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:

A thing or two
I thought I'd dump some ideas here since my activity may wane a bit over the next few months and I might as well say these things while they're fresh. (then I'll have exams late April-mid June, after that I'll resume to current levels with another semester's knowledge) First I wanted to say that I'm planning on maintaining the page User:Caliburn/Job List as well as I can. The intention is for new contributors to be able to come along and find what still needs working on and gaps that people may not have noticed. Also a handy list for myself so I know what still needs to be done. People are free to add to the list or take off stuff they've completed. I am not sure where to put it for maximum visibility, but I'll display it on my userpage and post it here.


 * There are already a number of contributors who have their own way of managing their to-do lists, but a global one may have a use. I say: go for it, but beware that it's just another thing that needs maintenance. There are currently few enough active contributors that this could be extremely useful, especially if they are in the same approximate areas of activity. I can see the points of overlap between measure theory, metric spaces, topology, normed spaces, prob theory, matroid theory etc. etc. where this would be worth applying, in particular. --prime mover (talk) 07:19, 4 January 2022 (UTC)


 * It seems that I am going to tackle some of your topics simply by following Sasane. Namely, I am almost done with distributions. One thing that has been nagging me is the definition of Dirac delta through limits of various functions. This was one of the main reasons why I decided to work on these topics. However, Sasane does not cover this at all. Hence, after I am done with a couple of exercises, I will briefly switch to a different source (not sure which one) to establish how definitions through limits work out in the distributional sense. Then I will work a bit on the Lebesgue integral and resume where I left off (this can be seen by inspecting hyperlinks in Sasane's book page). Most of the work will be less abstract involving normed vector spaces.--Julius (talk) 12:32, 4 January 2022 (UTC)


 * I was looking under Category:Distributions so I didn't realise how much you have got through, fair enough. (I think any category containing results about distributions should be a subcategory of this category) Distributions are a huge topic that have only just started getting worked on, so it is probably worth noting as an area to expand anyway. If you need ideas on sources for more work on distributions, the module at Warwick on distributions recommends Friedlander & Joshi's Introduction to the Theory of Distributions, among some Fourier analysis texts by Duoandikoetxea and also by Grafakos. I haven't looked at these myself yet, learning more about distributions is on my "to-do" list for the summer. Wikipedia's page on distributional limits gives an example of a sequence of functions converging in the distributional sense to $\pi \delta_0$ (not sure if it's the canonical one, if there is one) so that might also be a good jumping off point. Looking forward to seeing how it all turns out. Caliburn (talk) 15:50, 4 January 2022 (UTC)

Second I'm wondering how theorems could be catalogued so that they don't get lost. While having a descriptive name for each theorem makes the most sense, it can make navigation difficult since some pages have to be given unintuitive names, some more so than others. (sometimes leading to mistakenly duplicate pages) I like pages like Properties of Beta Function for this purpose. I'm wondering whether we could branch this out to have easily navigable collections of other results. No specific format to mind yet. My contribution backlog at the moment is massive, so I doubt I will get to this soon, (especially as it's a significant undertaking) I will return to this idea when it's been whittled down a bit. Caliburn (talk) 00:19, 4 January 2022 (UTC)


 * I too am a fan of the "Properties of ..." sort of page. The archetype is Subset Equivalences, which I have found very useful indeed.


 * While duplicate pages are a problem, it's not a serious one. It happens for minor stepping-stone results when multiple source are being used to flesh out an area -- but when we implement categories more incisively, these duplicates are usually caught. The problem mainly happens when a contributor puts every result in a high-level all-inclusive category called, e.g. "Real Analysis" or "Metric Spaces", then it's easier to miss stuff.


 * Best advice while an area is being fleshed out is: if you see a potential duplication, slap a template in there to flag it up and move on with what you're doing, then after all is in place, take a step back to see whether there is a common thread that would need to be refactored out. --prime mover (talk) 07:19, 4 January 2022 (UTC)


 * I think once measure theory is fleshed out I'll have pages like "Limit Theorems for (Riemann/etc.) Integrals" and "Properties of Measures", etc. As an aside - should we archive a few older discussions here? My browser is starting to lag a bit typing this response. Caliburn (talk) 15:50, 4 January 2022 (UTC)


 * Aside -- job done. Good call. --prime mover (talk) 17:16, 4 January 2022 (UTC)

Slow
I don't want to be irritating, but the site has been extremely slow on and off for the past few days. Could this be looked in to? It is making refactoring very sluggish. Caliburn (talk) 18:44, 18 January 2022 (UTC)


 * Haven't noticed it myself. I do hope I'm not the problem. --prime mover (talk) 20:23, 18 January 2022 (UTC)


 * Doesn't seem like it, happens on and off even if I'm the only one editing. Doesn't seem as bad right now. Caliburn (talk) 19:13, 19 January 2022 (UTC)

Weak convergence
Can we get macros for $\rightharpoonup$ (weak convergence) and $\stackrel \ast \rightharpoonup$ (weak-* convergence)? Caliburn (talk) 13:11, 30 January 2022 (UTC)


 * Yes okay, I'll get to it in a bit. --prime mover (talk) 14:03, 30 January 2022 (UTC)


 * ... all good? --prime mover (talk) 18:19, 30 January 2022 (UTC)


 * Yes that's great cheers Caliburn (talk) 18:24, 30 January 2022 (UTC)

Proofs of unsolved conjectures
Without trying to be rude to certain contributors, I'm wondering if codifying disallowing claimed proofs of famous conjectures (Goldabch's, Collatz, RH, etc.), and otherwise obvious crankery, (eg. the Bibhorr nonsense) is a reasonable step. Obviously we shouldn't discard the possibility of original theorems and proofs, (that being one of our selling points over Wikipedia of course - posting interesting-but-not-particularly-useful toy theorems should be encouraged) but I would draw the line before proofs that would very possibly win the poster a Fields Medal (or at least shoot them into international fame) if correct, on the basis that it almost certainly isn't. If by sheer miracle their proof is correct, they can get it published in a peer-reviewed journal, (I know this all might be harder for "outsiders", but Yitang Zhang managed despite being virtually unknown) claim their $\$1$ million dollar prize/Fields Medal/international infamy, and post it here. Thoughts? Caliburn (talk) 22:18, 31 January 2022 (UTC)


 * A well-crafted and coherently-written page to standards (or at least in literate $\LaTeX$) will always be given greater credence than an ungrammatical and careless page written by someone who does not care enough about the target audience to bother to communicate properly.


 * It is a matter of fact that the more unusual and improbable a claim of success at proving an unattainable, the more bletheringly incoherent and incomprehensible the language it is written in. This is not a matter of fluency in what may not be one's native language, this is either the complete inability to string thoughts together, or the writer's belief that they are so cool and awesome that they can write in their own version of street slang and as a result everyone will bow down in worship of the awesome light, brighter than a thousand suns, that emerges from their nether orifice.


 * Hence I give short shrift to crackpots. Life's too short to bother. --prime mover (talk) 23:43, 31 January 2022 (UTC)


 * We are not a peer-reviewed scientific journal. Even if we know a thing or two about maths, we are far from being competent to say anything solid about your favourite unsolved world-class problem. If anyone has proof, please go through the usual peer-review process, get your prize and recognition, and then we can discuss posting your result here. To my understanding, here we are interested in well-established results with anything we can interpolate in between. As for Bibhorr, I could see a historical reason if this was derived thousands of years ago, but to my knowledge, this is a claim to a revolutionary new result, which is not. It is simply an inspiration derived from approximation of standard trig functions.--Julius (talk) 07:46, 1 February 2022 (UTC)


 * This specific exchange was triggered by a recent posting about Collatz. If the post in question is written using standard mathematical symbols in $\LaTeX$ then maybe we'd have been able to have a stab at poking the necessary holes in it like we did Senojesse some months back. But the symbols used were non-printing and non-displaying and hence of zero value. Seriously, I may be getting old, but I have neither time, headspace nor tolerance. As for the request on my user talk page to discuss it over the phone, there's an orifice for such to be inserted. :-/ --prime mover (talk) 09:07, 1 February 2022 (UTC)