank, Andreas (2010), Tuning guitars and reading music in major thirds (html), Matheon preprints, vol. 695, Rosestr. 3a, 12524 Berlin, Germany: DFG research center "MATHEON, Mathematics for key technologies" Berlin, Postscript file and Pdf file {{citation}}: Invalid |ref=harv (help); Unknown parameter |month= ignored (help); Unknown parameter |urn= ignored (|id= suggested) (help)CS1 maint: location (link)

His would be an interesting biography.

Thanks! Kiefer.Wolfowitz 17:04, 24 July 2012 (UTC)

CV on Homepage. --LutzL (talk) 18:10, 24 July 2012 (UTC)

Indefinite logarithm at AfD

The article Indefinite logarithm has been nominated for deletion. Discussion is at Wikipedia:Articles for deletion/Indefinite logarithm.  --Lambiam 23:15, 25 July 2012 (UTC)

MathJax working

It looks like the bug fixes in MathJax implementation are now working so we can have less than signs $x<y$ and matrices ${\begin{pmatrix}1&0\\0&1\end{pmatrix}}$.--Salix (talk): 07:03, 26 July 2012 (UTC)

Good news! I'm trying the switch from Nageh's version to the built in support. So far it seems a little slower to render but no appearance glitches. —David Eppstein (talk) 07:39, 26 July 2012 (UTC)

Yep seems good. I just had a look at Help:Math and there are a few square boxes instead of characters for special characters and when doing \limsup and \liminf but the Nageh version does the same. Overall I'm very pleased and will use the system version of MathJax as default. Dmcq (talk) 08:36, 26 July 2012 (UTC)

Well it all depends on what renderer I've switch on. Seemingly that was with the SVG one. With the HTML-CSS they all come out okay though the special characters are half the size. And with MathML it warns me not all the features are supported by the browser. It's a hard choice, I think I'll try the HTML-CSS for a while. Dmcq (talk) 09:01, 26 July 2012 (UTC)

MathJax is excellent, but expensive. Sadly, nobody cares about such cheapie as class="texhtml", the font in which should match MathJax's one. Incnis Mrsi (talk) 09:05, 26 July 2012 (UTC)

You get that automatically if you use {{math}} and there's some ancillary templates that go with it e.g. {{mvar}} to just format a variable quickly. However some people here have a very strong dislike of serif font in the middle of non-serif. Not that MathJax will satisfy them immediately. There's also a couple of gotchas like having to put 1= in if one uses equal signs so it is another language again. As for me I'll be putting less effort into trying to use the math tempate in future and will use <math> more even if it is a little slower. Dmcq (talk) 11:43, 26 July 2012 (UTC)

Maybe we do not understand each other. I see x or x₁ markedly different from MathJax equivalents ($x_{1}$). I suppose, although not completely sure, than this can be cheaply fixed by altering texhtml's font-family to those used by MathJax. I hope, sysops just are not aware about the problem. But if someone is aware, but deliberately keeps a substandard appearance of {{math}}, then it is definitely an unfair trick to mount a prejudice against "texhtml" typesetting. Incnis Mrsi (talk) 13:07, 26 July 2012 (UTC)

You need italics as in {{math|''x''₁}} which gives x₁. I think it is fairly close but it depends on what method MathJax uses for rendering and your browser. By the way MathJax uses the STIX fonts and MathJax will run a bit faster if you install them instead of using web fonts. I guess texhtml could put the STIX fonts as the first ones to check for but they are close enough to the usual Times one for most purposes I believe, possibly the size needs to be tweaked slightly as currently it is set to match the old png render program. Dmcq (talk) 19:17, 26 July 2012 (UTC)

It was just a typo in x₁, sorry. Incnis Mrsi (talk) 09:17, 27 July 2012 (UTC)

The font of the {{math}} template could be made compatible with MathJax by adding the CSS rule span.texhtml { font-family: MathJax_Math, serif; }. You can try this in your skin.css and if we are happy with it roll it out to MediaWiki:Common.css or ask a dev to change skins/common/shared.css. I'm not sure quite how the MathJax_Math font is loaded so the font might only change if MathJax is enabled.--Salix (talk): 06:29, 27 July 2012 (UTC)

Thanks for explanations, Salix. I have MathJax's fonts locally. I will be completely satisfied if "texhtml" had to switch to MathJax's fonts if these fonts are currently available in the browser. So, do you recommend to proceed with bugzilla: and not wait for further conclusions in this discussion? Incnis Mrsi (talk) 09:17, 27 July 2012 (UTC)

P.S. apart of the problem of font-family, there is another problem with font-size in <sup>s and <sub>s. I'm afraid that, due to CSS limitation, the best solution is to supersede that explicit HTML elements by {{ssup}}s and {{ssub}}s respectively, such as x₁. Yeah, it is another language again, Dmcq is right. Incnis Mrsi (talk) 10:09, 27 July 2012 (UTC)

After yet some meditation I realized that, since class="texhtml" is defined in templates, not by the engine itself, it would be unwise to request changes to MediaWiki. So, I started small. Incnis Mrsi (talk) 11:30, 27 July 2012 (UTC)

Should we also ask for "font-size:larger" to be added. At least for me the following two match x $x$. (across multiple display settings). Not sure if this is true for all configurations of browsers/system.TR 12:36, 27 July 2012 (UTC)

I agree. Even in a browser without font-family:MathJax_Math this produces a serif text which does not looks too large. Incnis Mrsi (talk) 12:53, 27 July 2012 (UTC)

Just checked IE8 and Opera, neither of which actually pick up the mathjax font.TR 12:42, 27 July 2012 (UTC)

Did you install these fonts locally? It is useful also for the MathJax proper. Incnis Mrsi (talk) 12:53, 27 July 2012 (UTC)

Now I am in doubt again. Should font-size be better placed to {{math}} rather than to CSS? Incnis Mrsi (talk) 13:20, 27 July 2012 (UTC)

No, because then it cannot be customized by user CSS.—Emil J. 13:28, 27 July 2012 (UTC)

I see no difference between increasing font-size in CSS and doing the same in all <span>s which use the class. Both are subject to user customization. Actually, there are two templates, {{math}} and {{bigmath}}. What do you propose: To merge (effectively) these two presentations? Or to make {{bigmath}} even larger? Incnis Mrsi (talk) 13:43, 27 July 2012 (UTC)

What (I think) Emil was getting at, is that if it is conrtolled through the CSS a user/reader can specify a custom css style which changes the way math output looks. So, for example, if you detest seeing a serif font inline, you can load your own css style that set the texhtml class to a sans-serif font. As a user, you cannot load a custom version of a template.TR 15:33, 27 July 2012 (UTC)

With a bit of messing around the closes set of styles I've managed to come to is

span.texhtml {       font-family: MathJax_Main, serif; font-size: 123%;}
span.texhtml var {       font-family: MathJax_Math, serif;}
span.texhtml sup {       font-size: 70.7%; }
span.texhtml sub {       font-size: 70.7%; }

Using those styles in skin.css the following two are virtually indistinguishable.

$-3\sin(x_{2i})+\ e^{3t}$ MathJax

−3 sin(x_2i)+e^3t Using {{math}} {{math|3 sin(<var>x</var><sub>2<var>i</var></sub>) e<sup>3<var>t</var></sup>}}

MathJax uses a different font for variables, MathJax_Math, than for other content, MathJax_Main, and slightly different sizes 123% as opposed to 118%. The code is dynamically generated so it might be different in other browsers.--Salix (talk): 21:34, 27 July 2012 (UTC)

havel

what happened to V. J. Havel (see too: S. L. Hakimi) - --Rovnet (talk) 16:35, 27 July 2012 (UTC) (w:es)

It was deleted by WP:PROD in March with the rationale "Poorly-sourced BLP with questionable notability". I can undelete it for you, if you want. —David Eppstein (talk) 17:08, 27 July 2012 (UTC)

I've un-deleted it for now. I'll try to notify interested parties. Michael Hardy (talk) 17:16, 27 July 2012 (UTC)

I was the one who proposed the article for deletion. I'm not a mathematician, but at the time I found it frustrating that there was next-to-no information about the person. Havel still appears to fail WP:BLP1E and the WP:GNG, but if the article was fixed, a date of birth mentioned, and some external links offered to confirm any notability, of course I wouldn't mind if the article stayed. Jared Preston (talk) 18:42, 27 July 2012 (UTC)

He also appears to fail WP:PROF. Although I think unprodding was the right thing to do, unless more evidence comes up I'd support deletion in an AfD. —David Eppstein (talk) 22:29, 27 July 2012 (UTC)

There is also Václav Havel, a famous Czech writer who is not the same person. Sławomir Biały (talk) 18:55, 27 July 2012 (UTC)

thx . --Rovnet (talk) 04:33, 28 July 2012 (UTC)

Udita fractional operator

The article Udita fractional operator is at AfD. Please comment there. Sławomir Biały (talk) 13:56, 28 July 2012 (UTC)

In related news, more eyes would be appreciated on Fractional calculus and Erdelyi–Kober operator, where a gang of SPAs are POV-pushing to include mention of the so-called "Udita fractional operator". Sławomir Biały (talk) 17:05, 29 July 2012 (UTC)

These three SPA, namely MathProff, MathBuddy and Uditanalin lock like sockpuppetts. Can someone investigate this? D.Lazard (talk) 09:37, 30 July 2012 (UTC)

MAJOR merger!!

What a mess! Arabic numerals and Hindu–Arabic numeral system (with an en-dash, not a hyphen) are two separate articles, and Hindu-Arabic numeral system (with a hyphen) does not redirect to Hindu–Arabic numeral system (with an en-dash) but to Arabic numerals, and Arabic numeral system does not redirect to Arabic numerals but to Hindu–Arabic numeral system.

Welcome to the earliest days of Wikipedia. In 2002 and 2003 this would be expected. Michael Hardy (talk) 16:29, 28 July 2012 (UTC)

Not-so-major merger

Is there any reason why Hurwitz quaternion order and Hurwitz quaternion should be distinct article which don't even link to each other? Deltahedron (talk) 17:16, 28 July 2012 (UTC)

The first one was linked to the second one through a redirect. I have replaced it by a direct link. However the subjects are distinct: the first article consider a subalgebra in a quaternion algebra, while the second one consider only usual quaternions. As a non specialist of non commutative algebra, I have the impression that both articles concern the integral elements in a quaternion algebra, but none of the articles make clear if the notion of integer element make sense here. I have no opinion about a merger or not. D.Lazard (talk) 19:57, 28 July 2012 (UTC)

List of zero terms

List of zero terms is also at AfD. Please comment there. Sławomir Biały (talk) 19:08, 28 July 2012 (UTC)

The treatment of zero in mathematics on Wikipedia is more generally a bit of a jumble. We have:

• 0 (number)#In mathematics,
• Zero (disambiguation)#Mathematics,
• Zero element,
• List of zero terms,

each giving a list of zero terms, each incomplete, with a lot of overlap.

Note also this curious pair of redirections:

• Non-zero → 0 (number),
• Nonzero  → Nonzero: The Logic of Human Destiny.

 --Lambiam 15:52, 29 July 2012 (UTC)

Now closed as 'merge to Zero element. I've done the merge but it could do with some eyes. I also had to split off Zero order as a seperate article which is very stubby.--Salix (talk): 11:33, 7 August 2012 (UTC)

Holomorphic function

If I recall correctly, a function $f:\mathbb {C} \to \mathbb {C}$ is holomorphic in a neighbourhood of $z_{0}$ if $(\operatorname {d} \!f/\operatorname {d} \!{\overline {z}})(z_{0})=0$. There is no mention of this in the article. I'm assuming that this is a well known fact. Should we add something to the article? — Fly by Night (talk) 21:33, 29 July 2012 (UTC)

It is not sufficient that the Wirtinger derivative vanish at $z_{0}$, rather it should be zero in a neighborhood. Vanishing of the Wirtinger derivative is equivalent to the Cauchy-Riemann equations (and is mentioned in that article). Sławomir Biały (talk) 22:31, 29 July 2012 (UTC)

Elementary Algebra GA candidate

If anyone is interested, I've recently made what I consider to be a number of improvements throughout the article on Elementary algebra, and submitted it as a Good Article nominee (see the article Talk page template for details). --Iantresman (talk) 16:29, 30 July 2012 (UTC)

Real-valued function prodded

Deletion of the article titled Real-valued function has been proposed on the grounds that it's been only a dictionary definition for several years and it's unclear what to redirect it to. A problem I see with this is that a large number of articles link to it. So: (1) Is there some appropriate redirect target; or (2) Can it be expanded so that it becomes a proper article? Michael Hardy (talk) 16:57, 31 July 2012 (UTC)

I don't see any problem with letting those links go red, and removing them bit by bit. Maybe someone could get them all with AWB? --Trovatore (talk) 17:42, 31 July 2012 (UTC)

That's a difficult question okay. I think developing real analysis and redirecting there might be best. The real question is what do we actually mean by real-valued function is it instead the old idea of smooth functions including 1/x which is actually a partial function? I guess real analysis would be better for covering more classical stuff too. Dmcq (talk) 17:59, 31 July 2012 (UTC)

I just don't see much value in linking the phrase real-valued function, in most cases. I think these links probably should be removed, independently of whether there's a canonical place to redirect the search term. --Trovatore (talk) 20:16, 31 July 2012 (UTC)

Why shouldn't "partial functions" be considered real-valued if their values are real numbers? Michael Hardy (talk) 12:38, 1 August 2012 (UTC)

I think expansion would be difficult (if someone had something to say, it probably would have been said by now). A reasonable redirect would be to function (mathematics)#Types of functions. The current definition is the first line of that section.Bill Cherowitzo (talk) 18:10, 31 July 2012 (UTC)

And by the way, I didn't do the redirect I suggested because I think that Trovatore is making a good point. I've seen far too many useless wikilinks in the math pages and I would count this one as one of those. I'm sure that some discussion of standards for wikilinks in mathematics pages has already occurred - so if someone could dig it up for review I would appreciate it. Bill Cherowitzo (talk) 02:38, 1 August 2012 (UTC)

Is there such a thing as a "cross-reference page" (or should we call it by some other name?) that links to various pages that may be of interest to those who follow a link like this one? I.e. Someone clicks on real-valued function and they see a page that might look something like this:

In mathematics, a real-valued function is a function whose values are real numbers. See:

• Function (mathematics)
• Real number
• Real analysis

This is a cross-reference page.

If such a thing doesn't exist, should we invent it (along with a template for the footnote, a style manual for them, and mentions and links within the other appropriate style manuals)? Michael Hardy (talk) 12:38, 1 August 2012 (UTC)

I've raised the topic of multiple-cross-reference pages here. Michael Hardy (talk) 13:37, 1 August 2012 (UTC)

For now I've made the article into a multiple-cross-reference page and created this manual, which currently has "essay" status. Michael Hardy (talk) 00:18, 3 August 2012 (UTC)

The Real analysis article has a heading called "Key concepts." Adding a short section there on Real-valued functions, perhaps covering some of the issues mentioned above, would seem appropriate and would make a good redirect target. --agr (talk) 00:36, 3 August 2012 (UTC)

But remember that real-valued functions occur not only in real analysis, but also in other areas of mathematics and the sciences, so that can't be the whole account of real-valued functions. Michael Hardy (talk) 19:37, 4 August 2012 (UTC)

What about adding Random variable as another entry?--Kmhkmh (talk) 03:18, 5 August 2012 (UTC)

There is some similarity in these two cases. "Real-valued function" is a function to real numbers from an unspecified domain. "Random variable" is a function from the sample space to an unspecified codomain. But these are not the same. "Random variable" is a historically important concept, discovered well before modern probability space approach, and must be retained as an article. Moreover, a half of probability theory is explained with various random variables (actually, even with random events as a special case of Boolean-valued random variables), with little consideration about codomains. Contrary, "real-valued function" is not anything historically significant, nor is it important in modern mathematics. BTW, I do not see much sense in these bizarre "multiple-cross-reference pages" and would prefer to see just a red link to avoid careless inbound links, rather than such an explanation of a trivial notion. Incnis Mrsi (talk) 12:42, 5 August 2012 (UTC)

My point was not to equate those 2 concepts, but rather that a random variable is one of the most important and most examples of a real valued function. That aside I'm not sure why you'd s real valued function si historically insignificant. There would be no calculus or real analysis without it and historically it actually stand for the development of the function/map concept itself. In fact many books simply treat function as a synonym for real valued function (or a subset of them since the domain is restricted to the reals as well), i.e. if some calculus or analysis primer speaks of functions, they usually mean real valued functions.--Kmhkmh (talk) 17:18, 6 August 2012 (UTC)

The phrase real-valued function appears to be nothing more than the sum of its parts: the two links real number and function (mathematics) should in effectively every case be sufficient. To allow articles, disambiguation pages, redirects or cross-reference pages for such phrases that have not acquired a distinct notable meaning seems to be inviting a proliferation of valueless pages. (I've also seen redirects for "common misspellings" that I feel should be removed.) I am not arguing against the concept of a Wikipedia:Multiple-cross-reference page, but to me it seems that real-valued function does not qualify. — Quondum^☏ 13:25, 5 August 2012 (UTC)

Why would you delete redirects from commonplace misspellings? Michael Hardy (talk) 16:25, 6 August 2012 (UTC)

A course like "Real functions", "functions of a real variable", "real analysis", etc., has been standard in U.S. mathematics for 80 years. A disambiguation page is useful, as Michael Hardy stated. Kiefer.Wolfowitz 17:08, 6 August 2012 (UTC)

+1--Kmhkmh (talk) 17:19, 6 August 2012 (UTC)

@Quondum : It's more than the sum of its parts in that (1) there are lots of existing links to the phrase; and (2) Someone who knows that "real" should redirect to "real number" and who also knows what a "value" of a function is might not know how locutions like "real-valued" are used, and "real-valued" is not a suitable article title.

When I create a new article, I always immediately create redirect pages from (1) alternative names, (2) alternative spellings and capitalizations, (3) common misspellings, (4) common misnomers. I also add hatnotes to other articles with similar names saying "This is about X. For Y, see [[Y]]." or the like.

@Kieffer : Of course I agree, except that "disambiguation page" isn't quite what this is, since links to it are appropriate and it's not about unrelated things bearing the same name. It more like a redirect but with multiple targets for the reader to choose among. Michael Hardy (talk) 15:50, 7 August 2012 (UTC)

History of the function concept

The new article bearing this title is perhaps interesting. Some people implicitly believe that the concept of function that we know today is axiomatic and coeternal with the Father, but the true story is complicated and messy. Michael Hardy (talk) 12:28, 1 August 2012 (UTC)

Formalized form infobox experiment

A

Correct me if I am wrong in summarizing that the discussion we had at the Mizar system talk page raised two main concerns. The first is one of bias in favor of a particular formalized math system, in this case the Mizar system, violating WP:NPOV with respect to other competing systems. The second concern is that by granting permission to place these links we will be sanctioning en masse changes to almost all mathematical articles, which while may benefit a minority of readers, will probably not be of any benefit to the typical reader in the near future. One additional secondary concern was that if we want to expose the readers to formalized math it is better to develop it inside Wikimedia than sending the users to outside sources.

Before addressing these issues please allow me one personal note: I have an agenda. My agenda is to have formalized math accessible from Wikipedia mathematical articles. No more and no less. This is driven by a view that for some readers, like myself, reading code is more instructive than reading descriptive text. I am not here to write articles, but I am here to help build the best encyclopedia the world has ever seen.

I am not affiliated with any proof assistant and in fact my knowledge of Mizar is rather slim. My choice to promote the Mizar system was based on considerable groundwork I made in preparation for this initiative, but truth be told I like Coq much better. Without much understanding of how Wikipedia works, I made the judgment that the Mizar system is the one which is best suited to the task. I believe this choice can be defended on objective grounds, but seeking to avert single-purpose-account charges I will not attempt to do so here.

Next, the issues. Indeed, I realize now that Wikipedia cannot provide access to one particular formalized system, no matter its benefits, at the expense of other systems. Nor should it be in the business of picking winners. It must be either all in or all out. This does make the choice of inclusion much harder, but should not warrant, by itself, automatic submission to the deletion impulse. My answer to this concern is two-fold: yes, we will have to link to more than one system, and no, we cannot do so in the external links section. We will have to come up with some kind of infobox or an addition to an existing infobox that will accommodate these links and help keep the typical reader away from clicking them.

Second, clearly the initial scale of deployment is not to be left to individual decision making, but should result from the formation of consensus here, in the math project discussion forum. But consensus is built by discussion, so we will probably have to spend some time in deliberation. Thus, a measure of patience will be required and yes, a willingness to learn enough of a foreign formal language that it stops reading like gibberish. It is however not in the spirit of Wikipedia established policy to brush this initiative aside by not being willing to engage the other side.

Seeking compromise, I suggest that we limit the initial deployment to a small number of key non-trivial mathematical constructs, where access to a reference of formal definitions and properties can be most helpful to undergraduate math students who are working on problem sets. I further suggest that we try and measure take-up quantitatively and by field, by contacting professors and asking that they mention the links in class and ask students to make a note if they used them in the solution of a problem set. This experiment should be limited in time as well as scope, guaranteeing that the typical Wikipedia reader does not suffer too much.

Which brings us to the final concern of internal vs. external development of formal math structures. Frankly, I do not have much to say here. I wish I was in the position to help work on the developer side, but I am not. It does however seem odd to me to suggest that Wikimedia developers should put much efforts into something for which it is not clear if there is any need. First we need to establish that there is some demand for the product, then we go about building it. This seems common sense to me and provides additional impetus to running this experiment.

I thank you for taking the time to read this lengthy post and hope that I was able to address the main issues raised. Yaniv256 (talk) 21:12, 1 August 2012 (UTC)

If we are going to include Mizar system, Coq, or Metamath proofs by reference, then I think we should make sure that those proofs are available under the CC-BY-SA 3.0 License and the GFD License as are proofs contributed by other means.

I think that proof assistants are the wave of the future, but not the present or near future. They need to develop to the point that they can read proofs in English+TeX and translate them into their internal format (perhaps asking questions of the person running the program in the process). They do not appear to be there yet. JRSpriggs (talk) 04:34, 2 August 2012 (UTC)

Metamath is in the public domain, which is CC-BY-SA compatible. I can't speak to the others. CRGreathouse (t | c) 05:16, 2 August 2012 (UTC)

Formalization links
Structure	sigma-algebra
Definition in
Metamath	Coq	Mizar
Proof of properties
Metamath	Coq	Mizar
See automated proof checking for more information.

I know that Coq-Corn and the MML are open-source but I don't know much about which kind and if it is compatible. I'll have to look into it. Yaniv256 (talk) 06:26, 2 August 2012 (UTC)

To make the discussion concrete I am posting a prototype for the purposed infobox. Currently only the Mizar links will work, the others will just send you to Google. Yaniv256 (talk) 06:26, 2 August 2012 (UTC)

I am against the inclusion of formalized proofs in WP. Unless for "trivial" results they use to be too long to be read by humans. This is similar to the case of programs. On the other hand, for pages containing results that have been formally proved, we has to mention this with references (the non trivial computer aided proofs are usually published in scientific journals and/or conferences). D.Lazard (talk) 09:48, 2 August 2012 (UTC)

It's unclear to me exactly what is being proposed. Yaniv, are you suggesting that we add an infobox to lots of mathematics articles containing links to various proof assistants? I oppose this. The input to proof assistants is really not human readable, and adds nothing to the article. If you truly find it easier to read this kind of code than plain prose, and to understand its mathematical intent, then I applaud you. But that probably makes you one of a kind. Moreover, I should add that the consensus at Talk:Mizar system was decidedly against adding links to articles, largely because such links add nothing of value to the article. Now it is being proposed that a large infobox be added, taking up more valuable real estate with the same useless information. It seems most peculiar to me that you would think the consensus at Talk:Mizar system would support such an initiative. Sławomir Biały (talk) 12:03, 2 August 2012 (UTC)

That's pretty much my position too. It would be different if these systems were widely used and understood. That is if all, or at least a large number of mathematics educators used them to teach mathematics. But that would be reflected in mainstream sources: they should be used in many textbooks, and on many courses, in the same way. But this was not true when I was at university and I've seen nothing to suggest this has changed. These links are only relevant to the particular formal systems, not general mathematics articles.--JohnBlackburne^words_deeds 13:23, 2 August 2012 (UTC)

What I said on that talk page was I was against it as a general thing and pointed to WP:NOTDIRECTORY but would support such external links where formalized logic or proof seemed relevant, for example for things like variants of the axiom of choice. Sigma-algebra doesn't sound like something like that to me. 'Deployment' sounds exactly the opposite to what I was thinking of. Dmcq (talk) 14:26, 2 August 2012 (UTC)

I would support a small-scale experiment once the template is constructed. Add the template to a small number of articles where (as Dmcq says) formalized logic or proof seems relevant. CRGreathouse (t | c) 14:36, 2 August 2012 (UTC)

Please excuse my poor choice of words as I am not native to English. Let me be more precise: 7-9 pages, determined by consensus, for a period of 6 months. My choice to use sigma-algebra was probably misguided. Can I suggest that we defer the discussion of which pages to select until after we establish a consensus that running such an experiment would be desirable, in theory? Yaniv256 (talk) 19:17, 2 August 2012 (UTC)

I really don't see what all this is about. The articles in Wikipedia are all independent and there isn't really such things as experiments like this except to test out new Wikipedia features. I think you have some picture in your mind about Wikipedia that it is monolithic and organized. It isn't. Of course some people can discuss something but I think your best bet is just to go ahead and try it out, we'll all have forgotten whatever was here in six months, or at least I will as I have a dreadful memory and I don't suppose many others will care. Dmcq (talk) 20:02, 2 August 2012 (UTC)

Before attempts to try this, though, the box needs to be improved. In particular links to Wikipedia namespace (especially a redlink) from article space are not a good idea. —David Eppstein (talk) 20:41, 2 August 2012 (UTC)

Yes, that is true. Thanks! I changed it from WP:Formal math links to Help:Formal math links, which of course I will need to create before we will be done here. Any other suggestions? Yaniv256 (talk) 21:05, 2 August 2012 (UTC)

Still not good enough. Help: namespace is for help editing Wikipedia, not for explaining Wikipedia content, and should also not be linked from article space. See WP:SELFREF. —David Eppstein (talk) 21:28, 2 August 2012 (UTC)

What should I put then? Yaniv256 (talk) 21:36, 2 August 2012 (UTC)

Since we can only work in article space I think that the best we can do then is to just send readers to a page like Automated proof checking. They will have to work out the details by themselves. Formal proof and proof assistant are two other viable landing sites. Now that I took another look at these pages I see that I'll have to attend to them anyway, so don't judge them by their current form. Yaniv256 (talk) 00:39, 3 August 2012 (UTC)

Just link the title to one of those and remove the explanation at the bottom. People can click on things to find out. Dmcq (talk) 18:02, 3 August 2012 (UTC)

Sure, if you think that is better, thanks. Opening a new page and pasting prototype B. Yaniv256 (talk) 18:15, 3 August 2012 (UTC)

Maybe whats needed is a reference template like thouse at Wikipedia:WikiProject_Mathematics/Reference_resources#Citation templates?--Salix (talk): 04:26, 3 August 2012 (UTC)

I considered this option, but read in one of the guidelines that citations should only be used to support the text to the degree that one uses them in editing the text, and not as a way to hide external links. I could work on each page and edit it so as to find a way to place these links as citations, since they do count, in my mind, as quite reliable secondary sources. My concern, however, is that this might cause confusion to the typical reader, due to the fact that such citations would have to be placed in a way that somewhat obscures their nature and will not be consistent across pages. For this reason, in case someone would revert my citations, I fear that I will have little to say in defense, as I will probably agree with most of what they would have to say. Yaniv256 (talk) 16:32, 3 August 2012 (UTC)

The citation guidelines are irrelevant, as you note, as these are not being used as sources to what's already there. The relevant guidelines are the external links ones and those suggest that not even one of these should be added, never mind six, for the same reasons as given at Talk:Mizar system. If individual links are not appropriate then box highlighting them is especially so.--JohnBlackburne^words_deeds 18:34, 3 August 2012 (UTC)

B

Formalization links
Structure	sigma-algebra
Definition in
Metamath	Coq	Mizar
Proof of properties
Metamath	Coq	Mizar

Please excuse me. I thought the matter of legal compliance with the external links guidelines was behind us. My answer to these claims was and still is here. I fail to see a meaningful response to my arguments in the discussion we had, but then again I may be missing something. Since if this proposal is to fall due to legal objections we are all just wasting our time discussing it, I suggest we stop here and assert if John's argument does have consensual support. Yaniv256 (talk) 19:49, 3 August 2012 (UTC)

You just don't get it do you? Just because you think you are right does not mean others do. You have not convinced people of your case and those references would be removed if stuck on things like sigma algebra. The reason it would be okay for things like axiom of choice is because a person reading that might not know about it and would find it a useful link. A person reading about sigma algebra is very unlikely to find it of interest unless they were already deeply into that sort of business. Wikipedia is not a directory to other web sites or software or books, it is an encyclopaedia. We do not list every single book that defines sigma algebra so why on earth should we list Mizar? Dmcq (talk) 21:54, 3 August 2012 (UTC)

Thank you for making it clear. I will not waste your time any longer. Yaniv256 (talk) 22:17, 3 August 2012 (UTC)

Mathematical Manuscripts of Karl Marx | References

Dear Members of the concerned community, I request you to consider adding the following to the References part of <http://en.wikipedia.org/wiki/Mathematical_manuscripts_of_Karl_Marx>:

Marx, Karl (1994)[1968], Yanovskaya, Sofya, ed.,Mathematical Manuscripts[complete English translation]together with a Special Supplement <http://cfcul.fc.ul.pt/varios/Karl_Marx_FINAL.pdf> Calcutta/Kolkata: Viswakos Parisad, I S B N 81-86210-00-8.

Regards. Pradip Baksi — Preceding unsigned comment added by 223.180.185.44 (talk) 03:58, 4 August 2012 (UTC)

I would have thought the ideologues in Soviet Russia and China would have gone out of their way to destroy pure mathematics with their Gradgrind type outlook, but it seemed to survive very well. Is there a story to be or already told about that? Dmcq (talk) 17:41, 6 August 2012 (UTC)

Elementary algebra GA review

I was reviewing Elementary algebra and then I found that the editors used textbook language, such as "Let's" which would be changed to "Let us," but that means let me teach you. Article sounds a lot like a Wikiversity page. I would appreciate a second opinion on this. Obtund^Talk 04:39, 4 August 2012 (UTC)

Fundamental theorem of ideal theory in number fields

I created the article Fundamental theorem of ideal theory in number fields because this theorem is mentioned in Wieferich prime. Do others feel that this theorem should have an own article, or should I better include that information in Wieferich prime via a footnote? -- Toshio Yamaguchi (tlk−ctb) 07:10, 7 August 2012 (UTC)

This theorem appears in Dedekind domain#Some examples of Dedekind domains. Therefore a redirect to this link suffices. By the way, the Dedekind domains are just the rings in which this theorem hold and have mainly been introduced for the case of the integers in a number field. Therefore the lead of Dedekind domain should be expanded to mention this important example. D.Lazard (talk) 09:30, 7 August 2012 (UTC)

links to Hermite's identity

I deleted the "orphan" tag from Hermite's identity. Three articles link to it. But one of those is only a hatnote and otherwise the linking to it seems on the thin side. If someone can think of other articles that could appropriately link to it, could they add those links?

Also, it currently lacks references. Michael Hardy (talk) 15:21, 7 August 2012 (UTC)

I linked it from one other article that immediately came to mind. -- Toshio Yamaguchi (tlk−ctb) 15:53, 7 August 2012 (UTC)

Must y be an integer?

Take a look at this edit. If one adopts the definition

${\binom {n-y}{n}}={\frac {(n-y)(n-y-1)(n-y-2)\cdots (n-y-n+1)}{n!}}$

then this is well defined even if y is not an integer, and I'd have guessed the whole identity would still hold then. Maybe when I'm feeling less lazy I'll check it.

A good edit? Or not? Michael Hardy (talk) 16:38, 7 August 2012 (UTC)

If n > y >1 are integers, this binomial coefficient is null. Thus the series involved by this edit is finite. For small values of n, all factors are negative. It is not clear to me what the notation "choose" means in this case. On the other hand the formula you have written is clearly a polynomial in y, and thus defined for any n. Thus the edit is certainly not good. But it reveals that the involved formula has to be checked, as binomial coefficients are rarely used when all factors of the numerator are negative. D.Lazard (talk) 17:28, 7 August 2012 (UTC)

The last sentence is not entirely correct. For instance, the binomial series

$(1+x)^{\alpha }=\sum _{k=0}^{\infty }{\binom {\alpha }{k}}x^{k}$

is valid for any $\alpha \in \mathbb {R}$ and $|x|<1$.--LutzL (talk) 18:15, 7 August 2012 (UTC)

The expansion in question follows formally by expanding one factor of the integrand defining the beta function in a binomial series and integrating term by term. This would not require y to be an integer, though there would be some natural constraint on y to ensure convergence. Sławomir Biały (talk) 19:14, 7 August 2012 (UTC)

Yes, it uses ${\binom {y-1}{n}}=(-1)^{n}{\binom {n-y}{n}}$. Uniform convergence does not extend to the upper bound 1 of the integral, but I don't see a dependence on y. If convergence follows as some variation of the alternating harmonic series, then the argument should be valid for all y.--LutzL (talk) 19:55, 7 August 2012 (UTC)--Number of negative factors stabilizes.--LutzL (talk) 07:54, 8 August 2012 (UTC)

Well, the problem is that ${\binom {n-y}{n}}$ all (ultimately) have the same sign for fixed real y, so the series never converges on the real axis, except at $y\in \mathbb {N}$, where it's zero. Sławomir Biały (talk) 20:51, 7 August 2012 (UTC)

They all have the same sign, but it doesn't follow that the sum diverges. For example, if I'm not mistaken, ${\binom {n-1/2}{n}}$ grows like $c\cdot n^{-1/2}$, which certainly yields a convergent sum (as long as x isn't a negative integer). --JBL (talk) 22:52, 7 August 2012 (UTC)

Ah yes, of course. In general ${\binom {n-y}{n}}\sim n^{-y}/\Gamma (1-y)$. Sławomir Biały (talk) 00:50, 8 August 2012 (UTC)

Indeed, and convergence follows directly from the Raabe or Gauß tests, as long as $x,y>0$. For non-positive x or y even the defining integral would have a non-integrable singularity at t=0 or t=1.--LutzL (talk) 07:54, 8 August 2012 (UTC)

Presumably the formula in question is taken from a reliable source? What is that source and what does it say? Deltahedron (talk) 06:47, 8 August 2012 (UTC)

Knuth somewhere has a discussion of the binomial formula, perhaps in Volume One or Concrete Mathematics.... Sedgewick and Flajolet's 2-volume Analytic Combinatorics used to appear on the internet in draft form.Kiefer.Wolfowitz 10:01, 8 August 2012 (UTC)

2-volume ?? Their book, which is 1-volume, is available where it's been for years by following the link at Analytic combinatorics.

Knights and knaves

The lead for this article credits Raymond Smullyan with the invention of "this type of puzzle". Not knowing much about history of logic puzzles, and suspecting that the puzzle has been around a lot longer than Smullyan's books, I thought this sounded like a rather generous claim. Can anyone check into how important Smullyan's contribution to the topic is? He is pretty old, and my sense that this is a problem from antiquity could just be wrong. Rschwieb (talk) 16:46, 7 August 2012 (UTC)

I have a book by Maurice Kraitchik ("Mathematical Recreations") dated 1943, well before Smullyan appears to have committed his Knights and Knaves to print, in which one of the first problems is one of exactly this type. Although I remember as a child finding something similar in one of my grandmother's Arthur Mee encyclopedias (which was old-fashioned even before she acquired it: 1870-ish I believe) which also had a puzzle along the same lines. So no way did Smullyan invent such a puzzle, although he may well have been a pioneer in giving an exhaustive workout to the genre. --Matt Westwood 21:34, 7 August 2012 (UTC)