Talk:Main Page/Archive 18

This is an article of past discussions, from 12-Feb-2023 to 20-Nov-2023.
Do not edit the contents of this page.
If you wish to start a new discussion or revive an old one, please do so on the current talk page.

Looking for Algebra

I cannot find a variant of algebra defined in my source. Namely, it states that "An algebra is a vector space V in which an associative and distributive multiplication is defined". Do we have such a thing? Also, from Definition:Bilinear Mapping I can recover distribution, but not associativty ($(x \oplus y) \oplus z = x \oplus (y \oplus z)$). A disambiguation will be needed. --Julius (talk) 23:25, 13 February 2023 (UTC)

Have you seen this page? Definition:Algebra (Abstract Algebra) It looks like what you're talking about is an Definition:Associative Algebra. Is this right?

We use disambiguation if the same word is used for two completely different things. If what you're talking about *is* the same as an Definition:Associative Algebra, just that your work assumes associativity by default, then what you're looking to do is set up an "also known as" section, which we are now implementing as transclusions. --prime mover (talk) 06:23, 14 February 2023 (UTC)

Thanks. I will map the details accordingly without introducing a new definition. Although, technically, the given definition involves only one operation. Shouldn't we say "associative wrt $\oplus$" if there are multiple (not necessarily associative) operations involved?

Another addition that is really needed is a simple proof that a vector space with a bilinear product is an algebra over field. A lot of books only bother with vector spaces, but we don't, so we should establish this link and save ourselves from reinventing the wheel.--Julius (talk) 11:28, 14 February 2023 (UTC)

Change in behaviour of double-click in "Edit source" tool

A few days ago I noticed that the behaviour of double-click has changed subtly in the "Edit source" tool.

Previously, if you had for example a string "Definition:Circle", and you double-clicked "Circle", the editor would pick up the whole string "Definition:Circle".

Then the other day the behaviour changed, and double-clicking on "Circle" picked up only "Circle". This was a brilliant enhancement, because it then made editing so much easier.

But now it's back the way it was. Clicking on a string with a colon in the middle of it picks up the entire string, colon and all.

How easy would it be to go back to the way we had it a few days ago, where the editor recognises the colon as being a word delimiter? --prime mover (talk) 08:02, 15 February 2023 (UTC)

Sorry -- ignore this. It's browser dependent. I had logged on using Google Chrome this morning. That one behaves so as to pick up the entire string, colon and all.

When I use Brave, which I usually do but not earlier, it picks up the part of the string either side of the colon, which is what I want.

So, as I say, no problem. --prime mover (talk) 08:37, 15 February 2023 (UTC)

Incoming opinions from scientists using Proofwiki

During the previous week I took liberty of reaching out to various people who, accoriding to Google Schoolar, used Proofwiki in one way or another. The rate of response is modest, but there are a few distinct recommendations. I will not display all of them here at once. Instead, comments about specific articles will land in their discussion pages, while here I will gradually present those concerning the website as a whole.--Julius (talk) 00:27, 1 March 2023 (UTC)

Failure to pay attention to house style

I'm considering deleting with extreme prejudice some of these recent pages which are contemptuously non-compliant. Come on, everyone else can pick up the rules, so can you. --prime mover (talk) 21:43, 9 March 2023 (UTC)

"Left-Truncatable Prime/Various Number Bases" was amazingly bad. Just a wall of numbers. No proof. No logic. No coherence. I am in favor of deleting nonsense. --Robkahn131 (talk) 23:38, 10 March 2023 (UTC)

Okay let's talk about this: should we feel obligated to provide webspace for research projects? Good to support such endeavours in the philosophical, but are we going to go so far as to allow people to decide they are going to use $\mathsf{Pr} \infty \mathsf{fWiki}$ as their publishing platform? What's the consensus please, regulars? --prime mover (talk) 00:20, 12 March 2023 (UTC)

Too many contributors have put a great deal of time and energy into contributing something of value. Junk pages reflects poorly on all of us. I am in favor of holding each other accountable. All pages must adhere to house-style. If a page goes rogue and defines things differently, it should at least mention how the topic is defined elsewhere. --Robkahn131 (talk) 01:37, 12 March 2023 (UTC)

I'm not sure what openning up $\mathsf{Pr} \infty \mathsf{fWiki}$ to original research would mean and how it might impact me. So far much of the original research put up on $\mathsf{Pr} \infty \mathsf{fWiki}$ has been questionable or non-compliant. And that is deflating. Like yourself, in principle I want to support original research, but originality can't be allowed to trump quality.

Then there is the question of using $\mathsf{Pr} \infty \mathsf{fWiki}$ as a publishing platform for their work. This seems to be at odds with why most of us are contributing, which could become a source of conflict. --Leigh.Samphier (talk) 04:22, 12 March 2023 (UTC)

If you have reached the point where you are unable to give someone the benefit of the doubt that they are genuine then you have no choice but to delete the pages. If there is still some willingness to give them a small benefit of the doubt, then move the offending pages under the apropriate User: page. --Leigh.Samphier (talk) 04:22, 12 March 2023 (UTC)

It will be noted that I have temporarily blocked User:Richard47 as I am fed up of tidying up his non-compliant pages, most of which appear to be nothing but copypasta from OEIS and whatever other sources. The user a) has shown little willingness to write compliant pages, b) insists on asserting a non-standard definition of Definition:Minimal Prime because he "likes it", c) pastes up pages of unformatted lists of numbers with no attempt to justify their validity.

While there are one or two definitions raised of concepts that we currently have no record of, the effort of tidying them up for $\mathsf{Pr} \infty \mathsf{fWiki}$ compliance is too tedious to be contemplated.

IMO it is not unreasonable to expect that a mathematician should be intelligent enough to be able to learn how to use this site, particularly when encouraged to do so repeatedly.

If anyone has any reservations about this, and are concerned that we may be cutting off a source of valuable content, then feel free to comment. --prime mover (talk) 09:42, 14 March 2023 (UTC)

Problem uploading image

Just tried to upload a png file "Field-lines-negative-charge.png" but it throws an error:

Upload error

Could not store file "/tmp/phpPMUdp9" at "mwstore://local-backend/local-public/e/eb/Field-lines-negative-charge.png".

I have just successfully uploaded "Field-lines-positive-charge.png" which is practically identical, but for the directions of the arrows and the text in the centre.

Anyone able to troubleshoot? --prime mover (talk) 19:23, 22 March 2023 (UTC)

Yikes, looks like we're out of disk space. Give me a few minutes to fix. --Joe (talk) 19:29, 22 March 2023 (UTC)

Should work now! --Joe (talk) 19:31, 22 March 2023 (UTC)

Nice one, thanks bruv --prime mover (talk) 00:09, 23 March 2023 (UTC)

Proof-needed Template

Is it possible to add a template for assertions which do not have proofs in any section of the page nor is it linked on Proof Wiki, similar to the "Citation Needed" statement on Wikipedia?

We have {{ProofWanted}}, is that what you're after? Or {{TheoremWanted}} maybe? --prime mover (talk) 19:37, 25 March 2023 (UTC)

That'll work! --PeterJohnson (talk) 19:40, 25 March 2023 (UTC)

Adding Extension DiscussionTools

It should be a very easy process. Would it be possible to install DiscussionTools? This will allow users to write talk discussions like they would on Wikipedia. It requires very little setup on this current MediaWiki instance (see Special:Version). Of course, this is your wiki, so do what you please. However, I feel that it would make it much easier to contribute to talk pages.

What do you get that you don't got with what we got? --prime mover (talk) 17:48, 27 March 2023 (UTC)

I'm fine with installing this if there's general consensus. --Joe (talk) 18:05, 27 March 2023 (UTC)

No problem with this in theory, as long as the operational overhead does not outweigh the benefits, and as long as it does not compromise the look and feel. --prime mover (talk) 19:48, 27 March 2023 (UTC)

Setup

If you end up deciding to install DiscussionTools, the setup instructions are on the page, but I will write an install tutorial here as well, since I ended up adding it to my wiki as well.

1. Download DiscussionTools. If you are on Windows, the easiest way to do this is to use 7zip and extract the files. Depending on where your server(s) are hosted, it may be easiest to directly upload the .tar.gz file onto your server(s). This will only work if you are running a Linux server.

2. Download and add the Linter extension. This extension is required by DiscussionTools. Just add wfLoadExtension( 'Linter' ); to your LocalSettings.php wherever you prefer. You also need to add

$wgParsoidSettings = [
    'linting' => true
];

to your LocalSettings.php.

3. Load DiscussionTools with wfLoadExtension( 'DiscussionTools' );.

4. Something not said in the tutorial on MediaWiki is that you need to configure VisualEditor to work on Talk Pages. Otherwise DiscussionTools won't appear on the talk pages, which is the only thing it's supposed to do. This is very easy to do, you simply need to add NS_TALK the the list of namespaces allowed in wgVisualEditorNamespaces.

About that VisualEditor: is it possible to disable it from all but talk pages? Its use compromises the page layout and hence the consistency of our presentation. --prime mover (talk) 19:50, 27 March 2023 (UTC)

For example, my wiki currently has it set to:

$wgVisualEditorNamespaces = array( NS_MAIN, NS_TALK, NS_USER, NS_USER_TALK );

Then, just run the update script (located at maintenance/update.php from the directory you installed MediaWiki), and it will create all the necessary database tables for DiscussionTools to work.

Anyhow, feel free to do whatever you feel like, this is your wiki.

Oh and on a side note, I feel you should consider collecting donations over using Google Analytics, however, you may be for-profit instead of non-profit. I don't know, I'm not you. Is it simply the tax concerns from collecting donations is far too large?

Thanks for the write-up. With respect to the ads, I would also like to move away from them but I'm undecied on the best path. The simple issue with donations when I did them in the past is that very few people donate. It was spiratic and did not come close to covering the cost of running ProofWiki (not that it's a gigantic amount). I've consdiered memberships or Pateron but I'm not sure it's the right approach. --Joe (talk) 18:05, 27 March 2023 (UTC)

I see. That really sucks. I'm planning on running a large-scale wiki at some point, but the costs, and the setup pains (installing not just normal extensions but extensions such as WikiSeo) are immense, so I empathize with you greatly. Well, we'll see what happens in the future, and I wish you the best of luck (ProofWiki's super cool). Peter Johnson (talk) 21:31, 27 March 2023 (UTC)

Glad you like it. I'm almost getting to the stage where I'm generally happy with both content and presentation -- we've made a solid start in most areas now, at least of pure. I'm taking on applied and physics. Contribute whatever you have, we'll work out how to squeeze it into our format. --prime mover (talk) 22:31, 27 March 2023 (UTC)

Should we standardise the expression of the complex numbers?

While I was browsing pages on complex numbers, I noticcd that there're $a+ib$ pages like this; $a+bi$ pages like this. And I also found this page writing $\ds 2 i \, \map \Im z$.

So where on earth should we place $i$? --AuroraAeon (talk) 02:11, 5 April 2023 (UTC)

Multiplication in this context is commutative. --prime mover (talk) 05:24, 5 April 2023 (UTC)

Orthogonal Curvilinear Coordinates

I invite anyone with an opinion on or familiarity with the business of three dimensional coordinate systems to follow along behind me with a bucket, so to speak. I'm taking my time with this because I'm not fully convinced that I am filling in the details correctly. I do not know whether the underlying definitions of some of the objects that I am using are completely accurate, but have not found easily understood source materials.

First stop after this will be to define spherical coordinates, the absence of which makes the physics coverage embarrassing. Cannot really progress with electrostatics until we've properly pinned down spherical coords. --prime mover (talk) 21:54, 10 April 2023 (UTC)

Inequalities

I have found myself embarking on an exercise to rationalise the section on inequalities, e.g. Hölder's Inequality, Chebyshev's Inequality and so on.

We have a number of approaches: some are presented on the real number line, some extend to the complex plane, some are set in a Lebesgue space, some implicitly assume the underlying space is Banach, and so on.

Starting with the rationalisation of Definition:P-Sequence Space, I intend that each inequality is presented:

a) in the most abstract space to which it can be applied

b) in the specific context(s) of the real number line and/or complex plane

c) if applicable, to a general Cartesian space $\R^n$ or even $\C^n$

The above will of course depend to a certain extent on what sources we can find online.

I have already started using both Spiegel and Abramowitz & Stegun as my compendia, to which the various implementations can be added according to whatever sources we find them in.

I would like to encourage anyone who has the requisite knowhow (and sources to back it up) to (continue to) contribute to these pages as appropriate. --prime mover (talk) 08:35, 20 May 2023 (UTC)

AI editors

Are there any AIs out there? It occurs to me that some of our contributors may actually not be human. I wondered if they might want to introduce themselves? Be delighted to meet you. --prime mover (talk) 17:58, 25 May 2023 (UTC)

Pages and pages of empty definitions

Because of some well-meaning and industrious activity of one the newer members of our team, we have had a flood of new stub pages added for a whole host of new definitions (and some proofs). While on the surface this is all well and good and all, I am not sure this is completely welcome.

When there is a redlink on a proof, it is clear that a page has not been written and needs to be addressed. But if the links are all nice and blue, it is more likely that an editor is going to say: good, don't need to do that, someone has filled in that definition -- and in fact it's not there.

As for the poor reader, following link after link of empty contentless pages all with a neat path of links between them is probably worse than there being no material there at all.

What's the consensus on this? --prime mover (talk) 14:35, 1 June 2023 (UTC)

I don't like this at all. I think Theorem pages should have a theorem statement at the very least, and definitions include at least one complete definition. Otherwise I'd recommend users use their sandbox. Caliburn (talk) 15:50, 1 June 2023 (UTC)

I was fairly sure User:Cngzz1 was an AI but I'm not so sure now, as it has failed adequately to learn the rules of page structure, despite having received numerous corrected examples.

But I try not to discriminate based on nationality, gender, colour or nature of intellect substrate. --prime mover (talk) 16:15, 1 June 2023 (UTC)

I doubt they are an AI since they were able to reply to your talk page messages. Automated editing tools do exist, but they are not really editing in the volume or frequency that would make me assume that this is the case. Some people type a bit robotically/overly formally, I think this is just personal style and not really reflective of anything. I guess it's also natural when you've entered a space for the first time. Caliburn (talk) 16:37, 1 June 2023 (UTC)

Mind, it does make me think we may do well to create a consensus "template" page which can be used (although perhaps not using the WediaMicky Template object because it's just too fiddly to set up). I'll gather it together and put it in my toolspace, like my other bare-bones pages. --prime mover (talk) 17:46, 1 June 2023 (UTC)

Definition of Proper Subset

The current definition of proper subset specifies that $A$ is a proper subset of $B$ if and only if $A \subseteq B$ and $A \ne B$ and $A \ne \O$.

That is, that the empty set is not considered a proper subset.

However, I have been reviewing my sources, and it turns out that the overwhelming majority of my sources do allow $\O$ to be a proper subset of a non-empty set.

Hence I am going to investigate whether it is feasible to change our definition so that we follow the majority.

Please feel free to weigh in with whether or not this is a good move. --prime mover (talk) 10:19, 7 June 2023 (UTC)

The more I look at it, the more it makes sense to change it. I have gone through the results and ensured consistency with this. --prime mover (talk) 12:38, 7 June 2023 (UTC)

I have no objections against this, but I wonder if the current definition also find support in literature. If it does, maybe we can rename the current version as the nonempty proper subset.--Julius (talk) 15:40, 7 June 2023 (UTC)

I have found a total of 3 sources in my personal library that defines it as $\O \subsetneqq S \subsetneqq T$; all the rest give $S \subsetneqq T$. In the (few) places where the proof needs to be $\O \subsetneqq S \subsetneqq T$ I have deliberately used the terminology "nonempty proper subset". I have set up an "also defined as" page for now, which should be adequate. --prime mover (talk) 15:50, 7 June 2023 (UTC)

Moore-Smith sequences

I will need nets soon because of the non-metrizability of weak/weak* topologies, and I will be taking them out of Willard. On here we call them Moore-Smith sequences. What do I call a subnet? Caliburn (talk) 10:40, 16 June 2023 (UTC)

I've written essentially all that I could possibly need apart from the stuff on subnets, see Special:PrefixIndex/User:Caliburn/s/nets. Caliburn (talk) 16:31, 16 June 2023 (UTC)

All depends on what your source work says. Moore-Smith subsequence? --prime mover (talk) 16:41, 16 June 2023 (UTC)

I haven't found any source work that uses "Moore-Smith sequence" beyond just mentioning that it might also be called that and then going on to talk about nets and subnets. It seems like it was decided this should be used to avoid ambiguity quite a while ago. Moore-Smith subsequence was also my first inclination. Caliburn (talk) 17:11, 16 June 2023 (UTC)

Also worth mentioning that the page subnet already exists. Caliburn (talk) 10:31, 17 June 2023 (UTC)

Another possibility is Subsequence of Moore-Smith Sequence. --Usagiop (talk) 13:37, 17 June 2023 (UTC)

I thought of this too, but it would risk confusion with a subnet indexed on the natural numbers (even if the original net did not have index set $\N$). You could and probably would sensibly call this a "subsequence of a net". Since a net is a generalisation of sequences, I wouldn't want to use the word "sequence" to describe a net without the qualifier "Moore-Smith" either. Caliburn (talk) 13:47, 17 June 2023 (UTC)

I found a random paper that says "Moore-Smith Subsequence": https://link.springer.com/article/10.1007/s12220-022-01050-7. The notation is quite obscure but I believe they're still talking about subnets. This is good enough for me, any objections to moving subnet to this? Maybe ping User:Lord_Farin since they wrote about this some time ago in User:Lord Farin/Sandbox/Nets. Caliburn (talk) 12:02, 18 June 2023 (UTC)

Yep, he may well drop in if you do.

But I say: excellent find. Let's have this notation, it's fully in accord with the $\mathsf{Pr} \infty \mathsf{fWiki}$ way. --prime mover (talk) 14:58, 18 June 2023 (UTC)

I would prefer not to lmao, (it seemes awkward and untransparent from a first glance, IDK if it's because they're working in an area with agreed notation or what) but it's at least a source for "Moore-Smith Subsequence". I will check if they are indeed talking about subnets later on and if they are we can go ahead with "Moore-Smith Subsequence". They definitely mean "net" by "Moore-Smith sequence", as we do, at the very least, so I would be surprised if it didn't mean subnet. In this case, we would have "Topological Space is Compact iff every Moore-Smith Sequence has Convergent Moore-Smith Subsequence" and so on. Caliburn (talk) 16:22, 18 June 2023 (UTC)

Chipping in as requested, one of the reasons I never finished the whole nets topic is because it is kind of cumbersome and unwieldy to always say M-S sequence, and I wasn't satisfied with it.

The trouble is the ambiguity between order net and preorder net. It is possible and consistent to make "net" mean "preorder net" and then always qualify "order net" in the appropriate cases, with an "Also defined as" section.

One way or another, anyone who works in this field or is searching for things involving nets is going to use the word "net" and not "M-S sequence". So we might as well adopt that terminology and carefully qualify what we mean otherwise. There are more examples of this approach on PW, where we say "some sources define X as Y, on PW we choose X because it is better". — Lord_Farin (talk) 09:00, 29 June 2023 (UTC)

Those who are active in this area can make the decision as to exactly what we do. --prime mover (talk) 10:44, 29 June 2023 (UTC)

I am just going to switch over from Moore-Smith sequence to net, I think. "Moore-Smith sequence" sounds like a term that is hardly used nowadays and is mentioned for historical interest, so it feels pointlessly obscure to continue using it. Caliburn (talk) 12:38, 1 August 2023 (UTC)

Mostly done. Caliburn (talk) 18:38, 1 August 2023 (UTC)

Slow

Is someone doing something bigly database intensive? I'd been godawfully slow every time Iv'e tried to log in to do anything togay. --prime mover (talk) 21:00, 25 June 2023 (UTC)

Everythning is quiet on the servers. --Joe (talk) 14:07, 26 June 2023 (UTC)

It's fine now. Just yesterday first thing in the morning and last thing at night. --prime mover (talk) 21:50, 26 June 2023 (UTC)

Search improvements

Hi Folks, just stopping by with some user feedback -- I came to the site to find the rule for Derivative of Composite Function (it's been a while). I searched for "derivative of composition" but did not find the relevant result, and after searching again for "derivative of composite" the first two results are sub-pages (Derivative of Composite Function/Second Derivative and Derivative of Composite Function/Third Derivative).

I think it would be a great improvement to the site if it could be less strict on matching exact terms, and prioritise the parent page over child pages with derivative results (pun intended). I know everyone is busy so (if others agree) there might not be bandwidth for researching/testing/implementing options for improving search, just wanted to mention this as an option to make the site easier to use for visitors. --Linus44

I usually have better luck using Google with site:proofwiki.org. I think it's a MediaWiki issue but it would be nice to see if there are improved search plugins or etc. I think most results occupying subpages (except corollaries and lemmas) should eventually have redirects to them as well. Caliburn (talk) 06:50, 14 July 2023 (UTC)

Spam account applications are on the rise again

I have left 2 of these in the queue for an opportunity to see what we might need to do something about. --prime mover (talk) 07:45, 3 September 2023 (UTC)

Thought I'd mention the date

$2^3 - 3^2 - 23$ or in the MDY style $3^2 - 2^3 - 23$ --prime mover (talk) 22:14, 8 September 2023 (UTC)

And today in $2$ years time it will be $4^2 - 3^2 - 45^2$. --prime mover (talk) 15:35, 16 September 2023 (UTC)

GeoGebra logo

A lot of our artwork is done using GeoGebra. Should we put the logo on the corner of the screen with MathJax? Give them some basic acknowledgement? --prime mover (talk) 21:26, 26 September 2023 (UTC)

I think we should. Also, this is in line with our transparency concerning the source of material.--Julius (talk) 11:44, 27 September 2023 (UTC)

Sounds good to me. Can anyone find a logo that would fit well, preferably in a box like the others? --Joe (talk) 13:58, 27 September 2023 (UTC)

Just uploaded one now.

Lifted the image from their website. --prime mover (talk) 22:07, 28 September 2023 (UTC)

MediaWiki LTS Upgrade

I've upgraded ProofWiki to the latest MediaWiki LTS (1.39). There were some techincal issues with MathJax rendering that I hope are now working corrently. Please let me know if something is not wokring as expected. Thanks. --Joe (talk) 20:59, 28 September 2023 (UTC)

The commutative diagram on Condition for Mapping from Quotient Vector Space to be Well-Defined does not render for me. Caliburn (talk) 22:01, 28 September 2023 (UTC)

Commutative diagrams: it works if you put everything on one line. Adequate, but not optimal. --prime mover (talk) 22:10, 28 September 2023 (UTC)

It's not just commutative diagrams. It's every instance of a multiline $\LaTeX$ expression. The worst one is \begin{cases} \end{cases}, on pages such as Definition:Absolute Value/Definition 1. --CircuitCraft (talk) 01:31, 29 September 2023 (UTC)

Yeah, I've found the "Purge" tool is missing from the "More" menu. Also, I have the same trouble as Caliburn. So that's broken.

Apart from that it seems functional enough ... although the "Insert Link" tool has an annoying pop-up helper that gets in the way for a click. --prime mover (talk) 22:07, 28 September 2023 (UTC)

I've been one-line-ing multiline $\LaTeX$ expressions as I find them, but it would be good if we can find a solution to the above problem, because there's a mountain of them out there. --prime mover (talk) 22:20, 1 October 2023 (UTC)

I'll take a look at this tonight. My current fix works pretty good, but breaks the MathJax rendering in the ToC. I can switch if it's preferable for now. --Joe (talk) 14:41, 2 October 2023 (UTC)

It also breaks when you have a $\LaTeX$ string with two apostrophes next to one another. Parser seems to think it's the start of an italic tag. It can be simply addressed by putting a space between the quotes but it's a pain to have to do it. --prime mover (talk) 05:05, 3 October 2023 (UTC)

So I think everything should work now except for the rendering of the ToC if it has math in it. Looking into fixing. --Joe (talk) 12:57, 3 October 2023 (UTC)

Problem setting account up using Mac

I have been trying to get a student of mine to set up an account on $\mathsf{Pr} \infty \mathsf{fWiki}$ but every time he tries to enter the secondary anti-spambot question in the setup screen, his device hangs. I watched over his shoulder while he tried doing this several times over.

As I'm not a Mac user myself, I have been unable to get this to fail. --prime mover (talk) 07:26, 7 October 2023 (UTC)

Just try it on mobile or some other device? Login will work afterwards... — Lord_Farin (talk) 21:13, 7 October 2023 (UTC)

I'll suggest this, and see whether such an option is feasible. --prime mover (talk) 21:30, 7 October 2023 (UTC)

Circular reasoning

I noticed that Thales' theorem/Proof 2 relies on Inscribed Angle Theorem while Inscribed Angle Theorem/Proof 2 relies on Thales' theorem. --Telliott99 (talk)

Since there are independent proofs of both theorems this isn't a logical difficulty, but I wonder if there is some general philosophy about this on the site.

I think we should have a standard format of "if we use Proof 1 of [...], there is circularity introduced, hence refer to Proof 2". I think it's fine to cite a theorem for which one of the proofs relies on what is being proved provided there is an independent proof also sitting there. Caliburn (talk) 21:14, 14 October 2023 (UTC)

I think it's fine to have circular proofs, as long as the cycle is broken somewhere. Besides, there's value in demonstrating how related results connect to one another. I also don't think it's necessary to specifically mention that this is happening on the relevant pages; we should just try to put non-cyclic proofs at the top of the list, if present, to minimize confusion. --CircuitCraft (talk) 01:54, 15 October 2023 (UTC)

I'm with Caliburn (talk) on this one.

The current convention is that when we link to a definition or a result, we do not link the individual subdefinition or proof unless either there is a circularity or there is an equivalence proof going on or something. I will leave it up to someone else to craft a template for it.--prime mover (talk) 08:04, 15 October 2023 (UTC)

Archimedes

There is a famous theorem ascribed to Archimedes called Archimedes' Theorem of the Broken Chord from his Book of Circles. That book is lost, but the topic was later written on extensively by Al Biruni in his Book on the Derivation of Chords in a Circle. I cannot find a page about it here, but that usually means I just haven't looked in the right place. As I intend to do a lot with this, so I thought I'd ask before I get started. --Telliott99 (talk) 19:02, 18 October 2023 (UTC)

The field is open.

Please feel free to investigate the $\mathsf{Pr} \infty \mathsf{fWiki}$ technique of implementation of historical notes. Much of the above will clearly fall into that category. --prime mover (talk) 06:38, 19 October 2023 (UTC)

Converse Theorems

I'm not clear on how to handle the converse to a theorem that already has a page. Should they just link to each other or both be transcluded from one main page? And if the second, should they be organized as Theorem, Converse, Proof of Theorem, Proof of Converse, or something else? --Telliott99 (talk) 14:44, 26 October 2023 (UTC)

The short answer is: it depends. I can make the case for taking either approach depending on the context of the existing theorem and the actual statement of the converse. I can even envisage a situation where I might do both.

When transcluding a theorem and converse from a main page the preferred approach is exemplified in the Nagata-Smirnov Metrization Theorem.

To provide you with any more help it would be good to know the theorem and its context and the converse. --Leigh.Samphier (talk) 23:11, 27 October 2023 (UTC)

Thank you. I'm getting the idea. I see Menelaus's Theorem as a prototype, in addition to your example. I suppose it wouldn't hurt to create some redirects to help people searching for proofs. --Telliott99 (talk) 00:51, 28 October 2023 (UTC)

There are many examples of the approach taken in Menelaus's Theorem on $\mathsf{Pr} \infty \mathsf{fWiki}$ and many examples of the approach taken in Nagata-Smirnov Metrization Theorem. The approach taken in Menelaus's Theorem can invite a request to restructure the page as per Nagata-Smirnov Metrization Theorem, but not always. The criteria for such a request seems to depend on the complexity and length of the proofs. The approach taken in the Nagata-Smirnov Metrization Theorem has never invited a request to restructure the pages. --Leigh.Samphier (talk) 07:15, 28 October 2023 (UTC)

The first is the pair Opposite Angles of Cyclic Quadrilateral sum to Two Right Angles and Quadrilateral is Cyclic iff Opposite Angles sum to Two Right Angles where I made the mistake of simply citing the first in the proof of the second one. The latter page awaits renaming.

What I would do here is to leave Opposite Angles of Cyclic Quadrilateral sum to Two Right Angles alone as it is looks like this theorem is the historic proof from Euclid and tampering with this may not be appreciated.

Yes, I endorse that. The general approach is not to change existing proofs unless they are genuinely wrong or incomplete or whatever. Proofs which have been published, in particular, are to be left alone. --prime mover (talk) 21:57, 2 November 2023 (UTC)

I would change Quadrilateral is Cyclic iff Opposite Angles sum to Two Right Angles to be an iff statement, put the current proof under a Sufficient Condition heading and under the Necessary Condition add a simple statement that it follows follows from the theorem Opposite Angles of Cyclic Quadrilateral sum to Two Right Angles

No transclusion needed.

An Also see section in Opposite Angles of Cyclic Quadrilateral sum to Two Right Angles with reference to the theorem Quadrilateral is Cyclic iff Opposite Angles sum to Two Right Angles would be appropriate.

Then wait and see what comments from others are received, if any. Hope this makes sense. --Leigh.Samphier (talk) 21:30, 2 November 2023 (UTC)

The other is Thales' Theorem and Thales' Theorem/Converse where there is no link from the first to the second, although there is a link to Category:Thales' Theorem. --Telliott99 (talk) 16:24, 31 October 2023 (UTC)

Given that Thales' Theorem is a named theorem and assuming the theorem attributed to Thales was never an iff statement then I think it would be best to leave it alone.

I would do much the same as I suggested above. I would rename the page Thales' Theorem/Converse so that it was not a subpage of Thales' Theorem, and make it an iff statement; one of the Condition proofs could simply refer to Thales' Theorem. An Also see section in Thales' Theorem could reference the renamed Thales' Theorem/Converse theorem. --Leigh.Samphier (talk) 21:30, 2 November 2023 (UTC)

I've had a think about this.

Clearly there are ancient theorems for which the converse is considerably newer.

Technically, the converse of Thales' Theorem is a different proof from Thales' Theorem, but they are so obviously used with each other's name on them that you have to take one with all.

We have a "Necessary Condition" section and a "Sufficient Condition" section, and refer to it casually without taking the time to work out which direction is being used.

If necessary, add in the historical note "Thales only proved it in one direction, took till (whatever date) for someone to come up with its converse."

Then we wouldn't need to scatter the place with "/Converse", it is clear which is being used when we're using it.

Otherwise it becomes so much clutter. --prime mover (talk) 18:01, 20 November 2023 (UTC)

General philosophy

It seems there are some conflicting goals for the site. You welcome additional proofs for theorems that already have them. On the other hand, you obviously favor sophisticated proofs with a clear path from proof to proof and no room for error.

Undoubtedly, each new proof, including some that may not fit well with the site's existing Definitions, puts stress on the limited resources of administrators. Not to mention the learning curve for newbies.

What I would hope is that when a question admits a proof using only Euclid, then that proof should be welcomed without the addition of extra stuff --- like analytic geometry. It's fine to have a parallel proof of the same theorem. But let corect simple proofs of fundamental theorems remain simple.

If it is necessary to accomodate the limited domain of a simple proof, that can be done. --Telliott99 (talk) 00:41, 4 November 2023 (UTC)

Sorry, what's the problem? I don't understand what you're getting at. --prime mover (talk) 01:44, 4 November 2023 (UTC)

I think I understand what you're trying to say -- you can spend ages working out a "pure" proof in a discipline. I confess I cut a few corners in the Euclidean stuff because the geometric way of proving number-theoretic results (specially integral geometric progressions, the theory of which is as simple as it's beautiful when you don't have the onerous task of Euclidifying it).

Please feel free to point out specific instances of where modern methods have gone stomping over the beauty of an ancient proof. --prime mover (talk) 18:48, 20 November 2023 (UTC)

New maintenance template suggestion

I'm going through the entire site methodically at the moment, as you can tell, filling every single gap I can find.

Every so often I find a "Whoops this has gone badly wrong, we need to do some urgent maintenance on this," sort of thing, often caused by incomplete or unsupported work.

An example is the mess surrounding definition of topological continuity at a point.

Bear with me, this is my latest project to sort out.

Yeah it wasn't as bad as I thought it was, it was just horribly incomplete. It's sort of finished now and if anything looks a bit bland. Such is the nature of continuity. --prime mover (talk) 18:45, 20 November 2023 (UTC)

Be good to have a "urgent work under way" template, the status of which can be assignable.

Anyone want to have a go at that, let them go to it.

We are rocking. --prime mover (talk) 17:56, 20 November 2023 (UTC)