Talk:Main Page

New $\LaTeX$ macros for your convenience and our internal consistency
There are a number of new $\LaTeX$ macros which have been developed recently as a result of a lot of discussion some time back which never ended up happening at the time.

They can be found on the page Symbols:LaTeX Commands/ProofWiki Specific, transcluded here:

Others may happen as and when I think of them. --prime mover (talk) 03:48, 25 August 2018 (EDT)


 * This is awesome! Thanks!! — Timwi (talk) 19:27, 27 August 2018 (EDT)

Public outreach
I have found on this site that a certain user was motivated to set up a blog about this site. I know how the story ended, and that setting up a blog was denied. I wonder, to what extent a no-go for the blog was given due to special circumstances? I understand that this additional task requires extra time, while a decentralized option would slow down the process due to opinion incompatibility. I myself would rather work on maths material rather than encourage discussions on a social platform. However, to what extent can one's contribution here be advertised elsewhere, barring appropriate disclaimers? --Julius (talk) 18:59, 9 May 2020 (EDT)


 * Which user was that? --prime mover (talk) 01:21, 10 May 2020 (EDT)


 * Thinking further on this, discussions on a social platform should not be a bad thing. If there's something wrong with the site, that's how we'd find out. We have a poor reputation everywhere (which is obviously understandable), and it would give would-be contributors the chance to rant about how bad we are.


 * Though I seem to recall you taking some issue with StackExchange, is frequently mentioned there and got quite a positive review when users were asked about its reliability. Not to mention the fact that it is usually quite high up in google searches. I think this website is much better rated than you realise - though very few of these viewers go on to regularly contribute. It's expected that the majority of viewers will just find what they're looking for, and leave, (as is the case with Wikipedia) but it'd be useful to find out if there's any specific reasons people pass on contributing. Caliburn (talk) 09:07, 10 May 2020 (EDT)


 * Ouch. Yes, I've been looking at, and it's seriously embarrassing. If only the people who have found all these mistakes had told us about them. This is appalling. --prime mover (talk) 09:28, 10 May 2020 (EDT)


 * Here's an example:


 * Wow I do not like the way those statements are worded at all. I also think it is a grave mistake to package the statement that ∅,S∈τ with empty unions and intersections. – Cameron Williams May 5 at 12:23
 * @CameronWilliams: I agree it's not pretty (in fact, the whole concept of ProofWiki is not very pretty at all). But logically it's correct. – Lee Mosher May 5 at 12:32
 * @LeeMosher 100% agreed for sure. I've had my issues with ProofWiki in the past but this one blows those out of the water for me. Pedagogically this drives me up the wall haha. – Cameron Williams May 5 at 12:40


 * which says it all, really. Basically, then, is rubbish. --prime mover (talk) 09:51, 10 May 2020 (EDT)


 * There are only a few hundred results down that link. Let's say that each of them involves 10 distinct people (which is very generous). Assuming all of them have problems with this site, this would sum up to a few thousand negative comments over several years. Now based on Alexa ranking we have roughly 6k-10k visitors per day. So, we are drawing conclusions from a severely misrepresented sample. Instead, we can turn this into a constructive thing. Once in a while scan the field, look for a misunderstanding, if possible, fix it, and report it there. This way the question is addressed, and people notice that feedback works. As for others who do not like our style - this is not a theorem beauty contest, and they are welcome to look elsewhere. 6k per day is a good achievement, especially for such dry material.--Julius (talk) 11:19, 10 May 2020 (EDT)


 * I tried to get involved with StackExchange once. You can't actually contribute to a thread unless you have earned so-much reputation. To do this you have to ask questions. So I tried that. I posed up a question, had no replies, no messages, nothing. When I went to take a look at it a week or two later, I found someone had deleted it. At that point I decided life was too short to waste time on it. If it were only a little more accessible, then maybe it would be worth doing, but I'm obviously not of a high enough mathematical level for it. So I can fix stuff, but it will be up to someone else to post up a reply to SpackExchange. --prime mover (talk) 11:40, 10 May 2020 (EDT)


 * Note we already have a facebook group, as well as a twitter account. Nobody really seems to use them much. --prime mover (talk) 04:19, 10 May 2020 (EDT)


 * If someone (admin or someone who could be made an admin) is more social media savvy than me, they're welcome to post on our social media accounts. --Joe (talk) 11:44, 11 May 2020 (EDT)


 * I had this user in mind.


 * He had a lot of "good ideas" including incorporating this site into another, affiliating us with a university, selling us to a company, completely changing our presentational style and philosophy, and so on. We eventually had to disallow his continued contribution, as (among other things) he would not stop taking on colossal restructuring tasks and not following through, leaving the site in an inconsistent state, requiring a large amount of work of other people to put it right.


 * As for the comment about the blog, as I say, I started writing a blog but was told I was not allowed to, so I stopped. Don't know what the problem is myself, but I like my internet access and I didn't want it to stop just because of the whim of some fascist. --prime mover (talk) 05:52, 10 May 2020 (EDT)


 * Who was this down to? Sounds like an extremely counterintuitive move. This is a public wiki, we're not exactly sworn to secrecy. Caliburn (talk) 09:16, 10 May 2020 (EDT)


 * Someone on Quora, I believe. Something about copyright and attribution and so on, and the fines that can be imposed upon violators. --prime mover (talk) 09:28, 10 May 2020 (EDT)


 * It sounds weird that someone had a problem with a blog and not with the site itself. I mean, this site generates small income to keep the server running. Maybe low traffic actually helps us to avoid big fish. Either way, what can one man do?--Julius (talk) 11:19, 10 May 2020 (EDT)


 * I don't follow the issue with the blog. Who's not allowing who to have a blog? From ProofWiki's prospective a blog is fine so long as our license is not violated. I'm also not against starting/hosing our own blog, but we'd need to have people actually want to contribute to it. --Joe (talk) 11:44, 11 May 2020 (EDT)


 * As I say, I did start a blog at one point as a subpage of my user page but got told to take it down, so I did. That would have been back in, I dunno, 2012 or 2013 or something. It might have been because it was substandard or something. I'll see if I can reinstate it if you like. Don't know how it would increase site visibility though. --prime mover (talk) 12:04, 11 May 2020 (EDT)


 * I found your old blog and tried to pick though past discussions. I think this was around the time we were trying to figure out our format. Also maybe not all your blog posts were purely mathematical in nature :). Also, to be honest, that was a long time ago. Feel free to blog about whatever (within reason obviously) you want on your blog subpage. With respect to the above mentioned user. I suspect the primary issue (though I don't remember) was that we often get new people who don't stay around who want to totally rearrange everything. At this point in time I'd be happy to start of official blog assuming: primve mover and Lord_Farin agree, and we have someone(s) willing to write. --Joe (talk) 12:44, 11 May 2020 (EDT)


 * If anyone wants to start a blog, let them feel free, if they have something clever and interesting to write on a regular basis. I've looked back at my own effort and I can't see anything there particularly worth enshrining or even preserving, but if someone feels like rattling off a regular essay I'm not stopping them. --prime mover (talk) 17:59, 11 May 2020 (EDT)


 * I'm a bit confused too - ProofWiki's license is incredibly flexible (basically, do whatever you want as long as you attribute it and release it under the same license) so I can't see how a problem with licensing or the like would arise. I'd be happy to contribute. Caliburn (talk) 11:47, 11 May 2020 (EDT)


 * I believe that at the moment people simply cannot distinguish us from the noise. Those at higher echelon, like PhD students simply cannot find their stuff here, while undergrads often are not aware of our existence, or they consider us to be yet another personal wiki hobby. I am a PhD student in theoretical physics, and none of my colleagues have heard of this site. I even had to stress that we are not a branch of Wikipedia.


 * Considering how linear maths is (everything you learn builds upon what you've learnt before), to start adding in substantial amounts of research material you'd need a good amount of graduate material, for which you'd need a good amount of undergraduate material. Due to our lack of contributors, sometimes these foundations just don't exist and indeed users with the knowledge to add such content are scarce. You mention theoretical physics, but even our coverages of basic classical mechanics and electromagnetism are microscopic, so it'd take a lot of time and many dedicated contributors to build it up enough to have PhD-level content on there. Most of our problems boil down to a lack of contributors, for which I agree outreach can only be a good thing. Caliburn (talk) 09:07, 10 May 2020 (EDT)


 * I've started on both E-M and QM but the work is slow because that's what I'm like. I get to a concept that I think: that's too much like hard work I'm going to do something easier, and I go and do something else. Takes a while to get back to it. --prime mover (talk) 09:10, 10 May 2020 (EDT)


 * Yeah that's fair enough, these things take time and with a lot to do you can easily find yourself skipping between things. It's not really anything we're doing wrong (that I know of) - it's just a lack of active contributors. Caliburn (talk) 09:16, 10 May 2020 (EDT)


 * Then I also had a short conversation on Reddit. There were few responses, most of them telling "good job", and one with more basic comments about the website (e.g. what does $\leadsto$ mean, and why we don't have a link to a dictionary of such symbols on the main page). I think that regularly throwing out something on FB or TW, should it be more serious or just a shared meme, or referring to us in YouTube comment section in a reasonable way would show the world that we are alive (20000 theorems don't matter if nobody knows, that there are 20000 theorems).


 * I can't comprehend the mindset that claims (in the context it is seen) that they don't know what $\leadsto$ means. I mean, we make a pretty good job of declaring our definitions as we use them (this being one of the main bones of contention), but it becomes a bit much when our usefulness is seen to be limited because there are people who not only don't know, but can't even work out, what this most basic bit of mathematical punctuation means.


 * The reason why we don't have a link to a dictionary of such symbols on the main page is because we honestly never dreamed that mathematicians would need it. Although we say we include links to definitions of all terms used on every page, we never went to the detail of defining every single mathematical symbol used, on the grounds that some stuff we think everybody knows. But if it is indeed the case that mathematicians do need such an aid to understanding, then I expect it will fall to someone to have to take on this reponsibility. --prime mover (talk) 06:01, 10 May 2020 (EDT)


 * Also, there are more statistics-based tools to gauge this, like alexa ranking. Even on https://www.alexa.com/siteinfo/proofwiki.org I can see which websites we are giving up to, which keywords are missing here, and what traffic comes from various countries. Working on these numbers would improve popularity in an indirect way. --Julius (talk) 05:18, 10 May 2020 (EDT)


 * I'll leave that up to someone else, because, seriously, I don't care in the tiniest slightest. It is acknowledged that this site is of limited worth, and the only thing that will improve it is a complete redesign from the ground up (or even, as many commentators say, deleting the thing and completely removing it from the web), but for those of us with limited opportunity to interact with the outside world, it gives us something to do to fill our twilight years. --prime mover (talk) 06:01, 10 May 2020 (EDT)

Sorry I didn't respond earlier to this discussion, I completely missed it. If someone has ideas with what we should doing better for community outreach and wants to help, please let me know. --Joe (talk) 11:46, 11 May 2020 (EDT)


 * I made a Reddit community. If any of you use it, I can make you a moderator. It will take some time before it starts looking solid. In the nearest future I am planning to design it according to some simplified version of more established math communities. As for Twitter, I saw that Wikipedia simply puts fun facts on theirs. Not sure how to make this work for math. Since messages there are supposed to be brief, I guess a more humorous approach would work. Otherwise, I believe that we simply have to visit various forums and YouTube comment sections and refer to this site whenever there is a genuine relevance. I believe that since we would start this from scratch, we should simply look for channels used by more authoritative sites.--Julius (talk) 18:21, 11 May 2020 (EDT)


 * Good idea! Will be lurking on there. (supposed I should reduce my footprint so I'll be commenting under /u/PWCaliburn) Caliburn (talk) 18:34, 11 May 2020 (EDT)


 * I lurk on Reddit as /u/joejoebob —Joe (talk) 20:14, 12 May 2020 (EDT)

A bit late to the party, but please know I've caught up with all the above and I'm totally fine with any blog/Reddit/YT/FB presence as long as it is made in good faith. &mdash; Lord_Farin (talk) 13:47, 24 May 2020 (EDT)

Stackexchange
I've now been through the list of issues raised at Stackexchange. (Or at least, most of them, there was a lot.) I've fixed the obvious mistakes, but I'm not sure how to handle all of them. But issues fixed or not, there's no denying that we are very much considered substandard, to such an extent that it is believed we should not exist.

Is this the point where we decide to wrap it up and admit there's not much point trying to keep this site going? --prime mover (talk) 01:11, 11 May 2020 (EDT)


 * No, it isn't. For each successful fix the complaint is resolved and the old negative conclusion becomes irrelevant. I also find any constructive comment (or the link thereof) from elsewhere copied on the respective discussion page useful. Then everybody can see what is there to be done. --Julius (talk) 02:26, 11 May 2020 (EDT)


 * I think we can address issues that make sense to us. I'm sure we'll never be able to make everyone happy. --Joe (talk) 11:47, 11 May 2020 (EDT)


 * SE is also a place where everyone can disagree with whatever they want because their own style is supposedly superior. But without the responsibility of actually making something worthwhile that could be argued about. In that sense high-level criticisms are often not much more than a matter of taste. &mdash; Lord_Farin (talk) 13:47, 24 May 2020 (EDT)

Terminology: Real Number Line or Real Number Space?
For reasons of clarity of understanding, I am trying to emphasise the difference in concept between:
 * the real number line, which is the set of real numbers under the usual ordering

and:
 * Real Number Line is Metric Space, where $\R$ has the Euclidean metric imposed on it (which I never got round to defining as a definition page)

and:
 * the real number space, which is the topological space induced by the Euclidean metric $\map {d_2} {x, y} := \sqrt {x^2 + y^2}$ on the real number line.

I'm at a loss as to what to call these things. I have found that at one point I started to use real number space without any authoritative backup, and it can of course be confused with for example $\struct {\R^n, \d_2}$.

There's a good reason for separating them out: because for example:
 * you can define a metric space with the real number line with different metrics on than just the Euclidean one

and
 * you can define a topological space with the real number line without reference to a metric at all (for example, the real number line under the discrete metric, as is done for example in Double Pointed Discrete Real Number Space is not Lindelöf‎.

I want to refactor this whole area so as to be consistent, and merge a number of pages which are the same, for example Definition:Real Number Space and Definition:Euclidean Space/Euclidean Topology/Real Number Line but I need advice as to what to name these things for maximum clarity and minimum unwieldiness.

Advice? --prime mover (talk) 06:05, 31 May 2020 (EDT)


 * Further thoughts: Definition:Real Number Line, Definition:Real Number Line (Metric Space), Definition:Real Number Line (Topological Space) and similar for the plane and $3$-space? --prime mover (talk) 07:25, 31 May 2020 (EDT)


 * Actually I'm not sure about Definition:Real Number Line (Topological Space) because that doesn't leave it open for different topologies to be applied.


 * Could also go with Definition:Real Number Line (Euclidean Space) but that doesn't distinguish between that and the RNL as a Metric Space.


 * Yes I know they are the same thing, but as I say, I want to leave it open for different metrics and different topologies, and lumping the real number line, the RNL as a metric space under the Euclidean metric and the RNL under the topology induced by the Euclidean metric leaves us in danger of not being able to establish the specific chain of proofs which demonstrates rigorously that they *are* all the same thing. We also want to make sure we can provide the framework to equally rigorously prove that an "open set" in the context of a topological space is an "open set" in the context of a metric space is a union of "open intervals" in the real number line. Yes I know we've already got that chain of proofs in place, the point is the framework into which it is included is unstructured and duplicated. Similar applies to compactness. --prime mover (talk) 08:08, 31 May 2020 (EDT)


 * My suggestions would be Definition:Real Number Line, Definition:Real Number Line (Euclidean Metric) or Definition:Real Number Line (Euclidean Metric Space), Definition:Real Number Line (Euclidean Topology) or Definition:Real Number Line (Euclidean Topological Space) --Leigh.Samphier (talk) 10:04, 31 May 2020 (EDT)


 * Another thought: Definition:Real Number Line, Definition:Real Euclidean Line, Definition:Real Euclidean Topological Line --Leigh.Samphier (talk) 10:17, 31 May 2020 (EDT)


 * Or Definition:Real Number Line under Euclidean Metric, Definition:Real Number Line under Euclidean Topology -- but I wonder what the correct preposition or conjunction ought to be: "under", "with", "endowed with", "bearing", something along those lines, maybe. The "main" page perhaps ought to be Definition:Euclidean Space/Euclidean Topology/Real Number Line with a redirect, and similarly for the metric space. Then the 2d and 3d versions can be implemented similarly. --prime mover (talk) 15:28, 31 May 2020 (EDT)


 * In differential geometry, one usually endows or equips a manifold with a metric. In colloquialisms "with" is used very often, i.e. "A manifold together with a Riemannian metric is called a Riemannian manifold". I cannot remember anyone use "under" or "bearing".--Julius (talk) 17:42, 31 May 2020 (EDT)


 * "with" works for me then. When I'm less tired I'll go with that. --prime mover (talk) 18:22, 31 May 2020 (EDT)


 * I think "with" is standard. Its typically "real numbers with usual topology". --Leigh.Samphier (talk) 20:07, 31 May 2020 (EDT)


 * Another concern I have is with the term "Euclidean Space" which currently refers to the "Metric Space". The term "Euclidean space" refers to the fact that it satisfies the axioms of "Euclidean Geometry" which to me suggests that is should at least refer to the "Inner Product space". Subtly different things. We should think about how to distinguish the "metric space", the "normed vector space", the "inner product space" and the "Hilbert space" --Leigh.Samphier (talk) 20:07, 31 May 2020 (EDT)


 * Okay scratch "Euclidean Space", replace it whenever used with "Euclidean Metric" and "Euclidean Topology" or "Euclidean Norm" etc. unless used to encompass all concepts. OTOH there's already a refactor request for Definition:Euclidean Space, which should be either a (better crafted) top-level parent page for a complicated system of transclusion (hard work) or a disambiguation page (less optimal). --prime mover (talk) 01:25, 1 June 2020 (EDT)

So far so good. We now have Category:Real Number Line with Euclidean Metric and Category:Real Number Line with Euclidean Topology, and all references to "Real Number Space" in the context of the real number line have been removed.

I suppose the next exercise would be to do the same for "real number plane", although I can see that Definition:Rational Number Space is also crying out for the same treatment.

"Real number plane" has the added complication that there is more than one way to structure such a plane, standard Cartesian coordinates, oblique Cartesian coordinates, polar coordinates ... so I will also have to take into account Definition:Cartesian Coordinate Plane and all subsequent entities. Not today, I need a break. --prime mover (talk) 09:08, 1 June 2020 (EDT)

Linking books to pages
Is it allowed to endow chapters in the book section with a link to a page, say, corresponding to the first entry from the given chapter? This would make the navigation easier.--Julius (talk) 15:45, 25 June 2020 (EDT)