Talk:Main Page/Archive 2

LaTeX is broken again ...
Check out Properties of an Ordered Ring ... --Matt Westwood 06:29, 26 September 2008 (UTC)

On it again, I think it's the same problem. --Joe 10:10, 26 September 2008 (UTC)

Working again! --Joe 13:37, 26 September 2008 (UTC)

Good man ... --Matt Westwood 18:23, 26 September 2008 (UTC)

POTW Suggestions
Anybody have a suggestion for proof of the week? --Joe 19:51, 27 September 2008 (UTC)

Don't pick any of mine, they're well known for being badly flawed. --Matt Westwood 20:13, 27 September 2008 (UTC)

How about the Quadratic Equation? And Matt, considering that you've posted several hundred proofs, it's inevitable that some of them will have errors of varying degrees of seriousness. --cynic 23:30, 27 September 2008 (UTC)

Sounds good! --Joe 23:37, 27 September 2008 (UTC)

On a side note, how do you go about changing the POTW? --cynic 23:43, 27 September 2008 (UTC)

If you edit the main page, then go to the bottom, there is a list of transculded pages and templates. POTW is Potw. --Joe 00:30, 28 September 2008 (UTC)

New users
I was thinking, we should try to write on new users discussion pages welcoming them to ProofWiki, and let them know where they can go to ask questions and that kinda thing. Would you guys (namely Cynic and Matt) be up for that? --Joe 23:46, 8 October 2008 (UTC)

yep, no problem with that ... I see people join but not many seem to contribute. Perhaps encourage people to "submit any old stuff, just to get the info in there, no matter if it's not 100% rigorous, it can always be tidied", sort of thing? Up to you. --Matt Westwood 05:19, 9 October 2008 (UTC)

Great idea, I've started a small section on my page that I can copy to a new users page when they join. Feel free to take that and modify/use. --Joe 11:03, 9 October 2008 (UTC)

Should we interwiki?
Does anybody know how to create interwikis? For example, so that I can link to Knol, MyWikiBiz, and PlanetMath articles by using the forms:

Knol:&hellip;, MyWikiBiz:&hellip;, and &hellip; ? Jon Awbrey 12:30, 9 October 2008 (UTC)

It should be possible to add an interwiki feature, we should probably put it to a vote to see what others think on the matter. I'll put the question up on the main page discussion .--Joe 15:10, 9 October 2008 (UTC)

I've copied this text from the origonal page so we can chat about it here. --Joe 15:18, 9 October 2008 (UTC)

Okay, I finally looked this up. We can interwiki link to certain other wikis by default (wikipedia, mediawiki commons, wikibooks, etc.). Just use Mathematical proof or the like to create Mathematical proof Renaming the links works like normal, so Mathematical Proof creates Mathematical Proof. If we want to add other wikis, you can add them to the interwiki database manually or with an extension (see here and here). However, I think only Joe can do this, since I am under the impression that the interwiki list is on his end somewhere. --Cynic 22:58, 1 November 2008 (UTC)

Column Templates?
Another thing that might be nice to have &mdash; maybe some way to import from Wikipedia? &mdash; is the set of templates for creating evenly spaced columns:, ,. Jon Awbrey 13:04, 9 October 2008 (UTC)

It would be a good idea to implement these ideas here, I'm currently working on other parts of the site, so if someone else would like to set up these templates that would be awesome. --Joe 15:13, 9 October 2008 (UTC)

I confess I'm not a fan of just importing stuff from Wikipedia. If what we're providing is just another Wikipedia clone, then IMO we're not adding much value to the internet. I'd like to think that we're adding something, be it a pithy precis of something that may already exist (which is the direction I like to tend to go), or an expanded explanation of something that may already exist (probably not my bag, man), or something genuinely new that isn't so far netified (the holy grail). Just repeating something that's already out there doesn't stroke any of my erogenous zones, so to speak. What's anyone else think? --Matt Westwood 20:36, 9 October 2008 (UTC)

I agree that we shouldn't copy things, but the idea of column templates is a good idea. If someone where to implement that idea I would be fine with it. So long as they didn't just cut and paste wikipedia code. --Joe 20:41, 9 October 2008 (UTC)

Line Break
So I've figured out what causes the line break before nowiki tags every time a page is edited. It's a glitch in the extension used to suggest categories. If we get rid of this extension then we would have no problems, but would to manually add the categories like this instead:

Note that usually if you would like to link to that category page you would write Category:Proofs What does everyone think on the topic of keeping this extension? --Joe 19:27, 9 October 2008 (UTC)

I vote to just get rid of it. Would probably make it a little more work to add a category (you have to know if the category exists), but probably better in the end. --Joe 19:32, 9 October 2008 (UTC)

Actually, I was pretty used to adding them manually, so it's no nose off my skin to drop the assist. Jon Awbrey 19:34, 9 October 2008 (UTC)

Agreed, none of our category names are so long that it would be especially burdensome. --cynic 19:41, 9 October 2008 (UTC)

Okay, I'll take it out, the help page will need to be updated though to show the new(which is really the old) way. --Joe 19:43, 9 October 2008 (UTC)

Sorry mate, don't like it. I don't mind being in a minority of one, but I'd much prefer to have the automatic helper because I'm an idle sod. I'm happy to be overruled, I know I'm just one guy. --Matt Westwood 20:47, 9 October 2008 (UTC)

I agree that the other way is much easier, but it does cause some problems that I've been trying to fix for some time now. The line break before the nowiki, and when transcluding template pages, how to have it so that the template page is not included in the category(notably the stub, explain, tidy, and proofread templates). At the bottom of the editing page, I've added, so all you have to do is click on them to have them appear in the page code. Hopefully this will make life somewhat easier. --Joe 21:07, 9 October 2008 (UTC)

Yeah okay, guess that works for me. No worries mate. --Matt Westwood 21:31, 9 October 2008 (UTC)

Axioms vs. Rules
JA: I am noticing a problem about the usual distinction between Axioms and Rules of Inference. I have long been interested in systems where that distinction is finessed in various ways, but the fact remains that the distinction is very important in all the more ordinary logical systems. So I'm wondering if maybe we shouldn't have a Category for "Rules" ("Inference Rules" or "Rules of Inference"). Jon Awbrey 18:34, 10 October 2008 (UTC)

My incoherent two-penny-worth (it's been a hard week and my browser crashed just as I was about to post a particularly long entry and I lost the lot, had to do it again so I'm *tired* ...)

I understand that axioms are relative, in that the particular axioms you use depend on the particular field of maths you're undertaking a study of. I also understand that no (or very few) axioms are truly "standalone" in the sense that they can all be proved by more basic axioms in a more fundamental field. Examples being the axioms of number theory: "the natural numbers are well-defined", "addition is commutative" etc. (not documented yet, haven't quite got round to that yet) but those can be proved from more basic axioms rooted in abstract algebra. Those axioms themselves can be deduced from, for example, ZFC or whatever, and even the axioms of propositional logic depend on a "relative" perception of truth; the Law of the Excluded Middle, for example, may or may not hold in certain fields of study. (Apologies, I haven't explained myself very well - and I consider myself a professional communicator!)

Thus it was my suggestion that the "axioms" section be available to put any so-called "axioms" of whatever fields of mathematics we can muster the energy to document, but with the proviso that we can also provide proofs of those axioms from another mathematical field as we progress. (It's early days yet, we've barely scratched the surface of *anything* yet.)

If your particular angle of attack separates the concept of "axioms" from those of "rules", then I see no reason why not to separate "rules" out from "axioms", but I'd be interested in what way the rules of inference are anything but "axiomatic" as the concept of being "something taken as a truth and not needed to be proven" is what I see axioms as being, and if your rules of inference are a basis of where you start from, then they'd seem like axioms to me. --Matt Westwood 21:17, 10 October 2008 (UTC)

JA: Thanks for the extended reply. Life intervenes, as it will, and it may be next week or so before I can assemble a coherent response. Jon Awbrey 18:25, 11 October 2008 (UTC)

Latest Theorems and Internal-Internal Links
How easy would it be to do the following?
 * 1) Add a link to a page which gives not just *all* the latest changes to the wiki, but all the new theorems / definitions / axioms / categories etc., so we could have a front page or something saying: "Recently added: Fermat's Last Theorem ... A Proof of the Riemann Conjecture ... P vs NP ..." or whatever other trivia we've nailed up on the wall.
 * 2) Add a means of linking to other parts of the same page, so you can e.g. label equations as "equation 1", "equation 2" etc. and then be able to say "Substituting for x in equation 1 and subtracting equation 2" etc. without getting bogged down in wordy descriptions or just the vague "From the above ..."

Just thoughts ... BTW there's another POTW contender out there ...--Matt Westwood 18:10, 11 October 2008 (UTC)

I think I know of an extension that will allow us to create a news feed which will have just new pages. I'll try it out and what happens. In terms of the labelling I'm not sure yet, but I'll look into it. Right now your best bet might be to just put a manual label there after an equation, say "(1)", then later on just say, "by equation (1)". Only thing is that there is no linking for that. But I will look into finding something.

In the mean time, any particular POTW candidate in mind?

Yeah, I just put up the notorious Division Theorem. About time. Yep, that's right, I've got as far as elementary number theory. --Matt Westwood 21:51, 11 October 2008 (UTC)

I have the extension working that will tell us what are the newest proofs. Check the sandbox. Where one the main page should we put this list? --Joe 13:29, 12 October 2008 (UTC)

Nice one! How about the empty space in the community bulletin board? --Matt Westwood 14:16, 12 October 2008 (UTC)

Awesome, good thinking! --Joe 14:22, 12 October 2008 (UTC)

People
From some of the postings put up by Jon Awbrey I notice there's links to people, notably Charles Sanders Peirce. Seems like there's a case for including a list of mathematicians. What does anyone think about expanding PW to include such a category, or is it outside of the remit of this site? What we don't want to do is just haul in reams of undigested text copied in from somewhere else - I envisage a few lines only. What's anyone think? --Matt Westwood 05:28, 13 October 2008 (UTC)

I think that's getting a little far away from proofs. I suggest we just link to the wikipedia articles, ideally through the interwiki links people have been talking about, but if not, then just with standard style links. That avoids the cut and paste approach, but still lets people see what these mathematicians have contibuted. --cynic 15:13, 13 October 2008 (UTC)

What if we create a page in the ProofWiki namespace, say Mathematicians Have a giant table of mathematicians, listing their name, years alive, major area of study, and then a list of their theorems. Or something along those lines. I think a table would be good, since there are ways to set them up so that they can be sorted.

If not that way, then maybe just have a new section for each mathematician, and use the same information. I'd like to be kinda cautious though in terms of having too much information. I think we'd want to focus more on what they had proved, and say little about their personal biography. Thoughts? --Joe 19:06, 13 October 2008 (UTC)

That's exactly what I was thinking. Example:

Lagrange, Joseph Louis (1736 -- 1813)

Author of "R\'eflexions sur la r\'esolution alg\'ebrique des equations" (1770), a complete restudy of all the known methods of solving the cubic and quartic equations.

Proposed a prime number as the universally adopted number base. Thus every systematic fraction would be reducible and represent the number in a unique way.

Established some very general theorems on whether a number if prime from examining its digits.

Tried in vain to prove Fermat's Last Theorem.

One of the few exceptions of his time who was doubtful that a polynomial equation of degree greater than four was capable of a format solution by means of radicals.

Gave an insufficient proof of the Fundamental Theorem of Algebra.

Proved Wilson's Theorem, i.e. that $$p$$ is prime if and only if $$p$$ divides $$\left({p - 1}\right)! + 1$$.

Introduced two fundamental theorems:


 * 1) A congruence of degree $$n$$ can have at most $$n$$ distinct roots.
 * 2) If a polynomial of degree $$n$$ is divisible by $$p$$ for more than $$n$$ non-congruent values of $$x$$, then it is divisible by $$p$$ for any value of $$x$$.

He was led from this to discover a remarkable relation between Fermat's Little Theorem and Wilson's Theorem.

... etc. --Matt Westwood 19:44, 13 October 2008 (UTC)

Sounds like a plan, make sure you link to the proofs, at least those that we have. I still think we should link to Wikipedia for a bit of biography for those that want information. --cynic 20:28, 13 October 2008 (UTC)

Agree on both points. --Matt Westwood 21:10, 13 October 2008 (UTC)

I created a mathematicians page and mathematician template to use with it. It still needs to be modified and touched up a bit, but it's an okay start. What do you think of the approach?

Not sure about the table approach. Maybe it'll grow on me. I'd rather have been able to create a page linked to from the page where the appropriate theorem was proved. --Matt Westwood 05:29, 16 October 2008 (UTC)

Doesn't really bother me which way we go with the page. The table is nice because it can easily be sorted. It would also be nice to be able to link to the person, i.e. Have each mathematician as his/her own section, you could link like " Mathematicians ". This would be harder to sort, and possibly may make the page really large, but it would have better functionality for linking.

Then again, we could just create pages, /A,/B,...,/Z (relative to ProofWiki:Mathematicians), in which we could separate mathematicians. So the general page size would be smaller and easier to organize. Then each of the 26 subpages would easily be transcluded into the main page.

Thoughts/Suggestions?? --Joe 03:43, 18 October 2008 (UTC)

Deleting pages
I think we should try to keep pages whose names are not capitalized. I think the page should be redirected to a better name, but still keep the old page. It doesn't effect the proof counts and helps with links that are already out there on the www. This will help to avoid broken links. --Joe 15:22, 1 November 2008 (UTC)

I looked at wikipdia's manual of style (| see here) and it says that it will redirect on search to a page where each word in the title has the first letter capitalized or where the title is not capitalized at all after the first letter. Wikipedia suggests creating a page with just the first letter capitalized which redirects to the correct page. This won't help with direct links, but I don't think there are probably that many out there that it would mess with. --cynic 16:28, 1 November 2008 (UTC)

I think as long as we keeping both would be best. Since if someone has it bookmarked then if they try to go to it they will still be able to and wont' get a blank page. --Joe 18:07, 1 November 2008 (UTC)

Hadn't thought of the bookmarking issue. Will bear that in mind. Having said that, I went and deleted a Talk redirect earlier (on the grounds that it was less likely for talk pages to be linked, this seems reasonable). --Matt Westwood 22:27, 1 November 2008 (UTC)

I don't really think it would hurt to keep the redirects. As long as they're not categorized, it won't confuse people, and it will help for finding pages and keeping bookmarks functional. Unless of course it makes the site slower/more expensive to host. --cynic 22:43, 1 November 2008 (UTC)

Should be no problem for the server. I think that if a talk page exists it should be redirected also. Since it is related to the material for that particular page. --Joe 23:00, 1 November 2008 (UTC)

Algebra Categories
What does everyone think on moving the "Abstract Algebra" category to be strictly inside the "Algebra" category? I think it will make for better organization, since we will have both "Abstract Algebra" and "Linear Algebra" inside the "Algebra" category. --Joe 01:56, 6 November 2008 (UTC)

Sounds like a good plan. We don't want the categories to get to convoluted and un-navigable. --Cynic 02:58, 6 November 2008 (UTC)

A fine plan. --Matt Westwood 07:27, 6 November 2008 (UTC)

Standard texts lacking something
Anyone encountered stuff in standard textbooks that (if not wrong) don't tell the whole story? Produce weaker results than they could? Inaccurate examples? Pointless digression on subjects that are swallowed whole and shat out by mega theorems? We need to know where the lightweights are. We are going to be the definitive everything-that-is. Question unmercifully. Be prepared to defend your theses and theorems against the most acute deconstructions the universe has ever seen. Demand the impossible. Dream your destiny. Drink too much on a Friday night after performing Bob Dylan songs to a rapturous audience and post a pointless posting on ProofWiki. Enlighten the world with a mathematical breakthrough and defiantly name it after yourself. Mathematics is war and peace and violence and calm and brilliance and stupidity all at the same time. Go mad and be proud of it.--Matt Westwood 23:06, 7 November 2008 (UTC)

Motion to add this to About due to its awesomeness. --Cynic 01:23, 8 November 2008 (UTC)

(small voice) o dear did I really write that last night?--Matt Westwood 06:24, 8 November 2008 (UTC)

Missing definitions
The main page says there's 406 definitions. But the Definitions page lists only 398. There's obviously some uncategorized defs out there somewhere. Trouble is, if you search for "Uncategorized pages" from the "Special pages" page, it doesn't return any.

I know there's some out there, I found one earlier (Congruence Modulo m) which some silly dick forgot to add to the definitions. There's 8 more of these pages but I don't know how to find them. --Matt Westwood 22:33, 8 November 2008 (UTC)

I'll take a look and see if I can find them. I was working on a bot that could do this automatically, but it kinda got moved to the back burner. Maybe I'll see if I can get that up and running. --Joe

has all the pages in the definitions namespace. I've checked through everything starting with a, b, and c against, and have yet to find anything. I'll finish later (probably tonight) if no one else does first. --Cynic 22:58, 8 November 2008 (UTC)

I found all but one of the missing definitions :( The number of Definitions includes redirects, since they are in the same namespace. I am not quite sure Definition:N k really should exist since it links to Symbols:N. --Cynic 02:50, 9 November 2008 (UTC)

That explains it then. (Sorry I've missed out on discussing this further, my service provider went down soon after typing the original posting for this and it's only just come up again.)

I don't think we need to include the redirects in the dictionary, it just clutters it up. We could delete Definition:N k and I don't think anyone would mind. As for the 2 definitions for Sylow p-Subgroups we don't need them both in the dictionary. Thoughts? --Matt Westwood 10:15, 9 November 2008 (UTC)

Statistics
Special:Statistics Has a bunch of cool information. 0.999...=1 and the main page both have over 27,000 page views. --Cynic 02:50, 9 November 2008 (UTC)

Interesting. 0.999...=1 appears to be the most provocative statement you can make to a non-mathematician (and even many aspiring mathematicians) as it is probably the most accessible route to encountering the concept of infinity. I've been a spectator in many arguments on facebook and other places as to the relevance and meaning of this concept to "real life" and it all boils down to whether one allows oneself to be persuaded to accept the very notion of "going on for ever". --Matt Westwood 10:18, 9 November 2008 (UTC)

New Extension!
I wrote an extension that can search for definitions that are not in a category (It's a slight modification of the ones used for uncategorized images, categories and templates). It's a special page called Special:Uncategorizeddefinitions. This will make tracking down categorized definitions super easy! It's neat the bottom on Special:SpecialPages. I still have some modifications left to do on it, but nothing related to its functionality, just stuff to make it easier to update on the server. --Joe 20:30, 11 November 2008 (UTC)

Units and Measurement
Now we're in danger of breaking into the muddy waters of applied mathematics (we're discussing measurement of angles already), I wonder whether it might be a good idea to add another category: "Units".

Having done that, it might also be a good idea to define a "house style" for units, e.g. $$\pi \mbox { rad}$$ for "pi radians" - currently we're just writing the radians symbol as "rad" (no math styling) or rad. What does anyone think? --Matt Westwood 11:52, 15 November 2008 (UTC)

I think we should definitely use some sort of styling. Perhaps we need something like "ProofWiki:ProofStandards", where we can list our general conventions for things. --Joe 15:26, 15 November 2008 (UTC)

I'm inclined to just have a page, since we already have a lot of namespaces. As for radians, I realized that doing using rad outside of the latex adds a lot of work and doesn't look that good, so I took out the ones I saw. In fact, anything other than rad inside the latex or nothing will make things messier, I would probably leave it without units unless there is possibility of confusion. --Cynic 15:34, 15 November 2008 (UTC)

Sticking units in an mbox might be the most expedient way to go. Then they appear in non-italic mode and you can stick a space in front without trouble, and it's also obvious that they're part of the mathematical expression. And it's straightforward and doesn't take much work. An alternative is using tt which makes more it obvious that they're units, but may be more fiddly to insert into a mathematical expression. --Matt Westwood 16:24, 15 November 2008 (UTC)

Yeah, if you use tt, it seems like you have to use it ouside the math braces ($$1 rad$$). That's fine, except in fractions, where if you wanted, say, 5 meters over 2 seconds, which wouldn't be doable (I think). --Cynic 17:20, 15 November 2008 (UTC)

Definitions
Should we create pages like Definition:Radius of Circle which would just redirect to Definition:Circle in case people search for radius or the like? --Cynic 17:20, 15 November 2008 (UTC)

I was pondering the compromise between having an unwieldy definitions list and making the definitions more usable and inclusive. Actually, thinking about it, it looks like it may be a good idea to have "radius" and "diameter" and so on as extra pages with redirects. After all, redirects don't actually appear in the definitions list so it looks like a good plan to me. --Matt Westwood 17:30, 15 November 2008 (UTC)

Potw Suggestion?
Anyone have a suggestion for proof of the week? --Joe 05:17, 23 November 2008 (UTC)

First Sylow Theorem? --Matt Westwood 16:10, 23 November 2008 (UTC)

sounds good --Joe 16:26, 23 November 2008 (UTC)

Stubs
We now have 223 stub articles. I think we should probably go through and try to cut that number down. I don't know what Matt's plan for them was, but I feel that it sort of defeats the point of rigorously proving everything in terms of what has come before to have things relying on unproved theorems. --Cynic 17:19, 23 November 2008 (UTC)

Yeah I know, should be done ... it's either things which are easy but tedious, or tricky and, er, ahem, beyond me ... the plan was to build up to a few Named Proofs as soon as possible without getting too bogged down in detail, but ...

What I'm working towards now is (a) galois theory and (b) axiomatic definition of the complex field but I'm approaching out-of-my-depth and I need to go and do some more study.

Feel free to tackle any of the stubs yourselves, I'm planning on getting back to them once the basic framework is in place, but I won't complain if someone gets there first. --Matt Westwood 19:54, 23 November 2008 (UTC)

... got it down to 207 by shortcuts and general can't-be-arsedness. --Matt Westwood 23:46, 29 November 2008 (UTC)