Wikipedia talk:WikiProject Mathematics/Archive/2017/Oct

Someone wants to redirect Reciprocal rule to Chain rule

See Talk:Reciprocal_rule. Michael Hardy (talk) 03:22, 5 October 2017 (UTC)

Redirect Help

Currently the dualizing complex for wikipedia directs to the Verdier duality page. This is partially correct since this could also redirect to the Coherent duality page. Can someone create a disambiguation page for these two? — Preceding unsigned comment added by Username6330 (talk • contribs) 00:48, 10 October 2017 (UTC)

Has Erdős–Turán conjecture been solved?

Hello,

I am not a mathematician, but my friend is. The most current version of the Wikipedia article on Erdős–Turán conjecture states that it remains unsolved. Here is a published article written by my friend Dr. Martin Helm back in 1993, which might change this. I would love an expert comment on this. Thank you very much!

Best regards, Aleksandr — Preceding unsigned comment added by DocAZ (talk • contribs) 00:41, 9 October 2017 (UTC)

Your friend's paper is on the Erdős–Turán conjecture on additive bases, not the one you linked, the Erdős conjecture on arithmetic progressions. And it doesn't disprove the conjecture; it is about the tightness of a previous disproof by Erdős of a special case of the conjecture. —David Eppstein (talk) 03:47, 10 October 2017 (UTC)

User:Ujin-X and vectors

• Ujin-X (talk · contribs · deleted contribs · logs · filter log · block user · block log)

User Ujin-X (contributions) has been making a number of edits related to vectors, broadly construed; all of it has the taste of crankery (trying to get direction vector deleted, adding what looks like invented terminology to articles, etc.). Perhaps this could use a few more eyes. --JBL (talk) 12:39, 12 October 2017 (UTC)

I have just nominated for deletion an article by this user, see Wikipedia:Articles for deletion/Inverse vector (a prod would certainly not be successful, as this user is still active). D.Lazard (talk) 14:30, 12 October 2017 (UTC)

See also Talk:Cross product#Cross product does not exist. Seems Ujin-X has just rediscovered a number of basic results, then come up with names for them as if they were original, and thinks WP should be changed to match their esoteric findings.--JohnBlackburne^words_deeds 15:01, 12 October 2017 (UTC)

Note his summary to this edit: In the theory of vectors, significant changes take place. A number of new terms have appeared (rectilinear vector, angular vector, inverse vector). These changes are related to the publication "Angular vectors in the theory of vectors" Wow... Boris Tsirelson (talk) 15:10, 12 October 2017 (UTC)

Maybe also worth noting is that the editor's username is the same as the contact email on that publication, which I found surprising. --Deacon Vorbis (talk) 15:23, 12 October 2017 (UTC)

I suspected a WP:COI, this is a confirmation. D.Lazard (talk) 15:37, 12 October 2017 (UTC)

Dear judges, I thank you for your attention to my person, but in Wikipedia I do not discuss myself, but the result of scientific achievement in the theory of vectors. I'm sorry to see that many of you, without bothering to read the article "Angular vectors in the theory of vectors", delete or misinterpret new terms and definitions.
All these terms (angular vector, rectilinear vector, inverse vector, vector division) have appeared, because in the existing theory of vectors there are a number of problems.
The angular vector has appeared, since Euclidean vectors (direction vectors) can not correctly display angular physical quantities (angular velocity, torque, etc.) in the coordinate system. A rotating ball can not have a straight rectilinear direction.
With the advent of the term angular vector, it becomes necessary to distinguish it from the Euclidean vector, so it is logical to call it rectilinear vector, it has always been that way.
The term inverse vector appeared in the process of solving a problem with a cross product of vectors, when one of them is represented as a unit divided by a vector. The most valuable thing in the inverse vector is not that it was invented, but the output of projection of the inverse vector on the coordinate axis. Thanks to them, it was possible to solve unsolvable problems in classical theoretical mechanics. This is shown in examples № 7 and 9. Using the cross product of vectors and the inverse vector, we essentially obtain vector division.
Dear mathematicians, I did not really want to create this work. I understood that she would force to review a lot of scientific works and cause a wave of indignation. But the truth is that science must be truthful, and all these discussions are aimed at a better understanding of mathematics, better modeling of physical quantities. On the understanding of the material by students, and not on memorizing an illogical theory.
You probably will have to accept the fact that the theory of vectors will change significantly. It has increased.
By removing new information, you can only slow it down a bit. But create on the English version will already be yourself. If I make new pages, then only in Ukrainian.Ujin-X (talk) 17:30, 12 October 2017 (UTC)

Yes, according to the rules of Wikipedia, we should be slow. Yes, we'll create such articles, if/when the new approach will enter textbooks, or/and be awarded, or/and widely used by others etc. Boris Tsirelson (talk) 17:49, 12 October 2017 (UTC)

By the way, you can immediately delete and Draft:Angular vectorUjin-X (talk) 17:53, 12 October 2017 (UTC)

We already have Pseudovector. There I see: A number of quantities in physics behave as pseudovectors rather than polar vectors, including magnetic field and angular velocity. Boris Tsirelson (talk) 18:02, 12 October 2017 (UTC)

I have nominated Draft:Angular vector for speedy deletion, per WP:CSD G7. D.Lazard (talk) 18:14, 12 October 2017 (UTC)

An offline app for Mathematics

Hello everyone,

The Kiwix people are working on an offline version of several Wikipedia subsets (based on this Foundation report). It basically would be like the Wikimed App (see here for the Android light version; iOS is in beta, DM me if interested), and the readership would likely be in the Global South (if Wikimed is any indication): people with little to no access to a decent internet connexion but who still would greatly benefit from our content.

What we do is take a snapshot at day D of all articles tagged by the project (minus Biographies) and package it into a compressed zim file that people can access anytime locally (ie once downloaded, no refresh needed). We also do a specific landing page that is more mobile-friendly, and that's when I need your quick input:

1. Would it be okay for you to have it as a subpage of the Wikiproject (e.g. WikiProject Mathematics/Offline)? Not that anyone should notice or care, but I'd rather notify & ask
2. Any breakdown of very top-level topics that you'd recommend? (see Wikipedia:WikiProject_Medicine/Open_Textbook_of_Medicine2 for what we're looking at in terms of simplicity) Usually people use the search function anyway, but a totally empty landing page isn't too useful either. Alternatively, if you guys use the Book: sorting, that can be helpful.

Thanks for your feedback! Stephane (Kiwix) (talk) 12:26, 10 October 2017 (UTC)

For now let me only say that I have admired Kiwix for many years. Boris Tsirelson (talk) 14:25, 10 October 2017 (UTC)

The list at Wikipedia:Vital articles/Expanded/Mathematics is in fairly good shape as a starting point. power~enwiki (π, ν) 14:44, 12 October 2017 (UTC)

This is brilliant. Thank you. Stephane (Kiwix) (talk) 06:15, 13 October 2017 (UTC)

Pseudovector

The material in the first section of this article, pseudovector, that seems to try to pass for a definition is all handwaving. Can something more precise be added? Michael Hardy (talk) 21:13, 12 October 2017 (UTC)

One thing which is curious is Polar vector redirects to pseudovector even though it's precisely the opposite.--Salix alba (talk): 23:12, 12 October 2017 (UTC)

Why curious? It seems that "polar vector" means "vector" in contexts where the terms "pseudovector" or "axial vector" are used, and is used only in these contexts. Only 10 WP articles use this term, and all but use "polar vector" in connexion with "pseudovector" or "axial vector". The last article, Vector notation defines a polar vector as a coordinate vector in polar coordinates. This seems a misnomer, and I'll insert a hatnote in this article. D.Lazard (talk) 08:38, 13 October 2017 (UTC)

What happened to "Collection (mathematics)"?

This leads to a redirect "Collection (mathematics)", ending in "Collection", but there is no phrase "math" to be found.

Did the deliberate undefinedness within mathematics of "collection" carry over to WP? I hope I did not miss something. Thanks for checking. Purgy (talk) 15:09, 13 October 2017 (UTC)

This is an easy problem in binary search. The relevant edit is this one (from 2013). Since no one will ever put "collection (mathematics)" into the search bar and it is not linked from anywhere, I have trouble being very concerned about this. --JBL (talk) 15:26, 13 October 2017 (UTC)

Apparently many people put collection (mathematics) into the search bar, as this redirect is viewed, in the average, once every day. The section "Mathematics" of Collection has been removed in 2013 by a user that has been blocked for sockpuppetry. This section deserve to be restored and I'll do that. D.Lazard (talk) 15:45, 13 October 2017 (UTC)

Under no circumstances I intended to create any specific concern, only rarely I feel sufficiently competent to touch disambiguations, but in any case I am thankful for all of your caring, because now I can go on to safely link a collection, notated as an indexed family, with the least interference with the original text. For a given occurrence, I really wanted to know how a "collection" in math context is looked upon in WP, and -lo and behold- Collection (mathematics) was a suggestion, nowhere to be found. Purgy (talk) 15:05, 14 October 2017 (UTC)

RfC notification

See Talk:Muhammad ibn Musa al-Khwarizmi‎‎ § Request for comment: Should ethnicity of al-Khwarizmi appear in the lead? D.Lazard (talk) 17:53, 14 October 2017 (UTC)

call for abstracts

Posting this here since it would be great if someone could come along and talk about Wikipedia's mathematical culture.

CALL FOR ABSTRACTS (deadline: 30th June 2017)

ENABLING MATHEMATICAL CULTURES, University of Oxford, 5th-7th December 2017

This workshop celebrates the completion of the EPSRC-funded project “Social Machines of Mathematics”, led by Professor Ursula Martin at the University of Oxford. We will present research arising from the project, and bring together interested researchers who want to build upon and complement our work. We invite interested researchers from a broad range of fields, including: Computer Science, Philosophy, Sociology, History of Mathematics and Science, Argumentation theory, and Mathematics Education. Through such a diverse mix of disciplines we aim to foster new insights, perspectives and conversations around the theme of Enabling Mathematical Cultures.

Our intention is to build upon previous events in the “Mathematical Cultures” series. These conferences explored diverse topics concerning the socio-cultural, historical and philosophical aspects of mathematics. Our workshop will, likewise, explore the social nature of mathematical knowledge production, through analysis of historical and contemporary examples of mathematical practice. Our specific focus will be on how social, technological and conceptual tools are developed and transmitted, so as to enable participation in mathematics, as well as the sharing and construction of group knowledge in mathematics. In particular, we are interested in the way online mathematics, such as exhibited by the Polymath Projects, MathOverflow and the ArXiv, enable and affect the mathematical interactions and cultures.

We hereby invite the submission of abstracts of up to 500 words for papers to be presented in approximately 30 minutes (plus 10 minutes Q+A). The Enabling Mathematical Cultures workshop will have space on Days 2 and 3 of the meeting for a number of accepted talks addressing the themes of social machines of mathematics, mathematical collaboration, mathematical practices, ethnographic or sociological studies of mathematics, computer-assisted proving, and argumentation theory as applied in the mathematical realm. Please send your abstracts to Fenner.Tanswell@Gmail.com by the deadline of the 30th June 2017.

The event takes place in the Mathematical Institute of the University of Oxford on 5th, 6th and 7th December 2017, with a dinner on 5th December and an informal supper on 6th December.

The focus of Day 1 will be on success, failure and impact of foundational research with an emphasis on history and long term development. Days 2 and 3 will focus on studies of contemporary and prospective mathematical cultures from sociological, philosophical, educational and computational perspectives.

Confirmed speakers include: Andrew Aberdein, Michael Barany, Alan Bundy, Joe Corneli, Matthew Inglis, Lorenzo Lane, Ursula Martin, Dave Murray-Rust, Alison Pease and Fenner Tanswell.

Organising Committee: Ursula Martin, Joe Corneli, Lorenzo Lane, Fenner Tanswell, Sarah Baldwin, Brendan Larvor, Benedikt Loewe, Alison Pease

Further information will be added to the website at https://enablingmaths.wordpress.com

Previous "Mathematical Cultures" events can be found here: https://sites.google.com/site/mathematicalcultures/ — Preceding unsigned comment added by Arided (talk • contribs)

Does a Call for Papers belong here? If we allow, we'd be swamped by such calls as I get one a day. About each one would involve Wikipedians in one way or another. I suggest deleting.Limit-theorem (talk) 10:01, 21 October 2017 (UTC)

Women in Red November contest open to all

		Announcing Women in Red's November 2017 prize-winning world contest Contest details: create biographical articles for women of any country or occupation in the world: November 2017 WiR Contest Read more about how Women in Red is overcoming the gender gap: WikiProject Women in Red
		(To subscribe: Women in Red/English language mailing list and Women in Red/international list. Unsubscribe: Women in Red/Opt-out list)

--Ipigott (talk) 15:40, 22 October 2017 (UTC)

Lagrangian disambiguation help needed

Expert mathematical help is needed to disambiguate links to Lagrangian in the following articles:

• Skyrmion
• Accidental symmetry
• Generalized Noether's identity and non-classical Noether's conservation laws

Thanks! bd2412 T 18:45, 18 October 2017 (UTC)

The article Lagrangian should not be a disambiguation page. The primary topic is Lagrangian mechanics. A separate Lagrangian (disambigation) page might be called for, but someone typing "Lagrangian" into the search bar (or linking to this term) will almost always mean the Lagrangian in the sense of Lagrangian mechanics. In any case, all uses of the term are closely related, suggesting further that disambiguation is not the proper way to handle this topic. Sławomir Biały (talk) 19:01, 18 October 2017 (UTC)

The third page, Generalized Noether's identity and non-classical Noether's conservation laws, is rather odd and WP:ESSAY/WP:OR-ish. XOR'easter (talk) 20:26, 18 October 2017 (UTC)

If Lagrangian is miscast as a disambiguation page, it should certainly be fixed. As for the latter page, is there a topic that is salvageable from that? bd2412 T 20:31, 18 October 2017 (UTC)

Looking at it again, I'm inclined to AfD it. The creator and chief contributor to that page has never worked on anything else; of the four sources, only two actually address the specific topic, and those two are papers which have had zero impact (the only citation for the older is the newer). It has the very strong feel of someone promoting their own, otherwise unrecognized, work. Plus, it just doesn't make sense. XOR'easter (talk) 17:22, 20 October 2017 (UTC)

In fact, it follows the (difficult) phrasing of one source rather slavishly: "such as displacement, strain, stress, Airy stress function" versus "each of the displacements, stresses and strains as well as Airy stress function", for example. If it's not the author promoting their own work, it's functionally indistinguishable from that. XOR'easter (talk) 17:37, 20 October 2017 (UTC)

OK, I PROD'ed it. XOR'easter (talk) 18:26, 22 October 2017 (UTC)

Proposal at Talk:Complex number

Should complex number be divided into eight articles? And if so, are there competent volunteers willing to write the resulting eight articles? Opine at Talk:Complex number#Proposal: multi-way split. Sławomir Biały (talk) 01:43, 24 October 2017 (UTC)

Move request

There is a contentious move request afoot at Talk:Tensor#Requested move 25 October 2017. Please opine there. Sławomir Biały (talk) 19:15, 25 October 2017 (UTC)

E6

There is a contentious discussion on Talk:E6 (mathematics) about illustrations that perhaps other users would like to weigh in on. --JBL (talk) 00:49, 28 October 2017 (UTC)

Discussion on Science and Maths articles on Jimbo talk page.

There is a discussion at User talk:Jimbo Wales#Science and math articles folowing an article Wikipedia’s Science Articles Are Elitist. People might like to contribute. --Salix alba (talk): 11:55, 17 October 2017 (UTC)

My opinion is basically this: As long as content forking is disallowed, WP cannot provide textbook(s), nor popular science. Boris Tsirelson (talk) 13:01, 17 October 2017 (UTC)

Content forks are indeed allowed, as most of Wikipedia:Content forking explains. Introduction to general relativity is a featured article demonstrating the situation. Thincat (talk) 12:58, 20 October 2017 (UTC)

These are strongly discouraged, however, and tend to violate WP:NOT. What tends to happen is that a single editor tendentiously creates one and then is sufficiently argumentative to prevent others from merging it back. In the end they should be merged together, however. The other issue is that there is a difference between topics such as general relativity, quantum mechanics, etc. which are covered even in freshman-level summary textbooks, and topics which are only covered in graduate or postgraduate level texts. For the latter kind of topic, it is virtually impossible to write a sourced article at an elementary level (assuming it is possible to write any article at an elementary level). — Carl (CBM · talk) 13:06, 20 October 2017 (UTC)

@Boris Tsirelson: I agree, although I think that there are broader reasons why we can't give a textbook. I think another issue is that, in order to write a "neutral" article, which many people can agree to, we have to avoid injecting our own perspective and vision into articles we write here. But that perspective and vision is exactly what would be necessary to give a good course on a topic. We aren't trying to give a course here, though, just a reference. Even co-authoring a book can be very difficult when the co-authors look at the same topic in different ways - co-authoring a book with hundreds of anonymous editors, some of whom may not really understand the topic, would be impossible. We can only manage here by keeping neutral. — Carl (CBM · talk) 13:09, 20 October 2017 (UTC)

Yes, I agree. And for popular science, the problem is even harder. Every good popular science text is a very creative, very personal work of a talented author. An impersonal bunch of editors, mostly students, cannot produce it; and anyway, such an article cannot be sourced. Similarly to an exercise, it is destined to be either Original Research, or a Copyright Violation. Boris Tsirelson (talk) 17:37, 20 October 2017 (UTC)

One could use Wikiversity (WV). Yes, it is much less visited than WP. However, it is possible to provide a link from a WP article to a relevant WV article (if the WP community does not object, of course); this option is rarely used, but here is a recent example: the WP article "Representation theory of the Lorentz group" contains (in the end of the lead) a link to WV article "Representation theory of the Lorentz group". Boris Tsirelson (talk) 17:45, 20 October 2017 (UTC)

Another option is, to submit an article to WikiJournal of Science. For example see "Space (mathematics)" accepted there. Boris Tsirelson (talk) 17:52, 20 October 2017 (UTC)

We're always going to get people who complain they can't understand maths or science articles. Euclid is supposed to have said to Ptolemy that there was no royal road to geometry and one of his first theorems has been referred to as the pons asinorum because some people just wouldn't get it. If they don't get that they are not going to be able to skim and understand the result of another two thousand years of study.

There is a bit of a problem though with articles being aimed a bit too high. I would say that at least the first half of an article should be accessible to someone who is interested and whose knowledge would put them about six months away from getting to the subject if they were going to study it. Dmcq (talk) 18:28, 20 October 2017 (UTC)

I basically agree with Boris Tsirelson as well and the WMF has other projects for the textbook approach, namely Wikiversity and Wikibooks. Those can be used for that purpose and good pieces in Wikibooks and Wikiversity can be linked in the related WP articles.

Having said that however, I do think that some math articles tend to be unnecessarily complicated for wider audiences, in particular if they start off with overly generalized or abstract versions of a particular math topic. Imho math articles should aim for starting off its topic with the least abstract/least general treatment of subject that can commonly can be found in reputable literature and only after that move on to more abstract or generalized treatments of that subject. That assures that the first sentences of the lead as well as the first sections of article are readable and useful to larger audiences than just the "elite few".--Kmhkmh (talk) 11:44, 21 October 2017 (UTC)

Personally, I find the complaints about the lead of the article complex number to be rather incomprehensible. I think there is an attitude that readers somehow expect too much from the lead of a mathematics article. They want everything to be made clear, yet when perfectly precise and clear language is used to explain the subject, they complain that it's too technical. They also want the whole article to happen in the lead.

Readers without familiarity with a subject in mathematics will no doubt feel that there must be a simpler way to express it. But, this is often not the case. For example, to say what a compact space is, we must at some point say "A topological space X is compact if, for every collection of open subsets of X whose union is all of X, there is a finite subcollection whose union is still X." This is not a very complicated idea, but many readers unaccustomed to such things will not want to go through the arduous work of attempting to read and understand the sentence. So, my conclusion is that readers who say that the lead of complex number is too abstract simply don't want to understand things.

I worry that if there is ultimately a push to make technical topics "understandable" to general readers, it will result in a general degradation of quality in our articles. Making technical topics understandable is not easy to do, and is one of the areas in which we've seen the Dunning-Kruger effect. Mathematics novices often try to improve articles by making them more palatable to general readers, but the effect is usually a vague, poorly written mess, and often is just wrong. (Even experts have a hard time saying something that is not wrong when they use "plain English" to express mathematical ideas.) Novices should be encouraged to summarize and cite sources. Pedagogical or introductory sources can be used to introduce a topic, provided those meet the same standards of reliability as the rest of our sources. But editors shouldn't be encouraged to deviate from the presentation of topics found in reliable sources, but that seems to be where things are headed.

So, I propose that we should gather together a collection of bad edits that we've seen through the years that were aimed at making things more accessible (but usually with the opposite effect). Here is one that I found in my edit history. Sławomir Biały (talk) 18:24, 23 October 2017 (UTC)

Another such attempt. Sławomir Biały (talk) 18:43, 23 October 2017 (UTC)

A quote from myself: "Well, this is a math article. Not recreational mathematics. Not a textbook. Not a pearl of popular science. To a reasonable extent, it does contain elements of these three genres." Boris Tsirelson (talk) 19:37, 23 October 2017 (UTC)

On the other hand there are (too) many articles that seem having been written for being understood only by experts. My favorite example is this one. Although I know well this subject, I needed some time for understanding that the previous first sentence was correct. Another example is this one (I compare the 2012 version with the present version because several editors have been involved). Again, one may clearly consider the 2012 version as elitist. IMO, this is not elitism but incompetence of some editors. D.Lazard (talk) 20:14, 23 October 2017 (UTC)

@Sławomir  : as an example, the current version of "complex number" on Simple Wikipedia [1] manages in one lede to bring up normal numbers, to claim that complex numbers were invented (i.e. rather than discovered) and to claim that there is a "problem" with exponentiation. — Carl (CBM · talk) 15:08, 24 October 2017 (UTC)

CBM, the word "normal" is being used in its normal usage, to mean "typical, usual, what one is used to." Similarly, the claim that there is a "problem" is explained in the immediately following sentence, namely, it is referring to the problem of the algebraic unclosedness of the real numbers. The fact that we mathematicians assign meanings to words like "normal" does not mean that the cannot be used in other valid ways! Overall I think the simple wikipedia intro reads a bit stilted but is clear, covers a variety of important points, and is sufficiently technically accurate for an introduction of an encyclopedia article. --JBL (talk) 15:20, 24 October 2017 (UTC)

But complex numbers as just as "normal" in that sense as any other number. Imagine if I started an article with "New York is different than a normal city..." - that is not NPOV. Moreover, nobody writing an mathematical article should be aware that in that context the term "normal number" does have a specific meaning. The same NPOV issue happens with "problem" - this is the kind of writing that could be used in an expository article or popularization, or even in a textbook, but to use it here would go against the tone we are striving for as well as violating NPOV. This kind of thing is one reason why it is not as simple to write "clearly accessible" articles on Wikipedia as it would be on a personal blog. — Carl (CBM · talk) 15:27, 24 October 2017 (UTC)

This lede contains also the sentence "The complex number can also be written as a set (a, b)" ! D.Lazard (talk) 15:55, 24 October 2017 (UTC)

No, your first sentence is (obviously) wrong and that's the point: to you and me, the complex numbers are normal. To the world in the year 1550 they were not normal, and to my calculus students in the year 2017 they are not normal. They really are genuinely more abstract than real numbers, which are in turn genuinely more abstract than rational numbers, which are in turn genuinely more abstract than positive integers, and it is completely ok for the first sentence of the article to be written in a way that makes them approachable for people who are more like my calculus students and less like me. The objection you are raising involving normal number makes no more sense than if I started tearing up the lead of normal number by invoking normal (geometry) (since the number line is geometric after all). Similarly, I really don't know what to make of your claim "this is the kind of writing that could be used in an expository article" -- in what world is an encyclopedia article not an expository article? It is indeed difficult to write clearly accessible articles when one imposes standards that forbid accessibility. This is not to say that there could not be some better alternative phrasings -- I would describe the introduction to the simple wikipedia article as "reasonably decent and very accessible" and I would describe the introduction to our article as "reasonably decent but not very accessible." (The simple version doesn't discuss the geometry as much but does a better job of the history; the basic algebraic issues are covered in both.) -JBL (talk) 16:06, 24 October 2017 (UTC)

By an "expository article" I mean something that could appear as an article in Mathematics Magazine, or a senior capstone paper, or perhaps something that could be in the "What is" series of the Notices of the AMS. Essentially, a non-research-level summary of a topic, with no claim of originality in its mathematics, meant to introduce someone to a new area. Our articles, in contrast, are primarily meant to be references, not to be the first place someone learns a topic. People can sometimes use our articles to learn about a new topic, but that is a secondary purpose at best. Analogy: reference texts such as the Handbook of Combinatorial Designs vs. textbooks on design theory, or the Handbook of Mathematical Logic vs. textbooks on logic. The handbooks, like Wikipedia, are intended to be references first, and so they also can be quite inaccessible to people who don't have enough background.

As for complex numbers not being "normal", that is exactly the kind of claim that we remove routinely because of NPOV. It's simply not possible, in an environment where everything can be tagged for originality and POV, for editors to use flowery language of that sort. This is one reason that many of our articles seem to have a dry, uninspired tone: because they are written not only by a committee, but by an anonymous committee who have to agree on the wording. — Carl (CBM · talk) 17:33, 24 October 2017 (UTC)

I am mystified by why you think the category "encyclopedia article" is in conflict with the description "a non-research-level summary of a topic, with no claim of originality in its mathematics, meant to introduce someone to a new area." The description seems to me to fit exactly what an encyclopedia should aspire to: a first place someone can go to learn about a topic, with pointers to references for those looking for more depth. Normal people (used to) own encyclopedias! Normal people do not own the Handbook of Combinatorial Designs. There is a place in the world for reference works suitable for people who are already expert in a field, but that place is not a general purpose encyclopedia. --JBL (talk) 18:06, 24 October 2017 (UTC)

I do think that there is a difference between presenting a reference on a topic and presenting a textbook or expository essay. This difference is somewhat captured by the quote "The purpose of Wikipedia is to present facts, not to teach subject matter." from WP:NOT. Of course, people use Wikipedia for many purposes, and we make some concessions towards readers who have not seen the material before. I'm not arguing against that. But readers should also remember that our articles are not really intended to teach someone about a topic which they have no idea about. In some cases, it seems unreasonable to expect that this is possible, e.g. natural transformation — Carl (CBM · talk) 20:21, 24 October 2017 (UTC)

To add to this, I think that the matter is fairly conclusively settled at the policy level. WP:WEIGHT is to represent all viewpoints in a manner in proportion to the treatment in reliable sources. Reliable sources will certainly include some pedagogical sources, but generally should be sourced to standard academic literature, as these are the most reliable in the sciences. Our wording, likewise, must reflect what is in those sources. Sławomir Biały (talk) 20:55, 24 October 2017 (UTC)

Well, this has been a sobering conversation for me: I had always assumed that the perennial critics of the way math articles are written on wikipedia were simply underestimating the challenge of writing mathematics well for a lay audience. But apparently they are right: some of our contributors are actively opposed to writing mathematics well for a lay audience. This is sad. --JBL (talk) 22:18, 24 October 2017 (UTC)

I don't know that anyone is opposed to the general concept of writing mathematics for a lay audience - it is vital for the general public to see many aspects of mathematics. But that doesn't mean that the mission of Wikipedia is to write articles about advanced mathematical topics (e.g. natural transformation) for a lay audience. Some of our core policies, such as WP:V, WP:DUE, and WP:NPOV, require us to stay very close to existing sources, rather than writing our our personal interpretations and novel explanations. So, rather than underestimating the difficulty of writing for a lay audience, I think that many editors are well aware of that difficulty and edit accordingly. If anything, I think that editors sometimes overestimate the possibility of making articles on less-advanced subjects like complex number more clear. — Carl (CBM · talk) 01:15, 25 October 2017 (UTC)

While I don't have much to add to this particular debate, I'm sorry to hear that my owning a copy of the Handbook means I'm not a normal person . Be that as it may, I just wanted to point out that I have just made some edits to the simple Wikipedia page that makes part of this discussion moot. A better choice of terms in that article can remove some of the difficulties that have been noted. However, I did have to think long and hard about replacements that stayed within the limits of that project and I am not completely satisfied with the result. Portions of that page still jar my mathematical sensibilities, but I am trying to overlook those reactions. Although an advocate of mellower introductions to math articles, I don't see how I could keep this up in my more typical editing. --Bill Cherowitzo (talk) 18:52, 24 October 2017 (UTC)

. Your edits to that article are excellent. --JBL (talk) 22:18, 24 October 2017 (UTC)

Another example for Sławomir Biały's collection, which I have just fixed: [2]. For the record, I have done this edit after being told that a previous revert was wrong: although this article is intended for a public of beginners in mathematics, I was confused by the previous content of this section. D.Lazard (talk) 15:55, 24 October 2017 (UTC)

Comment: I don't have much to add to the above. But one aspect that exasperates the situation is that we are generally not allowed to make simplifying assumptions. For example, in algebraic geometry, sometimes, one can give simple definitions if one knows a variety is a quasi-projective variety. Similarly some expositions become obscure or obtuse because we are not assuming the base field has characteristic zero. If Wikipedia's mission is to provide learning materials, it might be a good idea to avoid some technicalities by making simplifying assumptions. Since our concerns here are to provide references, I don't know what can be done to the view that pedagogy and accessibility are secondary to presenting precise facts. -- Taku (talk) 03:35, 25 October 2017 (UTC)

I do know what to do: for pedagogy and accessibility use Wikiversity and Wikijournal (as I suggested above). But alas, I guess, you all do not like Wikiversity. It is indeed in a very bad state – just because you all do not participate. Boris Tsirelson (talk) 04:32, 25 October 2017 (UTC)

Well, Wiki seems to be a bad medium for writing textbooks or preparing learning materials. One reason I have not see mentioned is the tradinal teaching style doesn't mesh with collaboration: the great courses and textbooks are about personal touches and visions. Personally I don't know a textbook I like that has multiple authors. Of course, this can also mean "we're teaching math wrong!" I'm a bit irritated by a defeatist attitude of some editors (e.g., that of Professor S.B.) that the only traditional way to write math is the only way. Wikipedia is supposed to democratize knowledge; I think the root of the complain is that many of our math articles are failing this.

I know I know content forks are supposed to be "bad thing". Perhaps this policy needs to be revised; it is posssible that, given an inherent drive to generalization and abstraction, math articles are types of articles that benefit from content forks. -- Taku (talk) 23:46, 29 October 2017 (UTC)

About "courses and textbooks are personal" I agree, completely. About content forks, no, no chance to weaken this policy here; this is a fundamental principle of Wikipedia; this is why WP is much more coherent and successful than other wikis; no one will make an exception for mathematics. About "Wiki is a bad medium for textbooks" I disagree; probably you mean "Wikipedia", not "wiki" in general. If indeed "math articles benefit from content forks", then these should be on other wikis that welcome content forks. Wikiversity is flooded with very bad texts, which seems to be inescapable when content forks and original research are welcome, but really is not! For an escape see WikiJournal: WikiJournal of Science (again). For example see "Space (mathematics)" accepted there. By the way v:WikiJournal of Medicine succeeds; we could, too. On WikiJournal in general see m:WikiJournal User Group. Boris Tsirelson (talk) 05:50, 30 October 2017 (UTC)

To continue on "content forks", we do actually have de fact content forks in math articles in a way: mathematically, a vector space is simply a special case of a module and so all the materials on "vector space" can be covered in the latter. There are many similar examples in linear algebra topics; e.g., linear transformation v.s. module homomorphism, dual vector space vs. dual module, etc. Similarly, the notion of a connection on a fiber bundle (i.e., Ehresmann connection) subsumes connections on vector bundles and those on principal bundles. The connection situation in particular resulted in a lot of repetitions of definitions. In other words, we have varying treatment of the same/similar subjects depending on sophistication of approach. I don't think this situation is problematic but I think it's inevitable since readers of different backgrounds prefer different presentations. Also, "content forks" need not be "original research"; for example, a connection can be approached from either vector-bundle-pov or a principal-bundle-pov; either approach is standard. Personally I can see "content forks" depending on readers' backgrounds; say one "algebraic curve" article for the general public and the other for the readers with background in algebraic geometry. -- Taku (talk) 02:15, 31 October 2017 (UTC)

Those content forks are different from those originally discussed here, they aren't really simply (or at all) based on pedagogic or popular science take on the subject, but they arise from a the historic development of the field and its usage in practice.--Kmhkmh (talk) 03:25, 31 October 2017 (UTC)

For "accessible functor", the page Vopěnka's_principle links to Accessible_category, where accessible functors are not mentioned

See Vopěnka's_principle#Definition, the phrase "Every subfunctor of an accessible functor is accessible" marks "accessible functor" with a hyperlink to the wiki page Accessible_category. Unfortunately accessible functors are not mentioned there. Also unfortunately I do not know enough about accessible functors to add information about them. -- 109.172.129.80 (talk · contribs · WHOIS) 14:23, 24 October 2017‎