Langbahn Team – Weltmeisterschaft

Wikipedia talk:WikiProject Mathematics/Archive/2022/Jul

RFC at Fields Medal

Since I saw today that the Fields Medals will be awarded next week, I was reminded of an issue I brought up here earlier this year, without resolution. I've opened a RFC at the Fields Medal talk page to do with erroneous commendations, please feel free to comment there Gumshoe2 (talk) 20:24, 30 June 2022 (UTC)[reply]

@Gumshoe2: I started RfD related to Fields Medal. Should I withdraw this once and wait a while before re-nominated it? --SilverMatsu (talk) 05:00, 1 July 2022 (UTC)[reply]
Because Kodaira embedding theorem is one of the Fields commendation errors? I don't see any necessity to withdraw, I don't think either discussion has much effect on the other. Gumshoe2 (talk) 05:19, 1 July 2022 (UTC)[reply]
Thank you your reply. I'm worried about breaking the wiki-link in Fields Medal because RfD temporarily broke the redirect (example: "Achieved major results in the theory of harmonic integrals and numerous applications to Kählerian and more specifically to algebraic varieties. He demonstrated, by sheaf cohomology, that such varieties are Hodge manifolds.").--SilverMatsu (talk) 05:53, 1 July 2022 (UTC)[reply]

Editor adding junk content to 177 (number)

I have been working to remove huge piles of cruft that have been added over the years to many of our number articles (example diff). On 177 (number), Radlrb (talk · contribs) has been edit-warring to add back the cruft. I've reached the limit of my reverts. Help wanted. —David Eppstein (talk) 18:15, 28 June 2022 (UTC)[reply]

Yes, please help. See my comments on the Talk:177 (number). I am copy-pasting the non-junk David Eppstein does not understand to include. He reverted my edits 4 times.
I suggest we have the following properties for 177, since David Eppstein is warring my edits:
  • A Blum integer: 11th and less than 60 below 1000.
  • A Leyland number as there are very few below 1000.
  • A 60-gonal number as there are very few below 1000.
  • I added 177 as the sum of the three prime factors (41, 59, 71) whose product make the minimum faithful complex representation of the Monster group. This is not trivial, it is another set value of these digits. I.e. the group 2.B has a faithful representation under 96,256 dimensions, whose sum of digits is 196,560, the kissing number in 24 dimensions. Aliquot sums and sums of divisors are common properties of numbers, and 196,883 is a particularly important number within the monstrous moonshine as it is linked with the j-invariant under its 196,884 dimensional representation - if this is too OR then I am perfectly fine with not including it. It seems to me that David Eppstein just wants to remove "cruft" he doesn't like because, well, personally he doesn't like it. He removed plenty of other information like examples of .177 guns. It makes very little sense. People who come here and read these pages are often times not mathematicians, so yes, including information of numbers being odd, composite, and even semiprime, are important tidbits of information that inform people not well acquainted with mathematics.
These values are not unimportant. They define some of the characteristics of the number 177. To take out these properties leaves this number less notable. I am seeking mediation, as I have needed to continue reverting misguided edits by David Eppstein. He alone is not one to choose what goes on a page, or not; and neither am I. So if we can get proper input that would be great. Radlrb (talk) 18:24, 28 June 2022 (UTC)[reply]
I'd like to also add that he does not have a proper definition of that "cruft" entails, he seems to be the only person in all of Wikipedia enamoured with that phrase. Per Wikipedia:Notability (numbers), these sequences are in OEIS and have proper identifying names, and 177 is in their lists early on. Also, I tried to find middle ground and removed two properties, however it seems to not be enough for him, he wants to appropriate the page entirely. Radlrb (talk) 18:43, 28 June 2022 (UTC)[reply]
In fact, I do have a definition of "cruft": it is anything that would not be relevant to Wikipedia:Notability (numbers) and its requirement for "three unrelated interesting mathematical properties" or "obvious cultural significance". That notability guideline gives, for instance, the example of the number 9870123 as not notable. Yet, one can say many of the same things about it: it is odd, it is semiprime... the conclusion is that being odd and semiprime is not an interesting property of 3290041, one that makes it notable. In many AfDs, I have repeatedly expressed a specific and quantifiable version of this formulation: that to be interesting, the property must either have its own article here (or be deserving of an article through multiple in-depth publications) or be labeled as nice by OEIS, and the number having that property should be among the first half-dozen or so numbers with that property. The version of 177 that I cut it down to includes only properties meeting that criterion. The additional properties you have been adding do not. Therefore, they are cruft, as useless as stating on every biography on Wikipedia that the subject is human, with a head and two eyes. —David Eppstein (talk) 18:51, 28 June 2022 (UTC)[reply]
Ok. Radlrb (talk) 20:56, 28 June 2022 (UTC)[reply]
"they are cruft, as useless as stating on every biography on Wikipedia that the subject is human, with a head and two eyes." Well said! PatrickR2 (talk) 23:56, 28 June 2022 (UTC)[reply]
Just because other sums of prime factors are important when it comes to the Monster group, it doesn't follow that this sum of prime factors is important; that would have to be established and documented independently. So, it's very hard to see a case for why we should include that property. As for the others: OEIS does call the Blum integers a "nice" sequence, but 177 is 11th on the list, and while this will inevitably come down to a judgment call, it's not unreasonable to say that's too far down the line to be noteworthy. (I tend to find position in an OEIS list as more meaningful than how many there are below 1000, since the former is about the sequence itself.) 177 is the 8th Leyland number, but David Eppstein's most recent revision includes that property, so maybe we don't have a substantial disagreement there. XOR'easter (talk) 18:59, 28 June 2022 (UTC)[reply]
It's fine. No issue. I disagree, but agree to disagree - except for the point on the Monster I agree it's OR. To me, an 11th Blum integer is definitely noteworthy. In fact, I think any studied and well-defined detail is noteworthy as long as they can be incorporated in groupings if possible, even if it takes an extra 3 lines. This obsession with only highly distinguishable properties is absurd, and hurts the content of the page. A distinguishable property of say, polite numbers, or square-free numbers is precisely that they incorporate such a large universe of numbers - and I would like to know personally whether a property is unique or shared by many other numbers. That is my personal philosophy, and usually having a pool of data that is well organized and diverse tends to be of greater service than limiting it to only the most notable examples.
This is basic research philosophy, and the best way to present information - giving a comprehensive, and dynamic list of properties, even if some seem less important, there is still plenty learned from the way numbers mix with other numbers. Knowing 177 is a Blum integer and a polygonal number tells me that this number has geometric and arithmetic properties that otherwise I might be entirely unaware of. For a number like 177 it might not seem impressive, but over time one compounds properties of different numbers and one is able to make quick connections because one recognizes properties shared with other numbers. If you take these away, then you take away the possibility of making these connections. I've always appreciated and learned best when I am presented with a more universal structure of whatever I am learning. If it's too limited, then I get a perspective that is not true to the subject. Even if the notability of some points might be less than others, comparative analysis permits you to surmise a nuanced nature of the number that otherwise would be nearly impossible to feel. At the very least, every single page should explain whether a number is prime or not, since it is not evident immediately for numbers even above 20 for most people - and whether it has 2, 3 or x amount of prime factors matters, since this is the very basic elementary definition of a number. Without this, no one can really know if for example 101 is prime or not, even though those who are experienced mathematicians might recognize that it is. And let's be honest. There would not be a gargantuan amount of lesser-important sequences that we can tie with given numbers. There really, are a very few amount of such "bad examples" to include. I imagine that, say, some numbers above 30 have about an average of maybe 5 lesser important sequences and properties that could be included. Is it really destructive at all to include many of them if they're so minimal in count (they can take 1 single line - i.e. a simple list in one sentence)? This is why I think it's very silly to not include these properties - there won't be very many attributable minor properties to these larger numbers anyways (like parts of sequences, types of numbers, etc.). So why not include them to give a more holistic background of a number? It let's people know they are part of other large sets, which yes, it is important! Uniqueness and shared-properties are opposites, however they can be equal in power insofar as what they communicate. Radlrb (talk) 21:20, 28 June 2022 (UTC)[reply]
Mathematics is infinite. There are infinitely many properties, and infinitely many held by any number like 177. Even if one only goes by properties in OEIS, a search finds 6433 OEIS sequences matching 177. That is far too many to list. Your philosophy that we should list everything on the off chance that it sparks a connection is untenable, and more than that, wrongheaded: the more unimportant properties we list, the less likely that a reader coming to the article will notice and learn about the important ones, because they will be overwhelmed with unimportant minutiae. As for Blum numbers: their main significance comes in choosing keys for the RSA cryptosystem, for which the two prime factors should be large and independently random. Combining smallness and being a Blum number subtracts from the meaningfulness of the combination, rather than adding. So that is not a sequence where I am inclined to give a little leeway and say that maybe 11th is still early enough to be interesting, as I did for Leyland numbers. —David Eppstein (talk) 21:34, 28 June 2022 (UTC)[reply]

Sure. I rather choose to incorporate some minor points. Gladly you changed your mind on two properties you originally were against including. That's a win-win IMO. Radlrb (talk) 22:34, 28 June 2022 (UTC)[reply]

If we have an article on a natural number, then I think that that article should contain, near the top, its factorization into prime numbers. This is a property which is not dependent on an arbitrary choice of base. It is frequently needed and not obvious. JRSpriggs (talk) 22:41, 28 June 2022 (UTC)[reply]

That's done in {{Infobox number}}, which seems a reasonable place for it, though of course of a factorization has a further interesting property then we can expound upon that in the prose. XOR'easter (talk) 22:56, 28 June 2022 (UTC)[reply]
To XOR'easter: Thanks for pointing that out. I am afraid that I have gotten into the habit of ignoring infoboxes. JRSpriggs (talk) 23:00, 28 June 2022 (UTC)[reply]
That's true, I also forget to look at infoboxes. Thank you for reminding me as well. Looks like we're set there. Radlrb (talk) 00:00, 29 June 2022 (UTC)[reply]

Ah, I read David's's last response wrong, I was busy working. Well, it doesn't matter, given that he thinks he owns these articles himself, per how he says im giving leeway, as in "oh, let's please this little guy who doesn't know what he is saying;" and even worse, suggesting that I actually meant I would put thousands of minor points on a Wikipedia article, without realizing that I meant to add only several minor points, and then further saying I am wrongheaded. Ah, that passive aggressive nonchalance and condescending talk that just makes me think I wasted my time. Oh well, keep scruffing your cruft away, David. My time is better spent than trying to even bother with someone who is quite selfish as you are with coming to an agreement. But because you're an administrator, and I can tell you won't stop being selfish with your edits when others have a different perspective, I'm just going to spend my time otherwise. I hope you open your eyes to how rude you really can be on this platform, regardless of how much you have contributed here. Ciao. Radlrb (talk) 07:27, 29 June 2022 (UTC)[reply]

If others are interested in keeping the point on 177 as a Blum integer, feel free to edit it back if David removes it, and if you think it's notable enough. Else, I think this case is closed. Radlrb (talk) 07:48, 29 June 2022 (UTC)[reply]
And yet, despite claiming that you consider the matter closed, and resorting here to uncivil personal attacks rather than content-based discussion, you are still adding more uninteresting properties back to the article. —David Eppstein (talk) 19:36, 29 June 2022 (UTC)[reply]
I have to agree that both "60-gonal number" and "arithmetic number" fail the test of appearing early in a sequence the OEIS designates as "nice" (or interesting in any other way, like being related to a hard open problem). In the latter case, 177 is so late in the sequence it's not even in the part that the OEIS prints explicitly. The 60-gonal numbers are easy to calculate and don't seem to be among the polygonal numbers that have been written about; contrast, for example, how much the OEIS has to say about them with what it has on the hexagonal numbers, or the depth of coverage available for square triangular number and cannonball problem. XOR'easter (talk) 19:56, 29 June 2022 (UTC)[reply]
If a disagreement happens here, I rather speak of it here than move it elsewhere if there is a need of perspective for others to see abject behavior present. Moving it to another space for these types of issues I'd do if they continue, to take the matter at hand more directly if normal conversation fails to produce results. I'm trying to move on from trying to make sense of why others see notability where you/anyone would maybe not, and vice-versa, whether it's light notability, or even two minor points which together might bring some interest to a number that has such few highly notable examples (some of the examples you chose to include, as Gumshoe2 pointed out, could be interpreted as having average, or even no real notability - though I think they are good examples) - i.e. 60-gonal is a geometric representation of 177 in which its arithmetic average of its divisors also happens be a representation of 60, here as an integer itself. I find that interesting personally, especially since they arise from different operations. Take the example that 177 being a Leonardo number is 11th in its sequence (after two 1s), while the Blum example I wanted to include is also the 11th on its sequence.
The funny thing, is that, in fact, as math evolves and we learn more about large numbers, large numbers will have properties themselves that require relatively large numbers also to describe. So these numbers above 150 or so tend to have scant significant properties, and the ones that do have significant properties tend to come in sets, like for say the number 240, which is a geometrically important number (in E8 and icosahedral symmetry for example) as well as a number that is highly composite. So my internal intuition is to include minor examples not as fillers per se, but as giving at least some color to these 100s and 200s numbers that can be exceedingly bland. Now, I want to apologize because I usually try not to be so rude myself, usually I prefer to have a more civil conversation, and I become irritated when my edits are just blanketed with a negative tone - there are also more civil ways to express disagreement than by asking a rhetorical question that is afixed to an edit. If you think I do not enjoy contributing meaningful edits, see 15, 24, or even the golden ratio which I am trying to slowly bring to good article standing. I love editing here, and I love making these pages better. And I do actually appreciate you David (if I may refer to you with your first name). And maybe I am a little bland on some of these properties, however I try to provide good improvements. That is always my goal. Radlrb (talk) 05:43, 30 June 2022 (UTC)[reply]
Well, for what it's worth, I largely agree with Radlrb that David Eppstein can be rather condescending and rude in disagreement, sometimes not very nice to interact with as a fellow editor and especially not as an admin.
Anyway, as for the matter itself, radlrb's preferred version [1] (with exception of monster group sentence, although I personally happen to like it) is perfectly concise/readable and the properties seem to all have their own wikipage (and are well-cited). This is precisely what I as a wiki reader would hope for from a page like 177 (number). The four mathematical facts in David Eppstein's preferred version [2] seem just as randomly selected as any of radlrb's (and arguably even moreso). So I agree with radlrb's edits. From reading David Eppstein's replies here, it seems his main contention is that radlrb's properties fail to, in and of themselves, make 177 a notable number, and I agree with him on this. But I think it is a bad standard to use for the question at hand. Gumshoe2 (talk) 20:23, 29 June 2022 (UTC)[reply]
This is not the correct forum for making drive-by personal attacks. Perhaps a better forum, if that's what you want to do, would be WP:ANI. Also, given that the version you linked has an entire unsourced paragraph, multiple unlinked properties, and a WP:EL violation, I do not find your assertions that "the properties seem to all have their own wikipage (and are well-cited)" particularly convincing. —David Eppstein (talk) 20:55, 29 June 2022 (UTC)[reply]
Not any kind of personal attack, my action is only to support other editors having similar difficulties to what I have had in the past. For what it's worth, I think you make a lot of valuable edits to the website.
Anyway, the "entire unsourced paragraph" you refer to seems to be "177 is an odd composite semiprime with 3 and 59 as its prime factors" which as we are all aware amounts to totally rudimentary/routine computation on the elementary-school level. On the other hand, I see now that you are correct that "digitally balanced number" misleadingly links to external website, and so I agree with you that that sentence could/should be removed. I'm not sure what other unlinked properties you refer to. Gumshoe2 (talk) 21:09, 29 June 2022 (UTC)[reply]
One thing I don't like as a Wikipedia reader is indiscriminate piles of trivia. When an article is just a heap of factoids, it's darn near impossible to tell what is important — or, in this area, what mathematicians have agreed upon as important. The goal here is to build an encyclopedia, not the TV Tropes of math. The apparent concision of "it's a Leyland number, a square-free number, an Ulam number..." is an illusion; parsing it requires traversing the graph of bluelinks, and sifting the properties that are trivially verifiable from those that are not. XOR'easter (talk) 21:11, 29 June 2022 (UTC)[reply]
I strongly agree that indiscriminate piles of trivia are terrible on wikipedia, but strongly disagree that this counts as such (to the extent that I almost wonder if we're looking at the same thing). The "graph" (?) of bluelinks has as little complexity as ever present on wikipedia (you just have to click on one thing to have the concept explained). I think it would be fine and good to rephrase to clarify which properties are trivial and which are not. Gumshoe2 (talk) 21:17, 29 June 2022 (UTC)[reply]
Having to click on a link every three or four words to make it through a sentence is, I submit, not a good use of the hypertext medium.
If a property is trivial, why write about it? The only justification I can think of is if the number is an oft-cited example of having a property. (It is commonplace for natural numbers to have irrational square roots, but the fact that is irrational has been much remarked upon.) This is what the "does it appear early in the OEIS list?" question is trying to get at. XOR'easter (talk) 21:25, 29 June 2022 (UTC)[reply]
I agree with you for usual sentences, except that it would be strange to read the sentence in question in the usual way one reads sentences, as it is effectively (and very clearly, no matter one's comprehension of the content) a list only in sentence format. (It would be ok to convert to a literal bulleted list, but in my opinion it would not be an improvement.) Anyway, it seems we fundamentally have different criteria for what should go on a wikipage like 177 (number). For instance, given that a number page like 177 exists, I think it is totally irrelevant/uninteresting whether that number is early or late in an OEIS list. Also, I think it is universally accepted to include "trivial" information on wiki, and that the website is better for it. The question is which trivial information should be included or excluded.
It seems that the only relevant official wiki-rules (as linked above on this thread) are for whether such a number page should exist in the first place, and is not very well-suited for advising on page content itself. Maybe a RFC (on the issue of content of general number pages) would be the best way forward? Gumshoe2 (talk) 23:59, 29 June 2022 (UTC)[reply]
Given that there are 6433 OEIS sequences matching 177 (noted above), and others under dispute where 177 is too far along the list to even be mentioned at OEIS (e.g. odd numbers), we obviously cannot include them all. We need some standard. As a general principle, I think that properties that are more important as mathematical properties (say, being odd) should be preferred over properties that are unimportant (say, being a 60-gonal number) and that properties for which the number is particularly salient, likely to be cited as an example of that property, should be preferred over properties where the number is just one among many. My choice of "first half dozen members of an OEIS-nice sequence" is idiosyncratic, and I don't expect everyone else to agree with that exact choice, but it meets those principles. It also has the advantage of being somewhat objective; if we were going by my own opinion of what's interesting, for instance, I'd get rid of a lot more of the decimal-based properties (like "digitally balanced number"), but I recognize that others may find those more interesting than I do, and that's reflected in the fact that many of them are OEIS-nice. But obviously, you seem to think that my standard is the wrong standard. So can you please articulate a clear standard for what to include instead, one that is actually tenable rather than making a big pile of all properties that can either be sourced or calculated? It would not work to have an RFC with only a vague question rather than a clean yes-or-no question of whether some particular standard is a good one. My suspicion is that a general RFC is going to attract a lot of the kind of editors who have contributed to content like the current state of 155 which mixes easy-to-calculate unsourced mathematical properties held by most numbers with a large disambiguation-page-like random selection of links to bus routes numbered 155 and the like. The result of such an RFC could well be that any attempt to clean up this sort of mess would then have the weight of consensus against it. —David Eppstein (talk) 00:38, 30 June 2022 (UTC)[reply]
I see, perhaps you are right about RFC. Anyway, although I agree with OEIS that many of their nice sequences are actually nice, it seems that their deployment thereof is based on an informal poll of their mailing list (I may be wrong, I couldn't find clear info), so I don't think it's a good basis for anything here. And as I said before I also don't think that numbers towards the beginning of a sequence are more noteworthy. Anyway, my immediate thought is that it's reasonable to include named properties which have their own wikipage. Using [3] as a basis, here's where that would leave us for 177: (and just for fun, I have roughly ordered by how interesting I personally find each property)
  • 177 is an evil number, i.e. the binary expansion has an even number of ones; it is a sorting number, i.e. it arises as the worst-case number of iterations needed for certain non-optimal sorting algorithms; it is an Ulam number and Leonardo number, meaning that it comes up in certain recursions (the latter being small modification of Fibonacci); it is a Hilbert number, meaning that it is of the form 4n+1; it is polite number, meaning that it is not a power of two; it is an equidigital number, meaning that it and its prime factorization have the same total number of digits
  • 177 is an arithmetic number, so that the average of its divisors (1, 3, 59, 177) is an integer
  • Its prime factorization is which makes it semiprime (synonymously 2-almost prime). Since both prime factors are of the form 4n+3, it is the special kind of semiprime called Blum integer. The same fact makes it a nonhypotenuse number, so that it is not the hypotenuse of any integer-sided right triangle.
  • It is a Leyland number as . It is a cyclic number (group theory) since all groups of order 177 are cyclic. And it is an idoneal number, which seems particularly interesting as a (to my non-expert eyes) natural number-theoretic condition with only 65, 66, or 67 of them existing.
(I am not proposing the above text for inclusion on the page, it is just raw data for discussion.) These are (unless I miss a couple) the fourteen named properties which are satisfied from the linked list of 215 potential ones. I think that all of us present will agree that a couple of these "named" number types are totally uninteresting and perhaps should not even have their own wiki page!
However I believe that all of the above (in terms of basic content) is appropriate for inclusion, although I am sure some here will call it "crust". It is all very easy to absorb (with one or two more complicated things), easily citable to oeis, would take up only little space (couple of paragraphs) to write out well, and on a page which contains practically no other information anyway. I like the graph enumeration properties presently given but I think they are less appropriate. The monster group properties are original research and should not be present.
Two extra thoughts:
  • it seems some users here are using the criteria "what properties make 177 an interesting number". I am not using this criteria, since I think no natural numbers except probably 0 & 1 are themselves interesting. I think there are some interesting sequences (primes, Ramsey theory, etc) but the individual numbers seem not so interesting. The whole 177 page (along with many others analogous) could be deleted altogether without any real mathematical loss to wiki. But taking as given that we are talking about 177, the right choice is to send the reader to other pages for which 177 has some relevance. I may have no idea why someone would single out "Hilbert numbers" for significance, and it is absolutely not something which makes 177 interesting (I defer to previous few sentences), but wiki has singled it out so I think it is appropriate to send reader to "Hilbert number" page, despite my own distaste for the concept.
  • the criteria I suggest (properties with their own wiki-page) is almost certainly not practical for some very common numbers like 0, 1, 2, etc. But such wiki pages probably have to be written by a different standard anyway, being as they are at the intersection of many different things. In present case, and for similar numbers, I think it leads to a reasonable amount of information.
Apologies for the long message, I try to stay concise but it does not come natural to me Gumshoe2 (talk) 04:41, 30 June 2022 (UTC)[reply]
I don't think there's any need to apologize; it was interesting. I think idoneal should definitely be listed (finite sets of mathematical importance are different from the infinite and dense ones). Your approach is not unreasonable, but I think more difficult to implement: it takes a lot of effort to go through all of our number property articles (not all of which are listed on that template) and figure out which ones apply. You did miss some: it is also a deficient number and (as discussed above) a square-free integer. I do think there is actually a usefulness justification for including the combinatorial enumeration properties that would be dropped by your criterion: if one has a collection of 177 things, and looks up 177 to find that there are also 177 of some other kind of thing (star polygons, say), one might get a hint that the first kind of thing is secretly the same kind of thing as the second. —David Eppstein (talk) 05:34, 30 June 2022 (UTC)[reply]
Just to clarify two things: (1) if I were writing the page myself (and I do not anticipate making any edits) I probably would not include the graph enumeration properties but as is I have no strong suggestion on if they should stay or go; (relatedly, 2) I consider my proposed criteria as more if than iff -- to phrase the if/then carefully: I think that if someone adds a reasonably written sentence or two relating in this kind of totally direct way to the topic of another wikipage, then it is good/reasonable policy to leave it in. I don't consider it imperative to add such material, or that it should exclude against other content. (As I see it, my essential point is just that the suggested criteria does not let in an unmanageable mess of content, at least for numbers like 177) Gumshoe2 (talk) 06:13, 30 June 2022 (UTC)[reply]
I would tend to have the same opinion as David Eppstein in this matter. The page 177_(number) seems to be an accumulation of random (trivial?) facts about that number, which may not all be notable enough to be in this encyclopedia. But just for comparison, I wandered over to 178_(number), the next one in the sequence. And here it's becoming downright ridiculous. One of the claims of fame for that number 178 is that someone in 1946 claimed that there were 178 equivalence classes of something, and later that number was found incorrect. Makes no sense to have this in there. PatrickR2 (talk) 04:08, 1 July 2022 (UTC)[reply]
Suggestion to add for notability of the number 4: it's equal to the sum of the number of eyes and the number of ears of most vertebrates. :-) PatrickR2 (talk) 04:11, 1 July 2022 (UTC)[reply]
I have moved the information about the incorrect number of ... from 178_(number), where it did not belong, to Margaret Willerding. PatrickR2 (talk) 22:33, 1 July 2022 (UTC)[reply]
Recording the history of such things seems to make as much sense in 178 (number) as it does in Margaret Willerding, I think. Four_color_theorem#Early_proof_attempts covers failed proofs, i.e., "facts" about maps that turned out wrong; 178 (number) can record a "fact" about 178 that turned out wrong. XOR'easter (talk) 22:42, 1 July 2022 (UTC)[reply]
There's really very little to distinguish 178. If not for the history of quadratic form enumeration, we might better not have an article there at all. Only one of the other listed properties is OEIS-nice, and neither has its own article. Anyway, I think any reader likely to be misled by the claims in the literature on the number of forms, and in need of correction, is more likely to find that correction at the 178 article than at the article on Willerding. —David Eppstein (talk) 22:45, 1 July 2022 (UTC)[reply]
An analogy that just sprang to mind is that we wouldn't remove to the biography of Stanley Skewes just because that bound has been improved. XOR'easter (talk) 22:53, 1 July 2022 (UTC)[reply]
This is not the same situation at all. We are talking about whether a certain statement is a "mathematical fact" that belongs in one on the "number articles". Not other contexts. PatrickR2 (talk) 23:34, 1 July 2022 (UTC)[reply]
Not a problem to record this somewhere, and the Willerding article is a good place to mention this. But it is certainly not a "mathematical property" of the number 178, hence does not belong in that article. And let's be realistic, I doubt that any reader interested in integral quadratic forms would get their first information on that topic from the article 178_(number). Any reader interested in that topic would access detailed references to this topic from other articles. No need to clutter these number articles with more non-mathematical facts. PatrickR2 (talk) 23:25, 1 July 2022 (UTC)[reply]

"Kodaira embedding theorem" listed at Redirects for discussion

An editor has identified a potential problem with the redirect Kodaira embedding theorem and has thus listed it for discussion. This discussion will occur at Wikipedia:Redirects for discussion/Log/2022 July 1#Kodaira embedding theorem until a consensus is reached, and readers of this page are welcome to contribute to the discussion. SilverMatsu (talk) SilverMatsu (talk) 04:43, 1 July 2022 (UTC)[reply]

I believe the redirects are to Kodaira embedding theorem and are being discussed in the section Wikipedia:Redirects_for_discussion/Log/2022_July_1#Hodge_manifold. XOR'easter (talk) 16:08, 1 July 2022 (UTC)[reply]
@XOR'easter: Thank you for fixing the link. --SilverMatsu (talk) 00:07, 2 July 2022 (UTC)[reply]

Topology of ...

Topology of pointwise convergence redirects to an eponym section of Pointwise convergence.

Topology of compact convergence redirects to Compact convergence.

But Topology of uniform convergence does not redirect to Uniform convergence. Instead, it redirects to Topologies on spaces of linear maps. Moreover, the topology of uniform convergence is not explicitly mentioned in Uniform convergence.

This sets several issues:

  1. Coherency of redirect targets
  2. As far as I know, the topology of uniform convergence is defined for a much larger class of functions than the linear maps.
  3. Topologies on spaces of linear maps is an article almost entirely written by Mgkrupa. This article is awfully written: almost no context provided; much too WP:TECHNICAL; for finding the definition of the topology of uniform convergence (the subject of the first section), one has to read a long list of formulas without prose before reaching a definition involving notations defined many lines before. So, for understanding the definition, one needs to be an expert of the subject, or to spend several hours of hard work.

What should be done with these issues? D.Lazard (talk) 17:18, 30 June 2022 (UTC)[reply]

"one has to read a long list of formulas without prose before reaching a definition involving notations defined many lines before." I moved the section. Problem solved. Mgkrupa 17:45, 30 June 2022 (UTC)[reply]
"the topology of uniform convergence is defined for a much larger class of functions than the linear maps." Yes, there should be an article about this topic. I suggest that someone (not me) change "Uniform convergence" from a redirect into an article about this topic. Or maybe change it into a disambiguation page. Mgkrupa 17:45, 30 June 2022 (UTC)[reply]
Side note: I think that part of the reason by the article Topologies on spaces of linear maps is so technical is because there is no article dedicated to the more general theory of Uniform convergence for arbitrary classes of functions. If an article on this topic is created then we could link to it and simplify the presentation in Topologies on spaces of linear maps. Mgkrupa 18:12, 30 June 2022 (UTC)[reply]
"much too WP:TECHNICAL" The article Topologies on spaces of linear maps was intended to be about the various topologies that are used in functional analysis, which necessarily involves concepts such equicontinuous sets, bounded subsets, the Mackey topology, the ε-topology, and so on. I would like the article to be less technical and would love to hear suggestions on how to accomplish this. Mgkrupa 18:00, 30 June 2022 (UTC)[reply]
"almost entirely written by Mgkrupa. This article is awfully written" The article does need improvement. I suggest that we work together to improve it. Perhaps we can start by determining the best way to organize it? Mgkrupa 18:00, 30 June 2022 (UTC)[reply]
The material is too specialized for the subject matter. So I think that the solution is to not give the most general formulation possible. For instance, the primary context could be the weak convergence of continuous linear maps between Banach spaces, as is the context for many of the most standard textbook references on functional analysis. (At present, it seems Banach spaces are not even mentioned on the page.) Having said that, I personally like the nature of much of your contributions to this page and other similar ones. But I might suggest it is more appropriate somewhere like nlab, where it is still easily accessible to those who want it, but where wiki can have a space for (what I would call) writing more encyclopedia than knowledge database. Gumshoe2 (talk) 19:16, 30 June 2022 (UTC)[reply]
The Banach space cases should be mentioned. However, there are already multiple articles dedicated to such topologies. The article Operator topologies#List of topologies on B(H) lists many of them, including: Strong operator topology, Weak operator topology,Norm topology, Ultraweak topology, Ultrastrong topology, Weak convergence (Hilbert space), Weak topology. If I remember correctly, the reason why I originally created the article Topologies on spaces of linear maps was precisely because there was no article discussing uniform convergence in the general (non-normed space) setting of TVSs, and this was also why I did not add (norm space)-specialized content like what you suggested (i.e. weak convergence of continuous linear maps between Banach spaces). Having said that, this omission should be corrected as these cases are very important. I also suggest that links to articles like Operator topologies, Strong operator topology, etc. be mentioned early in the article (maybe the introduction) to help readers who are only interested in these special cases (and not the more general case) navigate to their desired article. [Update: I changed the introduction to contain a link to Operator topologies.] Mgkrupa 19:50, 30 June 2022 (UTC)[reply]
One comment about Topologies on spaces of linear maps, but which also applies to other articles written by you. The references are not targeted enough. Example: footnote 6 refers to "Narici & Beckenstein 2011, pp. 371–423.", and is refered to from about 7 places. Pages 371-423 is a huge range of pages, a whole chapter maybe? Each place that refers to something in that chapter should refer to a specific result on a specific page of that chapter, instead of forcing the interested reader to read the whole chapter to figure things out. PatrickR2 (talk) 04:30, 1 July 2022 (UTC)[reply]
You're right that large page ranges is bad practice. I have experienced the same problem you have (embarrassingly, a couple times with my own citations, which is why I've been doing that less frequently recently). But as you say, I should (and will) start making the page ranges more targeted. However, I sometimes include the proof or relevant definitions/author comments in a citation's page range. Is that considered bad practice?. Mgkrupa 21:42, 1 July 2022 (UTC)[reply]
Not sure I understand what the last sentence is referring to. Can you give an example? PatrickR2 (talk) 23:30, 1 July 2022 (UTC)[reply]
Consider "Grothendieck's Completeness Theorem" here: Complete topological vector space#Topology of a completion. The statement of the theorem was on page 176 (the proof is on the pages immediately after it). The citation for the theorem is given as "pp. 175−178" and this page range includes some - but not all - of the definitions/notation that are needed to understand the theorem as stated in that reference. The definitions of some the terms and notation that the reference used were defined elsewhere in hard to find locations (in this case as far away as pp. 151 and 157). If I didn't include these 2 pages then I think it likely that it would have been difficult for another person to verify that the statement and definitions were copied correctly. Now although in this particular case I used two separate citations (because of how many definitions were needed), there are occasionally other situations where this is not necessary and it would make much more sense to just use a single citation e.g. such as "pp. 151, 157, 175-176". I wish I could give a better example but I can't think of a better one off the top of my head. But did that clarify my question? Mgkrupa 08:15, 2 July 2022 (UTC)[reply]
Mgkrupa That sound ok in this case. But in general, if we don't refer to other concepts defined elsewhere in the book, I think it would be perfectly fine to just cite the page where the theorem in given. It's up to the interested reader to figure out where the proof is and where the definitions of any used concepts are in that source. No need to do it for them. The interested reader will learn more by looking things up themselves. PatrickR2 (talk) 04:35, 5 July 2022 (UTC)[reply]

RfC on Glossary of areas of mathematics

Glossary of areas of mathematics is an article that should concern all of use. Its state is presently awful. I have started an WP:RfC on inclusions criterias for this stand-alone list, at Talk:Glossary of areas of mathematics#RfC on inclusion criteria. Contributions are welcome. D.Lazard (talk) 15:28, 5 July 2022 (UTC)[reply]

Some verifiable explanation or definition of what constitutes an "Area of mathematics" would be useful if such exists. This appears to be the main subject of contention. Cheers · · · Peter Southwood (talk): 07:10, 6 July 2022 (UTC)[reply]

Endomorphism ring of an elliptic curve

The link in the title (as you can see) is red. I thought of redirecting it to elliptic curve, but as far as I can tell, that target has no info on the endomorphisms of elliptic curves (so the redirecting is unhelpful at best and misleading at worst). Is the topic not covered at all in Wikipedia (if so, that's very surprising.) -- Taku (talk) 08:32, 4 July 2022 (UTC)[reply]

Incidentally, the ring of differential operators also doesn't exist either (a special case is in differential operators but not the general one with the product given by the Leibniz rule with variable coefficients.) -- Taku (talk) 08:38, 4 July 2022 (UTC)[reply]

Deletion review of Łukaszyk–Karmowski metric

This discussion may be of interest to the community here. XOR'easter (talk) 14:26, 14 July 2022 (UTC)[reply]

Move of "Poincaré conjecture" to "Perelman's theorem"

A new user 廖培 (talk · contribs) has recently moved Poincaré conjecture to Perelman's theorem, since it is no longer a conjecture. I think this is unambiguously a bad move, since it is still (despite its status) universally called Poincaré conjecture and never called Perelman theorem; the user has simply decided that it ought to now be known as Perelman theorem instead. I don't understand well the technology of reverting page moves, hopefully someone else here does? Gumshoe2 (talk) 03:23, 10 July 2022 (UTC)[reply]

Thanks for flagging this. I have reverted. Presumably bots will clean up the redirects. --Trovatore (talk) 03:52, 10 July 2022 (UTC)[reply]
I suggest delete the Perelman theorem, because, as another example, I think the Geometrization conjecture are also known as Perelman theorem.--SilverMatsu (talk) 04:16, 10 July 2022 (UTC)[reply]
Much thanks, Trovatore! SilverMatsu, I believe there is absolutely nothing called Perelman theorem with any consistency. From google search "Perelman theorem" could be a classification of Ricci solitons, sometimes it is the existence of Ricci flow with surgery, in principle it could be either the geometrization conjecture or the Poincaré conjecture, and (by same principle) could be many other major results from his papers besides. I think there should not be any redirect or disambiguation page for "Perelman theorem." Gumshoe2 (talk) 14:20, 10 July 2022 (UTC)[reply]
Nominated for RfD. --SilverMatsu (talk) 16:37, 11 July 2022 (UTC)[reply]
I’d make Perelman's theorem and Perelman theorem redirect to either Poincaré conjecture or to Grigori Perelman#Geometrization and Poincaré conjectures. –jacobolus (t) 17:42, 11 July 2022 (UTC)[reply]
Is there evidence that these phrases are used in the wild for that? --Trovatore (talk) 19:32, 11 July 2022 (UTC)[reply]
Searching Google scholar for "Perelman's theorem" finds it continued:
  • ...that the metric projection of a non-negatively curved open manifold onto its soul is a well-defined Riemannian submersion (ProQuest 304537849, [4]); this seems to match Grigori Perelman#Comparison geometry.
  • ...that shrinking breathers of Ricci flow on closed manifolds are gradient Ricci solitons (doi:10.1007/s12220-017-9974-1)
  • ...that positively curved ancient solutions have vanishing asymptotic volume ratio and infinite asymptotic scalar curvature ratio ([5])
So it definitely seems incorrect to redirect to Poincaré conjecture. If we had enough links for these other things we could consider making a dab page. —David Eppstein (talk) 20:25, 11 July 2022 (UTC)[reply]
As a comparable example, both Wiles's theorem and Wiles theorem redirect to Fermat's Last Theorem (even though those terms are extremely rare in the literature even 25 years after the proof). The Poincaré conjecture is by far the most famous theorem proven by Perelman (since the mid 2000s and into the future, I would expect any use of the generic "Perelman theorem" to mean this, with other "Perelman theorems" named something more specific; for example in the three examples that David Eppstein found, the theorems there are explicitly called “Perelman’s Rigidity Theorem”, “Perelman's No Local Collapsing Theorem” and "Perelman’s Theorem on Shrinking Breathers in Ricci Flow" when introduced; none of these is presented as "Perelman's Theorem" without qualification). In a brief search of the current literature, there are a bunch of uses of "Poincaré–Perelman theorem" and a few direct uses of "Perelman theorem" to mean this result, but it is still commonly called the "Poincaré conjecture" after the proof, out of historical inertia. –jacobolus (t) 20:32, 11 July 2022 (UTC)[reply]
OK, if/when that happens, we can make those redirects. Wikipedia is not supposed to drive adoption of terminology. (By the way, I don't think it's wrong to keep calling it the Poincaré conjecture, given that Poincaré did in fact conjecture it. The assertions that it "was" a conjecture and "is now" a theorem are, I think, just wrong; if it's a theorem now then it has always been a theorem, even before there were humans. The proof has always existed; the only thing that has changed is that we now know a proof. Being a conjecture is more temporal; it's not a conjecture until someone conjectures it. Still, I don't think it stops being a conjecture just because we now know that it's also a theorem. --Trovatore (talk) 20:49, 11 July 2022 (UTC)[reply]
Adding redirects here seems easy and low-cost (low chance of causing confusion; does not make false implications; as just a redirect, does not give “undue weight” to some fringe/unestablished usage), while potentially helping some readers. If nothing else, it prevents people from trying to "helpfully" move the page there in the future. Titles to be redirected have a much looser standard than the text of articles: redirects are about helping people find what they are looking for, not telling them what terms are standard usage. If you think there will be some confusion about whether Perelman theorem should refer to Poincaré conjecture or Geometrization conjecture, then a redirect to Grigori Perelman#Geometrization and Poincaré conjectures should eliminate that concern. –jacobolus (t) 21:02, 11 July 2022 (UTC)[reply]
"The Poincaré conjecture is by far the most famous theorem proven by Perelman". That does not preclude a disambiguation page. That can be the bolded primary meaning (cf the treatment at Rabbit (disambiguation)). SpinningSpark 17:44, 13 July 2022 (UTC)[reply]
The fact that it's the most famous theorem he's proved (so far) doesn't make it the primary meaning for "Perelman's theorem". --Trovatore (talk) 17:51, 13 July 2022 (UTC)[reply]
If we called Poincaré conjecture as Perelman's theorem, I think we miss the contributions of Stephen Smale and Michael Freedman.--SilverMatsu (talk) 04:36, 14 July 2022 (UTC)[reply]
It really doesn't make any difference at all, for our current purposes, whether "Perelman's theorem" would be a good name. We shouldn't even be talking about that. I'm not at all a stickler for the rules on talk pages; I'm not objecting to you talking about what you find interesting. I just don't want it to get confused with what our articles should be called or what redirects/disambigs we should have and where they should point. --Trovatore (talk) 15:48, 14 July 2022 (UTC)[reply]
While I agree that a move of Poincaré conjecture to Perelman's theorem is inappropriate, a disambiguation page with links to, e.g., Poincaré conjecture, Thurston geometrization conjecture, might be appropriate. --Shmuel (Seymour J.) Metz Username:Chatul (talk) 11:18, 12 July 2022 (UTC)[reply]

σ

Looks like these should be unified. 1234qwer1234qwer4 20:49, 20 July 2022 (UTC)[reply]

I don't think so. At least σ-compact space is a concept from topology and should be kept separate from the other topics from measure theory. PatrickR2 (talk) 04:42, 21 July 2022 (UTC)[reply]
I'm talking about the naming of the articles; not sure how your point is relevant. 1234qwer1234qwer4 10:46, 21 July 2022 (UTC)[reply]
The naming is merely a matter of directions of redirects. In your above order, the following redirects exist (blue) resp. don't exist (red):
Moreover, I found Sigma-algebra of tau-past redirecting to σ-Algebra of τ-past (no idea what that is about). I suggest to create the red redirect. As for the direction of redirects, I don't care too much; either direction is ok (, and unification is nice to have, but not necessary). - Jochen Burghardt (talk) 11:14, 21 July 2022 (UTC)[reply]
You might pick one of these articles and start a discussion on the talk page, then put a link on all of the other talk pages directed at that one, to see if anyone has a preference between σ vs. "sigma" in the title or minds unifying the titles. –jacobolus (t) 21:46, 21 July 2022 (UTC)[reply]

If by "unified" you mean all of them should be merged into just one article, that seems like a very bad idea. Michael Hardy (talk) 00:16, 23 July 2022 (UTC)[reply]

I think he means, not merger nor any content change in the articles, but to change the titles to either (1) all use "σ" or (2) all use "sigma". JRSpriggs (talk) 05:55, 23 July 2022 (UTC)[reply]
My impression from glancing at some books is that "Sigma" is more likely to be used in titles and headings, "σ" in the body of texts. Am I correct about such usage? Limit-theorem (talk) 15:05, 23 July 2022 (UTC)[reply]

Colons

I may get around to fixing this eventually, but perhaps someone else would like to get there first: in Imaginary unit, one finds the amazing three-colon sentence The issue can be a subtle one: The most precise explanation is to say that although the complex field, defined as R[x]/(x2 + 1) (see complex number), is unique up to isomorphism, it is not unique up to a unique isomorphism: There are exactly two field automorphisms of R[x]/(x2 + 1) which keep each real number fixed: The identity and the automorphism sending x to −x. (It would also be nice if this statement were supported by a citation.) --JBL (talk) 22:09, 22 July 2022 (UTC)[reply]

Impressive!
The citation in complex number for that definition is actually to Bourbaki, which may be pedagogically suboptimal. XOR'easter (talk) 22:21, 22 July 2022 (UTC)[reply]
Thanks! I made a go at stripping out unnecessary technicality (after all, the property in question doesn't depend on how one chooses to represent C), so it's now a bit blander but perhaps more comprehensible. --JBL (talk) 17:44, 23 July 2022 (UTC)[reply]

Use of Latin in Mathematics

I was surprised that I couldn’t find any article concerning the use of Latin for writing European mathematics. From what I can tell the word “mathematics” does not occur in any of Medieval Latin, Renaissance Latin, Vulgar Latin, Ecclesiastical Latin, or History of Latin, and these articles have little if any discussion of the use of Latin for science in general. The article History of mathematics doesn’t really describe this in any detail. (There is an article Botanical Latin, and about 2 relevant sentences at Lingua franca#Historical lingua francas, and a somewhat related article at Latin translations of the 12th century.) I don’t read/speak Latin and know very little about this subject so I don’t feel I can meaningfully contribute about it. But it seems like a topic that belongs in Wikipedia, and I am sure there is a significant amount of secondary literature in English for anyone willing to hunt for it. Anyone knowledgeable about mathematical history want to take a crack at writing at least a few paragraphs? Edit: perhaps at Mathematical Latin or some similar title. –jacobolus (t) 21:25, 23 July 2022 (UTC)[reply]

See related discussion. In that discussion, the most recent mathematics paper I could find written in Latin was from 2006 (MR2214259). —David Eppstein (talk) 21:37, 23 July 2022 (UTC)[reply]

Bad typesetting

See this edit and the ones right after it. The typesetting in many many many places in the article is wrong by the standards of [[WP:MOSMATH]] and of standard typesetting conventions. Michael Hardy (talk) 00:41, 23 July 2022 (UTC)[reply]

Your changes are an improvement. But as an example, when changing the original ''n+2'', instead of manually inserting HTML "&nbsp ;" around each side of the plus sign, wouldn't be easier to just let Latex do the job with <math>n+2</math> PatrickR2 (talk) 02:39, 24 July 2022 (UTC)[reply]

Counting argument

Counting argument, a disambiguation page, currently links to two topics: the pigeonhole principle and combinatorial proof (mainly about bijections and double counting). There is another type of counting argument that is not linked: proof of the existence of an A that is not B, by counting both kinds of objects and finding that there are more A's than B's. Is there a good name for this type of argument, or better an existing article on it? —David Eppstein (talk) 01:05, 24 July 2022 (UTC)[reply]

Isn’t this just an application of the pigeonhole principle? –jacobolus (t) 17:41, 24 July 2022 (UTC)[reply]
It is related but I think not the same. The pigeonhole principle is about proving that functions from A to B are non-injective; here I'm more interested in proving that functions from B to A are non-surjective. —David Eppstein (talk) 18:09, 24 July 2022 (UTC)[reply]
Pigeonhole_principle#Alternative_formulations also mentions that version. —Kusma (talk) 18:25, 24 July 2022 (UTC)[reply]
So you think it would be enlightening to readers to link the phrase "counting argument" as occurring in Garden of Eden (cellular automaton)#Proof sketch or in the lead of P/poly? Probabilistic method seems closer in spirit (and would work for the P/poly example, at least). My feeling is that such a link would be baffling, because you have to pore very carefully through pigeonhole principle to find the relevant part. —David Eppstein (talk) 19:04, 24 July 2022 (UTC)[reply]
I don't really see a good place where the general argument "set B is contained in A, and strictly smaller in some sense (measure, cardinality, whatever), so A\B is not empty" is described, so perhaps better not to link it. For infinite sets (a typical application is that the algebraic numbers are countable, but the reals are uncountable, hence there exist transcendental numbers), this isn't covered by the pigeonhole principle. —Kusma (talk) 19:59, 24 July 2022 (UTC)[reply]

Moving Spinger series articles to new names

I think we should rename these two articles

to disambiguate them and then make the uncapitalized

names the "main" redirect" (with article possibility) or a disambiguation page.

There's a reason danger here of a person thinking these lists are a general listing of mathematical textbooks, e.g., "Undergraduate texts in mathematics" rather than the series "Undergraduate Texts in Mathematics". Since there are also similarly named series by publishers other than Springer, e.g., the Graduate Studies in Mathematics series, it also seems biased to me to have Springer capitalize on such general phrases. There a bit of tension here in our article title policy between our goal to be concise with titles and quickly get readers to the best article and our goals to be neutral and clear and unambiguous.

Similarly, I propose

with Graduate studies in mathematics becoming the "main" redirect (with article possibility).

Thoughts? Ideas? Jason Quinn (talk) 03:13, 28 July 2022 (UTC)[reply]

This seems like a bad idea. These are well-known book series, and nobody ever says "undergraduate texts in mathematics" when talking about anything other than the Springer books. You can easily come up with another title if you want to talk about generic undergraduate textbooks. There's a reason danger here of a person thinking these lists are a general listing. These articles state clearly at the top what they are about. Doesn’t seem like a real danger. –jacobolus (t) 03:34, 28 July 2022 (UTC)[reply]
[edit conflict] Wikipedia only allows disambiguators on article titles when there is some other article that they disambiguate against. It generally only allows disambiguation pages when there are at least three ambiguous meanings for the title. These things are based on syntax (the wording of the title), not semantics (the meaning of the title). Wikipedia rules also generally allow different articles to have titles that differ only in capitalization, as long as they have hatnotes pointing to each other (see WP:DIFFCAPS). So, in order to move these series names to disambigated titles, we need something else that would also be titled with the same exact wording and capitalization. What is that something else that you are thinking of? —David Eppstein (talk) 03:36, 28 July 2022 (UTC)[reply]
I was thinking that I would start new articles at the previous titles with a more general scope. But maybe you two are right. Perhaps it's a bad idea. Jason Quinn (talk) 03:47, 28 July 2022 (UTC)[reply]

Exterior of a set

The article Exterior (topology) has nearly identical contents with the section Interior (topology)#Exterior of a set. Should Exterior (topology) be merged into that section of Interior (topology) and then deleted? PatrickR2 (talk) 01:22, 28 July 2022 (UTC)[reply]

Not deleted, but redirected. Yes, given the article contents, that seems reasonable (and if someone later finds more to write about exteriors, they can expand it out again later). --JBL (talk) 19:11, 28 July 2022 (UTC)[reply]
Yes, I meant redirected. PatrickR2 (talk) 01:51, 29 July 2022 (UTC)[reply]
I simply redirected it, as there is no information for merging. Most of the Exterior article was taken from the Interior one in 2009, and the bulk of the remainder was added to both articles in 2021 in parallel edits. Felix QW (talk) 08:27, 29 July 2022 (UTC)[reply]
Quelle: http://en.wikipedia.org/wiki/Wikipedia_talk:WikiProject_Mathematics/Archive/2022/Jul