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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?"
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.
That's about it ... they must have gotten sick of webcomics.
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...)
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
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.
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.
The usual arguments for brevity don't apply here - are you worried about the "book" getting too "thick"?
They've started something - a compendium of knowledge - and they're preventing it from growing because they want it to fit a publishing model that no longer applies. Why limit yourself?
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.
I brushed my teeth this morning. This is an absolute truth. Should it be included in Wikipedia?
Knowledge is power. Knowledge shared is power lost.
Editing can be reverted ... the ability to do it doesn't give you a feeling of power. Deletion, now that's a power trip.
... hell they even thrive on the hatred. The fact that one of the deletionist in question even posted this story when it's obvious that no one here is going to agree with him is pretty telling.
They thrive on the attention, the ability to destroy
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.
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.
That you can't tell the difference between eye-witness testimony and a mathematical proof suggests you are an unreliable source. Which means that the alleged "fact" of your teethbrushing should not be included in Wikipedia.
Ok, devil's advocate - why not?
Is there any reason that absolutely ANY trivial fact can't be included in wikipedia?
Just have a ratings system to put less-noteworthy material someplace where people won't have to browse through it. Companies like google can specialize in finding data in these kinds of articles.
Disk space is getting to the point where an encyclopedia could be built capable of containing the continuous typing of every human on earth for the rest of time. So why not let them type?
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!
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".
The math is generally well-done in the sense that it is accurate, as far as it goes. It usually doesn't go very far, for the technically inclined, and it is usually far too abstract and technical for the general reader. It's sort of the worst of both worlds, really: It's impossibly shallow for the serious student, and impossibly jargon-rich for the layman. There are exceptions to both pessimialities, clearly, cases in which a given article is well-suited to one or the other audience, but in those cases, it has just lost one of its major audiences -- and really, the specialists are a major audience for wikipedia math articles, simply because there is nothing fulfilling that function for the serious student and professional right now, so that wikipedia math articles get more attention from this audience than they would, if such a facility existed. The result is that most of the articles become unusable for the general reader very quickly, but can never really satisfy the needs of the specialist audience.
-I like my women like I like my tea: green-
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?
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
Citation please?
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
So true. I wish each article would have two parts, an overview introductory explanation for general readers and an in-depth part for mathematicians. Trying to satisfy both audiences with the same explanation is impossible, and both audiences are important.
Terrorists can't threaten a country's freedom and democracy. Only lawmakers and voters can do that.
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 don't agree about mathematical proofs in wikibooks. Proofs for individual theorems only rarely require a book-sized volume of text. 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. Maybe there should be a separate wiki namespace equivalent to Mathworld, but proof of central math theorems certainly should be readily available from wikipedia.
I think this argument is fallacious. People contribute to Wikipedia because it is an open system to which anyone can contribute. The more open it is, the more people will choose to contribute. As long as articles are potentially useful and relatively unbiased, I can't see what harm it does to allow them. The argument about reverting vandalism rings hollow to me. Wikipedia could (but chooses not to) put in place technological measures to foil vandalism, preferring to rely on the efforts of volunteers to manually revert it. This seems monumentally inefficient. If it works, great. But if it doesn't work, the solution should be better technology, not filtering out potentially useful content.
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.
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