Slashdot Mirror
Should Wikipedia Allow Mathematical Proofs?
Beetle B. writes "An argument has arisen over whether Wikipedia should allow pages that provide proofs for mathematical theorems (such as this one).
On the one hand, Wikipedia is a useful source of information and people can benefit from these proofs. On the other hand, how does one choose which proofs to include and which not to? Should Wikipedia just become a textbook that teaches mathematics? Should it just state the bare results of theorems and not provide proofs (except as external links)? Or should they take an intermediate approach and formulate a criterion for which proofs to include and which to exclude?"
I don't see a problem with it, I just wonder why put the / in the article name the way they do. I understand that its to make a kind of sub page, but why?
Of course they should allow proofs. Proofs are useful and factual information and proofs alone don't really "teach" mathematics are far as I'm concerned. They should take care to properly separate proofs from higher level information, as not everyone is interested in them.
The most simple/efficient etc proof should be inserted, imo.
:p)
Simple should be easy to define, efficient may not. Maybe they should use some kind of voting system (but not like the one slashdot uses for its polls
They're obvious academic knowledge with clear educational merit. Where exactly is the problem?
Dealing with lawyers would be a lot less tedious if they all looked like Casey Novak.
For a website that supposed to be community created, they sure are worried about what should and shouldn't be in it. Why dont the just the community decide through thier actions of what the add?
I find wikipedia useful, and the math is generally well done. The biggest problem is that I hate reading math symbols in anything but latex generated documents.
As I see it, all three are essentially the same but vary in their level of details. Given that wikipedia is electronic, and can essentially (re)represent it's data in various forms, why limit the amount if information present (assuming its factually correct)? Surely the level of detail of an article should be up to the user. Perhaps a better solution in this case would be to include the proofs but make them 'rolled up' by default - IE 'click here for details'. I know 'rolling up' is possible in wikipedia; I've done it on my page there.
As a side note, its worth noting that the article submitter engaged in the discussion about the article for deletion. They voted to delete the article.
Windows in 6 Bytes (IA-32) : 90 90 90 90 CD 19
No one will RTFProof anyway.
I for one fail to see the problem here. For one, proofs help mark vandalism and give instruction by showing how the formula works. Why would you want to remove them? And to whoever wrote this: 1) What are you trying to prove by asking this, and 2) you SERIOUSLY need to get a life...
That's about it ... they must have gotten sick of webcomics.
I don't see why anyone besides the occasional Wikipedia purist of sorts would actually complain about this. It's convenient for proofs to be on there, and it's not like accurate information is degrading Wikipedia's "standards" at all.
To elaborate a little bit, some proofs are more elegant than others. Some require more knowledge than others. You can prove Pythagoras' theorem on two pages using only elementary geometry or in two lines using vectors. Which version you present depends on your audience, but that doesn't change the fact that you should present one. Proofs are useful, they help you understand not only that a theorem is correct but, much more importantly, why it is correct; so why is there even a discussion about whether or not to include proofs? Especially on a system like Wikipedia, where multiple versions of a proof can coexist peacefully (in theory) on a page - it's not like you'd have to choose one over all others (like you might have to, for instance, when teaching a class or giving a talk).
So - what's the problem? Unless it's political, in which case, well, you know, *yawn*.
Speaking as a postgraduate mathematician, it's clear that many people have made an effort with the mathematics articles, but they're almost always waffly. Mathematics is about the beauty of patterns, not a thousand cooks tweaking a proof to highlight their own difficulty or misunderstanding. It might be a good place for a paedagogical commentary on proofs - indeed, unbiased commentary on original research is precisely what an encyclopedia should be. It's not a place to post what is essentially the research itself, and then edit it out of all recognisability.
(Unfortunately, I don't feel Wikipedia comes close to that. But since you're asking...)
Lemme see if I got this right: posting absolute truths on Wikipedia is up for debate?
"There is much pleasure to be gained from useless knowledge." - Bertrand Russell.
yes they should. Wikipedia has always been my source for information, but when i need something in perticular, for example a guide to a method or a procedure, i've always used everything2.com since i have a largere chance of finding it there. I would love for wikipedia to have all the knowledge i need. Plus... wasn't just that their goal anyways?
Pure awesomenes
Wikimedia already has another project for this sort of thing. It's called Wikibooks.
The whole promise of wikipedia is that computers allow us to accumulate an incredible amount of knowledge. There's no need to draw an artificial line and say "no, you can't have this, because, book form encyclopedias don't have it". If volunteers were willing, it ought to have proofs. And, also it would be good if it had experiments in the other sciences as well. It would certainly make discussions over GW and evolution more accessible to more people as well. How does one infer historic atmospheric chemistry? How does one understand the genetics of evolution? Right now, a lot of this stuff is locked up in scientific journals and these are invariably organized more by article. Wikipedia could, hypothetically, allow us to apply a taxonomy to all of human knowledge. Donations welcome.
This is my sig.
As with most things in life the best solution is probably somewhere in the middle. Hundred page proofs are not really suitable for Wikipedia and a complete ban on proofs would leave the site lacking. If it is sensible to include the proof or part of the proof then it should be included.
The maintainers of Wikipedia really needs to ask themselves what they wants it to be. Do they want it to be an encyclopedia or does it want to be the source of all knowledge. Personally I think it should aim to be the best encyclopedia going as I suspect being the one source of all knowledge is probably impossible and there is a danger the real worth of the site will be swamped by too much detail.
Wikipedia should be the starting point of learning not the start, middle and end.
I used to have a better sig but it broke.
It seems that admins are recently too happy with removing information from wiki, than adding it.
Mathematical proofs are as much important and informative as their theorems. The proof allows for better understanding of the theorem, you can see why there are certain assumptions in the theorem and what is broken when these assumptions are not met. For some applications the proof is a blueprint for algorithm to solve problem stated in the theorem.
But I guess that biographies of fictional characters and detailed descriptions of Japanese cartoon episodes have much more important place on wikipedia.
What's the deal with wikipedia and deleting stuff anyway? It is not like this little bit of text is wasting space or something. I would think it would be much better to have too many articles than too little. One of the things that has made wikipedia sucessful is the sheer amount of information there.
They should have links to each mathematical symbol to explain what the symbol means in the current case... Trained Mathematicians are use to seeing this symbols and use them in their current focus. But the symbol can mean different things for different forms of Math. For example Pi in geometry is roughly the number 3.1415926535.... in statistics it is its own function, completely unrelated to the geometry pi.
Mathematicians seem happy to officiate their ideas so only Mathematicians can read them and leave the common man out of the loop, making math look that much harder and scarier. If wikipeadia took an approach of helping people understand the proofs vs. then just giving them but allowing someone to understand it, even on the more basic levels such as clicking on the Uppercase Sigma (looks like a big E) it should bring you to the link on summation.
Math is not actually hard it just has been formalized over thousands of years by Mathematicians to make sure their jobs stay relevant, keep the common man out of the study, and little work has been placed to opening up math for the common folk. Wikipedia has a great opportunity to break down this class structure and allow someone say in high school to lookup a College Level Proof and in time following links get a basic understanding of the proof and able to work it out. But as for the example wikipedia gave as a High School student or a college with a non math focused major it would be literarily all greek to me. And look it up I wouldn't know where to go next... Like knowing the Big E is actually sigma, If I would have guessed I would say it was an Epsilon Shaped like an E Epsilon logical connection huh...
I am actually quite tired of the "Dumbing Down" excuse to fix problems in education that are classically created complex just because some nobles wanted to seem special. Dumbing Down is saying just take this as fact and get the next step. What we can do is open up math so people can understand the details in language they understand or can jump into without having to be formally taught all the prerequisites.
Simplification is not Dumbing Down, but to dumb things down you need to simplify things. The Ven Diagram would be a Big Circle Labeled Simplification the little circle will be labeled Dumbing Down.
If something is so important that you feel the need to post it on the internet... It probably isn't that important.
Mathematical proofs are arguments, not facts. An encyclopedia should list provable facts with references. There are some notable methods of proving something (e.g. proof by induction), but an applied generic proof method or a "handcrafted" proof for a single problem is just an argument and should only be included if it adds insight beyond the proven fact.
Why, oh why, can't some people get that many things, cant, and don't need to be controlled. Indeed, Wikipedia is an example of this. In fact, it exists largely due to its decentralized design. Now people with an agenda want to do the very thing that is most opposed to the open ended system that Wikipedia is. Systems of control, or limits, as we are seeing now, will be the death of Wikipedia, mark my words. I guess, in the end, it comes down to the truth and those who believe they must control it. My guess is that they're afraid to let the people know what they're really doing.
Personally, I feel I should, and must, oppose those who oppose openness.
Maybe someone should start "proofopedia" - an online database of proofs. Is the URL still free? Soemeone register it, quick...
The big thing on Wikipedia right now is marking up articles for not quoting their sources. But for a theorem, the proof is the source. If you don't include the proof, then no one has any way of knowing the validity of your claim.
Also, slight changes in wording can drastically change the content of a theorem. By supplying a proof, it becomes very clear if the theorem has been stated correctly or not.
Isn't the point of wikipedia to let the users decide what to put up? Isn't the whole point to avoid one viewpoint?
Twinstiq, game news
Wikipedia has policies and guidelines for this. Include it if it's notable, and not original research, etc.
Patrick Doyle
I mod down every jackass who puts his moderation policy in his sig. Oh, wait a sec....
Err...what is the argument for _not_ including proofs? I can't come up with any good reason for that...
Please correct me if I got my facts wrong.
I do not understand the problem. A wikiproof site, just like wikiquote, could be a nice solution.
Existing articles are not 'polluted' with proofs and can link to the relevant wikiproof article. The wikiproof site can implement specific features that are usefull for mathematical proofs.
Reemi
If a topic is interesting enough for someone to take the time to research and provide for the site, given that it is factually accurate, why the heck would we limit the boundaries of the knowledge provided?
Wikipedia is all about user-generated content and lack of centralized control. There are certain rules in place to ensure that the site does not fall into anarchy, and those basic rules are enforced by site moderators. But once a central source starts deciding on the content itself, Wikipedia has lost its identity.
While I am sure that it is easy to argue that proofs should be included (I don't really mind either way), as a Wikipedia administrator I know that one of the hardest things to do is to find a source for something, especially something as specific as a proof. I don't mind the extra information that a proof provides, but it is a manhole up from which crackpot theories may crawl, looking more authoritative because they have a mathematical proof which might not even be valid.
The problem is verification, that editors are not violating the policy against original research (another barrier to crackpot theories). The idea of verification in Wikipedia is that if you look something up in Wikipedia, you should be able to find it elsewhere - and Wikipedia should provide a citation of that source to make it easy to check.
As long as they can be cited to some particular source, and don't otherwise disrupt the flow of the articles to which they are added, I think proofs are fine - there's no reason I can think of to exclude them. If they are used randomly or someone makes up their own proof, however, that is unverifiable original research that is much more likely to lead to errors.
I don't want to exclude information - I want the information there to be reliable.
Interesting proof of mathematical progression of cities
mathemacity
Why not choose one proof and show that in Wikipedia. Maybe the shortest or the one that will server the widest audience. Save the rest for one of the Wikibooks on mathematics. A good choice might be The Book of Mathematical Proofs
Mathematical proofs has filled volumes upon volumes of textbooks. How do you decide what to include? How does it not take over? I think links to 3rd party proofs is better. If you have math proofs, you should have proofs from other disciplines. Where does it end?
I like to use Wikipedia as a source of Mathematics, it's really convinient. I just hope that the information is correct.
:(){
Wikipedia has allowed mathematical proofs, for several years. I've found several of them useful, as it sometimes has nice proofs that would otherwise have been troublesome to track down without a more detailed literature search. I know other people who have found them useful as well. The fact that this useful information is now being opposed by some (including, apparently, the submitter) on the basis of "OMG, if we allow proofs, then there might be too many proofs, and then how will we stop it?!" is highly irritating to me. Proofs have been allowed for years without overwhelming the rest of the useful information. Wikipedia has not become a repository for opaque, useless 200-page proofs. Why are we suddenly worried about this? If you're really concerned, just put the proof on a separate page from the main theorem.
I still have never seen a coherent explanation of why Wikipedia is so concerned lately about deleting any material that is unworthy. It has greatly reduced the site's utility to me, and is the reason I use it less and less, and will refuse to contribute to its fund raisers until their deletion policy is substantially revised. The only explanation I've ever seen is a sort of question-begging, "But if we allow non-notable information without deleting it, then there will be non-notable information there!" Yes, so? Here's a nickel, kid, buy yourself a bigger hard drive. If you want to make "non-notable" information appear lower in search results, fine. That's useful. But a lot of information that I find useful is apparently now considered "non-notable" by the Wikipedia admins, and I'd rather there still be some way for me to find that information.
Also, what's with the policy of hassling articles with trivia sections? That seems so arbitrary to me. It's frequently a useful place to collect interesting information about the subject that doesn't fit neatly in earlier sections (and "if it's notable, you should merge it into the main article!" is just silly -- we should awkwardly insert this single notable and interesting factoid into an unrelated earlier section? That just makes it harder to find for those who care, whereas the people reading the earlier section will wonder why the subject jumps around. Trivia sections allow for cleaner editing and easier information searches.) Again, what is the harm in it being there? If you don't care about trivia, you don't have to read the section. And, again, if it bothers you that much, just put it on a separate page.
I'm a little bitter about this whole thing. Wikipedia used to be such a great resource, but lately all I hear is admins talking about ways to block useless information (for certain definitions of "useless"), not about how to actually strengthen the material that's there. Pretty soon, teachers won't have to tell kids not to cite Wikipedia....
I am the man with no sig!
As pointed out, the posed question is rhetorical. Having proofs (as long as they are not too tedious) is always useful. Interesting would be the question, whether Wikipedia should allow proof attempts and maybe get a proof of a previously unproved conjecture. The Web as a gigantic seminar, a modern Bourbaki group: Bourbaki 2. Currently, original material is not encouraged.
Wikipedia is run by a bunch of editors who are artistic in nature. They are very opinionated. I have not found a single one who will even let me post benchmark results. It was immediately deleted and one claimed it was an attempt to hack wikipedia. (The "hack" was the output lines from disk benchmarking utility "bonnie" which I added to an article I wrote.) I imagine in time wikipedia will open up and we'll get rid of the narrow minded idiots who think they are Gods but have no technical background bur for the time being it's a matter of understanding the limitations of the editors.
If we could find these editors and bribe them to make us editors with a couple bottles of wine we could turn wikipedia in to a much better place.
If its decided to be excluded from Wikipedia, maybe a sister site could be set up just for this.
For many people the inclusion of a proof could be far beyond their understanding, yet at the same time for some other people this is very useful. I believe that main content of Wikipedia should be easily accessible, in terms of explanation, to the average person and that specialist resources should help provide the harder more specialist content.
Jumpstart the tartan drive.
A proof is not a source of information, it's a reference. And as such, mathematicians should upload proofs elsewhere, and reference them in wikipedia.
Mathematical proofs are to be taken as a everlasting truthfull statement, and as succ doensn't benefint from being edited.
However ofcause it doesn't damage wikipedia when they are added, for informational purposes. This however should just not be common practice.
Should Wikipedia just become a textbook that teaches mathematics?
No, and including proofs won't make Wikipedia a fucking textbook. Who thinks up these asinine statements? Oh. Beetle Bailey does. I shudder to think that American education has sunk so low that Beetle Bailey is critiquing sites like Wikipedia.
With text and facts wikipedia sites places where it got the information as a resource to prove what is written is true, or they state when they can't site the source. Now with mathematical equations the source is the proof, so it doesn't make any sense not to state how it was proven. However, that being said, some proofs are very long and often people don't want to see them, so possibly put the proofs as a separate page (like clicking on an image to see it at higher quality) See what I've written, its called continuity in policy and I think it's the only way for wikipedia to gain/retain their credibility as a source for mathematics.
"Most people don't understand them" could be applied to most topics on Wikipedia, with or without proof. Just take any page about an advanced topic in philosophy, mathematics, astronomy, chemistry, biology or probably even history.
I agree that they should not be part of the *same page*, e.g. the previously mentioned proofs of the Pythagorean theorem should IMHO *not* be part of the page "Pythagorean theorem (http://en.wikipedia.org/wiki/Pythagorean_theorem)" (which currently includes 8 different proofs).
I don't think that something like wikibooks or wikiproof is a good idea. When I want to know more about the Pythagorean theorem, should I go to wikipedia? Or citizendium? Or MathWorld? There are already too many choices, and there is absolutely no advantage to having one more. I find it very useful to have *one* resource for "all knowledge". It's not like Wikipedia gets any heavier if it has more pages.
The reasonable thing to do would be to add a "Proof" section to things needing a proof, with one link per proof (e.g. "Euclid's proof of the Pythagorean theorem", "Garfield's proof of the Pythagorean theorem") etc. If using the current Wikipedia system is not good enough for that (but I think it is), it should be easy to introduce a new standard "Proof layout" e.g. something like this: If something is not in Wikipedia, it is *still* possible to link to Mathworld or wherever else you like. "No mathematic proofs because some don't understand them" is like saying "No dates in history pages because some can't memorize them".
They sould publish the proofs at Wikibooks and linf from the Wikipedia articles to the book.
"Should Wikipedia just become a textbook that teaches mathematics?"
Wikipedia should become whatever people want it to be. Who knows in advance what that is?
With the approval of the author of a well-known open-source program, I posted information about how to use the program. Next day that contribution was gone, removed by someone who said that Wikipedia should not become a place for software manuals. But my explanation was the clearest, most complete available at the time; the author of the software did not want to spend time re-writing his own manual.
The problem is not to decide which kinds of content to include in Wikipedia. Wikipedia does not have that problem of paper encyclopedias, paper and printing cost. More pages in Wikipedia are almost free. The only problem Wikipedia has with more content is organizing the content so that it is easy for the reader to make use of what he or she wants, and easy to ignore the rest.
The problem with Wikipedia is not with content, it is a social problem. There are many, many people with some kind of anger problem. Such people don't have many friends. But although they reject and discourage other people, they are still human and need to socialize. So, they spend time with open social groups like Wikipedia. They are there with the hidden and not-so-hidden purpose of having targets for their anger.
Angry people have plenty of free time because other people usually don't want to talk with them. Angry people have the time to dominate social groups, and destroy them. Wikipedia's problem is how to recognize angry, destructive contributors and how deal with their anger.
In some cases, proofs are totally unintuitive and do not provide insight into the result. In others, they are incredibly helpful! I say, let the authors decide.
Only a small percentage of the population on the earth will be able to tell if a wikipedia article is complete crap.
Allow them. Period. Otherwise you set up circumstances for vandals to thrive like they do around all other ambiguous rules. Put another way, if there are any rules specifying when you can delete proof, I guaran-frickin-tee that some kid will use them to remove articles about the four-color theorem and Godel's incompleteness theorem. They'll claim that they're doing it for nebulous purity reasons; that's just because you won't be able to see their smug little grins as they exercise their power.
The last think Wikipedia needs to do is give the Deletionists more ammunition. They're pissing off enough people as it is.
Dewey, what part of this looks like authorities should be involved?
This is part of the reason why I hesitated to donate to wikipedia this year and I think its why a lot of people get turned off by wikipedia these days. There is this group of people there that tries to edit and over police the site. Even the discussions on the discussion pages get policed by overzealous little shits and moderators who feel like this is their place to exercise some sort of powertrip, its really getting disgusting. Now, of course, wikipedia is a site that belongs to all of us, so if you don't like overpolicing fight back and argue against these people who think they know how to define wikipedia.
That is the real way to fend off these self-anointed policing pests, to join and get involved because as much as they want to edit it, fact is its NOT THEIR SITE, but if we allow them to go around and play admins then they win.
As far as the mathematical proofs. Of course, they should be in there. Wikipedia should approach a MAXIMUM of knowledge including math proofs. It should be a place where as much knowledge as possible is interchanged, described, sorted and edited.
Part of the problem is the insistence in Wikipedia that it cannot contain x,y or z. Here there is some rule that 'Wikipedia is not a manual, guidebook, or textbook.' It's very difficult to argue with people about this. When you point out that since wikipedia is not a paper encyclopedia it can contain a lot more information than a regular one and therefore can have characteristics of a textbook you get circular reasoning of 'Wikipedia is not a manual, guidebook, or textbook.' If you dare to ask to change the policy people say there is already consensus.
But this 'consensus' is 'weird'. Sometimes even when there is a clear majority in favor of saving some article or changing some policy admins will say that 'Wikipedia is not a democracy.' If you then ask well what does determine it you also end up with a tautology. I once asked someone why they wanted to delete article x and they said they were a 'deletionist'. Again I asked why and ended up with circular reasoning.
As far as this issue is concerned I think without proofs you are missing a whole lot in math. This also makes Wikipedia a difficult forum to discuss math and science in terms of what goes into an article. As someone in this area I often try to explain to people that their idea about y or z here is doesn't work because of some scientific concept.
The problems occur when they consider their generalist approach most important even if they are ignorant of the topic area. For example I might be talking about Unsolved problems in biology or Unsolved problems in medicine. Well to really address the issue you need expertise in that area. Generalists without it go in and presume to understand what is an unsolved problem in a field in which they lack knowledge. I heard all sorts of bizarre ideas from people in the unsolved problems in chemistry deletion debate about the 'nature' of chemistry, how chemistry itself was not very precise and easy to define. It's so crazy because Science magazine had a whole issue on the topic of big unsolved problems in chemistry. Oh well I guess those people who are actually scientists just don't get chemistry in the same way as a wikipedia admin.
It gets really crazy in that although the above articles got deleted enough people kicked up a fuss to save unsolved problems in neuroscience, unsolved problems in chemistry and unsolved problems in economics to save them. To really converse on these issues you have to really understand neuroscinece but wikipedia admins seem to think not. They play sneaky games. If they can't delete them the first time around keep on referring it for deletion. They did this with Unsolved problems in biology here and here. Then if you try to recreate the article you get slapped down by an admin because the article has already been deleted so you lose not matter what.
I finally gave up on getting any logical argument from the admins when I pointed out that if unsolved problems in neuroscience could exist then why not have unsolved problems in biology. I even talked to some practicing biologists about what these problems might be and low and behold they gave me some. Then the admins said well its not biology, its really biochemistry. Then I asked well why not have Unsolved problems in biochemistry. And it went
BTW The Totient_function Proofs was kept.
There are four sorts of people in the world: fools, lunatics, idiots and morons. - Umberto Eco, Foucaut's pendulum.
The real strength of Wikipedia shines through once again. "Editors" would rather see articles deleted than created. That is unless they're about Pokemon, in which case, create away.
Wikipedia is broken as a useful encyclopedia until it becomes easier to create articles than it is to delete them, but hey, at least we can find out everything there is to "know" about every obscure Pokemon.
The more good stuff the better. End of story.
Doesn't it make you feel good to know that our freedoms are protected by politicans, lawyers and journalists.
Wikibooks is a project under the umbrella of wikipedia which aims to create "a free library of educational textbooks that anyone can edit". Were it for me, the mathematical demonstrations will go there... (disclaimer: I have a degree in maths)
Why is this even an issue? I thought this is why links and hypertext and the like were invented. You read the theorem. If you want more, you click on the funny blue writing that says something mystifying like "Proof". If you don't want to read more, you move on.
Are they running out of space on the shelves?
I've calculated my velocity with such exquisite precision that I have no idea where I am.
The "meta" discussion wiki for Planetmath is AsteroidMeta. One topic of discussion I've seen is whether it should be Google-ad supported. It is qualified as a tax-exempt public charity in the U.S., and they are completely open about their finances with detailed reports.
I see no problem with mathematical proofs. It is a source of knowledge, and there is no reason to exclude mathematical knowledge from it. Most of the mathematical textbooks are copyrighted and unavailable to the majority of the people. Wikipedia is a nice fix for this issue.
...and the people interested in them generally have journal subscriptions and such to access details. I think a decent criteria to start with is if the proof takes less than a page, and uses high school level mathematics. University students or faculty have access to the university's subscriptions so a cite on Wikipedia suffices.
Higher Logics: where programming meets science.
Yea I agree, though perhaps the longer/more complicated proofs belong in Wikibooks.
I'm not a wikidolt so I obviously didn't read through whatever wikipolitics they're going through in their wikidrama, but an argument over whether or not to include a proof seems pretty silly. The question of whether or not a proof is correct is a silly question because Wikipedia decided a long time ago to not include original research, so they should never actually have to verify any. You also don't have to consider whether or not a proof is too long, because space shouldn't become a concern for any article that unpaid volunteers are willing to insert.
It seems like you'd just have to step back a minute and say
a) Is the source of the proof reputable?
b) Is the proof in the public domain?
If so, great, if not, delete.
This is however a pretty good example of why Wikipedia must ultimately fail at being the go to source for everything. While Wikipedia's design is great for creating an encyclopedia with various articles on culture, politics, regions, species, and other things that you can pigeonhole into relatively tight informational constraints, it is utterly useless once you want to go beyond scratching the surface in any particular discipline.
Overall, the wiki-effort would be better spent creating spaces for more specialized types of information, such as mathematical proofs and semi-research, as opposed to having endless cycles of subjective debates about notability.
Take a look at perlmonks.org, which is a pretty great example of how you can modify the everything engine to focus on a very specific subset of information.
The only legitimate reason I can see NOT to include a proof for any theorem discussed on Wikipedia is if the author of the article knows of no proof he is free to cite (because of copyright or attrribution). Proofs aren't something "extra" you add to a mathematical discussion, they ARE the math. Once you are discussing math on a serious level--say, anything beyond the elementary higher math usually taught to Engineers--it is nonsensical to say you know anything about a theorem if you have not read and understood a proof of it, or a good discussion of why no proof exists. The fact that some theorems are easy to state (see Fermat's Last Theorem, Goldbach's Conjecture, etc.) yet profoundly difficult to prove if you have not really understood the underlying ideas has led many an amateur mathematician toward becoming a crackpot.
In my opinion, articles about mathematical theorems without proofs are an invitation to circle-squarers and other well-intentioned but misinformed souls to contribute nonsense to Wikipedia.
Try using a zero-knowledge proof to show you don't know anything!
The maintainers of Wikipedia really needs to ask themselves what they wants it to be.
;) This isn't some great policy wide debate on Wikipedia, it's just the AfD of an individual article. Someone thought it shouldn't be there because of the policy, and the consensus disagreed. Big deal.
Sure - and they already have asked this, and put a lot of thought into it. See http://en.wikipedia.org/wiki/Wikipedia:What_Wikipedia_is_not , for example. The person who proposed the article thought that the proof made it count as a "textbook", but others pointed out that this didn't fall under "articles which read as textbooks, with leading questions and step-by-step problem solutions as examples".
But I'm curious why this issue is even on Slashdot - perhaps we should ask what sort of site Slashdot wants to be?
In fact, we can see the user Beetle B. voted delete - and now because the result was to Keep, he's running to Slashdot? (Okay, at least he's phrased it as an open debate - but it's not clear that this is some big "argument", and it's not clear a policy is needed specifically for mathematical proofs. Above all, this is the sort of thing that should be discussed on Wikipedia, not on Slashdot...)
I am a Physics undergrad student (so IAAP :P), and I've found Wikipedia to be an excellent source for mathematical information. The reason for this is the depth of information available. If, for example, I've forgotten a certain equation, my first port of call is Wikipedia:
The first section usually gives a concise overview.
The second gives the equations.
The third gives the derivation.
This is exactly what Wikipedia should be, in my opinion. I can get as much or as little information as I require, and I can't see any reason for intentionally removing or leaving out relevant data. I'm all for keeping articles free from pointless clutter, but derivations aren't pointless.
I thought Wikipedia was about "Free Access To All Human Knowledge", not "Free Access To A Good Percentage of Quite a Lot of Human Knowledge, But Some Things You'll Just Have To Accept, OK?".
Inclusion of mathematical proofs would be the last problem in the encyclopedical signal/noise ratio problem of Wikipedia.
The only problem is that errors in mathematical proofs are less forgivable (I can't explain why, maybe it's just a personal view but I strongly feel others would see it that way) than errors in literature. And they also require more proficient experts to check them out and find errors.
BTW, why not use MathML to mark up formulas, instead of images?
First, of course proofs are fair game for Wikipedia -- a proof is like the source code for a statement that is purported to be true.
I've seen a few nibbles around the edge with some of the answers but I think this topic leads to more fundamental questions, like "what things require proving" and "when is a thing proved", the latter of which sometims boils down to "to whose satisfaction must a thing be shown before it is accepted as proven"? The answer to these questions has driven a lot of the development of mathematics itself (as well as philosophy and the natural sciences), as things that were once accepted as axiomatic, after critical examination, have themselves been shown to be consequences of more fundamental axioms (or assumptions).
If people like you had their way, Wikipedia would run out of electrons in no time.
My view of Wikipedia, and this applies not just to proofs is that if someone is willing to write it and it is factually correct keep the article. The crackdown of "trivia" on wikipedia is ridiculous. It used to have some fairly esoteric knowledge, but no so much anymore.
There are 11 types of people, those who know unary and those who don't.
One of the problems with Wiki's math content is that too much of it is not acessible to someone who is looking up a concept out of the blue or landed on the article randomly. Heavy use of math notation is one of the reasons for this - it tempts authors to create what is technically a complete treatment of the topic but does not have sufficient plain-language content to be meaningful to non-experts.
I am by no means arguing for dumbing down of content, but it's important that at least the first few paragraphs avoid relying on heavy use of math notation in favor of giving a casual user an idea of (1) the gist of the math concept (2) why it's important and (3) some basic uses or a simple example.
The question of whether proofs should be allowed in Wiki depends on discipline of the average math author. Can they avoid the temptation of making the proof be the article? If they can, then there's nothing wrong with supplementing an already-good article with the proof. But if it's impossible to glean anything from the article other than by stepping through the proof - then the article is crap and the proof is what enabled the author to think he was done.
Perhaps there should be a separate sister site that housed proofs which are linked to from the main articles. I think that's probably the best idea - keeping the article meaningful to non-experts - and allowing those who care to "drill down".
-e
http://ed.markovich.googlepages.com
Why not just create another wiki just for mathematical proofs? You could just have wikiproofs.org and then put outside references to it where necessary in wikipedia. That way the entries would stay a manageable size, but one could easily get access to that information. From what I've seen it should even be possible to run a second wiki that links to the same user database.
Why not simply have another wikia site/mediawiki installation called "Wikiproofs" and put them there, and add a link from the wikipedia article?
That way, i can just look at that website and not have to bother with a lot of the cruft and garbage seen on wikipedia because of it's visibility and susceptibility to trolls and agenda-pushers. It continues to bother me that it's difficult to study/edit some of the excellently written technical/scientific articles on wikipedia without getting roped in to the cabalistic claptrap on non-technical subjects (often, editors agenda-pushing editors spam talk pages of technical-article editors to "call them to arms" for an edit war in a politics/religion/history article and fill it with ethnocruft or systemic bias).
It seems to me that a wikiproofs (or mathwiki) fork could be a peaceful place where pointy-haired academics could graze free of wiki-nonsense...
At least for a while.
l'Homme n'est Rien l'Oeuvre Tout: Gustave Flaubert to George Sand
An "encyclopedic" web site that explains what the Sword of a Thousand Truths is http://en.wikipedia.org/wiki/Make_Love,_Not_Warcraft could use a little hard mathematics for balance, in my opinion.
I have argued for too much time that Wikipedia should become a general knowledge base, since the encyclopedia is an out of date concept not suited for the 21st century. This can be implemented without significant software changes (although specialist software can greatly assist in the creation and management of a KB). Unfortunately, it seems that very few people really understand exactly what a KB is, so most people think of an encyclopedia as an ideal, rather than as a limitation.
With a wiki knowledge base, users could set their options to choose what level of details they would like to read, and the software could automatically retrieve exactly the level and depth of details that any specific user wants. For example, in wikitext, we could have the mathematical proofs tagged with a tag "nerds-only" and then only users who would have set the option "I am a nerd" in their account preferences would see these sections (anonymous users could still access the nerdy sections by clicking on a tab link or similar facility). This is how it could work with customised software (it really could be implemented simply as a mediawiki plugin only). Without software changes or additions, Wikipedia could implement some KB-like features right now by using namespaces, subpages, and other facilities (eg an article "Pythagoras theorem" could be accompanied by its "for nerds" counterpart in a "Nerds:Pythagoras theorem" namespace or in a "Pythagoras theorem/nerds" subpage. Once these basic features are in place, Wikipedia could start implementing more KB features, and perhaps also get incpiration from Cyc (in the past for some time I freely hosted a similar "wiki-style Cyc" project).
Encyclopedias are the result of old 19th century thought when people needed to limit the information they could put on paper simply because having thousands of volumes to carry around would be impractical. But now with computers there is no reason to limit how much information goes into a wiki, especially for one hosted by a biggish organisation.
Note that the fact that I am somewhat of a critic of Wikipedia's policies and sometimes also parts of its leadership doesn't mean that I don't support the project, I actually contribute and donate as well.
Now back to the original question... Whether Wikipedia (a project that unfortunately positions itself as an encyclopedia rather than a general KB, at least until its current leadership understands why KBs are important and why it is Wikipedia that should implement one) should include mathematical proofs. Well, I would say that since Wikipedia already contains articles in obscure porn stars, obscure music groups, politicians only known to their local communities, and little-known villages all over the world, it would be ridiculous to not include mathematical proofs of *all* theorems (including only the "important" ones is not viable because very few people are in position to understand what is important and what isn't). As a user, I expect to see mathematical proofs in every encyclopedia, especially online ones like Wikipedia.
On a similar fashion, Wikipedia currently does not accept articles on many free software and open-source developers based on notability policies. Yet it has articles for very obscure musicians etc (and it fails to properly accoutn for the correct name GNU/Linux in its Linux-related pages). Ridiculous.
Unfortunately Wikipedia has started to suffer from its own popularity (thanks to BBC): The project in beginning included a large proportion of users really caring about creating a useful resource. Now that so many new people have joined, the proportion of people genuinely interested in making Wikipedia useful is very small. Most people just want to push their agendas, write articles that they like being there (eg their favourite obscure porn star, politician, or artist) rather than on what *should* be there (eg mathematical theorems and chemical substances etc). This happens because the
I'd love it: Wikipedia not just as an encyclopedia but as a knowledge resource. This would mean that what is in Wikipedai is more than one would expect from an encyclopedia: more per entry and more entries. Both is already to some extent the case: some articles contain by far more information than your average encyclopedia (mostly articles about music bands etc.) ... and there are far more articles about e.g. TV series than any encyclopedia would want to contain.
So already, there is a grey area with regard to notability. And I say: thats good. I would welcome a policy change that allows even more and an even wider scope.
However, a few technical and organizational modificaitons would be necessary:
- seperate "notable" content from additional and detail content, dont put it all into the same huge article.
- create additional article types for background knowledge, related textbook-like information or proofs
- make the content markup less chaotic and less ugly for humans, and better parsable for computers
- allow "knowledge pieces", maybe in a separate namespace about every day knowledge and about entities that are not described by nouns, e.g. allow WP to contain articles about concepts represented by verbs or adjectives
- make the connection between the dictionary and the concept entries better
But most importantly: stop thinking about WP as an encyclopedia in the classical sense. Classical encyclopedias are what they are because their creation had to be done with limited resources: a limited number of experts, and you had to put it into a limited number of books so you can sell it. None of these limitations applie to WP.
WP is already something new, but it could be even more innovative.
fuck kdawson and his biased shit. he's ruined what little was still good about slashdot a few years ago. it's time that cmdrdildo wakes up and gives kdawson a kick to the nuts as he's shown to the door.
is the only man who can answer this question. http://xkcd.com/about/
The big danger is they could piss off a whole bunch of useful contributors over some pointless semantic spat.
I don't think anybody will see that as a wise decision.
No sig today...
The problem with Wikipedia is that Jimbo and his minions: Slimvirgin (aka Linda Mack the MI5 informant), Jayjg, JPGordon, and all the rest will make this decision FOR you. I can pretty much guarantee if it gives them a chance to put something Pro-Israel they will be for, otherwise if they can delete something you have done they will be for it as well. Everything else will be no.
Why not include a mathematical proof? or hundreds? As long as they are from verifiable sources, who cares?
Ask yourself this: What do they need all this money [donated] for if they don't have any intention of using it for storage and bandwidth? I have no intention of giving a dime to Jimbopedia. Here's the authoritarian BARNSTAR for your tireless work in supporting mindless automotons that spend 24/7 reverting and pushing their one-sided political agenda!
It seems to me the big deal is whether Wikipedia should include technical details, vs. just lay-introductions. This affects lots of areas of Wikipedia, not just mathematics. I have found the technical details that are available on Wikipedia to be invaluable to me at work and I would hate to see them go.
If they are afraid of turning people away from including too much technical details in articles, why not offer 1 or more layers of articles? For example, the lay-introduction, and then links to backing pages with more details. It seems silly to deliberately dispose of knowledge that people are offering, unless there are storage or bandwidth considerations, which I doubt will be a significant issue in the future (if it even is now).
Wikipedia is growing beyond the idea of a basic encyclopedia, into a type of knowledge base that the world has never seen before. I don't see why it can't serve as both a basic encyclopedia and as a source of advanced knowledge. People are pushing it that way, and it is incredibly useful. It has become very attractive to people wanting to share knowledge, and constraining it to the concept of a basic encyclopedia is just throwing away not only a lot of useful effort on the part of many contributors, but the momentum by those contributors to have a central store of knowledge. Wikipedia is where they are attracted to put their advanced knowledge. If Wikipedia shuts that down, it will be difficult to establish another central location, and when one is established, there will be conflicts of overlap with Wikipedia.
It shouldn't be that difficult to establish "knowledge layers" that satisfy both parties.
Let's wait and see what the secret mailing list cabal has to say before we worry our pretty little heads about such things.
Would someone please explain to me why anyone is resisting what I see as Wikipedia's inevitable ascent to Foundation (http://en.wikipedia.org/wiki/Foundation_(novel)) status?
Seriously, is there anyone having any difficulty answering such easy questions?
As Jimbo Wales once said, Wikipedia is - as an encyclopedia - only one book in our "wiki library", and one book is not a whole library. Of course mathematical proofs are important and should be freely available, but so is tons of other sort of information, too, and we can't just put everything in Wikipedia. Wikibooks offers a place for some book-like-stuff (and I think mathematical proofs belong there). There are also other projects for different kind of information, like learning materials and dictionaries. We should start to transfer Wikipedia's success to other free wikis and projects.
Surely proofs are more important than a lot of the crap in wikipedia. Do we really need entries like these: http://nostalgia.wikipedia.org/wiki/James_Cameron,http://en.wikipedia.org/wiki/Spice_Girls
Engineering is the art of compromise.
If the proof is too long for inclusion in article,add it to math wikibooks.
Put very short proofs in the article on the theorem. Put longer proofs in seperate articles. For very long proofs just provide a reference.
Warning: this article may contain humor, sarcasm, parody, and perhaps even irony. Read at your own risk.
I can visually see why the Wikipedia elite, might be disinclined to include formal mathematical proofs in general audience articles. They look intimidating.
It seems to me like the mathematics community on Wikipedia ought to be able to set up a new, top level Wiki-media project, along the lines of what Wikimedia Commons has become, dedicated to the sharing, presentation and interlinking of math proofs. The formal proofs could then be easily linked to from within Wikipedia, without making the Wikipedia articles harder for laypersons to understand.
Also such a top level project might be able to introduce some structure to proofs that would allow automated symbolic math processors to work directly with the public proof base. Also some enterprising Google geeks and/or college students ought to be able to bring some sophisticated search techniques along with the computing power of something like Amazon's Elastic Compute Cloud to the party. And that just might allow some truly amazing breakthroughs.
that way there won't be any suspect mods/edits...god himself will own the server.
SLASHDOT: news for people who can't concentrate on work or have no life at all and got tired of yelling back at the TV.
However, I wouldn't be surprised when a page is nominated for deletion, as there is always at least one person out there who would prefer to see a particular kind of page deleted. (Apparently the submitter wants proofs to be gone, for example, and that's senseless, IMO). I'd be more surprised if they were actually deleted, which they weren't in this case. And then, even if this particular page had been deleted, it wouldn't have created a precedent for deleting other proofs, so to say that there's a movement inside Wikipedia to delete proofs misses the mark by a wide margin.
there is no reason for wikipedia to turn down any true and factual information. why should they exclude some proofs? text books have to make these choices due to page constraints. wikipedia has no such problems. Being able to get more information from wikipedia than you can from a book is its greatest strength.
Ack for hitting Submit instead of Preview by accident...
About the manual: the decision was correct, but incomplete. The complete deletion/removal reason should have been, "Wikipedia is not a host for software manuals; however, Wikibooks is, and Wikipedia does not want to cannibalize its sister project." If you point me to the manual, I'll see what I can do to move it there.
otherwise, not sure. as has been pointed out several times in this thread, there many theorems whose proofs - if addressed to the audience with the minimal math background - are ill motivated, difficult to follow, in general quite long. you wouldn't even want to read them. the alternative proof can be literally two-liner by requires more advanced background. The simplest example I can think of is proving the Lebesgue conditions for integrability of Riemann integral. And many more examples like that. Worse yet, there are many theorems whose proofs - even on advanced level - are still quite complicated, like Jordan Curve Theorem. so the key question: unless the proof is short, sweet and kind of trivial, which version of the proof would you want to put online?
... always planetmath.org
I've never cared much for the term "computer science." I would love for someone to explain to me how CS could possibly be classified as a science. It's like when mathematics is called a science, which it is not. It seems to me (please correct me if I am wrong) that for something to be a science it must employ the scientific method. Neither mathematics nor CS makes use of the scientific method. No, I much prefer the term "computer engineering," or "software engineering."
isn't this really a case for svg?
I have discovered a miraculous solution to this problem, but this comment is too short to accommodate it.
MSIE: The world's most standards-complaint web browser.
Start a new wikimedia site: mathipedia with everything about math. Link to from the wikipedia. Problem solved.
I think a hyperlinked proof section is a really good idea, although they should probably replace the "citation needed" tags with "reference needed" tags.
Write out the various axioms on one page -- if there's a group of proofs that requires axioms different to what is already on the axiom page, create a new section (I guess if this gets too large, you'd need to split the axiom page into different pages).
Then, require every proof to reference back to a previous proof or axiom, at least once every line. That way, if someone asks "how do they get from step 5 to step 6?", it's a simple matter of clicking on the reference (and then following the references there as far back to the axioms as is required for them to understand).
Ask me about repetitive DNA
"Wikipedia is not a venue for publishing, publicizing or promoting original research." Either a proof is published elsewhere, in which case it should be referenced, or it has not, in which case it is original research, and should not be on Wikipedia.
The proofs go into WikiBooks on Math and the Wikipedia links to the WikiBook.
This way the book can go into far more detail and provide for more linear reading than the brief review expected from an encyclopedia
Notability itself is not a policy. It is only a guideline, and guidelines are a means to an end. In this case, the end is verifiability. If an article is deleted as non-notable, this represents a judgment that finding "reliable, third-party published sources" to verify claims in the article is unlikely. For example, if a local musical group's article got deleted, perhaps it was relying only on information published by the band or its label and not on any third-party sources. Such was the case for a bunch of articles related to bands on the label Serious Business Records that got proposed for deletion in November of 2007.
Another issue is that Wikimedia Foundation's mission is to provide free content, but popular culture is copyrighted and not available under a free content license. Too much reporting on popular culture brings tough questions of fair use for Wikimedia's legal department and for downstream users of Wikimedia content. However, facts are not copyrightable, which makes it easier for a free content project to report on fact than on fiction.
Less content is easier to maintain. You need to check if things written in Wikipedia are true, so you will need to use the references anyway. Just a mention of all those different proofs will be enough. What about another service to group those? Wikiproof sounds fine...
No. They are boring and politicians can't have staffers "tweak" them for the real truth.
Ok, I really don't agree with this, but nobody else was against it.
Mathematical proofs are original (and creative) work. Sure, they follow rules and are verifiable by other mathematicians, but Wikipedia does not allow people to publish original research.
If the proof is published in a referenced work, then I can see the justification for publishing an excerpt. However, if Wikipedia is to maintain its current policy toward publication of original research, then it must not permit the inclusion of proofs that are not referenced from another publication.
Why don't they just do what they normally do in these situations? Create a new project at www.wikimath.org and have the proofs live there. The Wikipedia pages can then reference the proof pages, just as they often do for wikibook, wikiquote, etc.
There's absolutely no reason for Wikipedia's admins to "allow" or forbid math proofs, or anything else, except perhaps where it's proven either libelous or clearly and presently dangerous - which has nothing to do with math.
If an article's author includes a proof, that's up to them. If later editors change or remove, it, that's up to them. If the proof isn't properly cited or otherwise corroborated, page updaters can correctly note that. And every reader should check the references of everything in the article before they rely on it.
Exactly like every other Wikipedia article.
This principle is fairly new, but it's pretty easy to understand. In fact, it's been the principle of any research source all along, no matter how "definitive", but for most math the citation was implicit in the publisher. Though the Web was in fact invented (at CERN) for precisely the problem of quickly linking citations of complex math (by physicists) among many online articles. without needing a central editor and "truth guarantor". And this is true of all publications, which have never been perfectly reliably "true", though their publishers usually liked to pretend they were - and didn't cite them.
--
make install -not war
If not, what's the issue. If I follow a link to an article and it goes over my head or is really long, I don't read it. That doesn't mean that it's existence disturbs me at some fundamental level that will make me stop using wikipedia altogether.
I really like Wikipedia too--but it seems to be becoming a bit of a religion for some people out there.
Even I don't understand wikipedia's articles on math sometimes.(and I have a degree in math) I had one of my professors tell the following joke...
"Wikipedia is proof that math majors can't find jobs."
Wikipedia articles on math/physics topics really need to develop a whole new format. One thing I would like to see is more casual articles on math topics. Sure, I can almost every popular mathematical proof on wikipedia....but wikipedia is a general knowledge database.
The proofs should DEFINITELY be on the same page, but a lot more care should be taken to make the articles more approachable. I used to use wikipedia in conjunction with my textbook...and several times I wound up preferring the textbook. This wasn't on instructional topics, but on rather general topics. The wikipedia article was simply to confusing, and too technical.
Basically, remember that wikipedia articles DO have an instructional quality. Most mathematicians aren't reading the wikipedia article on the "twin prime conjecture". Encyclopedia articles aren't written for people who know everything about the topic, they are written for people who need information.
**(BTW...this comment is written in the same manner as most of the articles. It has all the essential information, but in a very impractical format)**
like the Spice Girls' birthdays
Engineering is the art of compromise.
The admin adjudicating the argument has ruled in favor of keeping the proof. As far as I can see, there is no conflict. Proofs are arguments in mathematical language.
In most times, most places, by most people, liars are considered contemptible. - Ursula Le Guin
sorry, thanks for playing but theorems are not axioms, and you've made the assumption that a theorem must have meaning or a valid meaning or can even have anything to say about an axiom. no, all theorems are just false. here's your pointy hat, over to the corner, dunce.
President of Malawi: Bingu wa Mutharika
Vice-President of Malawi: Cassim Chilumpha
Not too sure about the Prime Minister though...
Taken from here.
w00t
There is a Mathematics Wiki that seems to accepting proofs, but doesn't have many articles created yet.
If Wikipedia doesn't accept proofs, why not just put them in one dedicated to Math?
Calling atheism and agnosticism a religion is like calling bald a hair color.
Ignore All Rules
CAn'T CompreHend SARcaSm?
"Does the article read well?" should be the acid test for wikipedia articles, math, or otherwise. Include what is necessary for the article with the general stuff up front. Make it easy to skim over, but don't worry about getting too in depth.
Wikipedia can handle depth because it can have an unbounded number of articles. If the article starts getting too long, move the details into it's own topic. Then they are easily skimmed over by not clicking the link.
Above all, if something is 'too in depth' DON'T delete it. Don't delete ANY correct or useful content ever. Find out where it goes, put it there, and link to it. Make it it's own topic if the topic doesn't exist. Since wikipedia can host an unbounded number of articles, the depth of knowledge it can contain is also unbounded.
This is something no paper encyclopedia can do. It is why, whereas I haven't opened a paper encyclopedia in years, I read wikipedia almost daily. One can't outgrow it.
Focused articles that are accessible to a general audience are a good thing, but I would be sad if wikipedia lost any of it's depth for the sake of keeping articles focused for a general audience.
The simple method of moving stuff to it's own topic and linking to it solves the problem. A proof that makes an article seem unfocused can easily be it's own topic. Just create a PROOF_OF_XYZ_THEOREM topic with the proof and have a link. It doesn't hurt the rest of wikipedia at all, and will help anyone who wants to see the proof immensely.
...
The who thing should be there. If somebody who understands it wants to, they can make a summary page.
The only god damn problem with Wikipedia is that has become a 'if in doubt delete' crap shoot.
When in doubt, do not delete.
In fact, I wouldn't let anyone delete anything more then once a day, and make them put in a better reason as to why they are deletingit. If the claim is that something is wrong, then they had better post a reference.
To people who post and delete on Wikipedia: It'.s not YOUR God damn site, it is all of ours. I don't care who you are or what you are posting, you don't know everything about what you are posting. No matter what it is. Keep that in mind. Also keep in mind you are driving monetary contributor. It would surprise me if Jeff Albertson would be glad he has more life then some of you people.
There is nothing like posting facts and having them removed as incorrect. Then citing references that require 1 fucking click and 30 seconds to verify get ignored and the data is deleted.
Fucking douche bags. NO, fucking Cowardly douche bags.
Delete that, wikibitch.
The Kruger Dunning explains most post on
The issue is real. How much depth should Wikipedia, as an encyclopedia, provide before one should seek-out more specialised sources. An encyclopedia entry on Albert Einstein might take up two or three pages. (I haven't checked Wiki's entry on Einstein). You could fill a library with books and papers about Einstein. It is not reasonable or useful for all this information to be provided comprehensively on Wiki. Most readers would be overwhelmed. Mathematical proofs to my mind are several levels down (or up) the knowledge chain in the realm of more specialised information requiring more specialised treatment
When it comes down to it, no one really cares about proofs. Proofs are very long. Proofs are very terse. If I want the proof, I"ll look up the real article from whatever journal or proceedings it was published in. Wikipedia is for quick overviews of subjects. Not for detailed technical discussions. It's an encyclopedia, not a science journal.
Then giving the quality of the math articles on Wikipedia, I can't imagine this would make the articles better. What I mean is, that while the articles are never wrong (or at least obviously wrong), they're always way like 10 times harder to understand they have to be. Seriously. Any undergraduate math book is way clearer.
Its the wrong question:
::))
The right question: Should mathematical proofs allow slashdot?
This is just simply based upon a "proof' by a beginning geomerty student that you can duplicate a cube, using only a ruler and a compass. ( The proof is left as an excercise... )
After 'cooking' everyplace where he cheated, i.e. used the ruler as a measuring device, he finally stumbled upon a 'special case' ( i.e. a cubic equation that had real roots ), and still hurled insults, coming from of all places, the 'general case' follows from the 'specific case.' Wikipedia is not a place for rigorus scolarly math anymore than Slashdot is. (Neither place being especially good for the spelling chalenged, just that wikipedia claims it is...
There is a project on wikibooks that aims to include mathematical proofs from various topics; http://en.wikibooks.org/wiki/The_Book_of_Mathematical_Proofs The goal is that one can link from wikipedia to this book, where all proofs are allowed.
Mathematical knowledge is one knowledge that is certain, universal and timeless. All other content on Wikipedia is subjective and biased.
Wikipedia should contain whatever it takes to have someone visit the article and UNDERSTAND what they read. On a similar note, I tried to include a layman's explanation of the Riemann Zeta Function on Wiki and got a lot of pushback for attempting to help non-math PhD's be able to understand the article. The response I got was 'this is just an encyclopdedia'. Thats crap. Wikipedia should be as accessible as possible to everyone, and that includes proofs.
First off "It also makes little sense to collect proofs of separate theorems into "books", or about as much sense as collecting articles on different subjects into an encyclopedia." ... collecting articles on different subjects does make a lot of sense for an encyclopedia. :P
How about WikiSource then, Wikipedia's repository of public domain archives. It was created when people would do things like copy and paste the entire contents of a treaty or something into Wikipedia.
Good afternoon, dear slashdotters!
;-)) of the comments you want to see.
As I heard, wikipedia is about collecting and sharing knowledge to make it accessible for everyone on the world.
When thinking about that, how can it possibly happen to have a discussion about deleting knowledge?
Is there a censorship going on, about which knowledge is too complex for the world?
In my opinion there should be a wiser solution than just dropping knowledge which does not fit wikipedia's style.
As a public source for knowledge, it should not care about style, the only thing that does matter should be correctness.
Maybe wikipedia should think once more about it's quality standards and develop a better system to categorize in-depth information for the appropriate topics.
Compare this to the slashdot moderation system: You choose the score (say complexity
On wikipedia, I'd like to have a choice too.
Seems to me that proofs would make math on wiki more reliable. If you show the proof, anyone who can follow it can notice mistakes in it. If you just show the completed theorems, people just have to take them as gospel.
And how are people supposed to actually learn math from wikipedia, if you don't show them any proofs? Without proofs, you're just giving them recipes, instead of understanding.
He's right to exaggerate, as it gives a sense as to how much *crap* wikipedia stores on certain topics, simply because they're close to the heart of the fanboy's among editors.
FANBOY EDITOR 1: "My god, they want to add math proofs to Wikipedia?! Someone needs to tell these fools that Wikipedia has strict limits on what we put in it, and math proofs simply aren't reputable enough for a page of any sort. DELETED!"
FANBOY EDITOR 2: "Hey, do you think that we really need a list all the names of these characters from *RANDOM OBSCURE ANIME* series and everything that they did?"
FANBOY EDITOR 1: "You're questioning the notability of minor characters from *RANDOM OBSCURE ANIME* series?? How did they let you be an editor?! I think I'll mention this to the boss and we'll see how long you make crazy talk like this!"
...I mean, there's only so much space in those tubes. If we don't want to run out, we have to limit what we put up there.
-Styopa
Why is this even an issue? What does it matter whether Wikipedia has proofs or not? I didn't think mathematical data for public use was something people had big opinions about. They're just theorems. I don't see the problem. Put whatever you want on Wikipedia- that's what it's for.
Obviously the optimal solution was for your writeup to have become (part of?) the new manual.
In Repressive Burma, it's not just your connection that dies. slashdot.org/comments.pl?sid=314547&cid=20819199
Wikipedia is not about creating an archive of all of human knowledge.
You are damn right it isn't! Which is why I am starting a new web site, called 'wikiallhumanknowledgica' to cover this oversight.We expect to put Wikipedia out of business inside of a month.
(I was going to make a joke about calling it the 'wikinet', but I realized that if your data store is the whole Intarwebz, you would have to call it the 'wikipornopedia'.)
HA! I just wasted some of your bandwidth with a frivolous sig!
The correct way to read mathematical theorems is to read the proofs. The only way to understand any (even the simplest one) theorem is to understand the proof. There is a reason that when mathematics is taught, you aren't just supposed to memorize a bunch of statements of theorems. Mathematics IS proofs. Wikipedia would be doing itself (and the mathematics community) a disservice by not allowing proofs. Knowing a good proof of a theorem is worth much more than knowing a statement.
The statements of the theorems are important for a reference, but for it to be complete, you need proofs, at least of the fundamental results. It is just as important when reading mathematics to look up proofs of theorems as it is to look up theorem statements. So a complete reference MUST include proofs.
BTW, anyone noticed that Planetmath does include (and does encourage including) proofs with theorems? While most theorems remain unproved there, it is more a lack of time on the part of the authors and everyone is encouraged to contribute proofs of anything on Planetmath!
I would not trust to wikipedia to assemble a collection of "mathematical" knowledge. I have been working on one myself due to the overt lack of such a system. Mine is called FRDCSA (frdcsa.org), its really a misnomer. "Database" is not apropos, but neither is KBS for that matter. I guess it's a working name. First of all, one should not simply store proofs in human readable format, but in machine readable format. There are many efforts, the names of which now escape my memory, but some come to mind, the best of which is FDL (Formal Digital Library), tho I can't be sure it's still in Operation. Then there is Mizar. Oh god I cannot remember. Of course the semantic web in theory does this. I would imagine if one would look they would find collections. The problem I ran into in assembling the collection is this, in theory, I'm not sure its possible to differentiate between proof systems and programs. Intuitively it would seem they are very different. But as Emil Post remarked, proof systems are equivalent to programs? Is that what he said, I don't remember. And then there is the Curry Howard isomorphism, which I've never really studied. Anyways, I took to collecting all kinds of software instead of just proof systems. The one thing I'm sure about is that the larger the system is, the better the chance it can behave intelligently. That is stated (without proof) in mathematical form on my site. Alright, I've done my best to drop hints to the wise.
Oh yeah, and regarding the formalization of arguments on Wikipedia, after talking with James Wales at a meeting, I walked away with the impression that wikipedia does not have as a goal the rederivability of their content, they would rather state it without proof. Specifically he made fun of me for asking whether any assertion that does not follow from its premises could be considered "idiotic", a word he was using. He said, let me remember, he said that was "what a programmer would think" or something to that effect. Made me quite upset.
Yes, of course they should be included. What is mathematics without the very logical arguments which make it mathematics ?