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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.
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.
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*.
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?
Why the hell not include ALL proofs that someone takes the time to type into Wikipedia? They're running low on hard drive space or what? And what's gonna be next, drop proofs from textbooks because they can't figure which one to include?
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!
"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".
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
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.