Wikipedia talk:WikiProject Numbers

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Interesting properties

Edits on the article 1234 (number) recently were disliked and questionable by some users; backgrounds can be seen in Talk:1234 (number)#Mock rational and WT:WPM#1234 (number). This curiosity leads me to question what are the facts not included in "interesting properties"? Do we have some guidelines or manual styles about this, or to put it plainly, how to distinguish between properties of a number that are very interesting? There are several articles, one of which is 59 (number) talking about the number of polyhedron classes or polytopes, each of which is 59 in total. Dedhert.Jr (talk) 10:36, 5 August 2024 (UTC)

Discussion at WP:ANI

The ongoing discussion at WP:ANI#User:Radlrb in WP:WPM, spawned from WT:WPM#1234 (number), is relevant to members of this WP, as User:Radlrb is responsible for a very large amount of the content on number pages. Mathwriter2718 (talk) 13:16, 5 August 2024 (UTC)

Help remove WP:CRUFT on number articles!

Hi, I'm looking for editors who can help me clean up some of the more problematic number articles and format their mathematical properties in a standard fashion, for an example, see 2, (before: [1] after: [2]). As this is a rather big task, I would love some help! Allan Nonymous (talk) 20:36, 6 August 2024 (UTC)

@Allan Nonymous: Why did you rm the etymology of two? I am thinking it remains relevant until we get to at least 13 (to explain the whole -teen suffix and why 11, 12 are unique). ❧ LunaEatsTuna (talk), proudly editing since 2018 (and just editing since 2017) – posted at 20:42, 6 August 2024 (UTC)

Never mind I am blind, pardon me. ❧ LunaEatsTuna (talk), proudly editing since 2018 (and just editing since 2017) – posted at

Although while I have you, what is your opinion on 69 (number), the only integer with GA status? ❧ LunaEatsTuna (talk), proudly editing since 2018 (and just editing since 2017) – posted at 20:44, 6 August 2024 (UTC)

Most of the information in the article is WP:DUE but is not always presented in the cleanest way (there are a lot of redundant statements). Some parts of the section on mathematics probably don't belong there. Allan Nonymous (talk) 21:30, 6 August 2024 (UTC)

Not a fan of the bullet points TBH, it looks too unencyclopaedic for WP. Also, everything in the lead is meant to be mentioned in the body as well, so it is not redundant to repeat it. IMO said article is a more preferred example of what the other integers should look like, at least having been through a peer-review and some editors have said so too – I think we should open a discussion on making any major changes/standardisations to our articles on integers first. We have no policy on what aspects of a number should count as being noteworthy so it might be worth discussing that first – I think a criteria is ultimately needed so we can better improve them :) ❧ LunaEatsTuna (talk), proudly editing since 2018 (and just editing since 2017) – posted at 22:20, 6 August 2024 (UTC)

What is the justification and what is the big idea about changing all of those prose into bullets? The section in mathematics about 69 is already well-known divided into elementary properties as a natural number, properties of its factor and its classes, numerical systems, and its classes in geometrical visual. I think article 69 is presented well, from which we should treat other number-topic articles. The fact that GACR1b stated the article complies with MOS, one of them is about the list embeddings (see MOS:EMBED). A somewhat relatable MOS can be seen in MOS:PROSE. Dedhert.Jr (talk) 02:28, 7 August 2024 (UTC)

I will say, whether the articles are in prose or in bullets is not terribly important to me. I would be fine with people rewriting them in prose if that's the general consensus (I'd be willing to put in the work to change them myself, even!) My main concern is the accumulation of mathematical trivia, not really the format of the articles. WP:NNUMBER WP:1729 all provide pretty good guidelines for this sort of thing. Allan Nonymous (talk) 04:08, 7 August 2024 (UTC)

That's ridiculous and reckless given myself and others have made extensive efforts converting bullet points into high quality prose, which you have subsequently deleted. We are aware of the issue with trivia but what you are doing is a backwards step. You are deleting high quality encyclopedic content. Don't throw the baby out with the bathwater! Polyamorph (talk) 12:08, 7 August 2024 (UTC)

• Oppose I disagree that the information you're removing is cruft, and I wish you would get consensus before making such large changes to so many articles at once. Also, as Dedhert.Jr said, I prefer prose to bullet points. Davey2116 (talk) 03:15, 7 August 2024 (UTC)

  Mass reverting edits, particularly from an individual editor is generally frowned upon per WP:HOUND as for the reasons behind those edits, see Wikipedia talk:WikiProject Mathematics#Cleaned up the article 7 where a general consensus on the mathematical worthiness of the content in question was established. As to whether the information ought to be presented in WP:PROSE I feel it would be better to have it in large paragraph bulleted lists, but would be perfectly fine with prose paragraphs. Allan Nonymous (talk) 03:45, 7 August 2024 (UTC)

You brag on your user page that you are a BOLD editor. If you make bold edits to more than a dozen articles in rapid succession you do not get to then complain when they are reverted. I do not think HOUND applies here because the edits in question are all directly pertinent to this issue, as opposed to unrelated edits reverted as part of some personal vendetta. BRD is more relevant in this case than HOUND, and really, you shouldn't be redoing this many bold edits after you know that someone has objected to them.

I assure you that I do assume AGF on your part, I simply disagree with what you're doing here. Overall, I find that most of the contributions in question are interesting, informative, and above all, useful; the reader who searches for individual numbers on Wikipedia is looking for exactly this kind of information. There can be discussions about how much weight to give the more specialized facts, but the wholesale indiscriminate deletions you've been doing are not helpful, in my opinion, and should be reverted.

As for the "consensus" you cite, while that is a lengthy discussion, there are only a handful of editors present, and some comments read like objections to your BOLDness (e.g. An edit removing that much material deserves a thorough review to ensure there is not any rescueable content that was deleted). As to your response to that particular comment (I 100% agree, feel free to go in and add back (in a more clear and concise way) some of the facts deleted if there is a consensus to do so): deleting 20,000+ worth of content is effortless; to put the burden on someone else to sift through all of it or else let your deletion stand is very unreasonable. That is why I attempted to revert your deletions; it is not that I think every single fact I restored should ultimately be kept, just that if we're going to delete things we should do it small steps at a time, with dedicated discussions on each article's talk page to deal with things on a case-by-case basis, rather than all at once in some obscure backroom discussion that didn't even get a RfC. Davey2116 (talk) 05:26, 7 August 2024 (UTC)

I agree 100% with you Davey2116 and is along the lines of how the wikiproject members have been operating. Polyamorph (talk) 12:33, 7 August 2024 (UTC)

• This is disruptive. Please stop removing content on mass. Several of us have been actively improving these articles, removing what you might consider to be WP:CRUFT, and improving the prose. You are removing this prose and replacing with lists, which is not an improvement and contrary to the GA standard we've been working towards. Your edits are disruptive and you must stop immediately. Polyamorph (talk) 11:54, 7 August 2024 (UTC)

@Radlrb, Certes, and Barnards.tar.gz: your attention is requested. Polyamorph (talk) 12:00, 7 August 2024 (UTC)

I haven’t had a chance to look at the edits in question in detail, but after a very brief spot check of a few removals I find myself agreeing that they are crufty. However, huge sweeping changes are difficult to assess so I understand the concern. Since there does not currently appear to be consensus, let’s discuss here. Perhaps some principles could be agreed, e.g. that a number appearing in an OEIS sequence is not sufficient for that to be a significant fact about the number. Barnards.tar.gz (talk) 12:34, 7 August 2024 (UTC)

Compare this with this. Completely removing the extensive prose in the "In mathematics" section (which incidentally I wrote) and replacing with an inferior list. Polyamorph (talk) 12:39, 7 August 2024 (UTC)

I agree that wasn’t an improvement. Barnards.tar.gz (talk) 13:18, 7 August 2024 (UTC)

Hi, I wish to introduce myself. I am Mathwriter2718, a relatively new editor to Wikipedia. I have worked at WP:WPM for a bit but I have been dragged towards this project, particularly from the Radlrb discussions, and I am joining it now.

I gently disagree with Allan Nonymous's style of making blowtorch removals, though I understand the motivation to act this way given the very large amount of cruft. I certainly agree that many number articles have large amounts of cruft on them. I personally believe the correct way to deal with this is to remove smaller amounts at a time, so that if edits are reverted, we can discuss the merits of specific content instead of getting into a spat about whether a 77,000 byte removal was a good change or not. I have recently made some (relatively) small, conservative removals from 5 and 7 that I hope the other editors will review.

Perhaps some of the chaos of the past week (or even months) could be minimized if this project's guidelines were expanded. Mathwriter2718 (talk) 15:29, 7 August 2024 (UTC)

Here are some relevant threads to this one:

• Wikipedia_talk:WikiProject_Mathematics#Cleaned_up_the_article_7
• Wikipedia_talk:What_Wikipedia_is_not#WP:NOTOEIS

Mathwriter2718 (talk) 15:37, 7 August 2024 (UTC)

Hi Mathwriter2718. I missed the drama at WP:WPM and so only just became aware after the reverts on my watchlist! Other relevant recent threads are:

• Wikipedia_talk:WikiProject_Numbers/Archive_8#Move_trivia_and_disambiguation_content_out_of_number_articles
• Wikipedia_talk:WikiProject_Numbers/Archive_8#Guidelines_for_entry_qualification

There is consensus that there is a lot of trivia that needs to be removed, and I have removed entire sections from articles myself previously. The ultimate aim of this project is to improve the articles on numbers. I worked a fair bit on 1 previously with the intention to improve the prose to GA standard, I think I was making progress. I think a systematic approach, starting with an overhaul of WP:WikiProject_Numbers#Template_for_integers for consistency with WP:Manual of Style/Trivia sections -Polyamorph (talk) 15:49, 7 August 2024 (UTC)

There was so much drama at WPM across many threads. Several comments were reverted and aren't visible anymore. I suspected things have been brewing for a while, and it seems from those threads you just sent that it goes back even further than I thought! I confess to being a fan of some trivia on articles, though the content on some of these articles is not even related to the article's subject. Specifically, the stuff that bothers me the most is "number X (the subject of the article) is related to Y, and now I am going to tell you several paragraphs about Y". Examples of this were removed in https://en.wikipedia.org/w/index.php?title=744_%28number%29&diff=1238550872&oldid=1230509719. Mathwriter2718 (talk) 16:05, 7 August 2024 (UTC)

Proposed update for integer guidelines

For the draft guidlines, see Wikipedia:WikiProject Numbers/Guidelines.

Polyamorph suggested that the inclusion guidelines at Wikipedia:WikiProject Numbers#Template for integers need to be updated. It does seem there's a big gap between what's recommended by the guidelines and what the most inclusive editors have been de facto keeping in articles. It also seems like there is material that inclusive editors have been restoring that they might agree can be removed, so it would help to get specific, and maybe the article conflicts can be resolved simply by following some new agreed-upon criteria. So, open question: what are the most important and interesting properties about integers that are missing from the guidelines? -- Beland (talk) 19:32, 7 August 2024 (UTC)

• For me, the Template for integers is fine for creating a brand new start class article, but most/all of these articles already exist now. For developing GA or FA quality content we should be using prose, not lists, and there are other important sections that would be expected in a GA, including etymology and history of symbols / representation etc. Polyamorph (talk) 19:44, 7 August 2024 (UTC)

  Would you say everything in [3] is covered by the existing guideline, then, other than that it uses prose instead of a list? It doesn't include etymology or history of glyphs - I assume that's only relevant for digits and numbers with irregular names (which the guidelines might want to say, and we also have English numerals to explain construction patterns). -- Beland (talk) 20:12, 7 August 2024 (UTC)

  The key guideline is that the subject of the article is the number — that is, the mathematical object — and not the numeral(s) that represents the string of characters or character commonly used to represent the number. To be honest, I think most of the content does satisfy that criteria. It could be written more accessibly or concisely, with some aspects like "concatenation of digits" section removed as it's not particularly relevant, but I don't see a justification for mass removal of content from this article making it a stub. Note, the PIN code that is in the current version fails these criteria since that is simply a string of characters and has nothing to do with the number as a mathematical object. Polyamorph (talk) 20:35, 7 August 2024 (UTC)

  I wonder if one reason the existing guideline envisions a list is that this encourages very short notes, deferring background information to linked articles. The preference for shortness may also be why editors who have been doing blowtorch trimming have been switching to list format sometimes? It sounds like small-article advocates are open to prose if it's focused on interesting properties. Is the level of detail for each factoid a matter of dispute? Or alternatively, what should the guideline say about prose? -- Beland (talk) 20:59, 7 August 2024 (UTC)

  The level of detail should be consistent with the GA guidelines in that it is broad in its coverage, covering all main aspects of he topic, mathematical or otherwise, without going into unnecessary detail - i.e., avoid straying too far from information about the number itself. Polyamorph (talk) 12:12, 8 August 2024 (UTC)

  It would be sensible to discuss how to deal with content such as 7#Religion and mythology. It is simply a list of factoids, most of which are uncited. There is provision for extra-mathematical associations in the guideline, but I'm certain most editors would consider this "cruft" ( I don't like the word but it is the one others are currently using). Yet this content was retained in the mass deletion event. Polyamorph (talk) 20:45, 7 August 2024 (UTC)

  Perhaps the detailed per-religion lists can be offloaded to detail articles if they seem a bit much for the number-article scope? We already have Significance of numbers in Judaism but it might be interesting to have a similar article for Christianity or other cultural domains. One argument for doing that is that it's interesting to compare how different numbers are considered in a given culture. One argument for not doing that is that it's interesting to see how different cultures have similar or conflicting views of the same number. -- Beland (talk) 21:30, 7 August 2024 (UTC)

  These sections should absolutely exist, but not as a long list of random factoids. Where a number is a key element of a religion or culture then it is of course important to include in the interests of breadth of coverage. Polyamorph (talk) 12:15, 8 August 2024 (UTC)

• The key guideline is that the subject of the article is the number — that is, the mathematical object — and not the numeral(s) that represents the string of characters or character commonly used to represent the number."

I do not think this is a good idea. I have said this before (in archive 8; please read) - just because something is a "mathematical fact" does not make it notable. Perhaps a good guideline to add would be "The presence of a number in an OEIS entry does not in itself give notability." OEIS is meant to be completely comprehensive; no-one is reading it as prose. Or again "A number x may not be cited as the nth member of an OEIS entry unless there are similar WP entries for the mth member of that sequence, for every m < n." Clearly there is a "cruft" problem with cultural stuff (football shirts and the like); I think some specific guidelines (not "rules") would help, like "No telephone numbers", "No bingo calls", "No billiard balls", "No age of majority stuff". (The last is a good example: pretty much any integer from 14 to 23 is available to pretty much every government in the world for age restriction more or less any sort of fun.) But there is also clearly a "cruft" problem with mathematical bits. Imaginatorium (talk) 03:39, 8 August 2024 (UTC)

• I'm not entirely clear on your objection to that existing guideline, I think it is that you feel it's too broad? I agree introducing a guideline as to what does and does not make a mathematical concept relating to a number notable for inclusion would be sensible. Polyamorph (talk) 11:53, 8 August 2024 (UTC)

  Sorry, I wasn't clear. I mean the "mathematical only" idea is too restrictive. Yes, the subject should obviously be the number, rather than just some connection to random other information. But significant facts about the number as a numeral should not be rigidly excluded. Imaginatorium (talk) 15:59, 8 August 2024 (UTC)

  Thanks for clarifying. I agree. Polyamorph (talk) 10:58, 9 August 2024 (UTC)

  Indeed, and maybe we should say that the focus should be on the mathematical object — and not the numeral(s) that represents the string of characters or character commonly used to represent the number. And that other associations are seconday. After all, we are talking about these articles as N (number). The identifier "number" is, I believe, more oriented to mathematical associations rather than other references that are not based in mathematical concepts, such as cultural, practical, or otherwise (in society). Scientific, as well as philosophical connections to the number rooted in mathematics are an order higher than purely cultural uses or applications (i.e. "high five" or "451" from the book Farenheit 451 as the cited temperature at which paper burns, though the scientific part itself is possibly worth mentioning prior first), I believe. As I mentioned, this is mostly, I feel, due to having the identifier of "number" as part of the Wikipedia article moniker for number articles (i.e., "10 (number)" for 10 instead, which in this view an article such as 5 could be slightly misrepresentative, as here really the article naming could all-along have been drawing readers to think its about anything to do with just "5", rather than principally its mathematical ascribed properties and relations). These, as examples aside from exceptional cultural connections that are themselves mathematical, or symbolic with a degree of arithmetic or geometric context, for example. Radlrb (talk) 03:23, 10 August 2024 (UTC)

A concrete proposal

I think it would be good to have a concrete first draft proposal that people can attack, modify, and affirm.

Number articles should typically have these sections in this order. All sections will be written in prose with subsections as necessary and will not be bullet lists.

1. History: history of the concept/symbol/word. Should only exist when there is something interesting to say.
2. In mathematics/In geometry: see below.
3. List of basic calculations: contains 1 row for multiplication, 2 for division, and 2 for exponentiation. Should only be on articles 1, 2, ..., 13.
4. In (some area other than math, Christianity, Judaism, Buddhism, science, technology, etc): I have no comments at this moment on what belongs in these sections.
5. Endmatter (see also, references, etc).

For the section "In mathematics", here is how I propose weighing facts. Facts should be frowned upon for being:

Routine. Routine means also being true for nearly every other number upon a slight modification.

Examples that are routine:

• On the page for 5: "the Collatz sequence for 5 is 5, 16, 8, 4, 2, 1".
• On the page for 9: "nine has the even aliquot sum of 4".

Examples that are non-routine:

• On the page for 3: "3 is the first odd prime".

Not about the subject of the article. Facts on the page for number X should be as much as is reasonable about number X and not about number or object Y, even if X and Y are related. It is fine to say that X and Y are related, but this doesn't mean we should go into tons of detail about Y.

Examples that are about the subject:

• On the page for 5: "5 is also the first of the three known Wilson primes 5, 13, 563".
• On the page for 9: "nine has the even aliquot sum of 4".

Examples that are not about the subject:

• On the page for 5: "the factorial of five 5! = 120 is multiply perfect".
• On the page for 5: "a magic constant of 505 is generated by a 10 × 10 normal magic square". (The connection here, I think, is that 505 contains two 5's in its base 10 representation.)

Only mentioned inside OEIS. Indicator of interestingness.

About a property or sequence that does not have a Wikipedia page. Indicator of interestingness.

Facts should be smiled upon for being:

Interesting, nontrivial, surprising, striking, or cool, as measured by editors' reactions.

Examples:

• On the page for 5: "In graph theory, all graphs with four or fewer vertices are planar, however, there is a graph with five vertices that is not: K₅, the complete graph with five vertices, where every pair of distinct vertices in a pentagon is joined by unique edges belonging to a pentagram."
• On the page for 777: "777 is the difference between the number of diagonals and edges in a regular 42-gon."

Non-examples:

• On the page for 1234: The infamous 1234 fact said that the square root of 1234 is approximately 35.128336140500 which, when you take the floor, is the first in some unspecified sequence to be composite.

About a connection to an important object

Example:

• On the page for 9: "A polygon with nine sides is called a nonagon".

Mentioned outside of OEIS. Indicator of interestingness.

About a property or sequence that has a Wikipedia page. Indicator of interestingness.

Facts should be thrown out right away for being:

WP:OR or WP:SYNTH: every fact should be stated somewhere other than Wikipedia prior to its inclusion in this section.

Mathwriter2718 (talk) 14:09, 8 August 2024 (UTC)

Support this is a great proposal. My only tiny concern is that "777 is the difference between the number of diagonals and edges in a regular 42-gon." doesn't strike me as a terribly interesting fact, as its about an arbitrary n-gon. Allan Nonymous (talk) 14:20, 8 August 2024 (UTC)

It's great to have your support. Shortly after you posted your response, I edited that criterion to make it clearer that it is the most subjective criterion (there are other more objective measures of interestingness I included). I personally find the 777 fact striking, but it is ok if we disagree. Mathwriter2718 (talk) 15:02, 8 August 2024 (UTC)

I incorporated your proposal into the draft Wikipedia:WikiProject Numbers/Guidelines. Allan Nonymous (talk) 19:22, 8 August 2024 (UTC)

The regular 42-gon is not an arbitrary polygon; see Euclidean tilings by convex regular polygons#Plane-vertex tilings, it is involved in the largest plane-vertex tiling, which does not make the 42-gon a trivial mathematical object as it is at the limit for regular vertex-only tilings. It contains the largest possible regular symmetry order of a polygon that can be used to tile the plane alongside other irregular polygons - see 1 for its construction. This makes a statement such as "777 is the difference between the number of diagonals and edges in a regular 42-gon" a worthwhile inclusion. Radlrb (talk) 02:40, 10 August 2024 (UTC)

• Comment All sections will be written in prose with subsections as necessary and will not be bullet lists. I think the important thing here is to note that prose is preferred. Lists can have their uses and for short articles with little content may even be a better way of organising the content. So it's just a matter of making clear prose is the preference where possible. The existing template in the guidance lists the following in the In mathematics section. Which of these if any are consistent with your proposal?
• A polygon with N sides is called an n-gon.
• N is part of the first few, or part of the last, members of a specific sequence.
• N is a Mersenne prime, or a Fermat prime, or a special and well-studied other prime.
• There are exactly N of (special groups, platonic solids, or other objects).
• There is a prominent mathematical object with N number of subobjects.

  Polyamorph (talk) 14:35, 8 August 2024 (UTC)

  Thanks for your comment. I agree with what you said about prose.

  A polygon with N sides is called an n-gon.

  This would be included for all N up to whenever people stop thinking that an N-gon for fixed N is an "important object". I personally think that 1-gons through 20-gons are probably important enough to merit inclusion, but 21-gons and higher are not very significant.

  N is part of the first few, or part of the last, members of a specific sequence.

  It is hopeless to decide this in general without knowing what the specific sequence is. My proposal intends to list criteria for how we would decide whether this sort of fact is included.

  N is a Mersenne prime, or a Fermat prime, or a special and well-studied other prime.

  This would definitely be included. It satisfies both "About a connection to an important object" and "About a property or sequence that has a Wikipedia page" and is not "Routine" or "Not about the subject of the article".

  There are exactly N of (special groups, platonic solids, or other objects).

  There is a prominent mathematical object with N number of subobjects.

  This is on the boundary. Again, I think we need to think about how important or interesting the specific fact is. For example, the fact "there are five platonic solids" is extremely widely said, but it is not interesting when S₂ has 2 subgroups, even though S₂ is definitely a "prominent mathematical object". Fwiw, its a bit bizarre that "object" links to Category theory and not Mathematical object. Mathwriter2718 (talk) 15:19, 8 August 2024 (UTC)

  Category theory objects are the most abstract (and thus inclusive), I think? Allan Nonymous (talk) 15:32, 8 August 2024 (UTC)

  OK Mathwriter2718, I've created Wikipedia:WikiProject Numbers/Guidelines using the existing text, feel free to blank and start from scratch but I thought this could be a good way to hack at the guidelines and come up with something we can all agree on. What do you think? A useful way to proceed? Polyamorph (talk) 15:36, 8 August 2024 (UTC)

  That might be a good way to proceed. At the moment, I've spoken enough, and I want to give others some time to share their opinions. Mathwriter2718 (talk) 15:44, 8 August 2024 (UTC)

  I think this is a good idea if we want to make more drastic changes to the guidelines here, which I think is a consensus that has emerged here and at WP:WPM. Allan Nonymous (talk) 16:50, 8 August 2024 (UTC)

  @Polyamorph Why not just write Wikipedia:Manual of Style/Numbers instead, similarly as Wikipedia:Manual of Style/Mathematics? Dedhert.Jr (talk) 01:55, 9 August 2024 (UTC)

  Topic-specific manuals of style are often hosted by WikiProjects, which can be helpful if general MOS participants are uninterested in a specific discipline or don't consider themselves expert enough to weigh in. -- Beland (talk) 02:50, 9 August 2024 (UTC)

  I think that is a very good point. Put this stuff somewhere like MOS and all sorts of well-meaning but not subject-informed people will make unhelpful changes or arguments. Imaginatorium (talk) 09:12, 9 August 2024 (UTC)

  @Beland uninterested in a specific discipline or don't consider themselves expert enough to weigh in So you are saying that MOS and guidelines are different in roughly speaking? Dedhert.Jr (talk) 23:57, 9 August 2024 (UTC)

  They are different in that they tend to be maintained by different communities, but other than that, they are the same - consensus rules that editors are expected to follow or discuss, with common-sense exceptions. Assuming of course that enough participation has happened among interested editors to create a durable consensus. The communities are different because many editors interested in discussing the nitty-gritty details of site-wide rules that affect all articles are not interested in discussing the nitty-gritty details of a specific subject, and vice versa, for a wide variety of personal reasons. (Different editors may also be interested in some site-wide MOS pages and not others.) -- Beland (talk) 00:14, 10 August 2024 (UTC)

• I think this is all a good idea. Please stress these are "guidelines", not rules, to be broken when clearly appropriate. I also suggest some neat "exclusion" reasons, which can make quick edit summaries when removing. E.g. "no phone numbers", "no road numbers", "no pool balls" etc etc -- please see my comment in the thread above.
• @Allan Nonymous: The examples you added in the "Assessing number facts" section are very helpful. I was a bit confused, though, about which number you intended to say that the examples were on-topic or off-topic for? -- Beland (talk) 20:48, 8 August 2024 (UTC)

  While acknowledging this is a draft, I don't agree with the wording that One of the purposes of number articles is to list facts about numbers. As with any Wikipedia article, their main purpose is to provide broad overview of key concepts, properties, and uses. Polyamorph (talk) 07:23, 9 August 2024 (UTC)

  The context about which numbers the on/off topic examples are in reference to - this has since been added, mostly by Mathwriter2718. Thanks! -- Beland (talk) 16:52, 9 August 2024 (UTC)

• Comment The problematic proposal you made is about the structure. For example, what if the article only contains mathematics topics? For example, if I implement my writing to 1729 (number), making sections in order becomes "As a natural number" --> "As a Ramanujan number", do I have to wrap them up into a huge section of "In mathematics"? I cannot find any manual of styles to avoid one big chunk section with more subsections and ended up with "See also" or "References" sections, but it reminds me about the WP:VGLAYOUT that we don't have to conform them into strictly and obligation order sections from the manual of style; otherwise, it is not an improvement at all. Take an example that most of the video game articles have a section "Reception", but OXO (video game) does not. Another content problem is most articles about numbers talk about the number of many objects; for example, 59 (number) says that there are 59 stellations of the regular icosahedron; this is not very amusing at all. Dedhert.Jr (talk) 02:10, 9 August 2024 (UTC)

  I agree with you that the structure set out in my proposal is not best practice in every case. Mathwriter2718 (talk) 12:10, 9 August 2024 (UTC)

  I added to the proposal: "If the article only has information about mathematical properties, the "In mathematics" section header can be omitted." Does that sound right? -- Beland (talk) 16:55, 9 August 2024 (UTC)

  I think that's fine, although if other sections don't exist simply because the article is incomplete then I feel the section header should be used. It's only in cases where there are no non-mathematical uses where the top level heading should be omitted (IMO). Polyamorph (talk) 17:03, 9 August 2024 (UTC)

  This, I think, is especially appropriate since our number articles explicitly have the tag "(number)", for most pages. Radlrb (talk) 03:41, 10 August 2024 (UTC)

  @Beland: I can't see where you added it to the proposal I suggest the modified version: "If there are no non-mathemtical properties or uses if the number, the "In mathematics" section header can be omitted." Polyamorph (talk) 17:12, 9 August 2024 (UTC)

  Whoops, I forgot to save my edit before posting here. I put in your modified wording. -- Beland (talk) 17:27, 9 August 2024 (UTC)

The editable version of this proposal is at Wikipedia:WikiProject_Numbers/Guidelines#Assessing_mathematical_number_facts. Thanks to @Allan Nonymous for adding most of it. Mathwriter2718 (talk) 14:02, 9 August 2024 (UTC)

I think I am still unsatisfied with NCONNECTION. I can't decide how I feel about "there is a prominent object with N subobjects" and "there are 59 stellations of the regular icosahedron". I also am not sure how I feel about "the aliquot sum of 9 is 4". Mathwriter2718 (talk) 14:31, 9 August 2024 (UTC)

Am I blind or is it listed twice? Once as routine (said to be avoided) and again as on-topic (said to be included). ❧ LunaEatsTuna (talk), proudly editing since 2018 (and just editing since 2017) – posted at 17:26, 9 August 2024 (UTC)

Yes, because some facts may be on-topic, but routine. Allan Nonymous (talk) 18:15, 9 August 2024 (UTC)

Exactly as @Allan Nonymous said. Mathwriter2718 (talk) 20:19, 9 August 2024 (UTC)

But this is a contradiction to include or not include, which of these supersedes the priority of the other, then? And when, what decides? Radlrb (talk) 03:44, 10 August 2024 (UTC)

I would interpret the guidelines as written to require a property to be both on-topic and non-routine to be included, so a "no" for either would take priority over a "yes" for the other. -- Beland (talk) 04:32, 10 August 2024 (UTC)

Read into the lines more, it's confusing. By this reading, it seems moot, because aliquot parts then cannot be included, though one of the guidelines says it's okay. Readers and editors wanting to follow these as potential guidelines will be confused, and will ask about it on the talk page. I suggest rewording these, or using other examples that will be explicitly used (or working these out more). Radlrb (talk) 16:35, 10 August 2024 (UTC)

If you mean aliquot sums, I don't see anywhere the guidelines say aliquot sums should be included. They specifically say they should not: "Facts that should not be included in a number article include: [...] the aliquot sum". Divisors are pretty much always included in the infobox, and the aliquot sum is trivial to compute from those.

Perhaps the confusion is that "aliquot sum" is listed under "yes, it's on topic". Just because something is on-topic doesn't mean it should be included. I'll clarify the wording of the intro to that list. -- Beland (talk) 19:44, 10 August 2024 (UTC)

My intention was for these guidelines to list pro and con factors to be weighed against each other. (Not that it needs to be that way, of course.) Mathwriter2718 (talk) 01:07, 11 August 2024 (UTC)

Hence in this discussion I was neutral about the inclusion of aliquot sums because it satisfies some pros and some cons. Mathwriter2718 (talk) 01:12, 11 August 2024 (UTC)

In articles across all topics, generally off-topic material is trimmed, and either moved to an article where it's on-topic or left out entirely if there isn't an entity with enough notability to justify an article. It would be odd to include off-topic material simply because it's interesting.

The section on routine facts seems to indicate aliquot sums should only be included if they are mentioned in academic literature more than once. Otherwise, it seems they are trivial to calculate from the list of divisors that's in the infobox. Yes, there's Wikipedia article explaining what an aliquot sum is, so it passes that test, but that doesn't make it non-routine or particularly interesting for inclusion.

The guidelines now say "In most cases, a number fact failing one of these criterion is a reason to remove it from an article." which doesn't seem to match your intention, but does match my intuition about what's interesting given this gauntlet of tests. Do you think that guidance is OK as-is, or would you propose some different wording? -- Beland (talk) 04:17, 11 August 2024 (UTC)

1. The proposed guidelines as they currently stand are pretty different from my original intention because I didn't/don't have the will or energy to edit war the proposed guidelines. I would rather express my opinions clearly and (hopefully) convincingly. My opinions have changed from my original intention, but there are still lots of little ways that the current guidelines differ from my current opinions.
2. Since my last message, I have changed my opinion. I think that in most cases, violations of NUM/ROUTINE and NUM/OFFTOPIC should on their own really should disqualify a fact from inclusion. I think NUM/NOPAGE should not disqualify but should increase our suspicion, as many interesting facts shouldn't have a Wikipedia page about them. As for NUM/OEIS: if an OEIS sequence has no or almost no mentions outside of OEIS, it shouldn't be on Wikipedia. If a sequence is discussed outside of OEIS but the fact that N is a member of the sequence is not discussed outside of OEIS, I think that is okay.
3. There has been some confusion or disagreement (not sure which) about the meaning of NUM/ROUTINE. I construe NUM/ROUTINE like this: articles should not include facts that fit naturally into a class of facts that hold for every other number too (or nearly every other number). It says nothing about whether the fact is obviously contrived, uninteresting, or routine to verify. For example, being a member of a class that doesn't hold for most numbers, such as being prime, can never be an NUM/ROUTINE violation. A typical NUM/ROUTINE violation is more like "12 is the sum of 4 squares, 12=1+1+1+9", because every number is the sum of 4 squares.

Mathwriter2718 (talk) 13:04, 11 August 2024 (UTC)

The biggest problem I have with the guidelines right now is that NUM/ROUTINE has been reinterpreted to be very different from what I think it should mean. It currently says this is an example of a NUM/ROUTINE violation:

• On 197: "197 is the smallest prime number that is the sum of 7 consecutive primes: 17 + 19 + 23 + 29 + 31 + 37 + 41, and is the sum of the first twelve prime numbers: 2 + 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 + 29 + 31 + 37"

It should be clear from my writing above that I do not think this violates NUM/ROUTINE, as the natural class of facts this falls into is a subset of the class of primes. Mathwriter2718 (talk) 13:24, 11 August 2024 (UTC)

I was going to modify NOPAGE per your comment, but then I was imagining a scenario where the application of that rule was disputed. If we say something like "violation of this rule alone is not necessarily disqualifying, but it is suggestive that a property is unsuitable for inclusion", I'm a bit worried that will give some people license to ignore this rule in all circumstances because it's "optional" (though all guidelines can have unstated common-sense exceptions if there is local consensus). Maybe that won't be the majority opinion in the end, but it might make for some unnecessary disputes if there's not enough guidance. I think 2-4 examples might clear things up adequately. Did you have any in mind? -- Beland (talk) 16:44, 11 August 2024 (UTC)

I have added a section on basic facts, but I do want to add, this section should be used sparingly (I can think of little more than 5 facts that belong in every article about a number). Allan Nonymous (talk) 20:06, 9 August 2024 (UTC)

@Allan Nonymous I have looked at your recent additions to my proposal and I think we disagree about key aspects of the proposal. At the very least, I should list our disagreements so that others may comment.

• You added "In most cases, a number fact failing one of these criterion is a reason to remove it from an article" and added it back after I removed it.
• You added "197 is the smallest prime number that is the sum of 7 consecutive primes: 17 + 19 + 23 + 29 + 31 + 37 + 41, and is the sum of the first twelve prime numbers: 2 + 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 + 29 + 31 + 37" as an example of a routine fact. The property here is "N is the smallest prime that is the sum of some number of consecutive primes". This property is definitely not true for most N, hence this fact is not routine. Maybe one thing that would make this more obvious is that I think primeness is non-routine, and this property is rarer than primeness.
• The same as the previous is true for "The number partitions of the square of seven (49) into prime parts is 744".
• I could list a few others about routineness, but I think what I have said suffices to show the disagreement.
• You added "Every 5 × 5 matrix has exactly 251 square submatrices" as an example of an off-topic fact. This implies that every fact of the form "prominent object X has N many subobjects" is off-topic. While I am not sure how I feel about the inclusion of such facts, they are not off-topic in the sense defined by the guideline, since they lay out a connection between X and N, which that guideline says is not off-topic. Maybe such facts should be explicitly addressed by the guideline.

I won't revert your changes because we are just drafting anyway. Mathwriter2718 (talk) 20:16, 9 August 2024 (UTC)

• I'm fine with dropping the "fails one" wording, as it can be a bit declarative.
• I agree with you that primeness is definitely not routine. Part of the problem here is that "rareness" can be hard to define when it comes to numbers. The sum of 7 consecutive primes may appear rare, but there are two things that give me pause, firstly, the fact that, cardinally, there are, in fact just as many sums of 7 consecutive primes as there are primes, and secondly, that there is no reason why 7 is special in this regard. We could look at sums of 2, through 1000 consecutive primes.
• The number partitions of 49 into prime parts is 744, feels like a very arbitrary fact that is more about 49 and partitions of primes than about 744.
• I agree, the fact on magic squares not off topic.

Allan Nonymous (talk) 20:29, 9 August 2024 (UTC)

Thanks for your comment. I now understand the difference better: you interpret "routine" to include things that I would call "not routine but arbitrary". Mathwriter2718 (talk) 20:43, 9 August 2024 (UTC)

Cardinality is of course a terrible way to measure the size of infinite subsets of the integers. Here is something more better. In my interpretation, if a fact is true for less than 1/2 of the numbers, it isn't a NUM/ROUTINE violation to include it. I measure "true for less than 1/K of the numbers" as follows: denote f_m the fraction of numbers below m that the facts hold for. Then if f_m is less than 1/K for all sufficiently large m, I say that it is "true for less than 1/K of the numbers". Now you can see that no subset of primeness is a NUM/ROUTINE violation to me. In fact, by the Prime number theorem, when the fact in question is primality, the limit of f_m is 0, so even if I had chosen a different K than 2, the discussion would be the same. Mathwriter2718 (talk) 13:36, 11 August 2024 (UTC)

Number, numeral, glyphs, linguistic representations

A.) There has been some argument above that articles should focus on numbers as math objects, not as numerals. This makes sense as not everything labeled "#7" - like every 7 bus and #7 sportsperson needs to be mentioned in a backwards index. But 7 does contain information about the Arabic glyph and its history. Is this information welcome, or should it be offloaded to e.g. Arabic numerals and Arabic numeral variations? Theoretically number articles would want to cover this number in all writing systems, e.g. Chinese, Babylonian, Roman, etc., but they don't seem to be doing that. 10 for example doesn't describe the history of any glyphs, even though "X" is a single glyph in Roman numerals representing ten.

B.) It also looks like we are not providing etymology or translation; Wiktionary does, so maybe we should be sure to always link there if there is a target? (Wiktionary covers up to 100, plus larger numbers that are single words - see wikt:Wiktionary:Criteria for inclusion#Numbers, numerals, and ordinals).

C.) Should we also try to put all of the non-Arabic number systems into every instance of {{Infobox number}}? I see there are many on 7 but none (other than the auto-calculated ones) on 111 (number). -- Beland (talk) 04:24, 10 August 2024 (UTC)

If it helps to have a mild opinion to react to, I'd say A.) offload glyph coverage to articles about writing systems, for NPOV (to avoid privileging any particular one) and avoid repetition (people excited about a number-writing system are probably going to want to read tidbits on all its characters), B.) yeah, maybe I could do a quick DB scan, and C.) yes, for NPOV in the sense of favoring the numbering system of any particular culture. I mean, obviously we are using the Arabic numerals in all our math content, so that system has a special role, but it seems obnoxiously Eurocentric to elaborate upon all the trivial aspects of what 7 looks like in the system we use in the West but say nothing about its appearance in Chinese numbering. -- Beland (talk) 09:11, 10 August 2024 (UTC)

That might be a good idea. Allan Nonymous (talk) 16:46, 10 August 2024 (UTC)

OK, I added the section "Visual and linguistic representations" to the guidelines and improvised some specific implementation recommendations. Tweaks and further discussion are welcome. -- Beland (talk) 20:52, 10 August 2024 (UTC)

I've thought about this for a while and it is a difficult question (granted, I am not a WP policy expert). Here's how I see it.

The case for including this information: the article 3 is named the symbol 3 and there is no reason a priori to think that it is about the number 3 any more than it is about the symbol 3. Hence, information about the symbol is a valid component of the subject of the article, in the same way that Algebra is about both abstract and elementary algebra instead of just picking one and declaring it the subject. We don't need to discuss other symbols for 3 because they are not the title of the article.

The case for NOT including this information: unless the subject of an article is obviously the reference, it should be the referent and not the reference. Mathwriter2718 (talk) 22:14, 10 August 2024 (UTC)

Good points; I'd certainly want people to be able to find information on the symbol 3 by going to 3. But I think that can be done with some prominent links, which makes things easier organizationally? The history of "3" is, after all, pretty much the same as the history of "4", or at least it's less verbose to cover them both at the same time. -- Beland (talk) 22:39, 10 August 2024 (UTC)

A disambiguation template at the top of the article that says something akin to "This article is about the number 3. For information about the symbol, see ..." sounds reasonable. In this case, we would be explicitly deciding that the article 3 is about the number and not the symbol. Mathwriter2718 (talk) 01:11, 11 August 2024 (UTC)

I've added to the guideline:

For the history and visual appearance of the digit 1 in the Hindu-Arabic system, see Arabic numerals.

Is that OK, or would you prefer a different phrasing or a different link target? -- Beland (talk) 04:19, 11 August 2024 (UTC)

I've modified this because the usual approach is to use summary style and a {{main}} template to target the main article on history or representation etc. I do not agree that there should be no information at all about the history and representation of the numbers, I think readers will expect to see this information. WP:SUMMARY is the ready made solution to ensure the pertinent information is included, with excess detail offloaded to the linked {{main}} articles. Please let me know if my changes are agreeable. Polyamorph (talk) 10:30, 11 August 2024 (UTC)

@Beland @Polyamorph I would happily support either of these solutions. Could any of the information from the pages 0-9 that is potentially being removed be added to Arabic numerals? Mathwriter2718 (talk) 13:40, 11 August 2024 (UTC)

Section for assessing information that is not pure mathematics, and aside from linguistics, etymology, and glyphs

I made some edits so that we can more comfortably move between assessing information that is not based on pure mathematics, i.e. the main subject of the number articles (hopefully for most, at least!). Lets maybe have a discussion of some WP points that can be deemed WP:DUE and acceptable, as well as accessible. For now, I dichotomized the subheadings as seen in the page Radlrb (talk) 07:17, 10 August 2024 (UTC)

1. Applied mathematics

Almost any field considered scientific that relies on mathematical knowledge, and facts found within. I think this is pretty straight forward, however we do need to include non-examples that are not really of interest, as they are either insignificant or not strongly-enough tied to mathematical facts of the number in question (kind of, like properties tied to bases only, here it would be maybe temperatures read in C instead of K, where temperatures in K can be of more significance and therefore be stronger and more WP:DUE). Radlrb (talk) 07:17, 10 August 2024 (UTC)

2. Philosophy and symbology

This part will likely need to deal with philosophy-oriented points, and be different from those that are symbolic strictly from a religious point of view, or spiritual (i.e. numerological). Questions such as, what is the meaning of unity in a deeper spiritual sense, or duality (from there, concepts of triality, as in the trinity in Christian doctrine, and so forth, become possibly relevant). Radlrb (talk) 07:17, 10 August 2024 (UTC)

3. Other cultural mentions

Things that are more in line with pop culture, but might be rooted in mathematical concepts, especially linguistic aspects that are passed on over time and might have "stuck" in society (this makes me think of common phrases, maybe even notable events in history known as "N", and so forth). Here can be included historical associations with the number, and even extend to myths in certain traditions or cultures, however they would need to be notable and truly worth mentioning (and at least minimally tied to a true mathematical aspect of the number). Radlrb (talk) 07:17, 10 August 2024 (UTC)

Note that I added specific terminology here that has not been introduced yet in this discussion, including pure mathematics and applied mathematics; I think these are worthwhile terms to include to dichotomize information optimally (i.e. purely mathematical, and otherwise). Unfortunately Allan went ahead and tried reverting some of this information, including the subheading "Relationships found in fields that are not pure mathematics" (and hiding it within his edit summary, 1). Can we discuss this terminology? I feel it is appropriate, elevating the word-choice we are implementing; it would be much appreciated, I believe. Radlrb (talk) 17:54, 10 August 2024 (UTC)

Also note: "Non-mathematical facts" is not a good subheading because of conflict with applied mathematics. Take for instance, Mathematical physics, Mathematical chemistry, Mathematical and theoretical biology, Mathematical sociology, and Philosophy of mathematics. I reworded the greater heading to "Relationships that are not pure mathematics", as these are based on pure mathematics. Radlrb (talk) 18:24, 10 August 2024 (UTC)

Please stop assuming bad faith, such as that Allan was "hiding" that change with an intentionally obscure edit summary. There are plenty of people watching text changes because we're actively drafting this document, and everyone can see the diff plain as day. No one can hide really anything here, even if they wanted to. The edit summary seems fine to me; Allan didn't specify in detail why they thought this text doesn't belong in this section, but that's a perfectly reasonable opinion to have. They didn't claim to be moving it somewhere more appropriate, just removing it. If the removal and the rationale needs clarification, it would be appropriate to simply ask for that here on the talk page rather than making a personal accusation.

The new subheading you put in is fine. The wording Allan removed is difficult to understand and I think is just making this section more verbose without clarifying anything. The subheaders immediately below already make it clear that applied math and philosophy and whatnot are being covered here. -- Beland (talk) 19:57, 10 August 2024 (UTC)

So just keep on doing that type of edit history, or mocking-style edit histories, keep removing information without consensus, and still not give the idea of bad-faith from Allan the attention it requires? Why did he not mention it in the edit history then, "oh, I forgot". He hasn't even said anything about it, and I suggest it is because it was too important an improvement that he did not make, and pushing weight out of his contributions here, vis-a-vis mine and those that are trying to bring more open perspectives on these guidelines (how he likely sees it). Radlrb (talk) 20:20, 10 August 2024 (UTC)

I'm so tired of this blind defense of his, that you are bringing forth. The converse is just as equally valid, assuming the potential for bad-faith. You are just requiring that he actually state it, which someone who is being willfully deceptive will never do. Radlrb (talk) 20:32 10 August 2024 (UTC)

You can have whatever personal opinions you might like, but if you are assuming bad faith, WP:AGF requires you to keep those opinions to yourself if you wish to continue editing here. It seems you feel disrespected by their removal of huge chunks of content you added, but cleaning up clutter is a valid and necessary editorial function for a crowdsourced encyclopedia, and I would hope that you would not take this personally. If you feel an edit has been made without or against consensus, feel free to politely say so, or better yet, give a specific reason why it should be undone. I'm not blindly defending anyone, I'm reminding everyone of the behavioral policies we're required to follow here. Allan has apologized on Wikipedia:Administrators' noticeboard/Edit warring for working "a bit to hard and fast", and agreed to have 1 locked for a few days while discussion proceeds. My advice is to accept that apology, stopping opining here about other editors' thoughts and motivations, and move on with a focus on content. Hopefully both of you can interact more cooperatively and smoothly in the future. -- Beland (talk) 22:30, 10 August 2024 (UTC)

Somewhat, fair. Fair. Radlrb (talk) 23:29, 10 August 2024 (UTC)

Assessment

Sorry for being off-topic, but do we have some kind of assessments in this WikiProject? Mathematics projects such as WP:WPM and WP:3TOPE have a template for assessment articles. It may be beneficial to sort the data of quality classes. For example, we do have e (mathematical constant), prime number, and regular number, and other sequence and number theory articles that have green badges, whereas Pi is the only featured article. For some reason, if our new guidelines are completed, my thought implies the fact that many articles about numbers can become GA, FA, or any high-quality classes. Dedhert.Jr (talk) 00:31, 10 August 2024 (UTC)

I would certainly support an Assessment of numbers articles section added to the Project Page. The revised guidelines will serve as a guide for assessment? Polyamorph (talk) 20:21, 10 August 2024 (UTC)

Fair point. Looking at WP:NUM/G on the start-template in which one line for each paragraph, each subsection, and each section, it is a somewhat absurd presentation for explaining what is the start-class article. We already have WP:QUALITY to describe considering an article is a start-class, according to which they are providing some useful information, though many weak areas as in lack of providing images (IF it is necessary since most of the number theory articles does not need it), multiple links helps to illustrate topics, subheading treats elements of the topic (this already explained before in the proposal of MathWriter2718, about my comments that we do not have to strictly uniform sections for each article), and multiple sections indicates material that could be added to complete the article (ditto). That being said, we have no idea whether they have the historical invention of symbols, applications in science, popular cultures, and many more. Not all numbers can have those. I am aware that this may lead to the reader's misrepresentation to create a similar or same way on that template, and not to avoid them instead.

Some short articles can be classified as C-class or B-class, depending on the topic, historical background, and source provision. Take an example of 1729 (number) is B-class in which short content includes "As a natural number" and "As a Ramanujan number" because it solely contains mathematical topics. It contains exactly its property about being a natural number, though it is questionable whether this could be expanded again because of the cruft content. It also contains the interpretation as a Ramanujan number, because of the anecdote between two mathematicians, along with its popular culture. Putting it another way, 69 (number) is the only GA article containing two sections only: "In mathematics" and "In other fields". Dedhert.Jr (talk) 00:39, 11 August 2024 (UTC)o

I understand your point about the template potentially being problematic. It can be removed altogether and instead simply list some sections which may be considered for inclusion (making very clear they may not be suitable for every number) with some guidelines on how they should be formatted? While 69 is currently the only GA, its likely other articles, particular the single digit integers, have potential to be much more expansive. Polyamorph (talk) 05:10, 11 August 2024 (UTC)

I've boldly removed the template from the draft guidelines. I've added the manual infobox back in under the Symbolic and linguistic representations section for now. Polyamorph (talk) 16:40, 11 August 2024 (UTC)

There should definitely be information on this WikiProject about assessment. Mathwriter2718 (talk) 01:14, 11 August 2024 (UTC)

Creating a new article

This currently states

Equally important are the cultural, scientific, or other significant associations related to the number. A complete number article should include at least one accompanying important cultural association aside from mathematical properties present. If you only know one interesting mathematical property, consider jotting it down in an article on a near round number. For instance, if you want to write an article on 1050, see if something about it has already been written on it at 1000. That's the point of the series of stubs at the ends of articles like 500 and 7000, to see if there are numbers outside the declared project range that might merit their own article.

I think this was raised by Dedhert.Jr above (in relation to their writing to 1729 (number)). We (Beland) addressed this in the template (which I've subsequently removed) but it was not addressed in this subsection. I was rewriting this subsection to reduce the verbosity, but now I'm needing consensus on how to handle this. I think we need to make it clear that it is not requirement for a number article to include non-mathematical associations described if they don't exist and this shouldn't prevent the creation of an article if its mathematical uses make it notable. Polyamorph (talk) 17:53, 11 August 2024 (UTC)