Wikipedia talk:WikiProject Mathematics/Archive/2019/Feb

Numerical modelling

Is numerical modelling the same as mathematical modelling? --Redrose64 🌹 (talk) 19:50, 31 January 2019 (UTC)

What is the context? In general, no. Mathematical models can be at the level of algebraic or analytic equations or even logical models, with no necessity for reduction to numbers. --{{u|Mark viking}} {Talk} 20:13, 31 January 2019 (UTC)

It's at Emily Shuckburgh which uses the term "numerical modeller" twice. I want to link it, because a previous editor removed the significant word "numerical", which could imply that Shuckburgh makes small-scale ships, trains or aircraft. --Redrose64 🌹 (talk) 20:28, 31 January 2019 (UTC)

I would say that numerical modeling is a sub-area of mathematical modeling. --JBL (talk) 22:06, 31 January 2019 (UTC)

Ah, I see. As a climate scientist, she uses mathematical models of the climate by simulating or solving those models on a computer (computational modeling or computer experimentation). The results of a simulation are numbers--e.g., temperature profiles over a region and across time. From my physics perspective, I would probably call her a "theoretician, computational modeller, and observational scientist." --{{u|Mark viking}} {Talk} 22:15, 31 January 2019 (UTC)

The source says that she does numerical modelling but it seems to be in the specific context of a climate model, possibly using numerical techniques to solve a box model. Certes (talk) 22:39, 31 January 2019 (UTC)

Thanks guys. Having found Numerical weather prediction, Category:Scientific modeling and its many subcats, I'm even more confused, so I've stuck with numerical modeller. Edit if you see fit, I just don't want the word "numerical" to be removed again, or it to be left without a link. --Redrose64 🌹 (talk) 14:09, 2 February 2019 (UTC)

Correspondence vs. binary relation

Currently, we have two articles: correspondence (mathematics) and binary relations. Set-theoretically speaking, there is no essential difference. Wikipedia insists a correspondence is an ordered triple (A, B, f) where f is a subset of $A\times B$, while a relation is just f or rather what f determines. While I can (a sort of) understand the difference, I don't think the distinction is enough for separate articles; basically the difference is like a difference between a function and the graph of a function (in fact, "binary relation" seems to be a bit confused about whether it wants to discuss a correspondence or a relation; see Binary relation#Is a relation more than its graph?). So, I'm inclined to just merge the two into one, except algebraic geometry bit in "correspondence (mathematics)" feels quite out of a place at "binary relation" and best to split off to correspondence (algebraic geometry). Thoughts? -- Taku (talk) 21:02, 30 January 2019 (UTC)

I'm not a huge fan of articles grouping together vaguely related things that share the same name. Maybe the bullet points could be merged into a glossary somewhere, with the specific content in the various fields merged into the articles on the individual fields? Or something?

I suppose having them all in one place could be useful to someone trying to read mathematical content who comes across the word "correspondence" and isn't sure what it means in context. I guess I don't object to that too much, as long as it doesn't try to abstract some commonality from them in an original-researchy sort of way. --Trovatore (talk) 05:45, 31 January 2019 (UTC)

Inspired by this comment (as well as the above thread), I have started Glossary of mathematics; I think it makes sense since some mathematical terms like correspondence are used across areas of mathematics. This at least gives us a merger target...

I will be splitting off the algebraic-geometry bit to correspondence (algebraic geometry), as I doubt there is an objection. -- Taku (talk) 00:45, 1 February 2019 (UTC)

In fact, Category of relations uses the term “binary relation” to mean a correspondence (so, it appears, Wikipedia actually doesn’t want to make this distinction). —- Taku (talk) 14:54, 3 February 2019 (UTC)

Amnon Pazy

Would someone from this WikiProject mind taking a look at this article and assessing it? It was created by someone hired by Pazy's family and it was not submitted for review via WP:AFC. I've done a bit of minor clean up, but there's still some issues that need sorting, particularly with respect to the sourcing (it seems that most of them are to documents, etc. uploaded to Commons). I'm assuming the subject meets WP:ACADEMIC and is notable for an article to be written, but some serious trimming/rewriting might be needed to bring the article more inline with current policies and guidelines. -- Marchjuly (talk) 13:06, 4 February 2019 (UTC)

Map (mathematics)

There is a dispute as to whether map (mathematics) should be a disambiguation page or not; i.e., should redirect to map (disambiguation). Note the content of the page has already merged with function (mathematics). To resolve the conflict, inputs from more editors are needed; the main objection is from an editor who claims “a function is not a morphism in the category of sets.” —- Taku (talk) 18:20, 1 February 2019 (UTC)

Wait, if a function is not a morphism in the category of sets, then what is? I hope this isn't some quibble about whether a function is just a set of ordered pairs versus also knowing its domain and codomain. --Trovatore (talk) 20:24, 1 February 2019 (UTC)

You nailed it. People (not me) believe two separate articles are needed (in part) because of this quibble... (the same problem for correspondence vs binary relation) —- Taku (talk) 20:34, 1 February 2019 (UTC)

Whatever happens with this proposed merge, do not make Map (mathematics) a redirect to Map (disambiguation), without first making sure that no articles link to it, since links to disambiguation pages are (generally) considered errors. Please see User talk:BD2412#Map (mathematics). Paul August ☎ 18:31, 1 February 2019 (UTC)

I think it's important that, in general-audience mathematics articles, the term "map" be linked to a useful article on functions or mappings that clearly explains the intended meaning of the term (the purpose of having an actual article as the target for Map (mathematics)). This is much more important than helping editors find the right link to add when they see the term "map" in a mathematics article but don't understand which kind of map is intended (the purpose of having a disambiguation page as target). Whether there is a separate article on maps and mappings or whether Map (mathematics) redirects to Function (mathematics) is less critical. I would lean to having a separate article, though, just because a redirect is going to entail a messy hatnote on the function article for all those other meanings of mappings. —David Eppstein (talk) 18:57, 1 February 2019 (UTC)

To add some context, I guess I just don’t see a point of an article explaining *terminology* as opposed to *concept* in Wikipedia. Wikipedia is a place to explain concepts, at least when math is concerned; terminology note is important, sure, but is of a secondary importance. For me, thus, this page is a disambig page in an effective sense since the concepts of a map are already discussed at other places like function (mathematics), morphism (category theory), homomorphism, etc. It doesn’t help that those “terminology” articles tend to be of low quality and low information (#Correspondence vs. binary relation above is another instance). Not to mention, our readers often complain about those article... —- Taku (talk) 19:33, 1 February 2019 (UTC)

See also: Talk:Map_(mathematics)#Suggestion to dedicate this article to the use of Map as a concept in mathematics when it is not a synonym of function. -- Taku (talk) 23:54, 2 February 2019 (UTC)

I’m probably sounding repetitive but here, a very similar type of an article: embedding. While there is a certainly a general concept of embedding, I don’t think it’s useful to use a “single article” to cover embedding in topology as well as those in other fields. Is there any benefit of doing (instead of having separate articles) that I’m not seeing? —- Taku (talk) 20:59, 4 February 2019 (UTC)

Are unedited drafts and disambiguations somehow related? Purgy (talk) 07:55, 5 February 2019 (UTC)

I was just saying it seems better to have "embedding (topology and geometry)" as a separate article instead of a single article. In fact, maybe I will split-off the topology-geometry stuff; the topic should be important enough for an standalone article. -- Taku (talk) 08:54, 5 February 2019 (UTC)

In the main embedding article, would you have a short summary for "Topology and geometry" with a "See also" pointing to the new article? The summary would be almost the same as the article in that case. Alternatively, if you made the main article a disambiguation pointing to several smaller articles then the other pages like embedding (algebra) or embedding (metric spaces) would be quite short! How would you structure the relationship between the "embedding" page and the "embedding (topology and geometry)" page?

On a barely-related point, why should it be written "Topology and geometry" rather than an alphabetized "Geometry and topology"? — MarkH21 (talk) 09:29, 5 February 2019 (UTC)

I didn't mean to propose that embedding be a disambig page. Also, "The summary would be almost the same as the article in that case" I don't think that need to be the case; there are so much embedding stuff in geometry and topology. (I didn't have any particular reason to write "Topology and geometry" instead of "geometry and topology". That was not a conscious choice and didn't mean to imply topology comes before geometry, for instance). -- Taku (talk) 10:28, 5 February 2019 (UTC)

I think the point was that there's very little content there now. And so the natural thing to do would be to add content in the current location, until such time as there is enough that the split can be done with a short summary section that doesn't duplicate the entire content of the new article.

For the question of what is the benefit of having several things in the same article, the answer is that it's easier to navigate: for example, the (not closely analogous, just illustrative) situation described here is one in which it can be hard to find the information one is looking for. --JBL (talk) 13:44, 5 February 2019 (UTC)

Ah, got it. My impression is that there was just going to be a split of the section as it is now into a new article. — MarkH21 (talk) 18:56, 5 February 2019 (UTC)

Possibly Taku was suggesting that; I was hoping that Taku would take my comment as a suggestion for a way to proceed with low likelihood of causing consternation. --JBL (talk) 19:56, 5 February 2019 (UTC)

First to JBL, I actually don't buy the navigation argument. Hypothetically, imagine there was an embedding (geometry and topology) and I proposed to merge it with embedding, to make it easier to navigate. I doubt there will be much support. So, the current setup is probably a historical artifact, rather than something out of the logical reason. So, for me, "geometry and topology" can be split off as is. Of course, you can do splitting-off after more content is added. But the topology section already has stuff beyond the typical summary (e.g., "proper embedding"). So, for me, it's time to split the section; replace it with a shorter summary; the rest of the sections will be untouched. Sounds like a plan? But yes I understand changes need to be implemented incrementally; so I will not do anything in an immediate future. -- Taku (talk) 20:21, 5 February 2019 (UTC)

You asked for a benefit; I have identified one. I have certainly experienced frustrations navigating Wikipedia articles on mathematics because of over-fragmentation before, so I'm not sure what there is to not buy. Moreover, I think that your hypothetical is just restating your views rather than adding anything new: I would certainly support the proposed merge you've described, given that the combined article is of such reasonable size. In fact, I don't really see that you've identified any benefit to splitting: two related-but-not-exactly-the-same ideas are covered in the same article, and that's bad because ... why, exactly? Given the nice size of the current article, anyone looking for an embedding is going to be able to find it easily. If you eventually manage to add so much material to the article that the geometry section overwhelms the rest (and so, for example, it becomes hard to find embeddings in category theory buried under sub-sub-sub-sections on geometry), then there would be a reason to split. But at present the article is nowhere near that, and the two half-articles would be very short. (FWIW, the chance of my intervening in any way more substantial than this conversation is 0.) --JBL (talk) 22:26, 5 February 2019 (UTC)

It didn't occur to me the fragmentation causes a navigation difficulty. I thought having focused articles is a preferred style here; in fact, easier to navigate, no distraction from unrelated topics. But, ok, I understand you see this differently. "Nice size" depends on one's position. For example, I imagine anonymous users will find discouraged to expand the geometry and topology section because of the size. Splitting-off the section gives a room for more growth. In any case, this comes down to personal preferences; I like big fancy rooms. I will however not be demanding that (got no right, obviously). Thank you for answering the my original question: yes, there is indeed some advantage (combining stuff). -- Taku (talk) 23:09, 5 February 2019 (UTC)

Map (mathematics) 2

User:Trovatore, yes, functions are not defined as the arrows of **Set**. Functions are defined, and then **Set** is defined as an emergent concept. This shouldn't be news to anyone. Now, the other thing that happens is that there are two types of references: (1) Those that (modulo wording) define functions as correspondences (<- beware User:TakuyaMurata has been vandalizing this page too.) with the 'unique image property' and (2) Those authors who define (modulo wording, although in this case they tend to be more explicit) functions as relations with the 'unique image property'. There is a third in which they explicitly state (2) and then hand-waving-ly add the codomain to the function. Those are essentially in (1). As a result, reliable sources have two positions, one in which there is a function for each arrow of **Set** and one for which there are many. It looks like it has to be reminded, specially to User:TakuyaMurata, that Wikipedia works by presenting what is contained in reliable sources, not what random editors imagine the concepts should be in Mathematics. Cactus0192837465 (talk) 13:23, 5 February 2019 (UTC)

+1 for relying solely on WP:RS. Paul August ☎ 13:34, 5 February 2019 (UTC)

@Cactus0192837465: I don't think the term "vandalism" applies here, I think you should strike it. Paul August ☎ 13:59, 5 February 2019 (UTC)

Vandalism? The definition of a relation in terms of a graph in the old version was not in a reference and so I simply replaced one in the reliable sources. How is it not an improvement? —- Taku (talk) 13:53, 5 February 2019 (UTC)

Again I have acknowledged a difference; we have merely chosen the most standard one and you’re advocating for a non-standard one, which will result in a function not being a morphism in the category of sets. —- Taku (talk) 13:56, 5 February 2019 (UTC)

User:TakuyaMurata, the very first reference in the article correspondences, which you have turned from an independent article into a redirect link, contains explicitly and precisely a definition for relation, and a definition for correspondence. I added links to screenshots in the talk page of that article for those who don't have access to the references and are literally pulling definitions out of what they can find online, in forums, or their imagination. Yes, you are pushing an agenda of smudging the boundaries of these concepts well beyond of what they are already done in the literature. Cactus0192837465 (talk) 16:51, 5 February 2019 (UTC)

Another thing. I am not advocating for any other definition. Actually, when I teach it, I use the definition of function as a correspondence (triple of domain, codomain, and relation). The vandalism is that you are trying to turn the article of correspondences into a redirect to relations. they are two different concepts. Very important, when consulting the literature, one must take into account that sometimes the word correspondence, just like mapping (as a verb), are sometimes used just as a common word, and not as a word loaded with concept. Cactus0192837465 (talk) 17:12, 5 February 2019 (UTC)

Again this is the difference between whether a function is a triple or a subset; what you call a map and a correspondence are also called a function and a relation by other authors (so a function is a triple). That’s just that. For example, Jacobson Basic Algebra defines a correspondence as a subset not as a triple (and Jacobson gives it as a proper definition). Sloopy? But I don’t have a strong reason to go again Jacobson and you need to know how reliable Jacobson is. Please also see category of relations where morphisms are correspondences in your usage but are called binary relations. So a binary relation is also a correspondence in your terminology. It shows even Wikipedia uses the terms “binary relation” and “correspondence” interchangeably: I know you want to make terminologic distinction; the fact is that your language is not universally adopted.

I do acknowledge the difference; in fact, binary relation has very explicit example showing why codomain matters. It only makes sense to have a redirect to a page where there is a discussion of this. —- Taku (talk) 17:24, 5 February 2019 (UTC)

This is similar to the situation that the terms "map" and "function" are frequently used interchangeably, you like it or not. We cannot claim your distinction is universally adopted one. That's ok if you are teaching, but saying that in Wikipedia is misleading (and in fact wrong as Wikipedia has to take a neutral stand). And, both in function (mathematics) and binary relation, we clearly indicate variations on the usage. -- Taku (talk) 21:02, 5 February 2019 (UTC)

To other editors, we (Cactus and I) need a tie-breaker for [1]. Please note we have Correspondence (algebraic geometry) and the rest in binary relation; my edit thus doesn’t mean any information loss. -- Taku (talk) 17:31, 5 February 2019 (UTC)

If I understand well the subject of the dispute is the following: for Cactus0192837465 a relation is a subset R of a direct product $A\times B$ of sets, while a correspondence is the triple $A,B,R.$ As, for Cactus0192837465, these are different concepts, two different articles are needed. My opinion is that the only situation where it is useful to distinguish between the two definitions is when using a proof assistant. So, there is only one concept and two slightly different formalizations of it. Cactus0192837465 provides a source that makes a distinction, but omits that most reliable sources do not care with such a distinction, and when they distinguish between the two definitions and/or between the two terms, it is not necessary done as presented by Cactus0192837465. So, presenting these two definition a different concepts with different named different articles, is not only confusing for the reader, this is also a biased presentation of the common mathematical usage.

So my opinion is that we must redirect Correspondence (mathematics) to Binary relation, as taku did. D.Lazard (talk) 23:24, 5 February 2019 (UTC)

Root 2 and Root two redirects

Root 2 and Root two are currently redirects to Square root of 2 and List of numbers respectively. They have been nominated for deletion at Wikipedia:Redirects for discussion/Log/2019 February 8#Root two where your comments are invited. Thryduulf (talk) 19:59, 8 February 2019 (UTC)

Is there a list of crap mathematics journals somewhere?

I'm currently expanding WP:CRAPWATCH (a project to detected predatory/unreliable sources) with various sources that document unreliable journals in various fields of research. Are there any such list mathematics for mathematics? Preferably externally sourced to reliable people, rather than personal opinion. Headbomb {t · c · p · b} 09:41, 5 February 2019 (UTC)

My preference for testing whether a math journal is crap is whether it is not listed in MathSciNet. But that isn't so good for finding a listing of all of the crap ones. —David Eppstein (talk) 19:13, 5 February 2019 (UTC)

Yeah, we need a list of crap stuff, not a list of good stuff. There's Beall's List in general, and medicine has Quackwatch's list for instance, just wondering if there is something similar for mathematics (even a blog post by a reliable person would be fine). I know about some weird math people like Florentin Smarandache and his Smarandache Notions Journal, but I really don't know enough about mathematics at this level to be able to be build a case-by-case list myself. If someone here wants to build it, and the math project agrees with the list, I could easily incoporate it in the crapwatch. Headbomb {t · c · p · b} 17:59, 6 February 2019 (UTC)

Why not build a whitelist first? "Not whitelisted journals" could be part of the report and then you can work either on blacklisting those or whitelisting those. --Izno (talk) 19:37, 6 February 2019 (UTC)

Mostly because a "not in MathSciNet" or whatever math whitelist you want to use would mean reporting a lot of non-mathematical journals as potential crap. And that's not really a workable solution. Headbomb {t · c · p · b} 20:33, 6 February 2019 (UTC)

I mean, there should be a general whitelist... --Izno (talk) 23:24, 6 February 2019 (UTC)

I think Google Scholar and Google Scholar Metrics take care of the problem. In math, if something is cited over and over, it is OK. Otherwise using these criteria of "where is it published" rather than "how cited it is", we would end up excluding people like Grigory Perelman and the greatest results of the past 120 years --Borel, Groethendieck, etc. Mathematics is much more robust than other sciences. Limit-theorem (talk) 01:55, 7 February 2019 (UTC)

True, but the idea isn't to have a YES/NO are publication always crap/always good, but rather YES/NO are there redflags about certain publications, e.g. pay-to-publish journals or journals edited by pseudo-mathematicians. For instance arXiv is a serious venue, but viXra is not. Doesn't mean you can't publish crap on arXiv, or good stuff on viXra, but the odds are if someone has cited viXra, they've cited crap. Headbomb {t · c · p · b} 04:33, 7 February 2019 (UTC)

Your statement about odds does not seem very well founded to me. It could almost be simultaneously true for vixra articles that being cited by a Wikipedia article implies that they are almost certainly non-crap, and that it also implies that they are almost certainly crap; see vacuous truth. However, currently there are at least some citations to vixra on Friedwardt Winterberg; I'm not sure whether they are crap. There is also at least one citation on Lebesgue's universal covering problem that is definitely not crap, and could go to vixra, but uses a different link instead. —David Eppstein (talk) 04:50, 7 February 2019 (UTC)

viXra is an unmoderated repository of preprints. That leads to things like this being very, very common on viXra. For something a bit less ridiculous, see [2], picked at completely random in the topology subgroup. Now I don't understand topology one bit, but I can't fathom that any person would consider this a solid source. Also the reason why only the Winterberg page has viXra links at the moment is because I removed most of the others a few months back. It is simply not a reliable source, generally speaking, although exceptions may certainly exist. Headbomb {t · c · p · b} 06:20, 7 February 2019 (UTC)

The moderation on arXiv consists only of checking whether the preprints are on-topic and (for some but not all classifications) whether they are not total crankery. So arXiv preprints should also not be considered to be reliable sources unless either the author is a known expert on the topic (WP:SPS) or they have been properly peer-reviewed and published elsewhere. In that sense, I don't see a qualitative difference from vixra in how we should treat them here. In particular, your "arXiv is a serious venue, but viXra is not" is either meaningless (seriousness is irrelevant for our standards on sourcing) or wrong (you are treating arXiv sources as being inherently reliable and you should not be doing that). —David Eppstein (talk) 23:31, 7 February 2019 (UTC)

And, by far and large, those posting stuff on the arXiv are published experts. The nonsense tends to get re-classified to [physics.gen-ph]. So yes, arxiv shouldn't be treated better than WP:SPS, the difference is that if you roll a dice and pick a random preprint on the arxiv, chances are it will be by a published expert. If you do the same on vixra, chances are you'll end up on a nonsense paper from a quack. Headbomb {t · c · p · b} 23:37, 7 February 2019 (UTC)

Certainly, arXiv should not generally be a fully reliable source but nowadays it is close to one when published by experts. However, viXra is not even close! Many serious academics will reference arXiv preprints in peer-reviewed published papers but very very few will reference viXra (I can't say that I've ever seen one). Of course, there are very bad preprints in both so neither can satisfy WP:RS and any citation of either can only really be used as a primary source (which means that they should both be on crapwatch based on its definition). Even Perelman's proof of the Poincaré conjecture, posted on arXiv, is only significant in conjunction with its recognition by the mathematical community. — MarkH21 (talk) 10:56, 10 February 2019 (UTC)

SPA

Assistance handling an WP:SPA at k shortest path routing and a related talk would be helpful. Johnuniq (talk) 09:16, 11 February 2019 (UTC)

I tend to agree with David Eppstein that this is probably the same obsessed sockpuppeteer. (Although maybe their English has improved over the last few months?) --JBL (talk) 02:15, 12 February 2019 (UTC)

Mathematics Wikiproject:probability and statistics at Wikipedia:WikiProject Statistics

Wikipedia:WikiProject Statistics includes a table of articles tagged as probability and statistics with the {{maths rating}} template. But the table shows no articles. Can someone here take a look and fix it? Thank you.--76.14.38.58 (talk) 22:01, 15 February 2019 (UTC)

It looks as if the table is transcluded from User:WP 1.0 bot/Tables/Custom/Mathematics-Probability. That page is updated by WP 1.0 bot, which removed the content in late 2017. More help may be available at Wikipedia talk:Version 1.0 Editorial Team/Index. Certes (talk) 00:35, 16 February 2019 (UTC)

Our article titled Wishart distribution needs some work!

Here I need to point out a conspicuous elephant in a room, but maybe that particular room doesn't get a lot of attention. Our article titled Wishart distribution contains this assertion:

[I]f n ≥ p, X has a Wishart distribution with n degrees of freedom if it has the probability density function

$f_{\mathbf {X} }(\mathbf {x} )={\frac {1}{2^{np/2}\left|{\mathbf {V} }\right|^{n/2}\Gamma _{p}\left({\frac {n}{2}}\right)}}{\left|\mathbf {x} \right|}^{(n-p-1)/2}e^{-(1/2)\operatorname {tr} ({\mathbf {V} }^{-1}\mathbf {x} )}$

where $\left|{\mathbf {x} }\right|$ is the determinant of $\mathbf {x}$ and Γ_p is the multivariate gamma function defined as

$\Gamma _{p}\left({\frac {n}{2}}\right)=\pi ^{p(p-1)/4}\prod _{j=1}^{p}\Gamma \left({\frac {n}{2}}-{\frac {j-1}{2}}\right).$

Anyone who wants to understand that or make any use of it or do anything at all with it will instantly wonder how in Hell we're supposed to integrate a thing like that, i.e. with respect to which measure is this a density, or to put it another way, with respect to which variables over which set are we integrating? Observe that the argument ${\textstyle \mathbf {x} }$ is a ${\textstyle p\times p}$ positive-definite matrix and we may denote its entries by ${\textstyle x_{ij}}$ for ${\textstyle i,j\in \{1,\ldots ,p\}}$. So a naive guess is we're talking about

$\int f(\mathbf {x} )\,\prod _{i,j}dx_{ij},$

so it would be just Lebesgue measure. But that raises question: since ${\textstyle \mathbf {x} }$ is symmetric, should we have $\displaystyle \prod _{i,j\,:\,i\,\leq \,j}$ or the like? So Lebesgue measure on a space of dimension ${\textstyle p(p+1)/2{\text{?}}}$ And what are the bounds of integration? The bounds may seem messy, but I think I may know a way to deal with that neatly. But is that what is meant, or is there some standard measure on the space of positive-definite symmetric matrices that anyone who knows about it would expect to be used here, or what? In any case, answers to these questions ought to be in the article.

Same problem in Inverse-Wishart distribution.

So maybe tomorrow I'll go to the library and look some things up, but maybe someone here knows something off the top of their head. Michael Hardy (talk) 18:47, 10 February 2019 (UTC)

Not a probability theorist nor a statistician, but there is a Lebesgue measure on positive definite matrices (corresponding to the Haar measure on the additive group). — MarkH21 (talk) 03:53, 11 February 2019 (UTC)

@MarkH21: The additive group? The set of positive-definite matrices is not a group under addition. Is the measure you have in mind the same as ${\textstyle \prod _{i,j\,:\,i\,\leq \,j}dx_{i,j},}$ as suggested in some of the other postings below? Michael Hardy (talk) 21:59, 11 February 2019 (UTC)

Whoops, ignore that - I think I had symmetric matrices in mind. So yes it should be that. — MarkH21 (talk) 00:44, 12 February 2019 (UTC)

I also think that you had symmetric matrices in mind. (The domain is another story.) On this (vector) space, the Haar measure is defined only up to a coefficient. By the way, on the plane $\mathbb {R} ^{2},$ the line $\{(x,y)\mid x=y\}$ is a one-dim Euclidean space, and carries its Lebesgue measure; but then, the segment from the origin to (1,1) has measure ${\sqrt {2}},$ while integrating $dx$ on it we rather get $1.$ This is the problem of the coefficient...

The Haar measure on a non-compact group is defined only up to a coefficient, this is the problem...

Indeed, most sources are silent on this point. But one (maybe not very reliable) is not silent; see here, equation (2.4) on page 8; is says:

For symmetric matrices, we are only concerned with the $p(p+1)/2$ independent elements of the symmetric matrix, thus $|d\Omega |=\prod _{k,l=1;k\leq l}^{p}\mathrm {d} \omega _{kl}.$

Boris Tsirelson (talk) 06:39, 11 February 2019 (UTC)

And now the same in the most reliable source, Wishart 1928 (ref 1 in our article); page 38 eq (8):

$\left|{\begin{array}{ccc}a&h&g\\h&b&f\\g&f&c\end{array}}\right|^{\frac {N-5}{2}}da\,db\,dc\,df\,dg\,dh$

in particular, and in general on page 38 eq (9): $da_{11}\,da_{12}\dots da_{nn}.$ Boris Tsirelson (talk) 07:09, 11 February 2019 (UTC)

And surely, the domain of integration is the set of all positive-definite matrices, a semialgebraic (see Sylvester's criterion), therefore Jordan measurable, open set in the dimension $p(p+1)/2;$ or equivalently, its closure, the (Jordan measurable closed) set of all positive semi-definite matrices (or any set in between of these two). Riemann integration applies (and Lebesgue integration as well, of course). Boris Tsirelson (talk) 07:15, 11 February 2019 (UTC)

Now added to the article. Boris Tsirelson (talk) 06:05, 17 February 2019 (UTC)

Draft:Oaxaca-Blinder decomposition

User:Legacypac was wondering if this draft is "useful/fixable" (I have no idea). So, is it useful? already covered in mainspace? -- Taku (talk) 00:41, 14 February 2019 (UTC)

Blinder–Oaxaca decomposition seems to cover it. Certes (talk) 01:03, 14 February 2019 (UTC)

Yep, the draft looks redundant with the existing article. XOR'easter (talk) 16:11, 14 February 2019 (UTC)

I've created a redirect at Oaxaca–Blinder decomposition (but not Oaxaca-Blinder decomposition) and thrown square brackets at a couple of relevant articles to create incoming links. Certes (talk) 16:37, 14 February 2019 (UTC)

(but not Oaxaca-Blinder decomposition) I do not know anyone who types en-dashes into search bars rather than hyphens. So I will create the other redirect. --JBL (talk) 17:15, 14 February 2019 (UTC)

@Joel B. Lewis: I often put en-dashes within search terms here. Michael Hardy (talk) 19:19, 14 February 2019 (UTC)

Wow... How do you put them? I do not see them on my keyboard. Boris Tsirelson (talk) 20:24, 14 February 2019 (UTC)

@Boris Tsirelson: They're not on my keyboard either. But when I click on "edit" I see a list of symbols right below the editing window:

– — ° ′ ″ ≈ ≠ ≤ ≥ ± − × ÷ ← → · §

The first one is the en-dash. You can also write &ndash; and when you save the article or click on "show preview" you'll see an en-dash. You can then copy that en-dash and paste it into the article, although that's not striclty necessary. Note that the minus sign is also there, and that differs from the en-dash. And from the hyphen, but that's obvious. Michael Hardy (talk) 06:37, 17 February 2019 (UTC)

I understand why do this fuss when editing articles. But in search bar?.. Moreover, when I search, I usually have nothing to edit yet; and I am reluctant to click "edit" without good reason. Boris Tsirelson (talk) 06:51, 17 February 2019 (UTC)

An en-dash takes me only one more keypress than a hyphen so I am likely to type it when appropriate, just out of habit, even when a hyphen would work. And also, keep in mind that it is pretty common to copy and paste into search bars. —David Eppstein (talk) 22:11, 17 February 2019 (UTC)

I see... probably I should develop the habit. Boris Tsirelson (talk) 07:03, 18 February 2019 (UTC)

WP:HTMD is useful for the dashophiles. --{{u|Mark viking}} {Talk} 20:33, 14 February 2019 (UTC)

Thank you for creating the hyphen redirect. I wondered whether it might seem rude when there was a draft of that name but you're right: it's more useful. By the way, I'm one of the rare people who do type en-dashes with ⇪ Caps Lock - - ., having repurposed my otherwise useless Caps Lock button as a compose key. Certes (talk) 21:08, 14 February 2019 (UTC)

When you huys are done merging please redirect the draft I found to tje mainspace page. Thanks. Legacypac (talk) 22:09, 14 February 2019 (UTC)

As I said at User talk:Michael Hardy, beware of time-traveling proofreaders accompanied by 5-meter ruminants. Robert McClenon (talk) 02:35, 15 February 2019 (UTC)

Where to request assessment

I've significantly expanded numerical linear algebra. Where can I request an assessment of it to revise its Stub Class label? - Astrophobe (talk) 22:05, 17 February 2019 (UTC)

@Apostrophe: I did a bit of copy-editing on it. I can't help wondering why you would write \underset_{\delta \to 0} {\lim} instead of \lim_{\delta \to 0} in a displayed (as opposed to inline) context. Michael Hardy (talk) 00:43, 20 February 2019 (UTC)

A TeX anomaly

In our system of mathematical notation coding, which is not LaTeX although people call it that, and is not actually TeX either, I found this in Barnes G-function:

${\begin{aligned}&z\log \Gamma (z)-\log G(1+z)=-z\log \left({\frac {1}{\Gamma (z)}}\right)-\log G(1+z)\\[5pt]={}&-z\left[\log z+\gamma z+\sum _{k=1}^{\infty }{\Bigg \{}\log \left(1+{\frac {z}{k}}\right)-{\frac {z}{k}}{\Bigg \}}\right]\\[5pt]&{}-\left[{\frac {z}{2}}\log 2\pi -{\frac {z}{2}}-{\frac {z^{2}}{2}}-{\frac {z^{2}\gamma }{2}}+\sum _{k=1}^{\infty }{\Bigg \{}k\log \left(1+{\frac {z}{k}}\right)+{\frac {z^{2}}{2k}}-z{\Bigg \}}\right]\end{aligned}}$

I changed it so that it says this:

${\begin{aligned}&z\log \Gamma (z)-\log G(1+z)=-z\log \left({\frac {1}{\Gamma (z)}}\right)-\log G(1+z)\\[5pt]={}&{-z}\left[\log z+\gamma z+\sum _{k=1}^{\infty }{\Bigg \{}\log \left(1+{\frac {z}{k}}\right)-{\frac {z}{k}}{\Bigg \}}\right]\\[5pt]&{}-\left[{\frac {z}{2}}\log 2\pi -{\frac {z}{2}}-{\frac {z^{2}}{2}}-{\frac {z^{2}\gamma }{2}}+\sum _{k=1}^{\infty }{\Bigg \{}k\log \left(1+{\frac {z}{k}}\right)+{\frac {z^{2}}{2k}}-z{\Bigg \}}\right]\end{aligned}}$

You see the difference on the second line: in the first version, the space between the minus sign and the z is what is normally followed when the minus sign is used as a binary operation symbol, rather the smaller amount of space that normally appears when it's a unary operation, thus:

${\begin{array}{r}5-3\\-3\end{array}}$

I tried the same code in genuine LaTeX and (as expected) this problem of incorrect spacing did not occur. The way I fixed the problem is that I changed this line of code:

= {} & -z \left[ \log z+\gamma z +\sum_{k=1}^\infty \Bigg\{ \log\left(1+\frac{z}{k} \right) -\frac{z}{k} \Bigg\} \right] \\[5pt]

to the following:

= {} & {-z} \left[ \log z+\gamma z +\sum_{k=1}^\infty \Bigg\{ \log\left(1+\frac{z}{k} \right) -\frac{z}{k} \Bigg\} \right] \\[5pt]

I found three instances of the same bug in the same section of that article and fixed them all the same way.

I don't recall that I've noticed this bug before. I'd hate to think that I'd encountered it without noticing, it, but such unpleasantenss can actually happen. How long has this been with us? Michael Hardy (talk) 20:24, 21 February 2019 (UTC)

Interesting. In the LaTeX world, this bug can be triggered in the amsmath multi-line environment.[3] Perhaps this only happens at WP in that environment? $=-z$ looks OK to me. --{{u|Mark viking}} {Talk} 22:34, 21 February 2019 (UTC)

RIP PlanetMath?

Our WP entry for the site describes it as inactive and apparently they moved their content last year to GitHub with the original website currently somewhere between dysfunctional and not maintained (and I suspect it being ditched in the future). Does anybody have any background on PlanethMath's exact status and planned future? We still have that collaboration project listed on our project page, but that seems to be inactive/dead for years now as well. Should we remove that? Do we still have an overlap of active editors or anybody doing work on the collaboration?--Kmhkmh (talk) 02:01, 18 February 2019 (UTC)

Planet Math restructured their website a few years ago and that left some of our external links not going to the right place. So far there are fewer than 250 pages which still use the obsolete {{PlanetMath reference}} template and I have replaced a few of them with the new one. For example, at Axiom of regularity, I replaced:

• {{planetmath reference|id=3485|title=Axiom of Foundation}}

with

• {{PlanetMath|urlname=axiomoffoundation|title="Axiom of foundation"}}.

This conversion still has to be done for the rest of the 250, which I hope to get to eventually. As to the continued importance of linking to Planet Math, probably that can be decided for each individual page. At Fano plane, the Planet Math link goes to a lengthy article and appears useful, but elsewhere some of the entries are very short. Those of our articles that actually use content taken from Planet Math need to keep whatever attribution template they currently have. EdJohnston (talk) 06:11, 18 February 2019 (UTC)

Thanks for the update on that, I completely forgot about the template in articles in my posting above. My question about removal however did not refer to the templates in articles but the whether we should still link Wikipedia:WikiProject Mathematics/PlanetMath Exchange on our project page or remove that link due inactivity/project having ended.

As far as the the templates in articles are concerned. Are we talking about the same change at PlanetMath? A few years back (2013) PlanetMath restructured its page and software (which probably requires older links to be adjusted). But I was talking about a more recent change seemingly from last year, when they moved their content to Github and seem to plan to shutdown/end their website completely (or maybe just to reorganize it again over a longer time frame). The information given on their website itself about this last change is scant and so is the activity on the related Github pages, hence i'm not really clear what's likely to happen there. For the templates/links currently existing in Wikipedia a possible fix might be to link them to archive.org, which seems to host a lot of former PlanetMath entries (probably all that were linked within Wikipedia).--Kmhkmh (talk) 09:36, 18 February 2019 (UTC)

Agree that the planetmath.org website does not seem to be updated very much and it's unclear whether anyone is home. Unsure that we would need to update our links to that site so long as it remains online. I'm leaving a ping for the people listed at WP:WikiProject Mathematics/PlanetMath Exchange#Participants who are still active on Wikipedia in case they want to comment: @Oleg Alexandrov, Paul August, Arthur Rubin, Tompw, and Rich Farmbrough: If it is correct that nothing much is happening, it may be time to remove the link to the WikiProject from the main page of WP:WPM. EdJohnston (talk) 16:35, 18 February 2019 (UTC)

I haven't contributed to our PlanetMath Exchange project in a very long time, and as far as I know the exchange project is moribund. Paul August ☎ 16:51, 18 February 2019 (UTC)

I haven't even looked at PlanetMath lately. No idea if there is anything there (any more) worth bringing here. — Arthur Rubin (talk) 10:17, 19 February 2019 (UTC)

Like Paul August, I haven't done anything relating to that project in a loooong time. It's a shame the site is inactive, but I agree any references should be replaced. Tompw (talk) 16:48, 19 February 2019 (UTC)

Concur. All the best: Rich Farmbrough, 09:27, 22 February 2019 (UTC).

Based on the discussion so far I removed PlanetMath from the project page now. As for the PlanethMath-Links in articles it might be best as suggested above to handle them individually on an article basis. Links that for now still works (at least most of the time) may be kept for now and those that hsve become completely dysfunctional/unavailable can be removed or replaced by copies on archive.org.--Kmhkmh (talk) 10:57, 22 February 2019 (UTC)

Discussion at Wikipedia:Village pump (idea lab)#Attention WikiProjects

 You are invited to join the discussion at Wikipedia:Village pump (idea lab)#Attention WikiProjects. We are designing a bot script to perform a few article assessment–related tasks and would appreciate your feedback. Qzekrom (talk) 08:56, 23 February 2019 (UTC)

Law of tangents

I've done approximately this same reversion three times, and I wonder if the user who added this stuff may persist. Michael Hardy (talk) 19:16, 21 February 2019 (UTC)

I've placed a warning on both IPs' user talk pages. — MarkH21 (talk) 23:12, 21 February 2019 (UTC)

Hi, Michael Hardy! The section IP users insert/restore into the article has been added 12 years ago (this edit Special:Diff/71696394 from 25 August 2006) by another anonymous user 202.135.111.2 and the same day hidden into a comment by yourself (Special:Diff/71730540). Good to see it deleted finally. :) CiaPan (talk) 07:42, 22 February 2019 (UTC)

Presumably, as an administrator, you (MH) have the ability to perform a short-term semi-protection of the article if disruption continues. --JBL (talk) 17:03, 23 February 2019 (UTC)

Gadi Moran is an AfD

Deletion of a new article titled Gadi Moran has been proposed at Wikipedia:Articles for deletion/Gadi Moran. Opinions can be posted on the latter page. Michael Hardy (talk) 17:52, 23 February 2019 (UTC)

Geometry of roots of real polynomials AFD

Geometry of roots of real polynomials is not a new article it as been proposed for deletion for the second time at Wikipedia:Articles for deletion/Geometry of roots of real polynomials. Opinion of editors that are competent in mathematics would be useful there. D.Lazard (talk) 20:45, 23 February 2019 (UTC)

Inclusion of Infobox mathematical statement in FLT

If you would like to contribute to reaching a consensus on whether Infobox mathematical statement should be included in Fermat's Last Theorem, please see this talk. — MarkH21 (talk) 05:09, 24 February 2019 (UTC)

Now nominated for deletion here by Deacon Vorbis (talk · contribs). — MarkH21 (talk) 05:31, 24 February 2019 (UTC)

WP 1.0 Bot Beta

Hello! Your WikiProject has been selected to participate in the WP 1.0 Bot rewrite beta. This means that, starting in the next few days or weeks, your assessment tables will be updated using code in the new bot, codenamed Lucky. You can read more about this change on the Wikipedia 1.0 Editorial team page. Thanks! audiodude (talk) 06:48, 27 February 2019 (UTC)

Portals added to math articles

New portals have been added in the "see also" section of several of our articles such as in e (mathematical constant), algebra, circles. There are more than twenty such automatically created portals. Please, participate to the discussion at Wikipedia:Village pump (proposals)#Hiatus on mass creation of Portals. Should we nominate for deletion all these portals that are related to mathematics? D.Lazard (talk) 15:49, 27 February 2019 (UTC)

• At the Portal:Burger King MfD an editor made some interesting points about pulling in barely related content, much like D.Lazard's points at the RFC. These things are based on Nav boxes but without the context of Nav boxes.

When WP:ENDPORTALS happened there were almost 1700 portals. Since then 4500 new portals have been created, about 3500 by one editor. Legacypac (talk) 16:23, 27 February 2019 (UTC)

• If you look closely at these portals, you see how terrible they are. I just nominated Portal:Circles for MfD. —Kusma (t·c) 17:07, 27 February 2019 (UTC)

Even the most advanced automated content creation is dangerous.User:Legacypac|Legacypac]] (talk) 18:27, 27 February 2019 (UTC)

References

• D.Lazard, are you suggesting deleting all math-related portals, or just the newly created ones? I think Portal:Set theory should stay. I would think all the "major branches" should probably have a portal — Algebra, Analysis, Geometry and Topology, Mathematical Logic, Number Theory. I haven't checked how many of these already exist or are newly created, but I saw algebra mentioned above among the newly created. --Trovatore (talk) 18:44, 27 February 2019 (UTC)

OK, Portal:Algebra is not new, although it has been widely edited by one of the creators of the new portals. About which portals should be delete, I have not a clear opinion. Otherwise, I would have been bold, by nominating them for deletion. D.Lazard (talk) 20:18, 27 February 2019 (UTC)

• I've seen the portals almost die over a long period, I've quite recently seen them revived by one(?) serious activist, I've seen dubious followers, and now I see mass-spamming. Maybe I am ametropic, maybe we should prepare to lean back and meditate while watching the AI-agents fighting their edit wars, installing infoboxes, partaking in RfAs, running the sanctions, ... I'd reduce the number of portals to just befor their near deletion, and watch their growth, before allowing for new portals. Purgy (talk) 19:29, 27 February 2019 (UTC)

Infobox mathematical statement

There is a sparsity of mathematical infoboxes and I think that one for mathematical statements (broadly construed, e.g. theorems, conjectures, propositions, lemmas, etc.) could be very useful on many particularly important mathematical articles. I've drafted a very simple one. Would other editors here welcome such a infobox? Feedback on its usage as well as its implementation (e.g. possible additional fields) would be very welcome as this is my first attempt at an infobox template! MarkH21 (talk) 06:17, 5 February 2019 (UTC)

I for one think that the sparsity is a good thing, and that adding more of them would be filling a much-needed gap. Infoboxes are inane. They're fine for filling out the details of inane subjects, like the teams a footballer has played on, but they are inherently a way of reducing material to a 5-second soundbite for readers who don't even have the attention span for a single full sentence at the start of the article. That's a bad fit for articles on technical topics in mathematics. —David Eppstein (talk) 06:31, 5 February 2019 (UTC)

Sure, I don't disagree with those statements! However, I do think that this would be a neat way of packaging a lot of the info for some major mathematical topics. Also, many of the articles for these problems are indeed technical and this would be a way to package basic information to a curious non-mathematician without requiring them to read through the history or current status. I'm sure many non-specialist readers look at articles about RH or P=NP precisely to get this kind of information quickly! MarkH21 (talk) 06:47, 5 February 2019 (UTC)

And indeed for important problems like P vs. NP you may find the Unsolved Problems box being used. --JBL (talk) 13:47, 5 February 2019 (UTC)

I've never seen that box used where the field given is mathematics (and in this case it's "Unsolved problem in computer science"). This is also an extension of that box, so if that merits use then shouldn't this? — MarkH21 (talk) 18:09, 5 February 2019 (UTC)

If you look at this you can see everywhere it is used, and find a bunch of math articles that way. For example, from the first 50 (and disregarding theoretical CS questions whose solutions will necessarily be mathematical in nature) uses I find these ten or so about mathematics: Sophie Germain prime, Hilbert's third problem, Sierpinski number, Collatz conjecture, Twin prime, Catalan's constant, Magic square, Catalan's conjecture, Mersenne prime, Perfect number. If that percentage is representative, then there are perhaps 50 or 60 total uses for mathematics. I was surprised to find it not used on RH, actually. --JBL (talk) 20:02, 5 February 2019 (UTC)

I see, although this is still not very widespread usage even for major problems (e.g. all 6 of the other Millenium Problems). Regardless, I see this infobox as an extension of the "Unsolved problem" box. Justification for the latter's existence and usage is pretty much also justification for the former's. — MarkH21 (talk) 19:56, 6 February 2019 (UTC)

Historically this Project has not been terribly enthusiastic about infoboxes, nav templates, and similar things, which can easily get spammy/crufty. That said, yours is plausible, and the RH example looks pretty good.

The "open question" field could get pretty controversial in some cases. Is the continuum hypothesis open, for example? Admittedly that particular problem is mostly concentrated in logic articles, and your format allows for explanation of the situation. But it might be good to explain that a problem being "open" doesn't necessarily mean the question is particularly in doubt (it would be shocking if, say, the Goldbach conjecture were false). Where one would explain that, I'm not sure. --Trovatore (talk) 06:38, 5 February 2019 (UTC)

Note that I just changed a few of the parameters and I changed the example since my first comment here. Sure, it could be controversial, in which case one could use something like Contested or just omit the field altogether until consensus is reached. A non-logic example would be the abc conjecture. I'm not sure evidence for/against validity would be a viable infobox field though.

Do note that many of the parameters are included for flexibility and that are optional. The example in the documentation includes all of them just for demonstration. MarkH21 (talk) 06:42, 5 February 2019 (UTC)

Heaven's blessings on the sparsity! Any single creation of such a box creates additional pressure an degrading substantial articles on math topics by stuffing real estate with boxes full of trivia, instead of structural content. I agree to the realm given above where these boxes may find a useful application, and I assume that there is nothing I can say beyond all the arguments already stated in the raging war against these infoboxes in serious articles. Maybe time has come where WP wants to degrade to trivia in boxes, I won't comment this. Diotimalives, Cassandra is dead. Purgy (talk) 07:51, 5 February 2019 (UTC)

I am in total agreement with David Eppstein and Purgy; the fewer of these things I see, the better. The kind of information that can be put into these sound bites is generally trivia, and while this may be useful in those articles where readers may be interested in trivia and trivialization of the subject, this just doesn't work in mathematical articles, not if you are trying to be intellectually honest. We work very hard, although not always successfully, at trying to make the lead accessible to a general reader and these infoboxes represent a repeat of that function in a highly formalized and abbreviated way. I don't think that this can be successfully carried out due to the inherent structural difficulties.--Bill Cherowitzo (talk) 16:49, 5 February 2019 (UTC)

I agree in general! But I do think that this particular usage would be helpful. I personally have looked up mathematical problems before just to remember who and/or when certain problems were posed and/or proven and the "simple answer" is not always obvious from the lead. I think that this particular usage would involve very little real estate and maintenance.

When the instance may not be "intellectually honest", then it can be expressed that way, the parameter can be omitted, or the infobox not used at all. — MarkH21 (talk) 18:09, 5 February 2019 (UTC)

I'm a bit late, and I'm not sure if I'm replying to anyone directly, but here goes anyway. I don't think I share quite the same level of disdain for infoboxes as some of the commenters above, but I do think that this one goes too far. They're good for examples of mathematical objects which have some standard bits of associated data – I think ones like {{Infobox probability distribution}} and {{Infobox graph}} work well. But for theorems, conjectures, etc., it mostly seems to be for information that's usually already in the article lead anyway, so I'm not sure much is really gained by having this. –Deacon Vorbis (carbon • videos) 19:17, 5 February 2019 (UTC)

Perhaps would the new "implied by", "generalizations", and "implications" parameters (that I just added be) useful as logical connectors between different theorems, axioms, etc.? I do think that such an infobox here could be revised to be appealing to most. — MarkH21 (talk) 19:31, 5 February 2019 (UTC)

I've thought about this some more, and I'd like to respond to the points brought up. The heart of the opposition seems to be that any infobox is a trivialization of the subject. However, the infobox neither detracts from the material of the articles for the knowledgeable nor expert reader, who may glance past the infobox just as one would for any biographical article. Meanwhile, the majority of articles on mathematical statements are too technical for the general reader (or even knowledgeable reader) to whom we should strive to make the articles more accessible. In particular, while basic details such as its history and its logical connections to other statements perhaps should be easily accessible in the lead (although I disagree for many cases), the fact of the matter is that they usually are not.

An implementation of the template, in great moderation and keeping the MOS purpose in mind, should add value to these articles – particularly for the general reader casually looking up math on Wikipedia. — MarkH21 (talk) 10:34, 10 February 2019 (UTC)

Bumping thread for 21 days. Referred to in a TfD listing –Deacon Vorbis (carbon • videos) 05:41, 24 February 2019 (UTC)