Talk:Normal subgroup

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WikiProject Mathematics (Rated C-class, High-importance)
WikiProject Mathematics
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Mathematics rating:
C Class
High Importance
 Field: Algebra


Too many articles in the math topics on Wikipedia contain the annoying complaint about citations. In fact, I think the complaint is entirely misguided. If needed the authors of any page should be asked for proofs of any assertions in question. Citations are circular. They prove nothing and especially so in mathematics. Think about it! It is entirely possible for nearly endless citations to support any statement and for the statement to be false. So in math a proof is what is needed (if there is any question) so let's get rid of these annoying citations complaints. apparently tildes not working my keyboard berrtus1 — Preceding unsigned comment added by Berrtus1 (talkcontribs) 16:53, 19 May 2016 (UTC)

A few notes, if I may:
  • First, this discussion is not new. Please see WP:WikiProject Mathematics/Proofs for an essay that tries to summarize past discussions on proofs in Wikipedia. Generally, with the exception of routine calculations (see WP:CALC), proofs in articles like any other content need to be backed by citations, as they otherwise would be considered original research, and that is prohibited by WP:NOR, and this is one of the three core content policies of Wikipedia, along with WP:V and WP:NPOV. Generally, the presence of a proof does not obviate the need for a citation. Furthermore, proofs (IMHO) should be included only if their presence makes the respective article more intelligible to the reader, or if they themselves are notable in the sense of WP:N, that is, if they are of encyclopedic interest.
  • Second, per WP:TALK, this talk page is not the place for a general discussion of our policy concerning the need for citations: "The purpose of an article's talk page … is to provide space for editors to discuss changes to its associated article or project page. Article talk pages should not be used by editors as platforms for their personal views on a subject."
Tea2min (talk) 08:46, 20 May 2016 (UTC)
Basically your saying the annoying citation can be placed above articles, but you can't talk about it even on the talk page. I suppose that indicates a top down policy where certain discussions are simply not allowed. I would suggest the following: Links to proofs where needed. Citations when a significant definition or theorem is referred to. But if it is just trivial consequences of well known theorems then constantly asking for citations is an insult, and really contrary, I believe, to the philosophy of mathematics, and the mathematical method, and pedagogical methods in general -- students should ask "why" or 'prove it' not 'where did you get that from'. — Preceding unsigned comment added by Berrtus1 (talkcontribs) 15:19, 22 May 2016 (UTC)
Wikipedia tries to be an encyclopedia, not a textbook. Wikipedia articles report what was written in reliable sources, and Wikipedia articles absolutely must provide references to those sources. The layman reader absolutely needs to be able to check that a given fact matches what is said in a reliable source. This applies to any article, including those reporting on mathematical topics.
Furthermore, Wikipedia is work in progress, mistakes happen, and Wikipedia articles are of very uneven quality. Tags like the one asking for more precise citations aim to point article authors to weak points of the presentation, and they sometimes help the reader as they sometimes warn him of articles of poor quality.
Now, are we talking about the need for citations in general or limited to the page Normal subgroup? If we are talking about the need for citations on articles about mathematical topics in general, then no, this talk page is absolutely not the right place for that. If we are talking about the need for inline citations on the page Normal subgroup, then yes, of course, this talk page is the right place for that.
So, let's talk about the page Normal subgroup. In my opinion, statements like
  • "Normality is preserved upon surjective homomorphisms, and is also preserved upon taking inverse images." and
  • "If H is a normal subgroup of G, and K is a subgroup of G containing H, then H is a normal subgroup of K."
clearly need to be backed by references as they clearly go beyond what I think can reasonably be called routine calculations. What do you think?
Tea2min (talk) 17:05, 22 May 2016 (UTC)