Wikipedia talk:WikiProject Mathematics

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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 [email protected] 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)

User:Hesselp again

• Hesselp (talk · contribs · deleted contribs · logs · filter log · block user · block log)

User:Hesselp has started nibbling at the edges of his topic ban from Series, at the article Cesaro summation, where he has some novel ideas of his own. The situation could use close monitoring. Sławomir Biały (talk) 11:27, 15 October 2017 (UTC)

It seems hard if not impossible to reason with him or explaining him how Wikipedia should approach a (math) topic. This issue has spread now over 3 Wikipedias, after starting out on the Dutch Wikipedia and being told off there, he moved to English Wikipedia and after the topic ban there on to the German Wikipedia. Now after his activities got largely stalled by other (math) editors in the German Wikipedia, he seems to be back in the English one.--Kmhkmh (talk) 14:23, 15 October 2017 (UTC)

This comment from Tsirel seems like a good summary of the situation. --JBL (talk) 16:47, 15 October 2017 (UTC)

Maybe an even better summary is his own (just above and below my one cited). He acknowledges that, first, he is "genetically" different from most of mathematicians. Second, that his adamant position did not change even a little after that discussion ("you helped me to get my views on the subject even more concrete, and to find more compact and to-the-point wordings"), in contrast to my position. Third, that there is, indeed, a chance that sometimes he will do according to my guess. Boris Tsirelson (talk) 18:04, 15 October 2017 (UTC)

Just some comment from an outsider: this seems to be mainly of a terminology issue. Is 1+1 the same as 2? Numerically speaking, the answer is trivially (I suppose) yes while the former is a sum and the later isn't; so in that sense they are different. The case of series is similar; for the purpose of discussion, a numerical series converges to pi need to be somehow distinguished from pi, even writing down pi itself involves some infinite expression. I don't think the language in mathematics that is currently in use is able to take these nuances into account. I guess one mathematically rigorous way is to somehow encode the construction that is used to obtain the results; i.e., histories behind objects. I'm sure the resulting approach to calculus should be called motivic calculus. (In case you thought this is a joke, actually I'm 1 percent serious about this concept.) -- Taku (talk) 05:28, 16 October 2017 (UTC)

This is very close to User talk:Hesselp#Maybe I understand; I suggested, he rejected (as usual...). Boris Tsirelson (talk) 05:40, 16 October 2017 (UTC)

This is very similar to what I also tried to articulate, only to find my wording picked apart, talked around in circles. Engaging with this editor is a pure waste of time. Sławomir Biały (talk) 10:53, 16 October 2017 (UTC)

An opinion

Some truth lurks behind his position.

• We do not have a singe, universally accepted (and rigorous, of course) definition of "a series".
• Sometimes $\textstyle \sum _{n=1}^{\infty }a_{n}$ denotes just a number (the sum of the series), but sometimes it denotes something much more informative ("the whole series") that determines uniquely each $a_{n}.$
• The language of "series" should not be interpreted literally; the meaning depends on the context; some mathematical maturity is needed in order to understand it correctly.
• This makes some troubles for teachers and students. Some students conclude that the series theory is non-rigorous, inconsistent etc.

However, whenever I try to elucidate such truth, he always disagrees: "but this is not my point". I fail to understand his point. In practice I observe that he attacks, here and there, an occurrence of the word "series" and insists on reformulating the text in order to remove this occurrence ("since this is consistent", or "more clear", or "less context-dependent", or "simpler", "more logical" etc). Maybe he hopes to gradually exterminate the word "series" this way. Anyway, he grossly exaggerates importance of all that. He believes that this is not just a pedagogical problem, but a mathematical problem, that mathematics is inconsistent (God forbid) because of that, etc.

Really, is it possible to reformulate everything (equivalently) in a "series-free" language? Yes, of course. Every mathematician can easily reformulate a statement accordingly. (And by the way, this is why consistency of mathematics is still safe.) Instead of a series one may use the sequence $(a_{n})_{n}$ of its terms, or alternatively the sequence $(s_{n})_{n}$ of its partial sums, or the pair ${\big (}(a_{n})_{n},(s_{n})_{n}{\big )}$ of these two (interrelated) sequences. Other possibilities are also available, of course.

The question is, does it makes our language more convenient, or less convenient. I tried to consider some examples ("User talk:Hesselp#Only a pedagogical problem?", near the end), but he missed my point completely.

As far as I see, it is possible to exterminate the word "series" from mathematics, but it is not worth to do, since ultimately it makes our language less convenient. This is not done for now, and I do not think this will happen in the (near) future.

Even if this seems helpful to do in textbooks, it is not. Textbooks should prepare a student to reading math literature. Thus, the word "series" (with all its intricacies) should be known to students. Boris Tsirelson (talk) 10:15, 19 October 2017 (UTC)

It is not up to Wikipedia editors no matter how knowledgeable or intelligent to reformulate mathematics in a more sensible or consistent way than is in current textbooks. They say series, we should say series. I really don't think there is very much more to it than that. As you pointed out right at the beginning of that very long discussion 'However, note a difference: on my courses I am the decision maker; here on Wikipedia I am not. Here a point of view cannot be presented until/unless it is widely used. And if it is, it must be presented with "due weight"'. Practically everything else there was irrelevant to improving the article which is the purpose of a talk page. The appropriate answer to him when he quoted Bourbaki and said though a definition was formally correct it was absurd is to say he needs a better source to say so than himself. No source was provided never mind a better one. Dmcq (talk) 11:27, 19 October 2017 (UTC)

I'm working on a reaction on the last two edits (19 October 2017). -- Hesselp (talk) 13:35, 20 October 2017 (UTC)

"They say series, we should say series." — Indeed: "There's no free will," says the philosopher; "To hang is most unjust." "There is no free will," assents the officer; "We hang because we must." q:Ambrose_Bierce   :-)   Boris Tsirelson (talk) 09:05, 21 October 2017 (UTC)

On 'An opinion' (Boris Tsirelson, Dmcq)
Thanks to both of you for your efforts to explain your position, in a clear way.  I'll make remarks on six points.

    On  "Sometimes $\textstyle \sum _{n=1}^{\infty }a_{n}$ denotes ..."
This symbolic form is used in three ways: the sum number, the sum sequence and the 'series' of sequence (a_n).
   Bourbaki has, in editions 1942 until 1971, the distinctive forms:  S$\textstyle _{n=0}^{\ \infty }a_{n}$,   $\textstyle \sum _{n=0}^{\ \infty }a_{n}$  and  $\textstyle \left((a_{n})\ ;\sum _{n=0}^{\ \infty }a_{n}\right)$.
   The object symbolically denoted by  $\textstyle \left((a_{n})\ ;\sum _{n=0}^{\ \infty }a_{n}\right)$,  is verbally described by:  the series defined by the
   sequence $\textstyle (a_{n})$  or  the series whose general term is $\textstyle a_{n}$  [or simply  the series $\textstyle (a_{n})$,  by abuse of language, if there is
   no risk of confusion].
As is this capital-sigma form, the adjective ‘convergent’ is ambiguous as well: "having a limit" and "having a sum". This double meaning has a long history, at least untill Euler and the Bernoullis. I cite (once more) Gauss, 18??: Die Convergenz einer Reihe an sich ist also wohl zu unterscheiden von der Convergenz ihrer Summirung, Werke, Abt.I, Band X, S.400.  In all his publications Cauchy used the verb converger for limittable and the adjective convergente for summable, but this seems to be never adapted at large.

    On  "We do not have a single, universally accepted..."
Is this really true? Or do we overlook Cauchy's observation? His famous Cours d'Analyse starts in CHAPITRE VI p.123 simply with: On appelle série une suite indéfinie de quantités ... . ("An infinite sequence of quantities is called series",  with 'quantity' = 'real number' as declared in PRÉLIMINAIRES p.2.)   Doesn't this fits with the (universal) practice: 'series' is used instead of 'sequence' in situations where it's essential that addition between terms is defined? And doesn't this fits with the contents of the chapters headed 'Sequences' and 'Series' in almost all textbooks on calculus? (Keep in mind that Cauchy used 'convergent' for 'converging partial sums' = 'summable',  not for 'converging terms'.)
You are going to qualify this as being OR, not allowed in WP?  It's nothing else than the observation that Cauchy's terminology (with his 'convergente' replaced by 'sommable') still fits with actual practice.

    On  "Maybe he hopes..." .
That’s your idea, Tsirel;  my comment: "Gedanken sind frei, wer kann sie erraten...".  Actually I'm quite convinced, and I wrote it several times, that a chapter "Series" (and a chapter "Cesàro summability" connected with Fourier-expansion especially) would be much easier to understand by using 'sequence', 'summable' and 'absolutely summable' instead of 'series', 'convergent' and 'absolutely convergent' (avoiding ambiguities). On the other hand, the objective "prepare a student (and a WP-user) to reading existing math literature", is as important to me as it is to you. That’s beyond discussion.

    On  "he misses my point completely".
I looked again at your questions of 9 October 2017 (18:16 and 19:54). You varied the wordings of your two phrases in a way I never thought of. Combined with your puzzling "identify a series with...." I missed your point, yes indeed.

    On  "They say series, we should say series".
They say series.   Literally yes, they use the word "series". But examining calculus textbooks you can find maybe a dozen different - non equivalent - attempts to describe its meaning. All of them pretending to present THE meaning; no one mentions Tsirel's "We do not have a single...".
So what do you, Dmcq, mean with "we should say series"?   Should the WP article choose for just one description (out of the 'dozen')?  Bourbaki's? as in the renowned EoM.
Or, current practice in WP, present a handful of non-equivalent descriptions, pretending their equivalence?  see:
- a series is, roughly speaking, a description of the operation of adding infinitely many quantities, one after one ([1]),
- a series, which is the operation of adding the a_i  one after the other (line 21),
- a series is an infinite sum (Basic properties, line 1),
- a series is the sum of the terms of an infinite sequence of numbers (line 1)
- a series is, ... an expression of the form  Σ_n=1^∞ a_n  or   a₁ + a₂ + ··· (section Series, line 1).
Or, distinguish explicitely the different roles of the s-word in: series-expression, series-representation, series-expansion, and more?   And mention that 'sequence' and 'series' are synonyms (though sometimes one variant is more usual) in: alternating se..., Fibonacci-se..., Fourier-se..., geometric se..., harmonic-se..., power-se..., trigonometric-se..., et cetera.

    On  "Bourbaki’s definition is absurd".
I cannot provide sources that support the qualification 'absurd'. Nor sources that comment on 'series' defined as a  sequence - sum sequence pair. I can show circa 10 titles of calculus books with their exposition on 'series' based on this pair; so it seems to be important enough to be mentioned in WP Series (mathematics).
One more remark on this quite unusual definition: Cauchy’s "sequence with real numbers as terms" implies that the partial sums are defined. So "a sequence with additionable terms" is close to "a sequence with a sum sequence", and in this interpretation of Bourbaki there’s nothing 'absurd' left anymore.
-- Hesselp (talk) 15:29, 22 October 2017 (UTC)

For goodness' sake. You just posted over 6000 bytes, and I have no idea what your point is, or if you even have one anymore. You've been overwhelming these discussions with walls of text, and it's not productive. Here's all you need to know: an (infinite) series is an expression $a_{1}+a_{2}+a_{3}+\cdots =\sum _{n=1}^{\infty }a_{n}.$ When the $a_{n}$ are numbers, this notation can generally denote either the series itself as a formal object, or the (ordinary) sum of the series. When the $a_{n}$ are functions (or operators, etc), there are often multiple common notions of convergence, so some care should be taken to indicate what's meant. This is all pretty standard; can we just drop this all now? --Deacon Vorbis (talk) 17:16, 22 October 2017 (UTC)

And not a single citation backing up whatever the view is. Ignore or revert on sight is my opinion. Dmcq (talk) 20:55, 23 October 2017 (UTC)

@Dmcq.   Your comment concerns Deacon Vorbis, 22 Oct., I suppose?   I agree, it wouldn't be possible to find reliable sources for his double cyclic:  An infinite series is an expression ....denoting either itself or its sum.
In case you meant my text (22 Oct.), you probably missed Cauchy, Gauss, Bourbaki, EoM. -- Hesselp (talk) 08:42, 24 October 2017 (UTC)

Some response to all of the above: I think it is useful to remember calculus that is currently taught and is in use is not the only one and not even necessary an optimum one. An example: is 0.999... the same as 1? This is mainly of the language problem. The "standard" interpretation is that the former denotes the limit of the sequence 0.9, 0.99, ... and so (trivially??) is 1. But one might resonantly argue the former should mean a "number" that is arbitrary close to 1 but is less than 1; namely, 1 - infinitesimal. This is a matter of what calculus we are using. In some edge cases, the interpretations need not be obvious: the typical example is the "series" $\sum _{-\infty }^{\infty }a_{n}$. I think by that one typically means Cauchy's principal value of the series. But arguably the best approach is to study such a series in the context of distributional calculus. In other words, it is fallacy to assume there is one unique consistent approach to calculus; we search for it in vain (no?) -- Taku (talk) 04:00, 25 October 2017 (UTC)

Rather intriguing: what is $\textstyle \sum _{-\infty }^{\infty }a_{n}$ according to the distributional calculus? Boris Tsirelson (talk) 04:45, 25 October 2017 (UTC)

By the way $a_{n}$ there should be distributions or some other kind of generalized function. The example I had in mind was the formula like $\sum _{-\infty }^{\infty }e^{2\pi in\bullet }=\sum _{-\infty }^{\infty }\delta _{n}$ where $\delta _{n}[f]=f(n)$ and $e^{2\pi in\bullet }[f]={\widehat {f}}(n)$, the Fourier transformation (the Poisson summation formula.) So here the sums/series denote particular distributions. My larger point was that the insistence on a unique interpretation seems unworkable not only atypical. For instance, I don't think there is a clean bright distinction between sum and series. The right-hand side in the above example seems better to be called sum than series. Likewise, any infinite sum involving partition of unity feels like sum than series. -- Taku (talk) 00:21, 27 October 2017 (UTC)

A sort of a corollary of the above is that a certain superfluous looseness between sum/series/infinite expression isn't because mathematicians are sloppy but because they are not completely distinct concepts. Trying to suggest there is a bright distinction is both a POV and misleading, I think (not only unsupported). -- Taku (talk) 21:07, 28 October 2017 (UTC)

G. Birkhoff's incorrect translation/interpretation of Cauchy

I invite everyone who criticizes my attempts to improve WP articles on 'series', to compare five sentences from Cauchy's text (1821) with Birkhoff's adapted (improved? modernized?) version (1973).

A.  Birkhoff's adapted translation (see Garrett Birkhoff A Source Book in Classical Analysis 1973 page 3;  this adapted text is copied by J. Fauvel, J. Gray in The History of Mathematics: A Reader 1987, p.567, no digital version of this section) reads:
A sequence is an infinite succession of quantities u₀, u₁, u₂, u₃, ...
which succeed each other according to some fixed law.
These quantities themselves are the different terms of the sequence considered.
Let  s_n = u₀ + u₁ + u₂ + u₃ + ··· + u_n-1  be the sum of the first n terms, where n is some integer.
If the sum s_n tends to a certain limit s for increasing values of n, then the series is said to be convergent,
and the limit in question is called the sum of the series.
[.....] By the principles established above, for the series   u₀ + u₁ + u₂ + ··· + u_n + u_n+1 + ···   to converge,
it is necessary and sufficiant that the sums  s_n = u₀ + u₁ + u₂ + u₃ + ··· + u_n-1  converge to a fixed limit s as n increases.

B.  Birkhoff's translation without his adaptations (see Cauchy 1821 (French) and Bradley-Sandifer 2009 (English)) reads:
Series is used as name for (Cauchy: On appelle série) an infinite sequence (Cauchy: suite) of quantities u₀, u₁, u₂, u₃, ...
which succeed each other according to some fixed law.
These quantities themselves are the different terms of the series considered.
Let  s_n = u₀ + u₁ + u₂ + u₃ + ··· + u_n-1  be the sum of the first n terms, where n is some integer.
If the sum s_n tends to a certain limit s for increasing values of n, then the series is said to be convergent (Cauchy: convergente),
and the limit in question is called the sum (Cauchy: somme) of the series.
[.....] By the principles established above, in order that the series   u₀ ,  u₁ ,  u₂ ,  ···,  u_n ,  u_n+1 ,  ···   be convergent,
it is necessary and sufficiant that the sums  s_n = u₀ + u₁ + u₂ + u₃ + ··· + u_n-1  converge to a fixed limit s as n increases.

Cauchy's nomenclature is consistent (although the adjective 'summable' instead of his adjective 'convergent' - close to the verb 'to converge' for 'tend to a limit' - could have avoided quite a lot of misunderstanding).   In the adapted text, the word 'series' pops up in the fourth sentence without any explanation.
Birkhoff remarks in a footnote  "Cauchy uses the word 'series' for 'sequence' and 'series' alike, ...". This is incorrect: Cauchy uses série in all his works only for "an infinite sequence of reals". -- Hesselp (talk) 15:13, 30 October 2017 (UTC)

If you want to write an article on the history of the words "sequence" and "series" and submit it to a journal about the history of science, be my guest. None of this has anything to do with editing Wikipedia, so please stop spamming it here. --JBL (talk) 15:24, 30 October 2017 (UTC)

Agreed. I can't figure out what Hesselp is trying to accomplish here, or how it relates to editing the encyclopedia. It seems to be a lot of long-winded rambling. Reyk _YO! 16:17, 30 October 2017 (UTC)

This editor is banned for editing Series (mathematics) and Talk:Series (mathematics). I suggest to extend the ban to all pages and discussions where series occur. D.Lazard (talk) 16:26, 30 October 2017 (UTC)

@JBL, @Reyk.   Isn't it desirable to inform WP readers that Cauchy's description is an alternative for no definition at all (or five contradictory)? -- Hesselp (talk) 17:25, 30 October 2017 (UTC)

None of your edits in the past couple of weeks relate in any identifiable way to the goal of informing WP readers about Cauchy's description of anything. Moreover, this is precisely the topic from which you are banned. Knock it off. --JBL (talk) 23:59, 30 October 2017 (UTC)

No one of the five attempts (in WP articles 'Series', 'Convergent series', 'Sequence') to describe the mathematical notion called 'series', is supported by any mentioned reliable and clear source. So Cauchy's (reworded by Bourbaki, used in the EoM) should be considered. That is my goal. -- Hesselp (talk) 15:33, 2 November 2017 (UTC)

"Cauchy's description" is already in use in the following sense (explained by me on Hessel's talk page, but apparently not understood). Mathematics works with notions rather than definitions. A notion is, effectively, an equivalence class of definitions. There is no gain in canonizing one definition and exterminating all others. It is better to know many equivalent definitions, and to understand their interplay (which needs mathematical maturity, sometimes missing). See Equivalent definitions of mathematical structures. For example, topological space has at least 7 definitions (which is good, not bad). Five (and more) equivalent (not at all "contradictory") definitions of a series is also a good, not bad, situation. One of these is "Cauchy's description" (which is just a historical fact of no special importance nowadays, I think so). Boris Tsirelson (talk) 05:53, 31 October 2017 (UTC)

@Boris Tsirelson.   Again, I agree with your general remarks on  "A notion is, effectively, an equivalence class of definitions."
But (1):   How can you write "Five (and more) equivalent .... definitions of a series is also a good ... situation." ?  For that seems to say just the opposite of your "We do not have a single, universally accepted (and rigorous, of course) definition of "a series" ".
But (2):  The 'five' refers (yes ?) to five actual descriptions in WP, summed up above almost at the end of. How can you say that this five are 'not at all "contradictory"' ?  For:
Don't you agree with me that an expression for a notion cannot define that notion itself ?
Idem, that the notion in question cannot be defined by "the operation of adding the terms" as well as by "a description of the operation of adding...." ?
Idem, that "the operation of adding the terms" comes much closer to the notion 'summing a series' than to the notion 'series' itself? -- Hesselp (talk) 10:03, 31 October 2017 (UTC)

Tsirel, on your judging "Cauchy's description" as a historical fact of no special importance nowadays:
You think the same for Bourbaki's description (as in the Encyclopedia of Mathematics) ?
And for which out of the cited 'five' as well? -- Hesselp (talk) 10:28, 31 October 2017 (UTC)

The mathematical notion usually named 'series' can be expressed/denoted by the symbolic form a1 + a2 + a3 + ··· . But equally well by the symbolic form a1 , a2 , a3 , ··· . The comma's-notation can be found in: A.R. Forsyth Theory of functions of a Complex Variable, 1918 page 21. Whatever the choice of symbolic notation, the denoted notion remains the same.
The same applies for the name of this notion: whether one says 'series' or 'infinite sequence with addable terms' or 'sequence with sum sequence', the notion does not change. -- Hesselp (talk) 20:21, 1 November 2017 (UTC)

I have asked for a ban extension at WP:ANI#User:Hesselp again. D.Lazard (talk) 17:46, 30 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 [2] 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: [3]. 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)

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)

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: [[Wikipedia:WikiProject Women in Red/The World Contest|November 2017 WiR Contest]] Read more about how Women in Red is overcoming the gender gap: [[Wikipedia:WikiProject Women in Red|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)

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)

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.

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)

"cas" typesetting

In this section of Hartley transform I found this line:

$2{\mbox{cas}}(a+b)={\mbox{cas}}(a){\mbox{cas}}(b)+{\mbox{cas}}(-a){\mbox{cas}}(b)+{\mbox{cas}}(a){\mbox{cas}}(-b)-{\mbox{cas}}(-a){\mbox{cas}}(-b).\,$

I changed it to this:

$2\operatorname {cas} (a+b)=\operatorname {cas} (a)\operatorname {cas} (b)+\operatorname {cas} (-a)\operatorname {cas} (b)+\operatorname {cas} (a)\operatorname {cas} (-b)-\operatorname {cas} (-a)\operatorname {cas} (-b).\,$

Obviously the reason for the deficiency of space between "2" and "cas" was the use of \mbox{} instead of \operatorname{}. But both before and after that edit, we see less than the usual amount of space before and after than plus and minus signs, as exemplified here:

${\begin{aligned}\cos(a+b)&=\cos a\cos b-\sin a\sin b\\\sin(a+b)&=\sin a\cos b+\cos a\sin b\end{aligned}}$

And the spacing deficiency in a + b is even worse after the edit than before. Note that the spacing in a + b is normal in the identities for sine and cosine.

Why is there that deficiency of space surrounding plus and minus signs? Michael Hardy (talk) 22:45, 27 October 2017 (UTC)

It looks ok to me. What are your math rendering preferences set to? —David Eppstein (talk) 22:49, 27 October 2017 (UTC)

@David Eppstein: Now I find that it looks correct when I'm logged out. As for preferences, I'm going to have to wait until tomorrow to look at that. Michael Hardy (talk) 23:17, 27 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)

Is it the gamma function or the Gamma function?

Opinions of this edit?

An argument for capitalizing the initial "G" is that it's a capital Gamma. Michael Hardy (talk) 22:14, 31 October 2017 (UTC)

Just to clarify a little, I noticed the vast majority of uses already in place that I happened to see were lower case, so I mainly did this for consistency. I'm about to run out, so I can't look in too much more detail right now, but I'll quickly note that Mathworld and the Springer EOM both use lower case (although EOM hyphenates it) (and we certainly don't have to do the same as them, but it seems to be more common this way). --Deacon Vorbis (talk) 22:28, 31 October 2017 (UTC)

I just did a quick spot-check of the mathematics textbooks I've got lying around, and most of them have gamma uncapitalised. So I would go with that. Reyk _YO! 22:33, 31 October 2017 (UTC)

I can't recall seeing a text that capitalizes the g, and spot-checking the books on my shelf, all the examples I find have the g lowercase. XOR'easter (talk) 03:56, 1 November 2017 (UTC)